Microwave Radiometer Systems - Design and Analysis 2nd Ed. by Niels Skou

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Microwave Radiometer Systems

Design and Analysis

Second Edition



For a complete listing of the Artech House Remote Sensing Library,turn to the back of this book.



Microwave Radiometer Systems

Design and Analysis

Second Edition

Niels SkouDavid Le Vine

a r techhouse . com



Library of Congress Cataloging-in-Publication Data Skou, Niels, 1947–

Microwave radiometer systems: design and analysis/Niels Skou, David Le Vine.—2nd ed.p. cm.— (Artech House Remote Sensing library)

Includes bibliographical references and index.ISBN 1-58053-974-2 (alk. paper)1. Radiometers—Design and construction. 2. Microwave detectors. I. Le Vine, D. M.II. Title. III. Artech House remote sensing library.TK7876.S5767 2006621.381’3—dc22

2005057085

British Library Cataloguing in Publication Data

Skou, Neils, 1947–Microwave radiometer systems: design and analysis.—2nd ed.—(Artech House remote sens-ing library)

1. Radiometers—Design and construction 2. Microwave detectorsI. Title II. Le Vine, David621.3’813

ISBN 1-58053-974-2

Cover design by Igor Valdman

© 2006 ARTECH HOUSE, INC.685 Canton Street Norwood, MA 02062

All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including pho-

tocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher.

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International Standard Book Number: 1-58053-974-2Library of Congress Catalog Card Number: 2005057085

10 9 8 7 6 5 4 3 2 1



Contents

Preface xi

1 Introduction 1

References 2

2 Summary 3

3 The Radiometer Receiver: Sensitivity and Accuracy 7

3.1 What Is a Radiometer Receiver? 7

3.2 The Sensitivity of the Radiometer 7

3.3 Absolute Accuracy and Stability 9

References 11

4 Radiometer Principles 13

4.1 The Total Power Radiometer (TPR) 13

4.2 The Dicke Radiometer (DR) 14

4.3 The Noise-Injection Radiometer (NIR) 16

4.4 The Correlation Radiometer (CORRAD) 18

4.5 Hybrid Radiometer 20

v



4.6 Other Radiometer Types 21

References 22

5 Radiometer Receivers on a Block Diagram Level 25

5.1 Receiver Principles 25

5.1.1 Direct or Superheterodyne 25

5.1.2 DSB or SSB with or without RF Preamplifier 26

5.2 Dicke Radiometer 27

5.2.1 Microwave Part 27

5.2.2 The Noise Figure and the Sensitivity of the Radiometer 295.2.3 The IF Circuitry and the Detector 30

5.2.4 The Extreme Signal Levels 32

5.2.5 The LF Circuitry 33

5.2.6 The Analog-to-Digital Converter 34

5.2.7 On the Sampling in the Radiometer: Aliasing 37

5.3 The Noise-Injection Radiometer 38

5.4 The Total Power Radiometer 40

5.4.1 DSB Receiver without RF Preamplifier 40

5.4.2 SSB Receiver with RF Preamplifier 42

5.5 Stability Considerations 43

References 44

6 The DTU Noise-Injection Radiometers Example 47

References 53

7 Polarimetric Radiometers 55

7.1 Polarimetry and Stokes Parameters 55

7.2 Radiometric Signatures of the Ocean 57

7.3 Four Configurations 57

7.3.1 Polarization Combining Radiometers 57

7.3.2 Correlation Radiometers 60

7.4 Sensitivities 62

7.5 Discussion of Configurations 64

vi Microwave Radiometer Systems: Design and Analysis



7.6 The DTU Polarimetric System 64

References 68

8 Synthetic Aperture Radiometer Principles 69

8.1 Introduction 69

8.2 Practical Considerations 72

8.2.1 RF Processing 72

8.2.2 Basic Equation 73

8.2.3 Image Processing 74

8.2.4 Sensitivity 758.3 Example 76

References 78

Selected Bibliography 79

9 Calibration and Linearity 81

9.1 Why Calibrate? 81

9.2 Calibration Sources 82

9.3 Example: Calibration of a 5-GHz Radiometer 86

9.4 Linearity Measured by Simple Means 87

9.4.1 Background 88

9.4.2 Simple Three-Point Calibration 89

9.4.3 Linearity Checked by Slope Measurements 92

9.4.4 Measurements 93

9.5 Calibration of Polarimetric Radiometers 96

References 98

10 Sensitivity and Stability: Experiments

with Basic Radiometer Receivers 99

10.1 Background 99

10.2 The Radiometers Used in the Experiments 100

10.3 The Experimental Setup 101

10.4 5-GHz Sensitivity Measurements 102

Contents vii



10.5 Stability Measurements 103

10.5.1 Discussion of the 5-GHz DR Results 103

10.5.2 The 5-GHz DR with Correction Algorithm 105

10.5.3 The 17-GHz NIR Results 109

10.5.4 Discussion of the TPR Results 111

10.5.5 Back-End Stability 113

10.6 Conclusions 114

References 115

11 Radiometer Antennas and Real Aperture Imaging

Considerations 117

11.1 Beam Efficiency and Losses 117

11.2 Antenna Types 119

11.3 Imaging Considerations 121

11.4 The Dwell Time Per Footprint Versus the Sampling

Time in the Radiometer 125

11.5 Receiver Considerations for Imagers 130

References 131

12 Relationships Between Swath Width, Footprint,

Integration Time, Sensitivity, Frequency, and Other

Parameters for Satellite-Borne, Real Aperture

Imaging Systems 133

12.1 Mechanical Scan 134

12.2 Push-Broom Systems 139

12.3 Summary and Discussion 140

12.4 Examples 143

12.4.1 General-Purpose Multifrequency Mission 143

12.4.2 Coastal Salinity Sensor 143

12.4.3 Realistic Salinity Sensor 144

13 First Example of a Spaceborne Imager: A

General-Purpose Mechanical Scanner 147

13.1 Background 147

viii Microwave Radiometer Systems: Design and Analysis



13.2 System Considerations 149

13.2.1 General Geometric and Radiometric Characteristics 149

13.2.2 Instrument Options 152

13.2.3 Baseline Instrument Specifications 156

13.2.4 Instrument Layout and Receiver Type 156

13.3 Receiver Design 157

13.3.1 The Direct Receivers (10.65–36.5 GHz) 157

13.3.2 The 89-GHz DSB Receivers 158

13.3.3 Integrated Receivers: Weight and Power 159

13.3.4 Performance of the Receivers 16013.3.5 Critical Design Features 161

13.4 Antenna Design 163

13.5 Calibration and Linearity 165

13.5.1 Prelaunch Radiometric Calibration 165

13.5.2 On-Board Calibration 166

13.6 System Issues 167

13.6.1 System Weight and Power 167

13.6.2 Data Rate 168

13.7 Summary 169

References 170

14 Second Example of a Spaceborne Imager: A Sea

Salinity/Soil Moisture Push-Broom Radiometer System 171

14.1 Background 171

14.2 The Brightness Temperature of the Sea 172

14.3 The Brightness Temperature of Moist Soil 175

14.4 User Requirements for Geophysical and Spatial

Resolution 177

14.4.1 Salinity Measurements 177

14.4.2 Soil Moisture Measurements 177

14.5 A 1.4-GHz Push-Broom Radiometer System 177

14.5.1 Sensitivity Considerations 177

14.5.2 The 1.4-GHz Noise-Injection Radiometer Receiver 178

Contents ix



14.5.3 Antenna Considerations 181

14.5.4 Layout of the System 181

14.6 Calibration 184

14.7 A Disturbing Factor: The Faraday Rotation 186

14.7.1 The Faraday Rotation 186

14.7.2 Correction Based on Knowing the Rotation Angle 187

14.7.3 Correction Based on the Polarization Ratio 189

14.7.4 Consequences for Instrument Design 191

14.7.5 Circumventing the Problem by Using the First Stokes

Parameter 191

14.8 Other Disturbing Factors: Space and Atmosphere 192

14.8.1 Space Radiation 192

14.8.2 Atmospheric Effects 193

14.9 Summary 193

References 194

15 Examples of Synthetic Aperture Radiometers 197

15.1 Introduction 197

15.2 Implementation of Synthesis 198

15.3 Airborne Example: ESTAR 200

15.3.1 Hardware 200

15.3.2 Image Reconstruction 204

15.3.3 Calibration 205

15.3.4 Discussion 207

15.3.5 Example of Imagery 208

15.4 Spaceborne Examples 211

15.4.1 HYDROSTAR 211

15.4.2 SMOS 214

References 217

Acronyms 219

Index 221

x Microwave Radiometer Systems: Design and Analysis



Preface

Two important microwave remote sensors are the radar and the radiometer.There have been a number of books written on various aspects of radar, butthere have been only a few written on microwave radiometers, especially on sub-

jects of how to design and build radiometer systems. This book, which is thesecond edition of a book originally published in 1989, attempts to fill this void.The background for this book is many years of work with radiometer systems

including design and manufacture of airborne imaging radiometer systems, lab-oratory as well as airborne field experiments with the systems, and design of future spaceborne imagers. This book would not have been possible without thesupport and encouragement of several colleagues. Søren Nørvang Madsen, whois working with synthetic aperture radar systems, and, before him, FinnSøndergaard have both contributed much to the work with radiometer systemsthrough many fruitful discussions and via joint airborne experiments. Muchsupport was received from Professor P. Gudmandsen, especially in the initial

phases. The value of fruitful interaction with Ph.D. students like Brian Laursenand Sten Søbjærg also cannot be overestimated. Finally, the partnership withCalvin Swift and several of his students in the development of the syntheticaperture radiometer, ESTAR, provided invaluable learning that helped makethis book possible.

xi



1Introduction

This book is the second edition of the book originally published in 1989. Thereason for updating the book is twofold: Certain issues are outdated, and new developments and concepts have emerged.

Of course, all the basic principles and concepts are still valid, and parts of the chapters are largely unchanged from the first edition. However, when itcomes to practical examples, like for example, the design of a spaceborne radi-

ometer system, significant technology developments must be taken intoaccount: A spaceborne radiometer will hardly still be assembled using individual

waveguide components, but it will be implemented using Monolithic Micro- wave Integrated Circuit (MMIC) technology in order to save significantly on weight and bulk.

A completely new concept has also received considerable attention lately,namely, the polarimetric radiometer measuring the full Stokes vector. A new chapter, Chapter 7, is dedicated to this important new technique. Most impor-

tantly, the synthetic aperture—also called interferometric —radiometer has beendeveloped for Earth remote sensing. This is indeed a very interesting and impor-tant new technique that does a lot towards solving the problem associated withhigh-resolution imaging, especially at low microwave frequencies requiring largeantenna apertures.

This book describes many years of work with microwave radiometers andradiometer systems. It concentrates very much on practical experiences and how to do it, not on the theoretical backgrounds. It is assumed that the reader isfamiliar with the basics of radiometry—to a level comparable with that given in[1]. Actually, this book may be seen as a continuation of [1], which ends where

1



much of the fun (and much of the trouble!) starts: namely, when the realizationof the ideas and theories is commenced.

This book deals with radiometers used for sensing the surface of the Earth.

Radiometers are also used for sensing the atmosphere and used within radioastronomy. There are, however, adequate differences, especially from a practicalpoint of view, to warrant a dedicated treatment for each application. Earth sens-ing receivers are typically characterized by relatively high brightness tempera-tures (100–300K), short integration times, and relatively large bandwidths.Radio astronomy receivers are often faced with very low brightness temperaturesand narrow bandwidths (spectral measurements) but large integration times(although there are also wideband examples like the observation of the cosmicbackground). Atmospheric sensors may face a mixture of the above: high tem-

peratures but narrow bandwidths (spectroscopy) and long integration times(although there are short integration time examples like spaceborne limb sound-ing). Radiometer receivers for radio astronomy are dealt with in [2], forexample.

The practical background for the book can be described in a few keynotes:

• Design and manufacture of airborne, multifrequency, imaging radiom-eter systems including polarimetric systems, imaging antennas, and syn-

thetic aperture systems;• Calibration exercises including linearity and stability assessments using

the radiometers of the airborne system;

• Several airborne experiments with the systems measuring sea ice aroundGreenland; oil pollution, wind vectors, and salinity in European andU.S. waters; soil moisture in Europe and United States;

• Design and evaluation of spaceborne radiometer systems for specificpurposes, based on the practical experience with the airborne systems.

References

[1] Ulaby, F. T., R. K. Moore, and A. K. Fung, Microwave Remote Sensing, Vol. 1, Dedham,MA: Artech House, 1981.

[2] Evans, G., and C. W. McLeish, RF Radiometer Handbook, Dedham, MA: Artech House,1977.

2 Microwave Radiometer Systems: Design and Analysis



2Summary

Overall the book can be divided into two main parts: one part consisting of Chapters 3 through 12 describing the fundamentals of how to make a radiome-ter system and leading up to another part consisting of Chapters 13 through 15describing how to arrive at a system design from certain specifications, whetherit is purely technical or whether it takes geophysical realities into account.

Chapter 3, “The Radiometer Receiver: Sensitivity and Accuracy,” explains

what a radiometer is, namely, a sensitive, calibrated microwave receiver. Radio-metric sensitivity is defined and explained. The basic sensitivity formula isdescribed. Absolute accuracy is explained and some of the problems associated

with it are stressed.Chapter 4, “Radiometer Principles,” describes the four major classical

radiometer principles: total power, Dicke, noise-injection, and correlation radi-ometers. Their sensitivities are derived from the basic sensitivity formula. It isalso discussed how modern technology enables circuit implementations that

softens the distinction between total power and Dicke radiometers (the hybridradiometer). Additional radiometer principles are only briefly mentioned (forthe sake of completeness), as they are not normally used for Earth sensing.

Chapter 5, “Radiometer Receivers on a Block Diagram Level,” is animportant engineering chapter. We discuss whether to use direct or superhetero-dyne receivers and how to combine double-sideband or single-sideband mixeroperation (in the latter) with a possible microwave preamplifier. After that, a Dicke radiometer is worked through in detail on a block diagram level. Somespecifications are fixed (frequency, bandwidth, and so forth) so that signallevels, gains, and signal-to-noise ratios can be discussed realistically. Signals aresketched and discussed throughout the receiver. The sampling process (and

3



possible aliasing) associated with the analog-to-digital conversion is discussed.The Dicke radiometer is enhanced to a noise-injection radiometer. This in turnre- quires new gains, new signal levels, and the stability of the feedback loop is

assessed. The total power radiometer is worked through stressing its specialfeatures and problems: dc stability, offset, tunnel diode detector, and so forth.The opportunity to discuss the differences between a double-sideband receiver

without preamplifier and a single-sideband receiver with preamplifier is takenhere: The total power radiometer is implemented both ways. Finally, some gen-eral comments about stability and the AC coupling in Dicke type switching radiometers are made.

The DTU (Technical University of Denmark) noise-injection radiometersystem is briefly reviewed in Chapter 6, “The DTU Noise-Injection Radiome-

ters Example,” partly to facilitate a discussion of important features in practicalradiometer design (temperature-stabilized RF enclosure and digital thermome-ter) and partly to introduce the radiometers that are used in the investigations of Chapters 9 and 10.

The radiometers discussed so far are traditionally used to measure the ver-tically and horizontally polarized brightness temperatures by connecting themto properly polarized antenna ports. Chapter 7, “Polarimetric Radiometers,”describes the extension associated with the measurement of the full set of Stokes

parameters. There are two fundamentally different ways of implementing thepolarimetric radiometer system: polarization combining or correlation radiome-ter systems. Also, within each fundamental category there are significant trade-offs. This chapter discusses the different implementation possibilities.Paramount issues are potential instrument stability and sensitivity as well as thetradeoff between increased microwave hardware complexity and fast digitalcorrelator circuitry. Another important issue is the isolation between channels.Finally, an airborne, imaging polarimetric radiometer system, used for ocean

wind direction sensing, is described and discussed.Chapter 8: “Synthetic Aperture Radiometer Principles” marks a significantchange in instrument design philosophy. The chapter introduces the basic con-cept of aperture synthesis and provides a motivation for why one would chooseto use it for remote sensing. The basic equations and the RF circuitry necessary for coherent processing are presented in simplified form. The approximationsand parameters (sensitivity, resolution, and fringe washing) needed to design a sensor system using this concept are presented. Chapter 8 concludes with anexample for an idealized system (uniform sampling on a Cartesian grid) to illus-trate the principles and performance that can be expected.

Chapter 9, “Receiver Calibration and Linearity,” explains the purpose of calibration and how to do it. Calibration facilities are presented and, as an exam-ple, a calibration curve for a 5-GHz noise-injection radiometer is shown. Linear-ity is often taken for granted due to the low signal levels in radiometers, but for




modern radiometers with tough calibration requirements, it may have to bechecked. Simple setups to do this are presented.

Chapter 10, “Sensitivity and Stability: Experiments with Basic Radiometer

Receivers,” is a substantive chapter, trying to answer the question that many must have posed: Is the noise-injection radiometer (NIR) really superior to theDicke radiometer concerning stability, which in turn is superior to the totalpower radiometer concerning the same issue—given real-life instruments withpossibly imperfect components and thermal conditions? Using thealready-described radiometers (properly modified for the purpose), extensivemeasurements of the stability against thermal variations inside the instrumentshave been carried out regarding the Dicke, the NIR, and the total power mode.The thermal variations were designed to resemble those that may be encoun-

tered in a satellite orbiting the Earth. The answer to the question is: Yes, theNIR is superior, but both the Dicke and the total power radiometers are wellbehaved; the variations in their outputs can be explained and modeled; hence,simple correction algorithms can be applied. Finally, the radiometer sensitivity formulas for the three modes are confirmed by measurements of sensitivities.

The antenna is an important part of a radiometer system, warranting a brief description in Chapter 11, “Radiometer Antennas and Real ApertureImaging Considerations.” Antenna types, loss, and beam efficiency are key

words. Imaging antenna systems are discussed: the line scanner, the conicalscanner, and the push-broom system. The dwell time per footprint is definedand the proper sampling of the antenna signal is discussed. We find that for real-istic antenna patterns a sampling time of 0.7 times the dwell time per footprintensures aliasing-free sampling. Finally, we discuss how the different radiometermodes each have their role to play in the different imagers: the total power radi-ometer in scanners and the Dicke type switching radiometers (especially theNIR) in push-broom systems.

Chapter 12 deals with the relationships between swath width, footprint,integration time, sensitivity, frequency, and so forth for satellite-borne, realaperture imaging systems, and it describes the differences between scanning sys-tems and push-broom systems: Small footprints and tough requirements to sen-sitivity favor the push-broom solution. Two examples illustrate this.

Chapter 13, “First Example of a Spaceborne Imager: General-PurposeMechanical Scanner,” deals with a system much like SSM/I—using a 1-m aper-ture and better receivers—and it is included to enlighten the special aspects of a mechanical scanner. The design is based on technical specifications (not specifi-cations to geophysical measurements). A tradeoff is carried out between thenumber of antenna beams (hence receivers) per frequency (at the highest fre-quencies) and sensitivity potential plus antenna scan rate. Rough designs of thereceivers are carried out, resulting in weight and power budgets. A few aspects of

Summary 5



the antenna design are covered, and calibration, prelaunch as well as in-orbitchecks, is discussed.

Chapter 14, “Second Example of a Spaceborne Imager: A Sea Salinity/Soil

Moisture Push-Broom System,” shows how we arrive at the design of a systembeginning with specific geophysical measurement requirements. From a modelfor the brightness temperature of the sea, we determine frequencies and polariza-tions to be measured. From a study of relevant literature, we find that soil mois-ture measurements are well supported using the same channels. Based on thisand user requirements for ground resolution and geophysical parameter resolu-tion, system considerations are carried out. A suitable 1.4-GHz noise-injectionradiometer is designed, weight and power budgets are made, some consider-ations are given for the highly specialized push-broom antenna, and a layout of

the total system is sketched. Calibration checks, once in orbit, are necessary foreven the best radiometer design, and aspects of this are considered with specialemphasis on the problems associated with push-broom systems. A dedicatedpush-broom calibration scheme, in which a relative intercalibration of all chan-nels (entirely done in the data analysis process) is carried out together with abso-lute calibration of one channel (using conventional sky horn and hot loadtechnique), is described. Disturbing factors like Faraday rotation, spaceradiation, and atmospheric effects are considered with special emphasis on the

Faraday rotation.Finally, Chapter 15, “Examples of Synthetic Aperture Radiometers,”

begins with a description of the trades that are involved in designing a syntheticaperture radiometer for Earth remote sensing. Then a description is given of three synthetic aperture radiometers. The first is a real (i.e., existing) aircraft sen-sor called, ESTAR. This is a well-known instrument that was critical in demon-strating the viability of this technology for remote sensing. The hardware isdescribed (with a picture) as well as the techniques employed for image recon-

struction and calibration. An image from a soil moisture experiment is also pre-sented. The second example is a sensor called HYDROSTAR that has beenproposed for remote sensing from space. Design parameters are given together

with expected performance. This instrument is similar in principle to the aircraftinstrument, and therefore, it is easy for the reader to imagine how it will per-form. Finally, the MIRAS/SMOS system, a spaceborne system with aperturesynthesis in two dimensions, is briefly described.




3The Radiometer Receiver: Sensitivity andAccuracy

3.1 What Is a Radiometer Receiver?

The objective of a radiometer is to measure power. However, in many microwave applications, such as remote sensing of the Earth’s surface, it is commonpractice to express power in terms of an equivalent temperature. This may be thetemperature of a blackbody that would radiate the same power, called the brightness temperature, T B , or the temperature of a resistor (termination) that has thesame output power as that of the receiving antenna, called the antenna temperature, T A . At microwave frequencies the Rayleigh-Jeans law is applied to expresspower in terms of temperature.

Now, consider an idealized antenna pointed towards an object of interest with equivalent brightness temperature, T B (see Figure 3.1).

The output power of the antenna is expressed in terms of its antenna tem-

perature, T A . The goal of the measurement is usually to relate the antenna tem-perature to the brightness temperature of the object. The task of the microwaveradiometer is to measure this antenna temperature with sufficient resolution andaccuracy that this connection can be made. In this sense, the radiometer is sim-ply a calibrated microwave receiver.

3.2 The Sensitivity of the Radiometer

The next step in the description of the microwave radiometer is illustrated inFigure 3.2.

7



The radiometer selects a certain portion of the available output powerfrom the antenna, that is, a certain bandwidth B around a given center fre-quency. This power is amplified (G ) and presented, in a suitable fashion, tosome output medium, here illustrated by a simple power meter. The metermeasures:

P k B G T A = ⋅ ⋅ ⋅ ( ) watts (3.1)

where k is Boltzmann’s constant: 1.38 × 10−23 J/K. Figure 3.2 shows a highly idealized radiometer. In real life the radiometer will generate noise, and thisnoise will add to the input signal (Figure 3.3).

As the antenna signal is also a noise signal and the two signals are inde-pendent, they will add and cannot be separated later. The meter now measures:

( )P k B G T T A N = ⋅ ⋅ ⋅ + (watts) (3.2)

To illustrate the sensitivity problem associated with all radiometer mea-surements, let us consider a case, where an antenna temperature of 200K isneeded with 1-K resolution. A possible value for T N is 800K. So we are faced

with the problem of finding a 1-K signal on top of a total signal of 1,000K; or,to put it differently, we want to see the difference between 1,000K and 1,001K.Note: It must continuously be remembered that the signals we discuss here arenoise signals having a well-defined mean but with a random fluctuation about


Object

Antenna

P power to be

measured

=

TB

Figure 3.1 The measurement situation.

TA

Radiometer

B, G P = k·B·G·TA

Figure 3.2 Idealized radiometer.

TA

TN

Radiometer

B, G P k·B·G·(T= A N+ T )

Figure 3.3 “Real” radiometer.



the mean. In the ideal case the fluctuations can be reduced by averaging (integration). The resulting sensitivity (standard deviation of the output signal)is:

∆T T T

B

A N =

+

⋅ τ(3.3)

This is the basic radiometer sensitivity formula, in which T A is the inputtemperature to the radiometer, T N is its noise temperature, B is its bandwidth,and τ is its integration time (how the integration is carried out will be shownlater). The sensitivity formula is quite difficult to arrive at, and it shall not be

derived here. For more information on the derivation of this result, see [1, 2]. A typical example using figures already quoted shall be given. Consider a radiometer having a noise temperature of 800K, a bandwidth of 100 MHz, andan integration time of 10 ms. An antenna signal of 200K can then be measured

with a resolution of:

∆

∆

T

T

= +

⋅

=

−

200 800

10 10

1

8 2K

K

3.3 Absolute Accuracy and Stability

Apart from sensitivity, stability and absolute accuracy are problems to consider.Let us take a closer look at the equation linking input and output quantities:

( )P k B G T T A N = ⋅ ⋅ ⋅ + (3.4)

If k , B , G , and T N are really constants, we have no stability problems: A given T A results in a certain P · k is, of course, a constant, and B is relatively sta-ble and need not worry us too much. The bandwidth of the radiometer is deter-mined by a filter, that is, a passive component, and if this is designed and built

with care, we can assume a stable bandwidth. What about gain and noise tem-perature? Both represent specifications for active components like amplifiers or

mixers, and both are dependent on, for example, supply voltage and physicaltemperature. Let us again consider the previous example with T A = 200K and T N

= 800K. The resolution was found to be 1K, and it would be reasonable to aimat an absolute accuracy also of 1K. This means determining 1K on 1,000K, andboth G and T N must be known and stable to within less than 1 per thousand,

which corresponds to 0.004 dB, and it is not difficult to see the problem in

The Radiometer Receiver: Sensitivity and Accuracy 9



keeping the gain of a 100-dB amplifier (a typical value in a radiometer) stable tobetter than 0.004 dB! However, there are ways around these problems, as will bedescribed in the following, starting with Chapter 4.

If k , B , G , and T N are not only constants but also known constants, weadditionally have no absolute accuracy problems: a given T A results in a given P that can be calculated. Such knowledge of the constants are rarely available,leading to the necessity for calibration (see Chapter 9). This illustrates the fun-damental difference between stability and accuracy: Stability is a highly appreci-ated virtue of an instrument, but a stable instrument need not be accurate. Thesteps towards accuracy includes the calibration process.

In the following we will describe a slightly different aspect of absoluteaccuracy, which stresses the care that must be exercised when designing or work-

ing with radiometers. Consider losses in a signal path—it could be the wave-guide connecting the antenna with the radiometer input or a passive componentin the radiometer front end (see Figure 3.4).

The symbol denotes the fractional loss (or the absorption coefficient)and T o is the physical temperature. T 1 is the input temperature and the outputtemperature is:

( )T T T o 2 1 1= − + ⋅ (3.5)

The difference between output and input is:

( )T T T T T D o = − = −2 1 1 (3.6)

If T 1 is 100K and T o is 300K, a loss as small as 0.01 dB ( = 0.0023)results in a difference, T D , of 0.5K. Bearing in mind that the losses of a real sig-nal path are much greater than 0.01 dB, the physical temperature of the path

must be measured and used for correction of the measured brightness tempera-ture. The corresponding losses must be known to an accuracy of better than0.01 dB and must remain stable within the same limits.

Consider a mismatch, for example, at the input of a radiometer, with a reflection coefficient ρ (Figure 3.5):

( )T T T RAD 2 1 1= − + ⋅ ρ ρ

(3.7)


T1 T2

T0

Figure 3.4 Lossy signal path.



( )T T T T T D RAD = − = −2 1 1 ρ (3.8)

where T RAD is the microwave temperature as seen from the point of reflectioninto the radiometer.

T RAD is typically 300K and if T 1 again is assumed to be 100K, a reflectioncoefficient of −26 dB will give an error (T D ) of 0.5K. Care must be exercised toobtain reflection coefficients better than −26 dB.

References


[2] Tiuri, M. E., “Radio Astronomy Receivers,” IEEE Trans. on Antennas and Propagation,Vol. 12, No. 7, 1964, pp. 930–938.

The Radiometer Receiver: Sensitivity and Accuracy 11

T1 T2

ρRadiometer

Figure 3.5 Mismatch at input.



4Radiometer Principles

The extremely simplified block diagram of a radiometer, as displayed in Figure3.3, will in this chapter be somewhat elaborated as a first step towards a fullblock diagram to be discussed in later sections. Some of the principles used toavoid degradation of accuracy due to gain and noise temperature instabilities

will be worked through.

4.1 The Total Power Radiometer (TPR)

In principle we are still talking about the same radiometer as discussed in Chap-ter 3, but the block diagram has been expanded in Figure 4.1, to explain betterthe function of the radiometer. The gain in the radiometer has been symbolizedby an amplifier with a gain G , and the frequency selectivity has been symbolizedby a filter with a bandwidth B (centered around some given frequency). Themicrowave power has to be detected to find some measure of its mean. Twostraightforward detector types can be made, using microwave semiconductordiodes: the linear detector and the square-law detector. In the present case, it isvery attractive to use the square-law detector. Then the output voltage will beproportional to the input power and hence the input temperature. Finally, weindicate where the integration takes place: The signal from the detector issmoothed by the integrator to reduce fluctuations in the output, and the longerthe integration time, the more smoothing there is.

The output can be expressed as:

( )V c T T G OUT A N = ⋅ + ⋅ (4.1)

13



where c is a constant. V OUT is totally dependent on T N and G . These can, forsome applications, not be regarded as stable enough to satisfy reasonablerequirements for accuracy. In other cases, however, the total power radiometer isvery useful, namely, where frequent calibration, for example, once every few sec-

onds, is possible.The sensitivity of the total power radiometer shall for completeness berepeated here:

∆T T T

B

A N = +

⋅ τ

(4.2)

4.2 The Dicke Radiometer (DR)

In 1946 R. H. Dicke found a way of alleviating the stability problems in radi-ometers [1]. By using the radiometer not to measure directly the antenna tem-perature, but rather the difference between this and some known referencetemperature, the sensitivity of the measurement to gain and noise temperatureinstabilities are greatly reduced (see Figure 4.2).

The input of the radiometer is rapidly switched between the antenna tem-perature and the reference temperature. The switch frequency F S is typically 1,000 Hz. The output of the square-law detector is multiplied by +1 or −1,depending on the position of the Dicke switch, before integration. The input tothe integrator is then


TA

G B x2

τ

VOUT

TN

~~~

Figure 4.1 Total power radiometer.

TA

TR

G B x2

τ

VOUT

FS

±1

TN

~~~

Figure 4.2 Dicke radiometer.



( )V c T T G A N 1 = ⋅ + ⋅

in one half-period of F S , and

( )V c T T G R N 2 = − ⋅ + ⋅

in the second half-period.Provided that the switch frequency F S is so rapid that T A , T N , and G can be

regarded as constants over the period, and that the period is much shorter thanthe integration time, the output of the radiometer is found as:

( ) ( )( )

V V V c T T G c T T G

V c T T G

OUT A N R N

OUT A R

= + = ⋅ + ⋅ − ⋅ + ⋅

= ⋅ − ⋅1 2

(4.3)

It is seen that T N has been eliminated, while G is still present, although with less weight. Now G multiplies the difference between T A and T R , where T R

is reasonably chosen to be in the same range as T A , while in the total power case,G multiplied the sum of T A and the rather large T N . The Dicke principle hasproven to be very useful, and Dicke radiometers have been used extensively over

the years. A price has to be paid, however, for the better immunity to instabilities.Since only half of the measurement time is spent on the antenna signal (theother half is spent on the reference temperature), the sensitivity is poorer thanfor the total power radiometer.

The output of the Dicke radiometer can be regarded as the differencebetween the outputs of two identical total power radiometers: TPR1 measuring the antenna signal and TPR2 measuring the reference signal. Each radiometeruses an integration time of τ/2. The standard deviation of the output fromTPR1 is [using (4.2)]:

∆T T T

B

A N 1

2=

+

⋅ τ

and for TPR2:

∆T T T

B R N 2

2= +

⋅ τ

As the output signals are statistically independent, the standard deviationof the difference signal is:

Radiometer Principles 15



( ) ( )[ ]( ) ( )

∆ ∆ ∆

∆

∆

T T T

T T T

B

T T

B

T

A N R N

= +

= +

⋅ +

+

⋅

=

1

2

2

2 1 2

2 2 1 2

2 2

2

τ τ

( ) ( )( )T T T T

B

A N R N + + +

⋅

2 2 1 2

2

τ

(4.4)

T R is, as mentioned earlier, selected as close to T A as possible, and T R isoften replaced by T A in (4.4), which then reduces to:

∆T T T

B

A N = ⋅ +⋅

2 τ

(4.5)

It is seen that the sensitivity of the Dicke radiometer is degraded by a fac-tor of 2 compared with the total power radiometer.

Alternatively, we can replace T A by T R in (4.4), and we find:

∆T

T T

B

R N

= ⋅

+

⋅2 τ (4.6)

which will be the conservative version of the sensitivity formula for Dicke radi-ometers since usually T R > T A . The truth lies between (4.5) and (4.6) but this isnormally ignored in real life, and either formula can be used.

4.3 The Noise-Injection Radiometer (NIR)

The noise-injection radiometer represents the final step towards stability; that is,the output is independent of gain and noise temperature fluctuations [2, 3].

From (4.3) it is seen that the output from a Dicke radiometer is zero (inde-pendent of G and T N ) if the reference temperature and the antenna temperatureare equal. The noise-injection radiometer is a specialization of a Dicke radiome-ter in which this condition is continuously fulfilled by a servo loop.

In almost any case encountered in Earth remote sensing, the antenna tem-perature is below about 300K (emissivities between 0 and 1 are multiplied by the physical temperature). The reference temperature in a Dicke radiometer isconveniently equal to the physical temperature in the microwave front end, thatis, 300–320K. In Figure 4.3 we show how the output T I of a variable noise gen-erator is added to the antenna signal TA, so that the resultant input ( )T A ′ to the




Dicke radiometer is equal to the reference temperature (T R ), and a zero outputresults from it. A servo loop adjusts T I to maintain the zero output condition, orrather the near zero output condition: The loop gain can be made large but notinfinite.

From (4.3) we have:

( )V c T T G OUT A R = ⋅ − ⋅ =′ 0

and as

T T T A A I ′ = +

we find:

T T T A R I = −

T R is a known constant, and knowledge of T I is required to find T A . Theaccuracies of the Dicke radiometer part of the NIR and of the loop gain are,given large loop gain, completely insignificant for the accuracy with which wedetermine T A . This is solely dependent on the accuracy of T I . Accurate and sta-

ble noise sources with variable output can be made, and they are used for“injecting” the required signal T I into the input line, so that T I and T A are added.

The sensitivity of the noise-injection radiometer is easily found using (4.5):

∆T T T

B

A N = ⋅ +

⋅′2

τ

But asT A ′ is equal to T R , we find:

∆T T T

B

R N = ⋅ +

⋅2

τ

(4.7)


TA

V 0OUT ≈Dicke

radiometer

TI

TA’

T T TA’ A I= +

Loop

gain

Figure 4.3 Noise-injection radiometer.



The sensitivity of the noise-injection radiometer is very close to that of theDicke radiometer; see (4.5) and (4.6) and the associated discussion.

The noise-injection radiometer includes a feature worthy of further elabo-

ration. The front-end circuitry in a radiometer is illustrated in Figure 4.4.If these components are surrounded by a temperature stabilized box keptat the physical temperature equal to T R , the radiometric reference can be a microwave termination. An isolator is added after the filter to obtain

well-defined output conditions. For the noise-injection radiometer the situationis then as shown in Figure 4.5.

The input signal can be substituted by a termination on the switch insidethe enclosure. The enclosure thus contains only passive components, all of tem-perature T R , and the output signal is:

P k T B OUT R = ⋅ ⋅

independent of details about the circuitry, and in particular independent of losses and reflections in the embedded Dicke radiometer. Of course, the accu-racy of the radiometer is still dependent upon the accuracy with which theinjected noise is known (i.e., upon the quality of the noise source and othercomponents in the noise injection circuitry).

4.4 The Correlation Radiometer (CORRAD)

The correlation radiometer is a multichannel system that finds use in the case where two brightness temperatures are measured as well as the correlationbetween them. This is the case in the polarimetric radiometer (see Chapter 7),


TR

TA FilterSwitch

Figure 4.4 Radiometer front end.

TR

TA’ R

T=

Tphys RT=

Switch Filter Isolator

Figure 4.5 NIR front end.



where the vertical and the horizontal brightness temperatures are measuredtogether with their correlation, thus finding the so-called Stokes parameters.This is also the case in interferometric radiometers like the synthetic aperture

radiometer (see Chapter 8), where the outputs of two different antennas point-ing in the same direction in space are measured.The correlation radiometer is shown in Figure 4.6. Two identical receiv-

ers, which here are total power radiometers, are connected to the two outputports of the antenna system. The outputs of the receivers are detected the usual

way to yield the normal brightness temperatures. The signals of the receivers arealso (before detection) fed into the complex correlator providing the real and theimaginary parts of the cross correlation between the two input signals from theantenna system.

For the two normally detected outputs, we, of course, find the usual sensi-tivity of a total power radiometer as shown in (4.2)—let us call it ∆T TPR (assum-ing identical receiver performance). The correlator outputs have a sensitivity that can be found by considering the analogy to the radio astronomer’s interfer-ometer with correlation receiver [4]: If the interferometer observes a smallsource in the boresight direction, and it is assumed that the two radiometerchannels collect equal but independent background noise, the sensitivity isexpressed as ∆T = ∆T TPR / 2 (the two receivers are identical with a sensitivity

∆T TPR ). It is thus assumed that the two input signals are only weakly correlatedand can be modeled as sums of large “background” signals (uncorrelated chan-nel to channel) and a small correlated signal. This is the case for the applicationsto be considered later in this book.

Concerning stability, the situation is much like that for the total powerradiometer, and proper attention to frequent calibration schemes must be exer-cised. Note, however, that the correlator outputs are relatively more stable thanthe total power outputs: Since the internally generated noise in the two receivers


real

imag

TA1

G B x2

τ

VOUT1

TN1

TA2

G B x

2 τ

VOUT2

TN2

~~~

~~~

Complex

corr.

Figure 4.6 Correlation radiometer.



is uncorrelated, these noise signals do not contribute to the correlator outputs.There will be more about stability in Chapter 7.

4.5 Hybrid Radiometer

The radiometers as described hitherto in this chapter are the classical receivertypes, and their implementation are indicated in the classical way using forexample analog integration after detection, and analog subtraction of antenna and reference signals (in the Dicke radiometer). Indeed, many radiometers arestill implemented this way. However, with the advent of analog-to-digital con-verters and digital processing, other implementation forms are possible and

often used. This is illustrated in Figure 4.7. As soon as possible following detection, the signal is analog-to-digital con-

verted—only a low-pass filter is indicated to condition the signal bandwidth tothe sampling frequency of the converter. The signal from the converter is led tosome kind of digital processor, typically a PC or a field programmable gate array (FPGA), where suitable data handling takes place. This can typically be digitalintegration to the required integration time τ, as well as subtraction of theantenna signal and the reference signal. Since these processes are under com-

puter control, flexibility becomes a keyword, and the distinction between totalpower and Dicke radiometer vanishes to some extent. If the processor operatesthe input switch rapidly and regularly, we can regard it as a Dicke case, while if the measurement situation is such that the antenna signal can be measured (withinterruptions when the switch points to the reference signal) without loss of data, then we have a total power case with frequent calibration. There will bemuch more about this in Chapter 13.

A classical Dicke radiometer spends half of its time measuring the well-known reference temperature and thus only half of its time doing its real job, namely, measuring the unknown antenna temperature. Thus, over the yearsresearchers have considered a better duty cycle for the antenna measurements (inturn potentially leading to improved sensitivity). See, for example, [5]. How-ever, having an analog subtraction of the signals, the 50% duty cycle is


TA

TR

G B x2

TN

~~~~~ A/D Processor

LPF

OUT

Figure 4.7 Hybrid radiometer.



instrumental to having simple and stable circuitry, but with the subtractiondone digitally, this is no longer a limitation, and optimized duty cycles can befound on a case-by-case basis. A word of warning: The naïve notion that spend-

ing more time on the unknown antenna signal will lead to improved sensitivity is not necessarily true! When more time is spent on the antenna, less time is leftfor the reference and this in turn leads to an increased standard deviation forthat measurement. Thus, the final standard deviation after subtraction mightnot decrease. This can actually be seen from the calculations in Section 4.2, butit can also be seen that for specific cases with specific values of T A , T N , and T R , anoptimization of the duty cycle and the sensitivity can be made. This will in gen-eral not be far from the classical values!

However, there are possible improvement schemes: Since the reference

temperature and the receiver noise temperature are assumed to be relatively sta-ble while the antenna temperature may change rapidly, averaging over severalreference temperature measurements will reduce the standard deviation of thismeasurement and thus allow a non-50% duty cycle to be employed. Initialinstrument fluctuations and averaging times must, of course, be considered care-fully. See a further discussion in [6].

In the present book only the classical radiometers will be discussed. Thereason is that this way all the difficult design issues are briefly covered. The cir-

cuitry for the hybrid radiometer is slightly simpler, so when the design of a clas-sical radiometer is familiar to the reader, the design of a hybrid radiometer isstraightforward.

4.6 Other Radiometer Types

The radiometer types already discussed are those that are widely used for sensing the properties of the Earth and are the ones that will be considered further in thefollowing chapters. However, other types have been suggested and they may find use for special purposes.

The two-reference radiometer [7] alleviates the problem with possible gaininstabilities still present in the basic Dicke radiometer. Two different referencetemperatures are alternatively selected and an extra synchronous detector willgive an output enabling determination of the gain and hence a correction of the

radiometer output. Also, the basic total power radiometer scheme can be modified to elimi-nate gain stability problems. In the noise-adding radiometer [8–10], a train of noise pulses is added to the antenna input signal. The ratio of the receiverdetected output during the noise “on” period to that during the noise “off”period is a measure of the gain. The added noise does, however, contribute to




the system noise temperature, and the full potential of the total power radiome-ter sensitivity cannot be exploited.

A variation of the noise injection radiometer suitable for correlation radi-

ometers should also be mentioned. This was developed at the University of Mas-sachusetts for use in the ESTAR radiometer (see Chapter 15). In this case, noiseis injected as described earlier (see Figure 4.3), but instead of using a Dicke radi-ometer, the switch at the front end (see Figure 4.5) is replaced by a hybrid. Thehybrid accepts two inputs (T A ′ = T A + T I ) and the signal from the reference load(T R ). The two outputs from the hybrid are the sum and difference: T A ′ ± T R .(The signals are labeled here as if they were power, but at this point, beforedetection, they are voltages.) The two signals (voltages) out of the hybrid thenbecome the input to a correlation radiometer such as that shown in Figure 4.6

but using only the path through the complex correlator. It is not difficult toshow that if the receiver noise in the two paths is independent, then the magni-tude of the output of the correlation receiver is V OUT = c ·(T A + T I – T R )·G 1·G 2

where G 1 and G 2 are the gains of the two paths in the correlation radiometer.Finally, the noise injection loop adjusts T I so that V OUT = 0. The special featureof this radiometer is that it does not require a Dicke switch and achieves the sta-bility of a noise injection radiometer. As in an NIR, the stability depends oncontrol of the reference load and noise source but is independent of receiver

gain.Even further radiometer types are possible—like the Graham receiver [11]

or different kinds of special correlation receivers [12–15]—but they only finduse within radio astronomy and thus clearly fall outside the scope of this book.

References

[1] Dicke, R.H., “The Measurement of Thermal Radiation at Microwave Frequencies,” Rev.Sci. Instr ., Vol. 17, 1946, pp. 268–279.

[2] Goggins, W. B., “A Microwave Feedback Radiometer,” IEEE Trans. on Aerospace and Elec- tronic Systems , Vol. 3, No. 1, 1967.

[3] Hardy, W. N., K. W. Gray, and A. W. Love, “An S-Band Radiometer Design with High Absolute Precision,” IEEE Trans. on Microwave Theory and Techniques , Vol. 22, No. 4,1974, pp. 382–390.

[4] Kraus, J. D., Radio Astronomy , 2nd ed., Powell, OH: Cygnus-Quasar, 1986.

[5] Bremer, J. C., “Improvement of Scanning Radiometer Performance by Digital Reference

Averaging,” IEEE Trans. on Instrumentation and Measurement , Vol. 28, No. 1, 1979,pp. 46–54.

[6] Tanner, A. B., W. J. Wilson, and F. A. Pellerano, “Development of a High-Stability L-Band Radiometer for Ocean Salinity Measurements,” Proc. of IGARSS’03 , 2003,pp. 1238–1240.




[7] Hack, J. P., “A Very Sensitive Airborne Microwave Radiometer Using Two ReferenceTemperatures,” IEEE Trans. on Microwave Theory and Techniques , Vol. 16, No. 9, 1968,pp. 629–636.

[8] Ohm, E. A., and W. W. Snell, “A Radiometer for a Space Communication Receiver,” Bell

System Technical Journal , Vol. 42, 1963, pp. 2047–2080.

[9] Batalaan, P. E., R. M. Goldstein, and C. T. Stelzried, “Improved Noise-Adding Radiome-ter for Microwave Receivers,” NASA Tech. Brief. 73-10345, JPL, 1974.

[10] Yerbury, M. J., “A Gain-Stabilizing Detector for Use in Radio Astronomy,” Rev. Sci.Instr., Vol. 46, No. 2, 1975, pp. 169-179.

[11] Graham, M. H., “Radiometer Circuits,” Proc. IRE , Vol. 46, 1958.

[12] Goldstein, S. J., “A Comparison of Two Radiometer Circuits,” Proc. IRE , Vol. 43, 1955.

[13] Fujimoto, K., “On the Correlation Radiometer Technique,” IEEE Trans. on Microwave

Theory and Techniques , Vol. 12, No. 3, 1954, pp. 203–212.[14] Clapp, R. E. and J. C. Maxwell, “Complex-Correlation Radiometer,” IEEE Trans. on

Antennas and Propagation , Vol. 15, No. 2, 1967, pp. 286–291.

[15] Aitken, G. J. M., “A New Correlation Radiometer,” IEEE Trans. on Antennas and Propa- gation , Vol. 16, No. 2, 1968, pp. 224–227.




5Radiometer Receivers on a BlockDiagram Level

The block diagram of a 17-GHz radiometer will be covered in some detail inorder to discuss the different aspects of designing a radiometer. The chapter willfirst concentrate on the design of an instrument operating in the Dicke mode,followed by comments to the necessary additions and special considerations

regarding the NIR mode. Finally, a total power instrument will be discussed. Inorder to enable the calculation and discussion of gains, signal levels, and so forththroughout the instrument, some major specifications will be given in Table 5.1.

Before proceeding to the specific examples, a few subjects of general natureare covered.

5.1 Receiver Principles

5.1.1 Direct or Superheterodyne

The radiometer is merely a very sensitive microwave receiver and, like any receiver, it employs front-end circuitry, which has two prime tasks: input fre-quency band selection, and amplifying the incoming signal to a proper level forthe detector and subsequent low-frequency circuitry. This amplification may have to be very large, typically 50–80 dB for microwave radiometers. It can beobtained by two entirely different schemes, either by direct use of amplifiers atthe input frequency (the direct receiver) or by use of a mixer, local oscillator, and

IF frequency amplifiers (the superheterodyne receiver). In the direct receiver, allamplification takes place at the input frequency, and all selectivity is determinedby filters in the same RF range. In the superheterodyne receiver most of the

25



amplification takes place at the much lower IF, and selectivity is determined by a combination of filters at RF and IF levels.

Regarding amplification, it has long been a desirable feature of the super-heterodyne receiver that most (or all) of the gain could be at IF level, due toeither unavailability of proper microwave amplifiers or very bulky and costly microwave amplifiers—at least until at few years ago. Now microwave FETamplifiers with excellent noise figures are available, covering the frequencies wellbeyond 40 GHz. Hence, the possibility of using direct receivers cannot beexcluded based on RF amplifier considerations.

Regarding selectivity, the direct receiver may run into problems. All selec-tivity is determined by the microwave filter meaning that many sections may berequired. Such a filter is lossy and bulky—the loss may deteriorate the noise fig-ure of the radiometer while bulky components should be avoided in some appli-cations like spaceborne instruments. The superheterodyne receiver includes a modest microwave filter for out-of-band suppression of strong signals, and thefinal selectivity is achieved by the IF filter. The microwave filter needs to only have a few sections (not excessively lossy or bulky) and at the IF level, filters of high order are small and easy to implement. Moreover, loss is of little concern.

Many microwave radiometers, and indeed most millimeter wave radiome-

ters (amplifiers not readily available), are made as superheterodyne receivers, andso too are most of the designs covered in this book. It should be noted that hav-ing understood the design of a superheterodyne receiver, a direct design will beregarded as a simpler effort, generally following the same guidelines. There willbe more about direct receivers in Section 13.3.1.

5.1.2 DSB or SSB with or without RF Preamplifier

Having selected the superheterodyne principle, the designer still has a funda-mental choice to make: double sideband (DSB) or single sideband (SSB) opera-tion. Again, this depends on whether a RF preamplifier is used.

In the receiver without RF preamplifier, the receiver noise figure is largely determined by the mixer in combination with the first IF amplifier. Hence, sucha receiver should use the DSB operation principle as the mixer-first IF amplifier


Table 5.1

Receiver Specifications

Frequency 17 GHz

IF bandwidth 500 MHzNoise figure 5 dB

Integration time 5 ms

Input range 0–313K



has a DSB noise temperature that is 3 dB lower than the SSB noise temperature.This can generally be exploited in radiometry as both input sidebands containinformation (the brightness input signal to the radiometer is wideband noise).

The radiometer has an input bandwidth twice the IF bandwidth, the local oscil-lator frequency is equal to the center frequency of the input band, and the IFfrequency is “DC” (IF band from DC up to B , the radiometer bandwidth). Itshould be stated at this stage that the radiometer bandwidth B in the sensitivity formula is the predetection bandwidth, that is, the IF bandwidth, and not thetotal RF bandwidth, which is 2B in DSB receivers. The benefit of the largerinput band has been used already in the DSB-SSB noise figure advantage andcannot be exploited again in the sensitivity formula.

Turning to the receiver with RF preamplifier the situation is very different.

Here the receiver noise figure is largely determined by the preamplifier andgoing from the SSB to the DSB mixer operation only results in a larger inputbandwidth to the radiometer with no gain in sensitivity. This may not matter insome situations, but should generally be avoided, as it results in larger suscepti-bility to interference from other sources. Spaceborne radiometers especially should use SSB operation and preamplification. The high gain antenna coverslarge areas on the ground, and in the low end of the microwave spectrum many active services are potential hazards to radiometric operations. Hence, the radi-

ometer input bandwidth should be as low as possible while still fulfilling sensitivity requirements.

In general, the SSB operation with a preamplifier should be used wheneverpossible/feasible, that is, at moderate frequencies, while the DSB option, having no RF amplification, is used whenever such amplifiers are unavailable ordeemed too expensive. This chapter will cover both possibilities: The Dicke typeswitching radiometers use DSB operation and no RF amplifier, while the totalpower radiometer will be designed likewise, as well as with an amplifier and a

SSB operation.

5.2 Dicke Radiometer

The block diagram for the Dicke radiometer is shown in Figure 5.1. The radi-ometer receiver is a superheterodyne receiver: The input signal is not directly amplified and detected, but rather converted to an intermediate frequency,

where the amplification takes place before detection.

5.2.1 Microwave Part

At the relatively high frequency of 17 GHz, the best performance is obtained by using waveguide technology. Here it is assumed that individual, off-the-shelf

Radiometer Receivers on a Block Diagram Level 27



microwave components are joined together using waveguide sections. This is thefast and straightforward method generally used by research institutions andcommercial companies. Today, however, there is an alternative: the MonolithicMicrowave Integrated Circuits (MMIC) technology. The big advantage is muchreduced bulk and weight; the drawback is the high cost of units from a few spe-cialized vendors. This directly points at the use of MMICs in space applications(see further discussions in Chapter 13), while ground and airborne instrumentsare still implemented as shown in the following.

The first component to be encountered is the Dicke switch. This is a latch-ing ferrite circulator, which is a circulator, where the magnetic field, and hence

the signal direction, can be reversed by electronic means. A typical switching time is 1 µs and 0.3 dB is a typical loss in a high quality latching circulator.

A trigger frequency (F S ) for the Dicke switch around 1 kHz is oftenreported in the literature concerning radiometer designs. Here a frequency of roughly 2 kHz is chosen and a few arguments for this choice are presented.

It is quite clear that the integration time of the radiometer has to be muchgreater than 1/F S to ensure a correct subtraction G ·T R – G · T A on the integrator.

With the integration time being 5 ms, F S has to be at least 2 kHz if “much” is

assumed equal to 10. Furthermore, the 1- µs switch time of the latching circulator requires an upper limit to F S . The finite switch time represents anuncertainty in the duty cycle of the Dicke switch, and exactly 50% is a precondi-tion for all calculations concerning Dicke radiometers. A 2.5-kHz switch fre-quency yields an uncertainty in duty cycle of:


±1

∆ Σ / DC

AFIFIF

17.0 GHz

10 MHz

500 MHzG 25 dB=

30 dB

7 mV/ µW50 dB

0.5 VDC/1 Vpp

5 msec

18 dB

10 V=100%

313 K

TA

DATA CK 205 kHz= FS 2225 Hz=

16.5 GHz

17.5 GHz

~~~

~~~

~

Mix - preamp2.4 V pp

1.2 V

0K

313 K 7.7mVpp 1.1 µW

9.5 V

↔

Figure 5.1 Dicke radiometer, T A = 0K.



2 1 0 4 5⋅ = µs ms parts per thousand.

which is not unreasonable, as would be a much greater value .

The Dicke principle involves great sensitivity to noise around the switchfrequency, and multiples of the power line frequencies, 50 Hz or 400 Hz,should be avoided when deciding upon the exact F S . A fair choice is 2,225 Hz.

The reference temperature T R is generated by a well-matched microwavetermination at the physical temperature T R (a microwave termination absorbs allincident energy; hence it has an emissivity of 1). The microwave front end, and

with it the reference termination, is enclosed in a temperature stabilized box toenhance stability. A reasonable operating temperature for the electronic compo-nents is 40°C and thus the reference temperature is 273 + 40 = 313K.

The microwave filter is included to prevent strong signals outside theinput band of the radiometer from saturating the mixer (the proper bandwidthlimitation is carried out at IF level). Hence it is designed for low loss (0.2 dB)and adequate bandwidth (0.1 dB limits at 16.5 GHz and 17.5 GHz). A five-sec-tion Chebyschev filter is a good candidate.

An isolator is situated between the filter and the mixer. For proper opera-tion, the filter requires well-matched output conditions, which a mixer cannotprovide. The isolator may have a loss of 0.3 dB.

Because a microwave preamplifier is not included, the mixer is very impor-tant for the performance of the radiometer. The best conversion loss figures canbe obtained if double sideband operation is possible, as it is in radiometers. TheIF band is 0–500 MHz and the two input sidebands (16.5–17.0 GHz and17.0–17.5 GHz) are added when DSB operation is used. High quality DSBmixers are often integrated with the first section of the IF amplifier (and nameda mixer-preamplifier), so that the manufacturer can optimize the interfacebetween the two, for best noise figure and conversion loss. A good quality

mixer-preamplifier exhibits a 4 dB noise figure and a total RF to IF gain of 25 dB. A 17-GHz local oscillator is needed. No special requirements to frequency

stability are present in this broadband application, and a standard dielectric res-onator oscillator (DRO) is adequate.

5.2.2 The Noise Figure and the Sensitivity of the Radiometer

The noise figure of the radiometer can now be calculated in Table 5.2 as thenoise figure of the mixer-preamplifier added to the losses of the componentspreceding this.

This noise figure is equivalent to a noise temperature of (5.0 dB ~ 3.2):

( ) ( )T NF N = − = − =290 1 290 3 2 1 640. K




The sensitivity of the radiometer is calculated using (4.6). T R is 313K. B is

the bandwidth before detection, which is 500 MHz. For 5-ms integration time, we thus find:

∆

∆

T

T

= ⋅ +

⋅ ⋅=

−2

313 640

05 10 10

12

9 3.

.

K

K

5.2.3 The IF Circuitry and the Detector

The IF filter finally determines the bandwidth of the radiometer. Here therequired steep cutoff is easy to implement, and losses are no problem after thelarge gain in the mixer-preamplifier. The IF band does not extend all the way down to DC. For practical reasons a 10-MHz highpass section is included in thefilter, and the IF band is 10–500 MHz. Further amplification takes place in thefinal IF amplifier stage, and the signal is ready for detection.

Schottky barrier diodes make good detectors and may yield a sensitivity of

7 mV/ µ W. They are quadratic for input levels up to some −20 dBm (where they become linear detectors). The decision of which signal level to put on thesquare-law detector includes a compromise. A low level ensures good square-law behavior but results in a very small output signal, which may cause noise prob-lems in the following amplifier. A level of −25 dBm is chosen. Then it is possibleto calculate the necessary gain of the IF amplifier.

The input power level is calculated from:

( )P k T T B A N RF = ⋅ + ⋅

where B RF is the total input bandwidth (1 GHz). Hence


Table 5.2

Radiometer Noise Figure NF

Mixer-preamplifier 4.0 dB

Isolator 0.3 dBFilter 0.2 dB

Latching circulator 0.3 dB

Waveguide 0.2 dB

Total 5.0 dB



( )P

P

P

= ⋅ ⋅ + ⋅

= ⋅

= −

−

−

138 10 313 640 10

132 10

79

23 9

8

.

.

W

mW

dBm

The total RF + IF amplification is found to be −25 dBm − (−79 dBm) =54 dB. The microwave components have a loss of 1 dB, and themixer-preamplifier has a RF to IF gain of 25 dB. Hence, the IF amplifier musthave a gain of 54 + 1 − 25 = 30 dB.

The detector dramatically changes the character of the signal. Figure 5.2(a)shows the signal before detection. It is a high-frequency signal with two levelscorresponding to the two different positions of the Dicke switch. The detector

reveals only the envelope of the signal as shown in Figure 5.2(b). The levels stillcorrespond to the input levels (T R + T N and T A + T N ). If, however, the output of the detector is AC-coupled, the signal now only contains information about thedifference between T R and T A , which is exactly what we want [see Figure 5.2(c)].This square wave signal of frequency F S has to be amplified by the subsequent,so-called AF (audio frequency), amplifier. To preserve the signal waveform, a frequency range of approximately 0.1 · F S − 10 · F S or 200 Hz–20 kHz isrequired (hence the name AF amplifier). Before proceeding with the AF ampli-

fier, it is necessary to calculate the extreme signal levels in the radiometer.


0

0

0c) After AC coupling:

b) After detection:

a) Before detection:

Peak amplitude ~ T TR A−

←T TR N+

←T TA N+

←T TA N+

←T TR N+

Figure 5.2 Waveforms around the detector: (a) before detection, (b) after detection, and (c)

after AC coupling.



5.2.4 The Extreme Signal Levels

The maximum dynamic signal arises when the antenna signal is 0K, which is thesituation shown in Figure 5.1. The difference in levels is ∆T max = 313K [see

Figure 5.2(a)], and this corresponds to:

∆

∆

P

P

max

max

.

.

= ⋅ ⋅ ⋅

= ⋅

−

−

138 10 313 10

0 43 10

23 9

8

W

mW

At the detector (54-dB total RF + IF gain), the signal is:

∆P max .= 11 µ W

After the detector, at the input of the AF amplifier, the signal is:

S

S pp

max

max

.

.

= ⋅

=

11 7

7 7

µ µ W mW W

mV

The minimum signal, which has to be handled without degradation by theradiometer circuitry, is reasonably assumed as equal to the sensitivity, 1K. This

situation arises when the input signal is 312K (see Figure 5.3). After the detec-tor, at the input of the AF amplifier, the minimum signal is:

S min = 24 µV pp


±1

∆ Σ / DC

AFIFIF

17.0 GHz

10 MHz

500 MHzG=25 dB

30 dB

7 mV/ µW50 dB

0.5 VDC/1 Vpp

5 msec

18 dB

10 V=100%

313 K

TA

DATA CK= 205 kHz F 2225 HzS =

16.5 GHz

17.5 GHz

~~~ ~~~

~

Mix - preamp7.6mVpp

24 V µ pp

3.8 mV30 mV

312 K

1 K

↔

Figure 5.3 Dicke radiometer, T A = 312K.



5.2.5 The LF Circuitry

The AF amplifier has, as already mentioned, a bandwidth of 200 Hz–20 kHz. Itis, however, not this bandwidth that is used to calculate the equivalent input

noise of the AF amplifier. Following the synchronous detector there is the ana-log integrator having a noise bandwidth of 100 Hz. Hence, the noise bandwidthbefore the synchronous detector (which can be regarded as a DSB mixer) is 200Hz centered around the Dicke frequency F S .

A good quality operational amplifier has an equivalent input noise of 10 8− V Hz. This gives an input noise of:

S

S

N

N

= ⋅

=

−200 10

014

8 V

V

RMS

RMS. µ

Recalling that the minimum signal at this stage in the radiometer is S min =24 µV pp, a comfortable margin is seen to be present.

A 50-dB gain in the AF amplifier results in the following minimum andmaximum signals to be handled by the synchronous detector:

S m

S

MIN

MAX

= ⋅ =

= ⋅ =

24 316 7 6

7 7 316 2 4

µV V

mV V

pp pp

pp pp

.

. .

The synchronous detector transforms the square wave signal from the AFamplifier into a DC signal (see Figure 5.4).

This is done by multiplying the signal by +1 or −1 in synchronism withthe switch frequency F S . The positive parts of the signal are left untouched,

while the negative parts are reversed in polarity. Figure 5.5 shows how the cir-cuitry can be realized.

It is seen that a 1-V pp signal is transformed into a 0.5-V DC signal. Hencethe extreme signals after the synchronous detector are:

S

S

min

max

.

.

=

=

3 8

12

mVDC

V DC


0

a) Before syn. det.:

0b) After syn. det.:

Figure 5.4 Waveforms around the synchronous detector: (a) before and (b) after synchro-

nous detection.



The analog integrator is just an RC lowpass filter, and the relationshipbetween noise bandwidth b , equivalent integration time τ, component values,and cutoff frequency f o is given by the formula:

b RC

f = = = ⋅12

14 2 τ

π0

In the actual design the integration time is τ = 5 ms, giving a noise bandwidth of 100 Hz and a cutoff frequency of 63.7 Hz.

The purpose of the DC amplifier is to condition the signal for the ana-log-to-digital (A/D) converter. This has a range of 0–10V, and the gain of theDC amplifier is chosen so that the maximum signal is amplified to just below

10V. A gain of 18 dB gives the following extreme signals on the A/D converter:

S

S

min

max .

=

=

30

9 5

mV

V

5.2.6 The Analog-to-Digital Converter

The A/D converter is implemented as a so-called ∆/Σ converter. The ∆/Σ con-verter is in fact a voltage-to-pulse rate converter producing a pulse train in syn-chrony with a clock, the number of pulses per time unit being proportional tothe input voltage.

The converter tries to maintain a constant voltage on the capacitor C when the input voltage varies. To achieve this, a reference current is presented to


+

−

AC INDC OUT

FS

Inverter

Op. amp.

Op. amp.

R

R

CMOSswitch

+

−

Figure 5.5 Synchronous detector.



the capacitor for a certain percentage of time, K . Hence, K is proportional toV IN . See Figure 5.6.

In this schematic diagram, A is an ideal operational amplifier, V IN is posi-

tive, V REF is negative, and the net voltage on C is zero. Then V OUT and I o are onaverage zero and I 1 = I 2. The input of the operational amplifier is a virtualground, and

I V

R

I K V

R

IN

REF

1

1

2

2

= −

= ⋅

hence

K V R

R V IN

REF

= − ⋅⋅

2

1

If K is synchronized to and gated with a clock frequency, two signals

emerge from the converter: (1) pulses having variable duty cycle proportional toV IN , well suited for controlling the noise injection in a noise-injection radiome-ter (this feature is the cause for selecting the ∆/Σ converter in the presenteddesign); and (2) a data pulse train consisting of a number of pulses N D equal to K multiplied by the number of clock pulses N C in any time interval.

A more complete diagram showing the ∆/Σ converter is given in Figure5.7.


+

−

I1

I0

I2

VREF

C

VOUT

VIN

AR1

R2

K

Figure 5.6 Explaining the ∆ /Σ converter.



The comparator decides when it is time to switch on the reference voltage,and the exact time of switching is synchronized to the clock pulses by the Dflip-flop.

A digital expression for the analog input is found directly by counting N D

relative to N C (see Figure 5.8). When the clock counter is full—after 2N clock pulses—the data counter

will contain an N -bit word representing the input voltage. This word is trans-ferred to the data register, the data counter is reset, and a new conversion starts.The data word in the data register may be read when convenient. The magni-tude of N is found by considering the resolution desired. The radiometer isdesigned for an input range of 0–313K and a sensitivity of 1.2K ( τ = 5 ms). It is,of course, not acceptable for the digital resolution to degrade this resolution of the more difficult part of the radiometer.

Ten bits will give a digital resolution of 1 in 1,024. Only 95% of the input

range to the converter is used so that as a result the 313-K input range to theradiometer corresponds to a digital range of 1,024 · 0.95 = 973 counts. Theconverter resolution is thus 313/973 = 0.3K, which is adequate.

The circuitry shown in Figure 5.8 is really a digital integrator of the inte-grate-and-dump type, and the integration time is equal to the conversion time.

Having selected N , the conversion time is determined by the clock fre-quency. If a 5-ms conversion time is required, the clock frequency is found to be1,024/5 ms = 205 kHz.

A simple modification of the circuit in Figure 5.8 will result in a digitalintegrator with variable integration time: increasing both counters (and the out-put register) with extra bits results in the integration time being multiplied by powers of 2 ( τ = 5, 10, 20, 40 ... ms). Externally selectable counter length is eas-ily implemented.


VREF

C

VIN

A

R1

R2

+

−

CK

K

DATA

Comparator

+

−

D

CK

Q

Figure 5.7 ∆ /Σ converter.



If the digital integrator has a range as assumed here (5, 10, 20 ... ms), it may

not be practical to allow the analog integrator to have an integration time of 5ms: The two integrators will influence each other when the digital integrator is inthe 5-ms position, resulting in a slightly increased effective integration time.Lowering the analog integration time to some 2 ms alleviates the problem, andthe radiometer’s integration times are determined solely by the digital integrator.

5.2.7 On the Sampling in the Radiometer: Aliasing

As already mentioned, the digital circuitry is an integrator of the inte-grate-and-dump type. Hence a sampling of the input brightness signal is carriedout, and the sampling interval is equal to the digital integration time. Due to thesampling, we need to discuss the response of the radiometer to time-varying input signals.

The transfer function of the analog part of the radiometer is determinedby the analog integrator, which is an RC lowpass filter with 63.7-Hz cutoff fre-quency. The function is shown as H RC in Figure 5.9. Assume that the digital

integrator is in its 10-ms position and the corresponding sampling frequency f S

is 100 Hz. The transfer function of the digital integrator (H I ) is of the (sinx )/x type with zeros at n · 1/(10 ms) = n · 100 Hz. The transfer function (H TOT ) of the entire radiometer is shown as the third curve in Figure 5.9. It is seen that theradiometer does not in itself provide adequate band limiting of the input signalto below f S /2 in order to avoid aliasing. We must ensure that the input signal isitself band-limited. When measuring in a stationary case (calibration, for exam-ple), this is, of course, no problem, but in considering an imaging radiometer, it

is an important issue. The band-limiting is carried out by the antenna throughits radiation pattern and the rate at which this sweeps across the scene to besensed; or, to put it differently, there are certain relationships between theantenna footprint dwell time and the integration and sampling time of the radi-ometer to be taken into account. More about this subject is covered in Section11.4.


DATA

CK N-bit counter

N-bit counter

N-bit register

Delay

Reset

Load

Figure 5.8 Output counter.



5.3 The Noise-Injection Radiometer

In Figure 5.10 we show the block diagram of a noise-injection radiometer, using the Dicke radiometer discussed in the previous sections as a basis. The Dickeradiometer has only been modified slightly: the gain in the LF section has beenincreased by 50 dB to account for the loop gain already defined in Section 4.3.In principle, we want the difference between the reference signal and the sum of


H(f)

−40

−30

−20

−10

00

fs

50 100 f(Hz)

HTOT

HI

HRC

dB

Figure 5.9 Transfer function of the radiometer.

±1

∆ Σ / DC

AFIFIF

17.0 GHz

10 MHz

500 MHzG=25 dB

30 dB

7 mV/ µW80 dB

0.5 VDC/1 Vpp

1.57 sec

38 dB

10 V=100%

313 K

Noise SwitchHI ON=

−2.5 dB

−3 dB

TA

Noise DiodeENR 28 dB=

DATA CK 205 kHz= FS 2225 Hz=

16.5 GHz

17.5 GHz

∼∼∼

∼∼∼

∼

Mix - preamp

−2 dB

-20 dB

24 µVpp

0.12 V9.5 V

95%

0K

312 K 1K

31200K

↔

∫

0.24Vpp

Figure 5.10 Noise-injection radiometer, TA = 0K.



the antenna signal plus the injected noise to be zero (the error signal in the servoloop is zero). This would, however, require infinite loop gain. Let us assume a maximum error signal of 1K—equal to the sensitivity of the radiometer. The

maximum error signal occurs when the antenna signal is 0K, requiring maxi-mum injected noise. Hence, the gain of the LF section has to be increased togive full output for a 1-K signal after the Dicke switch (and not for a 313-K sig-nal as was the case in the Dicke radiometer); 313 corresponds to 50 dB and the

AF amplifier gain has been increased by 30 dB, the DC amplifier gain by 20 dB.The loop gain (313 = 50 dB) requires that the integration time of the RC inte-grator be changed to 5 ms · 313 = 1.57 seconds to maintain the 63.7-Hz cutoff frequency of the radiometer.

The noise is injected in the antenna line through a 20-dB directional cou-

pler. Thus, the antenna signal is not attenuated to any measurable level. The sig-nal for injection is generated by a semiconductor noise diode giving a high,

well-specified noise signal. A typical excess noise ratio (ENR) is 28 dB, corresponding to 183,000K

(ENR = 10 log (T N /290 − 1)). The output from the diode cannot be changed,and the variable signal for the injection is obtained by rapidly switching thenoise signal on and off with a variable duty cycle: The zero duty cycle (i.e., theswitch is maintained in its off position) corresponds to no injected signal, and

the maximum duty cycle (in this design, 95%—the switch is on for 95% of thetime) corresponds to a signal loss of 0.2 dB. The noise switch is a microwavePIN diode switch, which typically exhibits very short switching times and a lossin the on position of some 2 dB. The switch is directly controlled from the K output of the ∆/Σ converter. Two fixed attenuators are finally selected to givethe correct signal levels: The generated noise is 183,000K, and the injected noiseis 312K (in the T A = 0K situation of Figure 5.10). This is a ratio of 27.7 dB.Hence,

20 0 2 2 27 7+ + + = ATT . .

and ATT = 5.5 dB, here selected as a 3-dB attenuator and a 2.5-dB attenuator.The noise-injection radiometer is really a servo system and an analysis of

the stability in the feedback loop is necessary. In the low end of the spectrum,the dominant frequency-dependent factor in the open loop transfer functionresults from the analog integrator—a simple RC lowpass filter. No stability problems will arise when closing the feedback loop because all circuit blocks of the radiometer—apart from the RC integrator, of course—have bandwidths farbeyond 63.7 Hz, which is the point of 0-dB loop gain.

The Dicke switch and synchronous detector complex may require someconsideration. The switching frequency (2,225 Hz) is much higher than any fre-quency of interest in this analysis. The switching (apart from giving a




contribution to the signal level from the reference temperature load, which isconstant and therefore can be omitted), results in turning on and off the inputsignal—including injected signal—with a duty cycle of exactly 50%. This is

equivalent to an attenuation by a factor of 2, which will clearly not disturb thestability of the closed loop.The sensitivity of the radiometer is 1.2K as was the case for the Dicke radi-

ometer counterpart (see Section 5.2.2).Other quite detailed descriptions of the noise-injection radiometer can be

found in [1, 2].

5.4 The Total Power Radiometer

As already mentioned earlier, the total power radiometer will first be designed asa DSB receiver without microwave preamplifier just like the Dicke type switch-ing radiometers covered so far. That way, the differences and similaritiesbetween the two classes of radiometers are best discussed. After that, the totalpower radiometer is designed with a microwave preamplifier and SSB mode of operation, and the differences from the earlier design discussed.

5.4.1 DSB Receiver Without RF Preamplifier

Figure 5.11 shows the block diagram of the radiometer operating in the totalpower mode. When comparing with the Dicke radiometer (Figure 5.1), greatsimilarities are obvious but also some important differences may be noted. Inthe RF circuitry the only difference is the lack of the Dicke switch. However, thetotal power radiometer requires frequent calibration and the latching circulator

is maintained, but now serves the purpose of a calibration switch (utilizing theformer reference load as a calibration load).

More substantial changes are found in the LF circuitry. As the signal is nolonger modulated with the Dicke switching frequency the circuitry after thedetector will have to be DC-coupled. Thus, Shottky barrier detectors are notvery useful; rather, the tunnel diode detector should be employed due to itslow-frequency stability being orders of magnitude better than that associated

with Shottky diodes. Furthermore, the low video resistance of the tunnel diode

facilitates low impedance levels at the first amplifier stage, which in turn resistsdrift problems. The price to pay is that the tunnel diode detector has lower sen-sitivity, typically 1 mV/ µ W, meaning that extra amplification is needed after thedetector to regain the signal level. This is illustrated in the block diagram by adding a 17-dB DC amplifier. The tunnel diode detector plus the 17-dB ampli-fier directly replace the original Shottky detector from a signal level point of




view, and the remaining gain (62 dB) can be compared directly with that of the

Dicke radiometer (50 dB + 18 dB − 6 dB in the synchronous detector = 62 dB).It is seen that due to the DC coupling, the AF amplifier and the synchro-

nous detector have been omitted and all gain has been attributed to the DCamplifier. Because the 640-K noise temperature of the radiometer itself is now also constantly present as a signal in the LF section, an offset is required forcompensation (otherwise, a very inefficient use of the A/D converter wouldresult).

The gains in the radiometer (although somewhat rearranged in the LF sec-

tion, as already mentioned) are the same as in the Dicke radiometer and a change in input temperature of 1K will again result in a change of 25 µV at theoutput of the detector—the detector now being understood as the tunnel diodedetector plus the 17-dB amplifier (see Section 5.2.4). The noise considerationsbrought forward in Section 5.2.5 are equally applicable here, but we addition-ally have to consider noise properties around this 17-dB amplifier. The 25 µV after the amplifier corresponds to 3.6 µV at its input, still comfortably largecompared with the typical 0.14 µV RMS noise of a good quality operationalamplifier. Due to the DC coupling, however, drift in the LF circuitry (including the offset) referred to the input must stay at the same low level. This is a strin-gent requirement, and careful circuit design, including thermal stabilization,and frequent calibration are needed.

The sensitivity of the radiometer is calculated using (4.2) and the parame-ter values also used in Section 5.2.2 to assess the corresponding Dicke


∆/Σ DC

DCIFIF

17.0 GHz

10 MHz

500 MHzG=25 dB

30 dB

1 mV/ µW 17 dB

5 msec

62 dB

10 V 100%=

313 K

TA

DATA CK= 205 kHz

16.5 GHz

17.5 GHz

∼

∼∼

∼

∼∼

∼

Mix - preamp

7.7mV9.7 V

0K

313 K

↔

23.1mVDC3.31 W µ

OFFSET -15.4mV

CALLOAD

TN 640K=

Calibration

953 K

640 K 2.22 W µ 15.5mVDC

0.1mV

0.13 V

∫

Figure 5.11 DSB total power radiometer, T A = 0K and 313K.



radiometer sensitivity. For T A we conservatively use the highest possible value of 313K, and we find:

∆

∆

T

T

= +

⋅ ⋅ ⋅=

−

313 640

05 10 5 10

0 6

9 3.

.

K

K

5.4.2 SSB Receiver with RF Preamplifier

In the final block diagram of this chapter (Figure 5.12), the opportunity is takento show the differences when the radiometer is implemented with a microwave

preamplifier. According to the discussion in Section 5.1.2, this also means singlesideband operation.

The obvious differences between the two implementations are the addi-tion of the microwave preamplifier and an associated redistribution of gainbetween this and the IF amplifier. Also the filters have been changed substan-tially: The input bandwidth is now 500 MHz, like the IF bandwidth. The inputband has here been selected to be 17.0–17.5 GHz, corresponding to the upperhalf of the original radiometers input band. The IF is no longer at DC but here

is selected to be 100–600 MHz, and the local oscillator is at 16.9 GHz. Animportant function of the RF filter is now to cancel the lower sideband(16.3–16.8 GHz). Requirements to out-of-band suppression in this filter is


∆/Σ DC

DCIFIF

16.9 GHz

100 MHz

600 MHzG=25 dB

15 dB

1 mV/ µW 17 dB

5 msec

57 dB

10 V=100%

313 K

TA

DATA CK 205 kHz

17.0 GHz

17.5 GHz

∼∼∼

∼∼∼

∼

Mix - preamp

13.8mV9.8 V

0 K

313 K 21.0mVDC2.96mW

OFFSET -7.2mV

CALLOAD

TN 168K=

Calibration

481 K

168 K 1.03 W µ 7.3 mV

DC

0.1mV

0.07 V

RF

20 dB

∫

Figure 5.12 SSB total power radiometer, T A = 0K and 313K.



determined by the lower cutoff frequency of the IF filter. It is not attractive tomake this cutoff frequency too low, as that will lead to a requirement for a very rapid cutoff in the RF filter, that is, a filter of high order (cost, loss, bulk).

It is important that the RF filter is after the preamplifier in order to filteraway the lower sideband noise from this amplifier. Also, this arrangementensures the lowest possible noise figure as the filter loss will not contribute. Itcan be discussed whether a modest, low loss filter might be required in front of the preamplifier in order to suppress strong out-of-band interference that mightotherwise overload the preamplifier. Experience shows that this is generally notnecessary, but it might be in specific cases.

The calculations of signal levels in the radiometer follow the same proce-dure as outlined previously. A typical good quality low noise amplifier exhibits a

noise figure of 1.5 dB. Adding to this 0.3 dB for the latching circulator and 0.2dB for miscellaneous waveguide losses, we find the noise figure of the radiome-ter to be 2.0 dB. This is equivalent to a noise temperature of 168K. The gain of amplifiers before the detector is then calculated so that the maximum inputnoise (168 + 313)K leads to −25 dBm on the detector. The gain after the detec-tor and the offset is then determined so that reasonable use of the A/D converterrange is ensured. All these gains and levels are indicated on Figure 5.12.

The sensitivity of the radiometer is again calculated using (4.2) but the sys-

tem parameter values are now changed due to the improved noise temperatureas a result of incorporating a high quality preamplifier. For T A we again conser-vatively use the highest possible value of 313K, and we find:

∆

∆

T

T

= +

⋅ ⋅ ⋅=

−

313 168

05 10 5 10

0 3

9 3.

.

K

K

A good quality microwave preamplifier is an important improvement!Note that as the instrument noise temperature is improved, the choice of

antenna temperature becomes increasingly important. If it is known that theradiometer in question will only measure a low antenna temperature, this shouldbe used in the sensitivity formula in order to yield a more realistic sensitivity than the conservative value calculated above.

5.5 Stability Considerations

Having become more familiar with radiometer circuitry, at this stage it is appro-priate to discuss further the merits of each radiometer type to elaborate someof the subjects covered in Chapter 4. We stated that the stability of the Dicke




radiometer depends only on gain stability (provided that the reference tempera-ture is known). With reference to Figure 5.1, this is not the whole truth: afterthe synchronous detector, the circuitry is DC-coupled, and drift in the DC

amplifier (and A/D converter) will result in offsets in the radiometer output thatare independent of the changes associated with gain variations. This is not a big problem, however, as the signal levels are rather high and the gain is modest.

Turning to the total power radiometer, we found in Chapter 4 that thestability depended on both the gain and noise temperature of the radiometer.

With reference to Figure 5.11, we see that a drift in the DC coupled low-fre-quency part of the radiometer will have the same effect on the radiometer out-put as a drift in the noise temperature. Now the problem requires a little moredesign effort as the signal levels in the DC-coupled circuitry are small and the

gain is comparatively high.From a radiometer designer’s point of view, the AC coupling in the Dicke

type of switching radiometer is an interesting feature. Although the drift prob-lems in the total power radiometer can be alleviated by careful design and differ-ent countermeasures (such as frequent calibration), stabilities as we find in evena rather simple Dicke design is difficult to achieve. This is not to say that ade-quate stability for a given purpose cannot be achieved, but it requires effort andperhaps complexity. Also it must be noted that accuracy requirements/stabil-

ity/calibration schedule must be considered together: Even a relatively unstableradiometer may be useful for a certain application if calibration can be carriedout very often. This is discussed in detail in [3].

Finally, it shall be stressed that good stability and the quality of tempera-ture stabilization of radiometer components in practice are closely tied together.

Although many tricks can alleviate effects of inadequate thermal control, theimportance of the latter cannot be disregarded if one strives for the ultimate inradiometric stability. In [4] the design goal is not the usual 1K or a fraction of a

Kelvin stability, but rather milliKelvins! This leads to a design where the thermalstability of the front end is measured in milliCentigrades. Of course, such con-trol is often not possible, and ways to alleviate the resulting problems must befound, like frequent calibration or modeling; see, for example, Chapter 10.

References

[1] Hidy, G. M., et al., Development of a Satellite Microwave Radiometer to Sense the Sur-

face Temperature of the World’s Oceans, NASA Report No. CR-1960, 1972.

[2] Harrington, R. F., “The Development of a Stepped Frequency Radiometer and Its Appli-cations to Remote Sensing of the Earth,” NASA Technical Memorandum No. 81837,Langley Research Center, 1980.




[3] Racette, P. E., “Radiometer Design Analysis Based upon Measurement Uncertainty,”Ph.D. thesis, George Washington University, 2005.

[4] Tanner, A. B., “Development of a High-Stability Water Vapor Radiometer,” Radio Sci- ence , Vol. 33, No. 2, 1998, pp. 449–462.




6The DTU Noise-Injection RadiometersExample

As an example of realization of the design considerations in Chapter 5, thenoise-injection receivers employed in the first generation of the DTU airbornemultifrequency radiometer system will be reviewed. A more detailed descriptioncan be found in [1, 2]. The system comprises three receivers at 5, 17, and 34

GHz. The major electrical characteristics are shown in Table 6.1.The design of the 17-GHz radiometer is very close to that given in Chap-ter 5 (NIR mode only). The two other radiometers are of equivalent design. Theonly major differences between the radiometers (apart from the frequencies, of course) is that the 34-GHz radiometer features two antenna inputs and an asso-ciated switch, while the 5-GHz radiometer has half the bandwidth of the othersand employs a microwave preamplifier before the mixer to enhanceperformance.

One of the basic assumptions in the noise-injection radiometer concept isthe stabilization of the front-end microwave components to a temperature equalto the radiometric reference temperature. Hence, a temperature-stabilized enclo-sure is designed for these components. The directional coupler, Dicke switch,reference load, microwave filter, and the isolator have to go inside the enclosurebut other components may well be included if advantageous.

It is reasonable to keep the mixer-preamplifier (and possible RF amplifier)close to the other microwave components to minimize waveguide losses and toavoid an extra waveguide through the isolation of the temperature stabilized

box.

47



The noise generating diode represents a special problem. The ENR of thediode has a typical temperature dependence of 0.01 dB/°C which on a 312-K level amounts to:

312 0 0023 0 72⋅ = °. . K C

Thus, temperature stabilization of the noise diode is obviously important,and the components in Table 6.2 will be mounted in the temperature-stabilized

enclosure (see Figure 6.1).Note that the discussion about which components should go inside the

thermally stabilized enclosure was specific for a noise injection radiometer. Fortotal power and Dicke radiometers—being dependent on noise figures and gains


Table 6.1

DTU NIR Specifications

Frequency 5 GHz 17 GHz 34 GHz

Bandwidth 250 MHz 500 MHz 500 MHzNoise figure 4.5 dB 5 dB 5 dB

Sensitivity ( τ = 8 ms) 1.15K 0.95K 0.95K

Sensitivity ( τ = 64 ms) 0.41K 0.34K 0.34K

Integration times 4, 8, 16, 32, 64 ms

Input range 0–313K

Table 6.2

Components in Enclosure

The RF chain Probe couplerDicke switch

Reference load

Filter

Isolator

(RF amplifier—if included)

Mixer-preamplifier

Local oscillator

The noise injection branch Noise diode

Attenuator

Switch

Attenuator



that are again very dependent on physical temperature—the choice is clear: Allmicrowave and IF components have to be carefully thermal stabilized.

The components are mounted in an inner aluminum box having heating wires glued to the face-plates, and this box is mounted in a foam lined outer box.The heating wires are supplied from a power supply regulated from a thermistor

The DTU Noise-Injection Radiometers Example 49

Heating wires IF

OUT

Pre-ampliferMixer

N o

i s e

g e n e r a

t o r

Isolator

Local

oscillator

FilterATT

ATT

S w

i t c h

Dicke

switch

Reference load

40°C

Probe

coupler

Silver

coated

pertinax

Temperature sensor

Foam isolation

Input

Figure 6.1 Microwave components in temperature-stabilized enclosure.



at one of the faceplates. A temperature of 40°C is thus maintained. The microwave components are mounted without metallic contact to the box and all heattransfer takes place via the air, forced to circulate inside the enclosure by a fan.

The system is quite slow in reaching temperature equilibrium, but a very uni-form temperature distribution is ensured.To prevent heat flow in the input waveguide, it is made out of silver-

coated Pertinax and it includes a Mylar window. However, temperature gradi-ents inside the stabilized enclosure cannot be fully avoided in practice (somecomponents are active and generate heat) and a thermometer monitoring theactual temperature of different components is incorporated. The data from thisthermometer may then form the basis for later corrections of the measuredradiometric temperatures. Small platinum sensors are glued onto eight

components in the enclosure.The digital thermometer has a range of 38.0 to 46.0°C and a resolution of

32 counts/°C (the temperature is found as T = counts/32 + 38.0°C). The accu-racy has proven to be better than two counts, that is, somewhat better than0.1°C. The thermometer is wired as shown in Table 6.3.

Table 6.4 shows the temperature distributions inside the radiometer frontends as measured by the digital thermometer. Two cases are shown:

1. The temperature without power to the microwave components, in which case a very uniform distribution is to be expected;

2. The temperature with the components powered.

As may be seen from the table, the temperature distribution is indeed quiteuniform in the case of no power. Note especially that the thermally isolating input waveguide is working satisfactorily (see sensor 00).

With the microwave components powered, the temperature differencesare 1.6°C maximum. Recalling also that the antenna noise temperature at thisstage—after injection—is in the 40°C range (actually close to the temperaturemeasured by the sensor at the reference load), the deviations from uniformity aresupposed to be of no importance. Assuming a component having a loss of typi-cally 0.2 dB and a physical temperature (T o ) 1°C off the noise signal passing through it, we have the following situation:

( )

( )

T T T

T T T T T

T

o

D o

D

2 1

2 1 1

1

0 047 1 0 047

= − + ⋅

= − = −

= ⋅ =

l l

l

. . ,K which is satisfactorily small




The temperature distributions shown in the table have proven to be very stable with time, and the absolute level marginally dependent on environmenttemperature.

In addition to the eight channels for measuring the internal temperaturesin the front end, the digital thermometer of each radiometer also has eight chan-nels for measuring external temperatures. The range of these external sensors is–34°C to +30°C with a resolution of 4 counts/°C. The external channels areintended for measuring temperatures of lossy input devices like antenna feedsand waveguide runs, thus enabling later corrections of radiometric data.


Table 6.4

Temperature Distributions in the Front Ends

Sensor

Number No power Power

34 GHz 17 GHz 5 GHz 34 GHz 17 GHz 5 GHz

00 39.6 40.3 39.9 41.8 42.0 40.5

01 39.6 40.4 40.0 41.3 41.9 40.6

02 39.6 40.3 40.0 41.6 42.8 40.3

03 39.6 40.3 40.0 41.7 41.8 40.3

04 39.6 40.3 40.0 42.0 41.2 40.1

05 39.6 40.3 40.1 41.5 41.2 40.3

06 39.5 40.5 40.1 41.5 42.2 41.4

07 39.7 40.3 40.1 41.9 42.0 41.7

Table 6.3

Guide to Sensor Numbers

Sensor

Number 34 GHz 17 GHz 5 GHz

00 Dicke switch Probe coupler Probe coupler

01 Mux switch Reference load Dicke switch

02 Reference load Dicke switch Reference load

03 Isolator Microwave filter Microwave filter

04 Mix-preamplifier Isolator Isolator

05 Diode switch (1) Mix-preamplifier Mix-preamplifier

06 Diode switch (2) Diode switch Diode switch07 Noise generator Noise generator Noise generator



Figure 6.2 shows a photo of the 17-GHz radiometer telling more aboutthe mechanical layout than words can.

In the overview photo of the radiometer system (Figure 6.3), we see all

three receivers plus two additional units necessary for the operation of the receiv-ers: a digital processing unit and a power supply unit. The radiometer system isset up in the lab for a simple calibration as shall be described in Chapter 9.

The digital processing unit collects the digital data from the three radiom-eters (transmitted in serial form by the ∆/Σ converters). It contains the countersof variable length (selectable integration time). The radiometer data is mixed

with auxiliary data from the digital thermometer, and from an interface to theaircraft inertial navigational system (INS) before being formatted properly for a suitable recording system. The unit contains all controls for the radiometer sys-

tem and displays for monitoring the receiver operation.


Figure 6.2 A view inside the temperature stabilized box of the 17-GHz radiometer. From left to

right: probe coupler, latching circulator and reference load, filter, isolator, Gunn

oscillator, and mixer-preamplifier. Following the semirigid line from the probe cou-

pler, note the attenuator, diode switch, attenuator, and noise generator.

Figure 6.3 From right to left: the 5-GHz radiometer, the 17-GHz radiometer on top of the

34-GHz radiometer, and the digital processing unit on top of the power supply

unit. The radiometers are via waveguides connected to calibration loads in a

freezer for calibration purposes (see Chapter 9).



The central power supply unit converts the primary power to preregulatedvoltages for the radiometers and the processing unit. Only linear power suppliesare used. Switch mode power supplies should be avoided in radiometer designs

due to possible interference.

References

[1] Skou, N., “Design of an Airborne Multifrequency Radiometer System,” ElectromagneticsInstitute, Tech. Univ. of Denmark, R 221, 1979.

[2] Skou, N., “Airborne Multifrequency Radiometry of Sea Ice,” Electromagnetics Institute,Tech. Univ. of Denmark, LD 42, 1980.




7Polarimetric Radiometers

7.1 Polarimetry and Stokes Parameters

Generally, the radiation from an object is partly polarized, meaning that thebrightness temperature at vertical polarization T V is different from the bright-ness temperature at horizontal polarization T H . A well-known example is the sea surface. To describe scenes with partial polarization, it is convenient to use the

Stokes parameters. The Stokes vector is:

I

I

Q

U

V

z

E E

E E

E E

E

V H

V H

V H

=

=

+−

⋅ ⋅⋅

1

2

2

2 2

2 2

Re

Im

*

V H E ⋅

*

(7.1)

where z is the impedance of the medium in which the wave propagates. It is seenthat I represents the total power, Q represents the difference of the vertical andhorizontal power components, and U and V represent, respectively, the real andimaginary parts of the cross correlation of the electrical fields.

Assuming that the Rayleigh-Jeans approximation is valid for signals in themicrowave regime, the Stokes vector for the fields in (7.1) can be converted toan equivalent brightness temperature Stokes vector:

55



T k

I B = ⋅ λ2

(7.2)

where λ is the wavelength and k is Boltzmann’s constant. The parameters of T B

are termed I B , Q B , U B , and V B where I k

I B = ⋅ λ2

and so on. It can be shown that:

U T T

V T T

B

B r

= −

= −° − °45 45

l

(7.3)

where T 45° and T −45° represent orthogonal measurements rotated 45° withrespect to the reference directions for V and H polarizations, andT l and T r refer

to left-hand and right-hand circular polarized quantities. It is common in theradiometer literature to use the notations I , Q , U , V to mean the brightnessStokes parameters (rightfully termed I B and so on), so we can write:

T

I

Q

U V

T T

T T

T T T T

B

V H

V H

r

=

=

+−

−−

° − °45 45

l

=⋅

+

−

⋅ ⋅⋅ ⋅

λ2

2 2

2 2

22

k z

E E

E E

E E E E

V H

V H

V H

V H

ReIm

*

*

(7.4)

and we shall adopt this notation here.This definition directly points to two fundamentally different ways of

implementing the polarimetric radiometer system. In both cases the first andsecond Stokes parameters are measured conventionally using vertically and hori-zontally polarized (that is, normal linearly polarized) radiometer channels, fol-lowed by addition or subtraction of the measured brightness temperatures. Thethird Stokes parameter can be measured with a conventional two-channel radi-ometer connected to an orthogonally polarized antenna rotated 45° with respectto the V and H directions, and subtracting the measured brightness tempera-tures. The fourth Stokes parameter can be measured with the two-channel radi-ometer connected to a left-hand/right-hand circularly polarized antenna system.In the following sections we shall use the term polarization combining radiometer for this case, and we note that we are dealing with a fully incoherent case, as all

Stokes parameters are found by addition or subtraction of brightnesstemperatures (i.e., detected power).

Alternatively, returning to (7.4), we observe that all Stokes parameters aremeasured by a two-channel correlation radiometer (employing a complex correlator) connected to a conventional horizontally and vertically polarized




antenna system. We shall use the term correlation radiometer in the following sections, and we note that this is partly a coherent case, where we have to pre-serve phase and keep coherence between channels up to the correlator, in order

to find the product between the vertical and horizontal electrical fields.

7.2 Radiometric Signatures of the Ocean

As an example to illustrate typical signal levels, let us consider the ocean surface.The brightness temperature of the ocean depends on the wind speed and direc-tion. At incidence angles around 50°, and in the frequency range Ku- andKa-bands, the dependence is some 0.5K per meters per second wind at vertical

polarization, and somewhat larger at horizontal polarization: 1–1.5K per metersper second; see, for example, [1]. This means that traditional radiometer mea-surements with an accuracy of 1K allows determination of the wind speed tobetter than 1 m/s (excluding other error sources), which can be regarded as quitesatisfactory. However, the measurement of the Stokes parameters, in order toassess wind direction, places more stringent requirements on the accuracy of the radiometers. Typical variations in Q and U are 4–6K peak to peak and lessregarding V (see [2–4]). This means that the measurement accuracy must be a

fraction of a Kelvin, which is not easy for traditional radiometers.

7.3 Four Configurations

7.3.1 Polarization Combining Radiometers

The first configuration to be discussed is the full multiplex polarization combin-ing radiometer outlined in Figure 7.1. The outputs from a normal horizontally and vertically polarized antenna are connected via a switchable microwave com-

bination network to a single radiometer carrying out all necessary measurementsin sequence. The switches can be PIN diode switches, which have good isolationproperties. By combining the horizontal and vertical signals in a magic tee, pro-viding the sum and difference signals, we obtain +45° and –45° linear polariza-tions (phase shifter, PS, set to 0°). With the phase shifter set to 90°, thecombined signals from the magic tee become right-hand and left-hand circularpolarizations. Table 7.1 gives an overview of switch positions versus measuredbrightness temperature component. Finally, a switch and reference load for

Dicke operation or frequent calibration is shown in front of the receiver.The positive aspects of this radiometer system are:

• With a suitable switching sequence we obtain a very satisfactory deter-mination of the important second and third Stokes parameters even

Polarimetric Radiometers 57



without Dicke switching: they are found by subtracting the output val-ues from one single receiver where the input is switched rapidly between two signals—quite analogous to the situation in a traditionalDicke radiometer, and gain and noise drifts/fluctuations are largely cancelled.

• Only one radiometer receiver is required.

Also note that, on a neutral note, with Dicke switching or frequent cali-bration we also get a good determination of the normal T H and T V signals.

The negative aspects of this radiometer system are:


RX0/90°

∆Σ

ver

hor

ver/hor

−45 or

+45 or r+ − / 45 or r/

Dicke/cal

REF

OUT

1

2

1

2

1

2

1

1

2

2

SWA

SWB

PS

SWC

SWE

SWD

Figure 7.1 Full multiplex polarization combining radiometer.

Table 7.1

Correspondence Between Positions of Switches in Figure 7.1

and Measured Brightness Temperature Component

SWA SWB SWC SWD SWE PS

T V 1 d.c. 1 d.c. 1 d.c.T H d.c. 1 2 d.c. 1 d.c.

T45° 2 2 d.c. 2 2 0°

T−45° 2 2 d.c. 1 2 0°

Tr 2 2 d.c. 2 2 90°

T l 2 2 d.c. 1 2 90°

(d.c. = don’t care)



• The system sensitivity is hampered by substantial loss in the polariza-tion combining network (may be alleviated by preamplifiers up front).

• The potential sensitivity is very poor due to low duty cycle because allmeasurements have to be multiplexed through a single receiver. Sensi-tivity may be regained with long integration time, precluding the use of this configuration in imaging systems where short integration timenormally prevails.

• The system requires complicated microwave combining and switching hardware.

A system of this type has been used with great success by JPL for their air-borne, profiling (nonimaging) measurements of ocean waves [2, 3].

The second configuration to be discussed is the parallel receiver polariza-tion combining radiometer as shown in Figure 7.2. This is an alternative versionof the system described above, where the same polarization combinations areproduced, not sequentially by switching, but simultaneously using power divid-ers (and again magic tees and a 90° phase shift). Preamplifiers (with substantialgain) up front are a necessity in this configuration or the power divider scheme

would strongly degrade the sensitivity. Six identical radiometers—these couldbe total power or Dicke—are required to measure the different polarizationcombinations.

The positive aspect of this system is that parallel channels ensure optimumsensitivity (no duty cycle problems) appropriate for applications in imaging sys-tems be it airborne or spaceborne.


ver

hor

REF

REF

3 wdiv

90°

RX 1

RX 2

RX 3

RX 4

RX 5

RX 6

TV

T−45

T+45

Tr

T

TH

Σ

Σ

∆

∆

3 wdiv

Figure 7.2 Parallel receiver polarization combining radiometer.



On a neutral note, Q , U , and V are found by subtraction of individualreceiver’s outputs, leading to potential stability problems. The problem is partly alleviated by proper design where identical receivers track in temperature and

supply voltages, and by Dicke switching or frequent calibration. In the presentcase Dicke switching may not be attractive due to the sensitivity penalty, whereas frequent calibration is readily possible while the scanning antenna looksaway from the useful swath anyway (see Chapter 13). Also, frequent calibrationensures good determination of T V and T H .

The negative aspect of this system is that the system requires six receiversand complex microwave hardware.

7.3.2 Correlation Radiometers

The first system to be described under this headline is the basic correlation radi-ometer shown in Figure 7.3 (based on Figure 4.6). Two identical total powerreceivers are connected to the horizontal and vertical outputs of the antenna sys-tem. The outputs of the receivers are detected the usual way to yield the normalhorizontally and vertically polarized brightness temperatures. The outputs of thereceivers are also (at IF level) fed into the complex correlator providing the U and V Stokes parameters after multiplying the real and the imaginary outputs by

a factor 2 [see (7.4)]. The complex correlator consists of two sections each hav-ing a multiplier and an integrator. The real section operates directly on the out-puts from the receivers, while the imaginary section multiplies the output fromone receiver with the output from the other phase-shifted 90°. The correlatorcan be implemented in analog or digital technology. In the following, digitalimplementation is assumed due to better stability, and technology is no longer a problem for typical radiometer bandwidths around 500 MHz or less. See, forexample, [5] for a brief description of such circuitry. The radiometers are gener-

ally implemented as superheterodyne receivers to enable the correlator to work


Real

Imag

ver

hor

RX 1

RX 2

TV

TH

U/2

V/2

complex

corr.LO

REF

REF

∼

Figure 7.3 Basic correlation radiometer.



at a suitable IF frequency. The correlation technique requires phase coherencebetween the two receivers. This is achieved by using one common localoscillator.

The positive aspects of this configuration are:

• Parallel channels ensure optimum sensitivity.

• U and V are very well determined. This is associated with the way in which the correlation radiometer works. The output of the digitalcorrelator is the correlation coefficient ρ (typically around 0.01) whichmust be multiplied with the total system temperature T S (typically around 500K) to yield the true cross correlation between the two chan-

nels. The error in U can be expressed as δU = δρ · T S + ρ · δT S , whereδρ is the error in the correlation coefficient, and δT S is the error in theknowledge of the system temperature. Due to the small values of ρ typi-cal of measurements when observing natural scenes, the second termvanishes with any reasonable radiometric error, and the first term is very small, as a digital correlator can be made almost perfect.

• The system requires only simple microwave circuitry.

On a neutral note, Q is found by subtraction of individual receiver’s out-puts—see the earlier discussion concerning the parallel receiver polarizationcombining system. Also, frequent calibration ensures good determination of T V

and T H . A negative aspect of this is that a fast digital correlator is needed. In the

past, digital circuitry with clock frequencies around 1 GHz was bulky andpower-consuming. However, with present-day technology, a three-level com-plex digital correlator can be implemented in a single chip consuming no more

than 1W of power. A system of this type has been used with great success by DTU for air-

borne, imaging measurements of ocean waves [6].The final system to be considered here is the switching correlation radiom-

eter outlined in Figure 7.4. It is just a small enhancement of the basic correlationradiometer in which a crossover switching arrangement is added between theantenna and the receivers, and corresponding synchronous demodulatorsare added after the detectors. The crossover switches and synchronous

demodulators operate simultaneously. A fast switching sequence as in a Dickeradiometer is assumed. Each of the two radiometers will now act as a Dicke typeswitching radiometer on the difference between vertical and horizontal polariza -tion with the associated, well-known stability. The correlation processes are notinfluenced by the switching (the imaginary signal must be demodulated like theQ signals, which is easy in the digital circuitry, and not shown in the figure). A




potential problem is multiple reflections between the antenna, the switchmatrix, and the first amplifier. Phase changes due to the switching action may lead to unwanted offsets. This must be further considered in an actual designand trade-off phase.

The positive aspects of this configuration are:

• Parallel channels ensure optimum sensitivity.

• The important Stokes parameters Q , U , and V are all very welldetermined.

Some neutral notes are that frequent calibration ensures good determina-tion of T V and T H , and the system requires slightly more complicated microwave

circuitry than the basic correlation radiometer. A negative aspect of this system is that there are possibly problems with

reflections within the microwave circuitry.

7.4 Sensitivities

The sensitivity of the full multiplex polarization combining radiometer will not

be discussed further here. It has already been mentioned that the potential sensi-tivity is poor, due to the fact that all measurements are multiplexed through a single receiver. Hence, this configuration is only useful where sensitivity is notan issue (nonimaging airborne or ground-based systems).

Concerning the parallel receiver polarization combining radiometer, thesensitivity is assessed rather easily assuming identical receivers and identical


ver

hor

RX 1

RX 2

LO Complex

corr.

±1

±1

Q

Q

U/2

V/2

TV

TH

REF

REF

∼

Figure 7.4 Switching correlation radiometer.



preamplifiers. Thus, the sensitivity of any radiometer channel (vertical, horizon-tal, +45°, ....) is that of a standard total power radiometer: ∆T TPR . Going to theStokes parameters, this means that ∆I = ∆Q = ∆U = ∆V = 2 · ∆T TPR [∆I is the

sensitivity (standard deviation) of the first Stokes parameter and so on], as they all are found by addition or subtraction of statistically independent signals withidentical standard deviation ∆T TPR .

For the basic correlation radiometer, we find as above ∆I = ∆Q = 2 ·∆T TPR assuming identical receiver performance. The correlator outputs have a sensitivity that (as already described in Section 4.4) can be found by considering the analogy to the radio astronomer’s interferometer with correlation receiver: If the interferometer observes a small source in the boresight direction, and it isassumed that the two radiometer channels collect equal but independent back-

ground noise, the sensitivity is expressed as ∆ ∆T T TPR = / 2 (the two receiversare identical with a sensitivity ∆T TPR ). In this case we also have a correlationreceiver, but now one connected to the V and H ports of one antenna observing for example the sea surface. The V and H signals are only weakly correlated andcan be modeled as sums of large “background” signals (uncorrelated channelto channel) and a small correlated signal. As before, we then find ∆T =∆T TPR / 2, only assuming that the system temperatures in the two channelsare equal, which is a fair assumption, although not fully correct, as the vertical

and the horizontal brightness temperatures of the sea surface generally are somewhat different. However, the difference is relatively small and the addition of thereceiver noise temperatures to find the system noise temperatures tends to fur-ther equalize the signals. Recalling the factor 2 in (7.4), we then find for thethird and fourth Stokes parameters: ∆U = ∆V = 2 · ∆T TPR .

We note that concerning sensitivity, there is no difference between theparallel receiver polarization combining radiometer and the basic correlationradiometer. They are both optimal in this respect.

In the switching correlation radiometer each of the Q outputs will exhibita sensitivity corresponding to that of a Dicke radiometer (i.e., 2 · ∆T TPR ), assum-ing a radiometric performance of the receivers as before; but there are two of them, and they are statistically independent (when one channel measures thevertical brightness temperature, the other measures the horizontal and visa versa), so by combining them, we gain a factor of 2, and obtain a resulting sen-sitivity of ∆Q = 2 ⋅ ∆T TPR . As before, we find ∆ ∆ ∆U V T TPR = = ⋅2 as thecorrelation process is not influenced by the switching. Concerning sensitivity,this configuration is also optimal. The main advantage of this configuration isthat we get the three important Stokes parameters Q , U , and V with “Dicke”stability yet without loss of sensitivity. However, in all fairness, it should benoted that the crossover switches have been assumed to be lossless. In real life a small sensitivity penalty will have to be sustained due to inevitable losses in theseswitches.




7.5 Discussion of Configurations

For basic airborne measurements of polarimetric signatures using circle flights

with a staring (nonimaging) radiometer, the first configuration, the full multi-plex polarization combining radiometer, is a strong candidate due to its relativesimplicity and its very good determination of the important three Stokes param-eters: Q , U , and V .

For any imaging applications, as, for example, a future spaceborne missionto measure wind over the ocean, only the three other configurations are candi-dates due to severe requirements on sensitivity. The correlation technique seemsto be a strong candidate, trading substantial microwave hardware for fast digitalcircuitry. With present technology, the required digital correlator is definitely

feasible, and the development of digital technology is rapid, making it evenmore feasible in the near future. However, it should be noted that the presentand future development of MMIC technology makes implementation of complex microwave hardware feasible.

It must also be mentioned that the statement that the parallel receiverpolarization combining radiometer and the correlation radiometer exhibit iden-tical sensitivity is based on the assumption that they have identical bandwidths.If the bandwidth requirements are in excess of 1 GHz, which could be the case

at Ka-band and above, it is felt that the digital correlator may be difficult to real-ize with present technology. Finally, it is noted that an ideal digital correlator

with a sufficient number of bits has been assumed. If only a few bits (typically 1or 2 bits for wideband applications) are used, some sensitivity degradation isobserved [5]. The degradation can typically be 15%, as discussed later in Section7.6, but it is dependent on the oversampling rate and the actual number of bits.The detailed trade-off between the parallel receiver polarization combining radi-ometer and the correlation radiometer requires technical studies including

bandwidth, weight, volume, and power budgeting on a case-by-case basis.The choice between the basic correlation radiometer and the enhancedswitching version is also not straightforward. No doubt, the switching system issuperior in determining the Q parameter, but the question is, whether a mod-ern, well-designed, paired set of receivers cannot do an adequate job. Thisrequires further investigations of real hardware.

7.6 The DTU Polarimetric System

As an example of polarimetric radiometer systems, aspects of the DTU ocean wind sensing system will be briefly described. The radiometers are of the basiccorrelation type as described earlier. This does not reflect a choice based on a detailed technical trade-off as described in the previous sections. Actually, the




radiometers were designed and built first, and these considerations were carriedout afterwards—inspired by discussions with other researchers who were infavor of other implementation possibilities. The main reason for the following

description of specific hardware is that—apart from the fact that real examplesalways further understanding—this gives an opportunity to touch on severalaspects of proper radiometer design.

The airborne, imaging, polarimetric DTU system features radiometers atKu- and Ka-band. They are of identical design. The correlation radiometeremploys two single sideband superheterodyne receivers (see Figure 7.5). Thelocal oscillator frequency is 16 (or 34) GHz and the IF band is 75–475 MHz.The two total power receivers are connected to the vertical and the horizontaloutputs of a dual polarized feed horn. Fast switches (latching circulators) are

included for frequent calibration.It can be stressed that, in order for the correlation radiometer to work

properly, the two receivers must be of the single sideband type. If DSB receivers were employed, the fourth Stokes parameter would always be zero since the


U/2

V/2

Real

Imag

REF

ver

hor

REF

LO

Σ∆

ϕComplexdigital

corr.

TV

TH

0°

90°

0°

90°

A/D

A/D

0/180°

0°

RF

RF IF

IF

~

∼∼∼∼∼∼

∼∼∼ ∼∼∼

∼∼∼

∼∼∼

∫

∫

Figure 7.5 DTU correlation radiometer.



contributions from the upper and the lower sidebands cancel due to the phaserelationships in the system.

The correlation technique requires phase coherence between the two

receivers in order to measure the complex correlation between input signals.This is achieved by using one common local oscillator. The phase shifterbetween the local oscillator and the mixer in the horizontal channel is used toachieve phase balance in the two channels. It is adjusted to maximize the realpart of the output signal (minimize the imaginary output) for equal, correlatedinput signals. These signals are generated by an external calibration system: A noise diode feeds a power divider, and the two identical signals are connected via identical attenuators and transmission lines to the inputs of the correlation radi-ometer. Experience has shown excellent phase stability and that the phase shifter

only has to be checked and possibly adjusted when cables or components of theradiometer have been disconnected and reassembled.

High isolation between the two channels is required. If a signal in onechannel leaks to the other channel, this leaked signal and its source will correlate,and the output from the correlator will exhibit an offset, that is, a nonzero valueeven for completely uncorrelated inputs to the radiometer system. The localoscillator distribution circuitry is especially critical as it provides a direct pathbetween the radiometer channels. A minimum isolation of 70 dB at RF as well

as IF frequencies is obtained by a combination of isolators and waveguide filters.The isolators take care of RF frequencies, but cannot be expected to operate wellat the much lower IF frequencies, while even the simplest waveguide filtereffectively will cut off IF stray signals.

When considering isolation issues, examine Figure 7.6 and recall that thedetectors in a radiometer operate in the square law range. Assume identicalreceivers and system noise temperatures of 500K. Hence, the outputs T 1 = T 2 =500K, while the correlator outputs are nominally zero, since the signals in the

two receivers are assumed uncorrelated. At some point in receiver 1, where theleak to receiver 2 takes place, the 500-K output signal corresponds to a voltage


Real

Imag

RX 1

RX 2

T1 500 K=

T2 500 K=

V1

V2

70 dB

g·V1

g·V2

+0.00032·g·V1

x2

x2

Complex

corr.

Figure 7.6 Leak signals in the correlation radiometer



V 1 and if the total gain between this point and the square law detector is g , wehave: ( g · V 1)

2 = 500K, and likewise in receiver 2. Assuming a leak of 70 dB (cor-responding to 0.00032) between receivers, we have at the input of the detector

and of the correlator in receiver 2 a signal 0.00032 · g · V 1 and accordingly at thecorrelator output: g · V 1 · 0.00032 · g · V 1 = ( g · V 1)2 · 0.00032 = 500 · 0.00032 =

0.16 K . This signal may be in the real or in the imaginary channel dependenton phase details in the leak path. A similar signal arises via the leak from receiver2 to receiver 1. The signals add according to phase details, and it is seen that the70 dB of isolation will ensure a worst-case offset on the correlator output with a value of 0.3K (which seems reasonable, bearing in mind the small polarimetricsignals that we intend to measure). This value is actually further reduced due tothe fringe washing effect: The leak signal is not a monochromatic signal, but has

in the present case a bandwidth of 400 MHz, and this, in combination with theleak signal electrical path length, causes decorrelation. Thus, we observe lessthan 0.1-K offset in practice.

The network used to feed the analog detectors and the digital correlatorconsists of: (1) an in-phase two-way power divider used to divide the signalbetween the digital correlator and the analog detector circuit, and (2) a quadra-ture hybrid to make in-phase and 90° out-of-phase signals for the correlator.The analog detector is a tunnel diode detector, and this is followed by an

integrator.The digital correlator consists of a multilayer printed circuit board with a

three-level (2-bit) A/D conversion at the input and proper multipliers. The sam-pling rate is 1,540 MHz and an 8-ms averaging is carried out on the correlatoroutputs. The circuit board also holds circuitry for monitoring the quantizationlevels. This information is used for the normalization of the correlation values.

Offsets on the output of the correlator are reduced significantly by phase-switching the local oscillator signal to one of the channels and properly

demodulating after the correlator. This is implemented by switching the localoscillator at a 1-kHz rate between the sum and difference ports of a magic tee.The demodulation is done inside the digital correlator. The injection of uncorrelated noise in the two receivers from two independent loads is used tocalibrate for the remaining offsets. The loads may be the same as those used forfrequent calibration checks as well.

The correlation radiometer concept requires a matched pair of receivers,and phase characteristics are especially important. The phase difference betweenreceivers is described by a mean phase difference over the receiver frequency band, and an RMS term. The mean phase term cause a shift of U signal into theV channel and V into U . This is compensated for by the phase shifter in the localoscillator section. The RMS phase term causes some decorrelation betweenchannels [5]. To find the correct correlation between measured signals in theradiometer system, a correction factor has to be applied. This correction factor is




found by coupling known amounts of correlated noise from a common noisediode into the two radiometer inputs and checking the correlator outputs.

The analog integration in the total power radiometers is 4 ms, and later a

digital integration to 8 ms is carried out. The resulting radiometric sensitivity for the vertical (or horizontal) channel has been measured to 0.35K, which isvery close to the theoretical value found using measured system noise tempera-tures and the normal sensitivity formula for a total power radiometer. The sensi-tivity of the correlation measurements (i.e., the third and fourth Stokesparameters) is then, following the discussion in Section 7.4, expected to be 0.35· 2K . However, this figure must be further degraded by a factor of 1.15 due tothe three-level digital correlator with a factor 1.6 oversampling rate [5]. Thus,the final sensitivity is expected to be 0.57K, which is in fair agreement with mea-

sured values of 0.59K (U ) and 0.52K (V ).The radiometer system just described is combined with a 1-m aperture

scanning reflector antenna system, designed for operation from the open rampof a C-130 Hercules transport aircraft. Several campaigns have been carried outover the ocean in order to investigate how well wind direction can be deter-mined by an imaging, polarimetric system; see, for example, [6].

References

[1] Sasaki, Y., et al., “The Dependence of Sea-Surface Microwave Emission on Wind Speed,Frequency, Incidence Angle, and Polarization over the Frequency Range from 1–40GHz,” IEEE Trans. on Geoscience and Remote Sensing , Vol. 25, No. 2, 1987, pp. 138–146.

[2] Yueh, S. H., et al., “Polarimetric Measurements of Sea Surface Brightness TemperaturesUsing an Aircraft K-Band Radiometer,” IEEE Trans. on Geoscience and Remote Sensing ,Vol. 33, No. 1, 1995, pp. 85–92.

[3] Yueh, S. H., et al., “Polarimetric Brightness Temperatures of Sea Surfaces Measured with

Aircraft K- and Ka-Band Radiometers,” IEEE Trans. on Geoscience and Remote Sensing ,Vol. 35, No. 5, 1997, pp. 1177–1187.

[4] Skou, N., and B. Laursen, “Measurement of Ocean Wind Vector by an Airborne, Imag-ing, Polarimetric Radiometer,” Radio Science , Vol. 33, No. 3, 1998, pp. 669–675.

[5] Thompson, A. R., J. M. Moran, and G. W. Swenson, Interferometry and Synthesis in Radio Astronomy , Malabar, FL: Krieger, 1991.

[6] Laursen, B., and N. Skou, “Wind Direction over the Ocean Determined by an Airborne,Imaging, Polarimetric Radiometer System,” IEEE Trans. on Geoscience and Remote Sensing ,Vol. 39, No. 7, 2001, pp. 1547–1555.




8Synthetic Aperture Radiometer Principles

8.1 Introduction

In remote sensing, situations arise that require radiometric measurements withlarge antennas that must be scanned (moved) in order to form images. An exam-ple occurs in remote sensing of soil moisture where science requirements forspatial resolution lead to antenna systems so large that they may not be practi-

cal. Requirements already exist for antennas in excess of 10m in diameter forremote sensing from space [1]. Aperture synthesis is a technique for overcoming the limitation that a large

antenna aperture places on passive microwave remote sensing from space. Thisis an interferometric technique in which pairs of small antennas are usedtogether with signal processing to achieve the resolution of a single large aper-ture antenna. In this technique, the product of the signal from each pair of antennas is measured using a correlation radiometer (see Figure 8.1 and also thebasic correlation radiometer in Chapter 7). The complex product (real andimaginary part) is recorded for pairs of antennas at many different spacings. Thespacing is called a baseline and both the magnitude and orientation of thedistance between the antennas is important.

It can be shown that the output signal at each baseline produces a samplepoint of the Fourier transform of the scene at a “frequency” that depends on thedistance between the antennas. Realizing this, the idea is to collect measure-ments at enough baselines to obtain a reasonable representation of the Fouriertransform and then to form an image by inverting the transform. The latter is a

relatively simple numerical integration of the sample data. The technique is sim-ilar to “Earth rotation synthesis” developed in radio astronomy [2].

69



The critical feature for remote sensing applications is that the eventual spa-tial resolution does not depend on the antenna size but on how well the Fouriertransform is sampled (number and choice of baselines). One can achieve highspatial resolution with sparse arrays of small antennas. Sparse arrays are possiblebecause only one measurement is needed at each baseline. Small antennas can beused because the individual antennas do not determine resolution. In fact, smallantennas can be an advantage by providing a wide field of view. Finally,mechanical scanning is not needed because an image of the entire field of view is

obtained in software as part of the inverse transform.The concept is illustrated in Figure 8.1. Imagine two antennas L m apart,

receiving radiation from a scene with an effective surface temperature, T (x ), thatis to be measured. The voltages out of each antenna are multiplied together andaveraged. Both phase and amplitude are measured, which is equivalent torecording the real and imaginary parts. In aperture synthesis applications, theoutput complex number is often called the visibility. Figure 8.2 is a block dia-gram showing how this measurement could be implemented in hardware (this is

a portion of the basic correlation radiometer described in Chapter 7). As in a conventional receiver, the signals from the two antennas are mixed to a


T(x)

V(v )x

Figure 8.1 Basic viewing geometry for aperture synthesis: Two antennas separated by a

distance, L , receive radiation from a scene with effective temperature T (x ).

H(f)

H(f)

LOQ

I

∼

90°

∼∼

∼∼

Figure 8.2 Block diagram showing how the measurement needed for each antenna pair

could be implemented in hardware.



convenient IF and then amplified and filtered. The process is represented in thefigure by the effective transfer function, H(f). The IF outputs of each receiverare then multiplied together in-phase (no phase shift) and also after shifting one

channel by 90° (quadrature). The products are averaged (equivalent to a lowpassfilter). The output visibility is a complex number whose real part is the in-phaseresponse (labeled “I” in the figure) and whose imaginary part is the output of thequadruature channel (labeled “Q”).

When the radiation incident on the two antennas is incoherent (true formost natural scenes), the visibility is proportional to the Fourier transform of the temperature profile, T (x ), evaluated at a “frequency” νx (for example, see [2,3] for derivation of this result). The frequency, νx , is often referred to as a “spa-tial frequency”, and is given by:

ν λx L = (8.1)

where L is the distance between antennas and λ is the wavelength at which themeasurement is made (i.e., corresponding to the center frequency of the receiv-ers in Figure 8.2). Since νx depends on the antenna spacing, L , the point at

which the Fourier transform is given by the output (visibility) can be changedsimply by repeating the measurement with different L . In principle, one couldmake measurements at many different antenna baselines, L , and obtain a goodrepresentation of the transform. Then, the temperature profile itself, T (x ), couldbe obtained by inverting the Fourier transform.

The important point for aperture synthesis is that the resolution obtainedin the image formed after Fourier transforming is determined by how well thetransform has been sampled (i.e., by the number and spacing of the samplepoints, νx ) and not by the size of the antennas used in the measurement. In prin-ciple, one could use very small antennas to obtain a wide field of view and by

making many measurements closely spaced in spatial frequency space, one couldobtain a map of T (x ) with very high spatial resolution.

Figure 8.3 illustrates how this technique might be applied for remote sens-ing from space. Imagine two antennas in orbit, one spiraling around the otherand each looking at the same region on the surface. At intervals indicated by thedashes, the signals from the two antennas are multiplied together and averaged,producing a sample point in the (two-dimensional) Fourier transform of thescene. After the spiral is complete, the data are assembled and the sampled trans-

form is inverted to produce an image of the scene. The individual antennasdetermine the field of view (oval on the surface in Figure 8.3). The resolution(boxes inside the oval) is determined by the longest baseline in the spiral. Hence,in principle, one could use small antennas to obtain a large field of view and a spiral with a large radius to obtain high spatial resolution.

Synthetic Aperture Radiometer Principles 71



8.2 Practical Considerations

8.2.1 RF Processing

Figure 8.2 indicates the processing needed in aperture synthesis. The front endis a standard receiver in which the RF input is mixed to a convenient IF withappropriate gain and filtering. This must be done using a single side band mixer

to preserve phase information and one common local oscillator (LO). If morethan one LO is used, the LO signal at each front end must be “phase locked” tothe same reference so as not to introduce phase errors. The net effect is repre-sented in the diagram by the front-end filter, H ( f ). The IF signals from eachantenna-pair are then multiplied together twice: first directly (no phase shift)and then after shifting one arm by 90°. The products are then averaged (a lowpass filter). The principle is the same as discussed in Chapter 7 for the basiccorrelation radiometer (see, for example, Figure 7.5).

The output from the in-phase channel (no phase shift) is the real part of the complex product of the output of the antennas and is proportional to A 12

cos( ϕ1 − ϕ2). The output from the quadrature channel (90° phase shift) is theimaginary part of the product and proportional to A 12 sin( ϕ1 − ϕ2) where A 12

represents the magnitude of the product, and ϕ1 and ϕ2 are the individualphases. The complex number formed from these two parts is V (u ,v ) in (8.3).


Figure 8.3 Illustration showing how aperture synthesis might be applied for remote sensing

from space.



The noise in the output of the correlator in Figure 8.2 is computed as inthe case of a total power radiometer. However, in this case it is reasonable toassume that the noise in the two RF channels following each antenna (i.e.,

equivalent receiver noise) is independent. In this case, the receiver noise cancels when the product is averaged and one finds that the sensitivity of the measure-ment at each antenna pair is [4, 5]:

∆T T B sys = 2 τ (8.2)

where T sys = T A + T N , B is the system (noise) bandwidth, and τ is the effectiveintegration time represented by the lowpass filter. Equation (8.2) is similar to

the result for a total power radiometer except for an improvement of a factorsquare root of 2. However, this is not the sensitivity of the image. It is the sensi-tivity of the RF electronics in a single measurement (a single point in the Fouriertransform). To obtain the sensitivity of the image, one must include the patternof the individual antennas and the image processing (Fourier transform). This isdiscussed in Section 8.2.4.

8.2.2 Basic Equation

Assuming a geometry such as shown in Figure 8.1, it is a relatively straightforward exercise in electromagnetic theory to compute the output of the two anten-nas when connected to a receiver such as shown in Figure 8.2 (for example, see[3]). Expressing the integration over the antenna field of view in a spherical coor-dinate system (θ, ϕ), one can write the correlator output in the form [6, 7]:

( ) ( ) ( ) ( ) ( ) ( ) ( )[ ] ( )V u v C T P e d d j u v , , , sinsin cos sin sin= +∫ ∫ θ ϕ θ ϕ θ θ ϕ π θ ϕ θ ϕ2 (8.3)

In this expression, u ,v are “spatial” frequencies that depend on the distancebetween the antennas: u = (x 1 − x 2)/ λ and v = ( y 1 − y 2)/ λ where λ is wavelengthand x 1,2 and y 1,2 are the coordinates of the two antennas in this pair. P (θ, ϕ) is theproduct of the voltage patterns of the individual antennas and T (θ, ϕ) is theeffective temperature (physical temperature times emissivity) of the surface. Thein-phase (I ) and quadrature (Q ) outputs of the correlator (Figure 8.2) are thereal part and imaginary part of (8.3), respectively. Finally, C is a scale factor that

depends on the details (shape and amplitude) of the effective passbands of thereceivers, and the lowpass filters.Equation (8.3) is an approximation valid for most remote sensing applica -

tions from space. It assumes that the incident radiation is incoherent and thatthe antennas are identical and that the distance from the antenna array to thescene is large compared to the maximum baseline. (The latter is commonly




referred to as the far-field approximation in electromagnetic theory. It neglectsthe curvature of the wave over the extent of the antenna array.)

Another assumption inherent in (8.3) is that the effective bandwidth of

the system can accommodate the time delay between signals arriving at pairs of antennas in the array. In general, there will be a time difference when comparing the signal arriving at the two antennas in a pair from a given point on the surface(e.g., the two ray paths shown in Figure 8.1 will be of different length). If theantennas are sufficiently far apart and the receiver impulse response is suffi-ciently short (very large bandwidth), it is possible for the response of receiver “a”due to the signal arriving at its antenna to decay before that signal arrives atreceiver “b.” There will be a consequent decay in the correlation, which is calledfringe washing after its counterpart in optics. One can obtain a rough idea of the

limitations this imposes by approximating the impulse response of the receiverby the inverse of its bandwidth, B. Then, in order to have a nonzero signal, oneobtains the limitation:

( )L c B sin θ < 1 (8.4)

where L is the distance between the antennas and θ is the angle between the lineof sight to a point on the scene and the normal to the array. Problems associated

with fringe washing arise when trying to employ large bandwidth to reducenoise (8.2). In this case it is possible for the right-hand side of (8.4) to be smalland limit the maximum baseline (L ) or the field of view (θ). For example, in the

window at 1.413 GHz used for passive remote sensing of soil moisture and sea surface salinity, the available bandwidth is 27 MHz. This implies a maximumbaseline on the order of 10m. One could employ a larger baseline by restricting the field of view (e.g., 15m if limited to 45°). The assumption made in (8.3) isthat (8.4) is satisfied and there is no fringe washing (the fringe washing function

is unity).Finally, differences among the antennas are not taken into account. Equa-tion (8.3) assumes identical antenna patterns. Among the possible effects is elec-tromagnetic coupling, which causes the pattern of an antenna to be changed by nearby antennas. This can be an issue especially for very short baselines [8].

Another possibility is thermodynamic coupling, in which case T (θ, ϕ) in (8.3)can be effected by the presence of the other elements in the array [9].

8.2.3 Image Processing

Equation (8.3) has the form of a Fourier transform. The resemblance of (8.3) toa Fourier transform can be made more obvious by rewriting it in terms of thedirection cosines ξx = sin(θ)cos( ϕ) and ξ y = sin(θ)sin( ϕ):




( ) ( ) [ ]V u v K e d d x y

j u v

x y x y , ,= ∫ ∫

+ ξ ξ ξ ξ

π ξ ξ2(8.5a)

where the kernel K( ξx

, ξ y

) is:

( ) ( ) ( )K CT P x y x y x y x y ξ ξ ξ ξ ξ ξ ξ ξ, , ,= − −1 2 2 (8.5b)

and the integration is over all values inside the “unit circle” (i.e., ξ ξx y 2 2 1+ ≤ ). In

principle, the image is formed by inverting the transform to obtain the kernel K and then solving for the scene brightness temperature, T:

( )( )( )[ ] ( ) [ ]

T

CP V u v e du dv

x y

x y x y

j u v x y

ξ ξ

ξ ξ ξ ξ π ξ ξ

,

,

=

− − − +

∫ ∫ 1 2 2 2(8.6)

There are a number of practical considerations that impact one’s ability toobtain the inverse transform. First of all, in practice one will only have measure-ments of the visibility function V (u ,v ) over a limited range of values (e.g., thediscrete points indicated by dashes in Figure 8.3 and only to some maximumradius). The implications of this type of limitation are well known in antenna theory (e.g., finite arrays of discrete elements) and in a more general form in“sampling” theory. The consequences include a limit on resolution (set by themaximum baseline) and the possibility of aliasing if the spacing between base-lines is not small enough.

A more serious problem that occurs in the practical application of thistechnique is that the antennas and even the receivers may not be identical. Inthis case, the kernel K in (8.5) is not the same for each baseline and the equation

is no longer a Fourier transform. One approach for obtaining an image in thiscase is to replace the integral by its approximating sum. Then (8.5a) becomes a set of linear equations in which the sample values of the kernel, K , are unknownand the visibilities, V (u ,v ), are known (obtained from the measurements). Thisapproach has been employed successfully in practical applications such as forremote sensing of soil moisture. It is discussed in Section 8.3 and again in moredetail in Chapter 15.

8.2.4 Sensitivity

The trade one makes for employing aperture synthesis is a decrease in radiomet-ric sensitivity. Each measurement employs a pair of antennas that are small com-pared to an antenna with the resolution of the final, synthesized array. Hence,




other factors being equal, one would expect the signal-to-noise ratio of eachmeasurement to be lower than would be obtained with a real aperture of the sizethat is being synthesized. This is the case; however, because the image is recon-

structed using many baselines much of the penalty in signal-to-noise associated with using small antennas is recovered [5, 6].In general, the noise in the image will depend on the processing. However,

a reasonable approximation can be obtained by assuming an ideal discrete Fou-rier transform for the inversion. In this case, the RMS noise, ∆T , in the imagecan be written [5]:

[ ] ( )∆T T B A NA sys syn e = 2 τ (8.7)

The term in brackets is the ideal response of a coherent correlation receiver(8.2) with system noise, T sys , effective bandwidth, B , and integration time τ. Theterms to the right of the brackets represent a factor that occurs during the imagereconstruction. In this expression, A syn is the effective antenna area correspond-ing to the synthesized beam (i.e., roughly the area covered by the spiral in Figure8.3), A e is the effective area of the actual individual antennas, and N is the squareroot of the number of independent baselines that were used in image reconstruc-tion. In general, A syn /(N A e ) > 1 and represents the penalty in noise performancepaid for using aperture synthesis. Examples of the factor, A syn /(N A e ), for severalantenna configurations can be found in [5]. In general, one finds that the pen-alty grows with the amount of thinning.

8.3 Example

To illustrate the procedure, consider a configuration in which the potentialantenna positions are uniformly spaced on the principle axes of a Cartesian grid

with center-to-center spacing d x and d y , respectively. That is, the individual an-tennas lie along the x - and y -axes with centers at x = p d x and y = q d y where p , q are integers. The baselines u ,v possible with such an array can take on values (n ∆u , m ∆v ) where ∆u = d x / λ and ∆v = d y / λ and n , m are integers. [See the defini-tions after (8.3).] Suppose that measurements are made so that the availablebaselines fill the space −N ≤ n ≤ N and −M ≤ m ≤ M . This could be done with

pairs of antennas arranged along the arms of a cross “+” or a tee “T.” Assuming that the antennas and receivers are identical, (8.5) applies.However, this configuration provides only a limited set of discrete samples of V (u ,v ), one value for each available baseline. As mentioned earlier, an approachthat is convenient in this case is to replace the integrals by their approximating sum. Doing this with (8.6a), one obtains:




( ) ( ) [ ]′ = ∑ ∑ − +K V u v e u v x y

n m j u v x y ξ ξ π ξ ξ

, , 2

∆ ∆ (8.8)

where u = n d x / λ = n ∆u and v = m d y / λ = m ∆v and the sums are over all the n and m . The symbol, Σn is used to indicate that the sum is over all the values of n .

Also, note the prime on K in (8.8). K ′ is the image generated from (8.8) as dis-tinct from the unprimed K in (8.5) that is the actual value.

It is possible to obtain a particularly useful form of (8.8) by substituting (8.5a) for V (u ,v ) and rearranging. Substituting (8.5a) and introducing “delta”functions δ(u − n ∆u ) to denote the sample values of V (u ,v ), one obtains [3]:

( )

( )[ ] ( )

′ = −K F V u v D x y x y ξ ξ ξ ξ, , * ,1 (8.9a)

( ) ( )= K D x y x y ξ ξ ξ ξ, * , (8.9b)

( ) ( )= ′ − ′ − ′∫ ∫ K D d d x y ξ ξ ξ ξ ξ ξ ξ ξ, (8.9c)

where F −1 denotes an inverse Fourier transform and the asterisk * denotes a con-

volution. The significance of this rearrangement is that (8.9c) has the conven-tional form for the response of an antenna with gain D ( ξx , ξ y ) when viewing a scene K ( ξx , ξ y ) (for example, see [10, 11]).

The function D in the expression above is the Fourier transform of a sumof delta functions:

( ) ( ) ( )[ ]D F u n u v m v u v x y m m ξ ξ δ δ, = − −− ∑∑1 ∆ ∆ ∆ ∆ (8.10)

The sum is over the all n and m : −N ≤ n ≤ N and −M ≤ m ≤ M . Equation(8.10) can be factored into separate sums and analytic expressions can beobtained by recognizing that the resulting sums over n and m are geometricprogressions. One obtains:

( ) ( ) ( )( )[ ]

[ ]

( )[ ]D h g

u

N u

u v

M v

x y x y

x

x

y

ξ ξ ξ ξ

π ξ

π ξ

π ξ

,

sin

sin

sin

=

=

+ +

∆

∆

∆ ∆

∆2 1 2 1

[ ]sin π ξ∆v y

(8.11)

Note that the components h ( ξx ) and g( ξ y ) of D are the antenna array fac-tors of a uniformly spaced, linear array with 2N + 1 elements. Hence, in this




example the synthesis array behaves (mathematically) like a real aperture lineararray of 2N + 1 elements. However, notice that measurement in the synthesisarray is of power (e.g., brightness temperature) and that the functions h ( ξx ) and

g ( ξ y ) are, in antenna theory, the array factors for the electric field. Hence, if a realaperture linear array was used to make this measurement, the antenna pattern would be h ( ξx )

2. The power pattern of a real antenna has only positive side lobes;however, the sidelobes of the effective pattern in the synthesis array can be bothpositive and negative (see Chapter 15). On the other hand, there is a greatamount of flexibility in designing a synthesis array and in choosing the imagereconstruction algorithm. For example, weighting could be used in the sumsabove to control the sidelobes.

The resolution of the synthesized pattern, D , is determined by the number

of elements in the array and the spacing, d , and not the actual antennas them-selves. Of course, the antenna pattern is part of the kernel K and it will beneeded ultimately to retrieve a map of T. However, if small antennas are used

with P ≈ 1 over the area of interest, then the antenna pattern itself is not a factorin determining the resolution of the synthesis array.

Also, notice that in the limit that ∆u N → ∞, the function h ( ξx ) becomesa delta function [similarly for g ( ξ y )]. In this case, the measurement is perfect (K ′≡ K). In the more general case, the image is a representation of K that is blurred

because of the finite width of h and g. The width of these functions can be usedas a figure of merit for the inversion. The distance between nulls is a convenientchoice. In the case of h ( ξx ) these occur at ξx =1/ [(2N + 1)Du ]. Using ∆u = d x / λand ξx = x /R where R is the distance between the scene and the antenna array,one obtains the following expression for the resolution in x :

( )[ ] ρ λx x R d N = +2 1 (8.12)

with similar results for the y -direction. ( λ is the value at the center frequency of the measurement).

Finally, notice that h ( ξx ) and g ( ξ y ) are periodic functions. In order toavoid aliasing of the image, it is necessary to keep the effect of the grating lobes(peaks) out of the image plane (−1 < ξ < 1). This imposes a limit on the spacing between antennas and therefore on the minimum baseline. For example,restricting the image to the halfway point between peaks results in the restriction(− π/2 < π ∆u ξx < π/2) from which it follows that d x,y < λ/2.

References

[1] Le Vine, D. M., “A Multifrequency Microwave Radiometer of the Future,” IEEE Trans.on Geoscience and Remote Sensing, Vol. 27, No. 2, March 1989, pp. 193–199.




[2] Thompson, A. R., J. M. Moran, and G. W. Swenson, Interferometry and Synthesis inRadio Astronomy, New York: Wiley, 1986.

[3] Le Vine, D. M., and J. C. Good, “Aperture Synthesis for Microwave Radiometers inSpace,” NASA Tech Memorandum 85033, 1983 (Avial. NTIS 83N-36539).

[4] Tiuri, M. E., “Radio Astronomy Receivers,” IEEE Trans. Antennas and Propagation, Vol. AP-12, 1964, pp. 930–938.

[5] Le Vine, D. M., “The Sensitivity of Synthetic Aperture Radiometers for Remote Sensing Applications from Space,” Radio Science, Vol. 25, No. 4, 1990, pp. 441–453.

[6] Ruf, C. S., et al., “Interferometric Synthetic Aperture Radiometery for Remote Sensing of the Earth,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 26, No. 5, 1988,pp. 597–611.

[7] Le Vine, D. M., et al., “ESTAR: A Synthetic Aperture Microwave Radiometer For Remote

Sensing Applications,” IEEE Proc., Vol. 82, No. 12, December 1994, pp. 1787–1801.[8] Wiessman, D. E., and D.M. Le Vine, “The Role of Mutual Coupling in the Performance

of Synthetic Aperture Radiometers,” Radio Science, Vol. 33, No. 3, 1998, pp. 767–779.

[9] Corbella, I., et al., “The Visibility Function in Interferometric Aperture Synthesis Radi-ometry,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 42, No. 8, 2004,pp. 1667–1682.

[10] Kraus, J. D., Radio Astronomy, New York: McGraw-Hill, Chapter 6, 1966.

[11] Collin, R. E., and F.J. Zucker, Antenna Theory, Vol. 1, Chapter 4, New York:McGraw-Hill, 1969.

Selected Bibliography

Bara, J., et al., “The Correlation of Visibility Noise and Its Impact on the RadiometricResolution of an Aperture Synthesis Radiometer,” IEEE Trans. on Geoscience andRemote Sensing, Vol. 38, No. 5, 2000, pp.2423–2426.

Camps, A., et al., “RF Interference Analysis in Aperture Synthesis Interferometric Radi-ometers: Application to L-Band MIRAS Instrument,” IEEE Trans. on Geoscience and

Remote Sensing, Vol. 38, No. 2, 2000, pp. 942–950.

Corbella, I., et al., “Analysis of Noise-Injection Networks for Interferometric-RadiometerCalibration,” IEEE Trans. on Microwave Theory and Techniques, Vol. 48, No. 4, 2000,pp. 545–552.

Perley, R. A., F. R. Schwab, and A. H. Bridle, (eds.), “Synthesis Imaging in Radio Astron-omy,” Astronomical Society of the Pacific Conference Series, Vol. 6, 1989.

Rohlfs, K., and T. L. Wilson, Tools of Radio Astronomy, 3rd ed., New York: Springer,2000.




9Calibration and Linearity

9.1 Why Calibrate?

The purpose of calibration is to establish the connection between the inputbrightness temperature and the output quantity (volts, watts, digital counts) of the radiometer.

In principle, a full knowledge of all component specifications, waveguide

losses, reflection coefficients, and physical temperatures would render calibra-tion superfluous, as the behavior of the radiometer then could be perfectly pre-dicted by modeling. In real life, however, such accurate predictions are very difficult, and modeling is best suited for prediction of relative dependencies suchas: how the radiometer output will vary with the temperature of a certain ampli-fier. Thus basic absolute calibration becomes a vital and often time-consuming part of a radiometer development and maintenance.

For Dicke radiometers we have from (4.3): V OUT = constant · (T A − T R ), where T R is known. For noise-injection radiometers: T A = T R − T I , where T R isknown andT I is proportional to some output quantity, usually digital counts. Inboth cases only one calibration point is needed, and the input-output relation-ship can be adequately described. It is then assumed that the radiometer in ques-tion is perfectly linear—an assumption that it would be nice to verify throughcalibration at several points.

For total power radiometers we have from (4.1): V OUT = constant · (T A +T N ), where T N cannot be regarded as well known (i.e., to better than a fractionof a Kelvin). Hence, two calibration points are required, again assuming a linear

calibration curve to be checked.In general, we need an accurate noise source with a variable output. The

output range should ideally be 0–300K.

81



9.2 Calibration Sources

The most obvious solution is a cooled microwave load. As described earlier, a

well-matched microwave load will generate a noise temperature equal to its phys-ical temperature—and the physical temperature can be measured accurately. Fig-ure 9.1 shows the simplest and cheapest possible setup. A microwave load ismounted in a freezer. A suitable liquid, continuously stirred by a motor-drivenpropeller, ensures a uniform temperature, which is measured by the thermome-ter. The temperature range of the simple setup is quite limited, but useful—espe-cially for calibration and stability checks during a radiometer’s development.

The microwave load can also be cooled by submerging it in a liquid with a low boiling point, that is, using cryogenic techniques. Figure 9.2 shows a low temperature calibrator with the load in liquid helium.

It is evident from the figure that now the concept is far from being simple.Great care must be exercised to prevent heat flow and condensation of gasses inthe waveguide. The temperature and the loss of the rather long waveguide mustbe carefully measured and used to correct the calibration temperature (see Sec-tion 3.3). This example is an extreme, going all the way to liquid helium tem-peratures. Usable loads cooled to liquid nitrogen temperatures around 77K arecommercially available. Well-made cryogenic loads are far from being cheap.

An alternative solution is a cooled target viewed by a suitable antenna con-nected to the radiometer (see Figure 9.3). A microwave absorber (normally usedto cover the inside walls of radio-anechoic chambers) will emit a brightness tem-perature equal to its physical temperature T o . Under ideal conditions, theantenna will sense nothing but the brightness temperature from the absorberand T A = T B = T o .

Figure 9.4 shows a practical layout of this concept. The radiometer is con-nected to an antenna horn through a short waveguide (very low losses!). The

horn views a microwave absorber soaked with liquid nitrogen. The absorber andthe liquid nitrogen are contained in an insulated metal bucket, and the excessopening of the bucket is covered by aluminum foil. In this way the antenna isonly able to pick up energy from the absorber, which is cooled to 77K by the


RadiometerInput

Thermal block

MotorThemometer

Freezer

Figure 9.1 Simple calibration setup.



nitrogen. There is generally no problem with losses and heat flow in the antenna

and the waveguide, liquid nitrogen is readily available, and the setup is cheapand simple. Overall this is a very useful radiometer calibrator. A slightly morerefined version of this calibrator is discussed in [2].

Calibration and Linearity 83

Figure 9.2 Low temperature microwave noise standard. (From: [1]. © 1968 IEEE. Reprinted

with permission.)

Antenna

TATB

TO

Microwave

absorber

Radiometer

Figure 9.3 Antenna target calibration.



A very important parameter concerning a radiometer calibration target isits emissivity ε (or its reflection coefficient 1 − ε). If we assume that we are deal-ing with a liquid nitrogen cooled target at 77K and that the noise temperature

being emitted from the radiometer out of the antenna towards the target is300K, the radiometer under test will measure the following brightnesstemperature:

( )T B = ⋅ + ⋅ −77 300 1K K ε ε

The error in the measurement can be expressed as:

( )∆∆

= −= −

T B 77233 1

K K ε

A return loss of 20 dB corresponds to an emissivity of 0.99, and to an errorof:

∆ = ⋅ =233 0 01 2. K K

which normally is unacceptable. However, already as we pass the 30-dB reflec-tion coefficient, the error drops below 0.2K, and we approach reasonablefigures.

Calibration targets are typically constructed using more or less standardmicrowave absorbing materials. Typical flat panel absorbers have a reflection


Radiometer

Antenna horn

AL foil

Liquid nitrogen

Microwave absorber

Foam insulation

Figure 9.4 Antenna target calibrator.



coefficient of 20 dB, so they can generally not be used. Typical pyramidalabsorbers can exhibit a 35-dB return loss at L-band with a pyramid height of 30cm. The 35 dB corresponds to an error of 0.07K. In general, the pyramidal

height needs to approach twice the wavelength for such a performance.The liquid nitrogen (LN2) is soaked up into the pyramids, but it is advis-able to let the level of LN2 be such that it is clearly visible between the pyramids.This is allowable since the reflection coefficient of LN2 is very small, and itensures that even the tips of the absorbers are properly cooled.

A more in-depth discussion of target reflectivity errors is found in [3]. Another solution to the calibrator problem is sky calibration. In fact, this

is a derivation of the antenna target calibration just described in which thecooled target is “replaced” by the sky (see Figure 9.5).

Again the radiometer is connected to a microwave horn antenna through a short waveguide. The antenna is pointed toward the cold sky. A large metalbucket ensures that nothing but the sky radiation is incident on the antenna.The brightness temperature of the sky, as viewed from the surface of the Earththrough the atmosphere, is indicated in Figure 9.6.

In the 1–10-GHz range the low temperature of the sky (∼6K) is ratherundisturbed by the atmosphere. At higher frequencies, care must be exercised.

At high altitudes (mountain tops) and in dry areas (deserts, arctic regions) prob-

lems with water vapor are minimized, but even in more normal areas, the con-cept is useful, especially on cold, clear winter days. (On satellites, there isno problem with the atmosphere, and a view of free space is often used for cali-bration checks on satellite-borne microwave radiometer systems.) The buckettechnique has been brought to “perfection” on a mountain peak in New Mex-ico; see [4].

As already mentioned, in other areas of the world the concept can also bequite useful. This is illustrated in Figure 9.7, showing a bucket on the rooftop of

a building at DTU. In the actual case the bucket was used to assess smallantenna reflector losses by radiometric means [5].


Radiometer

Metal bucket

TSKYTSKY

Antenna

Figure 9.5 Sky calibration.



9.3 Example: Calibration of a 5-GHz Radiometer

In Figure 9.8 we find a calibration curve for the DTU 5-GHz noise-injectionradiometer carried out using the simple setup displayed in Figure 9.1. The use-fulness of the method is clear: The linearity of the radiometer is confirmed(within a rather limited temperature range, though) and the slope of the curve isfound to be 6.56 counts/°C. Zero counts correspond to 41.8°C.


1,000T

(K)SKY

10

100

10.1 1 10 100

F(GHz)

H 02 02θ 0°=

60°

85°

90°

Low

humidity

Figure 9.6 Sky radiometric temperature with zenith angle θ as a parameter.

Figure 9.7 Sky measurements using an aluminum lined bucket on a rooftop.



Also the sky temperature was measured, using the setup of Figure 9.5. Theradiometer output was 2,026 counts. Hence, the measured sky brightness tem-

perature is found to be: T S = 41.8 + 273.2 − 2,026/6.56 = 6.2K, which is ingood agreement with the expected sky temperature (see Figure 9.6).

Normally the determination of the slope of the calibration curve is carriedout the other way around, namely, using the sky temperature as a primary point.This gives a better estimate due to the large temperature difference between thesky and the reference load.

9.4 Linearity Measured by Simple Means

Although a radiometer in principle need not be linear in order to carry out use-ful measurements provided it is properly calibrated throughout its range, linear-ity is a highly warranted virtue often strived for: A linear radiometer is mucheasier to calibrate in the first place. A radiometer launched into space must have


−30

−20

−10

0

10

20

100 200 300 400 Counts

°C

Figure 9.8 Calibration curve, 5-GHz DTU radiometer.



its calibration checked regularly, and this can in practice only be done if linearity prevails. Hence, linearity issues are important during a radiometer design phase,and a primary task to be carried out during calibration activities is a verifica-

tion/check of radiometer linearity. This section describes two ways of measuring linearity of microwave radiometers only requiring relatively simple equipment.The calibration situation for a typical spaceborne radiometer is used as anexample.

9.4.1 Background

This section deals with alternatives to the traditional way of calibrating radiome-

ters. The traditional method is based on the principle of pointing the radiome-ter’s feed horn towards a target simulating a scene with variable temperature. Although conceptually simple, it is not technically simple. The target mustexhibit excellent VSWR and be variable in temperature over a large range withextreme precision (in some cases ∼0.1K). Such a target is expensive, and more-over its operation is expensive as it requires a thermal vacuum environment.

The on-board calibration in present spaceborne, scanning radiometer sys-tems—like the well-known SSM/I, and as described in Chapter 13—is carriedout in an almost ideal fashion: The feed horn cluster sequentially views the main

offset parabolic reflector for the actual measurement of scene properties, the hotload for one calibration point, and the cold sky reflector for a second calibrationpoint. The output of the hot load is known by careful measurements of thephysical temperature of the absorbing elements, and by design taking into con-sideration the emissivity of the load and the VSWR of the load in conjunction

with the noise temperature of the radiometers as seen through the feeds. Theoutput from the main reflector is the antenna temperature modified by the mainreflector loss. This loss can be quantified very accurately [5]. The output from

the cold reflector is the sky temperature, which is known by design (feed/reflec-tor radiation pattern, satellite geometry, orbit geometry), modified by the coldreflector loss. No VSWR problems are foreseen for the two reflector cases due tothe offset geometry. Thus, as the losses and physical temperatures of the tworeflectors are known with good accuracy, a perfect calibration takes place. This isin strong contrast to most earlier radiometer systems, where a switch matrix selects whether the antenna, the hot load, or the separate sky horn is connectedto the radiometer receiver. This results in large problems with losses, switch

isolations, and the fact that different signal paths when calibrating and whenmeasuring the antenna temperature must be sustained. Ground calibration inthis case becomes an intriguing exercise in determining all possible losses,isolations, and radiometer transfer function properties. In the first case, how-ever, due to the “perfect” calibration scheme, the ground calibration exercise

would be not necessary if the radiometers were known to be perfectly linear.




Unfortunately, the radiometers cannot be assumed perfectly linear, so themain task of the ground calibration is to determine the transfer function of theradiometers with sufficient accuracy (plus the precise determination of the losses

in the two reflectors, which is not the subject here).

9.4.2 Simple Three-Point Calibration

The purpose of this calibration procedure is to make a rough calibration of theradiometers and check their linearity with good accuracy yet using simple,low-cost, primary targets. The principle is illustrated in Figure 9.9. Two targetsmade of microwave absorber material in isolated metal buckets are used. Filling liquid nitrogen into a target provides a cold calibration temperature T C (∼77K)and leaving it without the liquid nitrogen provides the hot calibration tempera-ture T H (= T 0 ∼ 293K). Two identical antennas are connected with equal

waveguides to a magic tee, the radiometer is connected to the sum port, and thedifference port is terminated. The power from one antenna is split between thesum and difference ports.

As the signals from the two antennas are uncorrelated, the sum port willprovide to the radiometer the average value of the two antenna signals (in the

ideal, lossless case and with an ideal, symmetrical magic tee). The noise signalfrom the termination is split equally between the two antennas.


T or TC H

k

l1 l2

+

Radiometer

lM

T0

T or TC H

T1

T2’

T2

TM

T1’

TM’

Figure 9.9 Setup for simple three-point calibration.



The calibration procedure includes four cases: the hot case (HH) whereboth antennas view T H and the radiometer measures T H , the cold case (CC)

where both antennas view T C and the radiometer measures T C , and two mixed

cases (CH and HC) where one antenna views T C and the other views T H and theradiometer measures (T C + T H )/2 or (T H + T C )/2 that are equal in the ideal case.It is assumed that the transfer function of the radiometer looks like the

“possible situation” shown in Figure 9.10. It is a very likely situation considering the way a radiometer is built. A dominating factor in the transfer function willbe the square law detector. It is expected to be something between square law and linear, and “good” square law behavior is obtained for sufficiently low signallevels. A transfer function like the “impossible situation” shown in Figure 9.10cannot be dealt with by the calibration method under discussion here. It is not a

likely situation, and for many good reasons it must be avoided. Returning to thelikely function of the figure and the procedure described earlier, it will be shownnext that one can measure three points on the calibration curve with good accu-racy even under nonideal conditions, that is, lossy components and nonperfectbalance in the magic tee (k is not 0.5). The losses (l 1, l 2, and l M ) are here repre-sented by their transmission coefficients (i.e., 0.2-dB loss means −0.2-dB trans-mission and l = 0.95).

By an inspection of Figure 9.9, the following set of equations can be

established:

( )T T l l T 1 1 1 1 01′ = ⋅ + − ⋅ (9.1)

( )T T l l T 2 2 2 2 01′ = ⋅ + − ⋅ (9.2)


*

*

Impossible

situation

Possible

situation

77 K 293 K

Output (N)

Input (K)

Figure 9.10 Radiometer calibration curves.



( )T k T k T M ′ = ⋅ ′+ − ⋅ ′

1 21 (9.3)

( )T T l l T M M M M =

′

⋅ + − ⋅1 0 (9.4)

By proper insertion, the following expression for the input to the radiome-ter is found:

( ) ( )

( ) ( )

T k l l T k l l k l l T

k l l T

M M M M

M

= ⋅ ⋅ ⋅ + ⋅ ⋅ − + − ⋅ ⋅ ⋅ +

− ⋅ ⋅ − ⋅

1 1 1 2 2

2

1 1

1 1 ( )0 01+ − ⋅l T M

(9.5)

Let us assume the hot case: T 1 = T 2 = T H = T 0, and by insertion and reduc-tion we find:

T T M HH = 0 which is not surprising!

By letting T 1 = T 2 = T C in (9.5), we find an expression for the radiometer

input in the cold case:T M CC . Likewise, T 1 = T H = T 0 and T 2 = T C givesT

M HC ,

while T 1 = T C and T 2 = T H = T 0 givesT M CH . By proper insertion and reduction,

it is straightforward to show that the average value T M av of T

M HC and T M CH is

equal to the mid-point value T m of T M HH andT

M CC , that is:

( ) ( )T T T T M M M M HC CH HH CC + = +2 2 (9.6)

so with our radiometer under test we measure the extreme (hot and cold)cases—T

M HH and T M CC —we calculate the mid-point value Tm, and we expect

the radiometer to yield this value as an averageT M av of the two measurements of

the mixed (hot/cold, cold/hot) cases. If not, the radiometer is nonlinear. A precondition for this to be able to work is that there is reasonable bal-

ance in the system, that is, k ≈ 0.5, which means that T M HC ∼T

M CH , and thatthe radiometer has a “decent” nonlinear characteristic.

A sensitivity analysis is warranted. Assume the magic tee imbalance to be±0.1 dB corresponding to k = 0.51. Assume equal length waveguides so that l 1 =

l 2 = l M = 0.95 (corresponding to a 0.2-dB loss). Let T H = T 0 = 293K and T C =77K. We can then calculate that T

M HH = 293K, T M CC = 98.06K, and the

mid-point value T m = 195.53K. Likewise, we findT M HC = 197.48K andT

M CH =

193.58K. The average value is T M av = 195.53K as we would have expected. It is

seen that a realistic imbalance will result in a small difference in the T M values,




that is, we can average the results from a slightly nonlinear radiometer and thusget a measurement of the deviation from linearity midway between T C and T H .

Further comments: l 1, l 2, and l M include the ohmic losses in the three ports

of the magic tee. A lack of isolation between the difference port and the sumport will result in loss of some signal to the termination and generation of somesignal in the sum port from the termination, that is, just like loss in the transmis-sion line between the tee and the radiometer. Hence, this effect can be regardedas included in l M and, as the calculations show, has no effect in the present case.

It shall be noted that the calibration method under discussion does notsolve the problem of finding the transfer function below 77K, which could be a problem as the cold calibration point in space is only a few Kelvins.

9.4.3 Linearity Checked by Slope Measurements

Figure 9.11 shows another setup by which a roughly calibrated radiometer canbe checked for linearity. An antenna horn points towards a simple liquid nitro-gen target and a variable attenuator (Att2) with a low insertion loss and at anambient temperature are able to produce any brightness temperature from ∼77K to ∼ 293K. The accurate value of the brightness temperature is not known, but

can be assessed by the roughly calibrated radiometer. Through a directional cou-pler with a coupling value of 20 dB (in order not to attenuate the signal in themain arm unduly) a noise signal of variable amplitude is injected. The signaloriginates in a noise diode [typical excess noise ratio (ENR) larger than 20 dB]and is attenuated in a variable attenuator Att1. A PIN diode switch selects eitherthis signal or the signal from a load at ambient for injection

When the ambient load is on, the net result is that practically no extra noise is added to the signal from the antenna horn, while as the switch selects the

signal from the noise diode a certain noise is added. The attenuators could be of the rotary vane type for low insertion loss and good stability.

Figure 9.10 shows the transfer function for the radiometer under test. By the rough calibration, two points are established corresponding (as an example)to 77K and 293K. For simplicity the calibration constant (N /T i ) is assumed tobe equal to 1. If the transfer function is linear (dashed curve), then the outputchange ∆N corresponding to a certain setting of Att1; hence, a certain inputchange ∆T i will be the same for all settings of Att2 and hence all values of Ti.

This is not the case if the transfer function is not linear.Let us assume a “nice” curve that deviates 0.1 from the linear curve midway between the two known calibration points (shown in Figure 9.10 strongly exaggerated as the “possible” curve). An input of 185K will result in an outputof 185.1. If we select Att1 to give ∆T i = 108K, we will observe a ∆N of 108.1and 107.9 for two suitable settings of Att2.




This difference of 0.2 corresponding in the present example to 0.2K canbe clearly detected. Hence, by this method we can readily detect deviations froma linear curve down to the 0.1-K level. Actually, we can measure the true devia-tion and assess the transfer function by proper selection of attenuator settings.

It is noteworthy that, if the antenna horn is pointed towards the sky, thecheck can be extended almost down to the cold calibration point in space.

9.4.4 Measurements

9.4.4.1 Three-Point Method

A noise injection radiometer (NIR), a Dicke radiometer (DR), and a total powerradiometer (TPR), all Ka-band, have been subjected to linearity checks

as described in Section 9.4.2. In fact, the NIR and DR cases are not independ-ent as we deal with one Dicke type switching radiometer able to operate inboth modes. Figure 9.12 shows an example of the experiments with the NIR

instrument. First, the hot case is measured to T M HH = 295.10K. Then fol-

lows, after filling one target with liquid nitrogen, a series of cold-hot/hot-cold


LN2

Att2

Att1

Noise

diode

Termination

20 dB

Dir. coupler

Radiometer

Figure 9.11 Slope measurement setup.



combinations by moving the targets around. We find T M HC = 188.43K and

T M CH = 191.11K (averages over the three measurements of each). Hence,T M av

= 189.77K. Filling the second target with nitrogen enables the three measure-

ments of the cold case, and T M CC = 88.17K. Finally we show a case where a

low-loss horn is connected directly to the radiometer input and pointed to thecold target to yield 77.27K as result. This, together with the hot case, providesthe basic calibration of the radiometer. From the hot and cold cases are seen that

the mid-point value is T m = 191.64K, meaning that there is a deviation from lin-

earity of 1.87K halfway between the hot-and-cold calibration point. As stated earlier, several experiments with different radiometer types werecarried out, and representative examples are summarized in Table 9.1.

It is seen that the NIR and the DR consistently reveals a nonlinear behav-ior, while the TPR is quite linear. The first hardware is from the 1970s based ona Schottky diode detector, while the TPR is a recent development with a high-quality tunnel diode detector. It is seen that the NIR and DR calibrationcurves bend upwards and not downwards as would be the case if the cause fornonlinearity were compression in low frequency circuitry or the fact that the

detector law were somewhere between 2 and 1 (between square and linear law).However, Schottky detector diodes are known to be able to exhibit a transfer law exceeding square law (an exponent more than 2) in the transition regionbetween square and linear under certain impedance conditions. This is probably the case here.


295.1

191.2 189.3 191.1 187.8 191.1 188.1

87.8 88.0 88.7

77.3

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11

T M

Figure 9.12 Example of an NIR three-point experiment.



9.4.4.2 Slope Method

Only the TPR has been examined by the slope method. The reason is that thisradiometer already by design includes circuitry for injecting noise at the inputfor calibration purposes. Thus, only an attenuator between the radiometer andthe antenna horn is needed to realize the setup of Figure 9.11 (with the limita-tion that only one value of injected noise is possible, as Att 1 is not present).Table 9.2 shows results from one experiment. By measuring liquid nitrogen andan internal calibration load, the radiometer is calibrated the usual way. Thevalue of the injected noise is ∆T i = 161.2K at low levels. The attenuator is set atdifferent values with some (unknown) accuracy, but the cold point is measuredby the now-calibrated radiometer.

It is seen that at first (steps a through c) the injection of the noise results inthe same change in radiometer output, indicating the linear behavior we expectfrom the three-point measurements. The measurement uncertainty is some 0.1K based on experience from repeated experiments. The last attenuator setting (d)

reveals beginning compression, but note that the injected noise brings the totalinput to the radiometer up to 343.1K, which is beyond the design limit corre-sponding to natural Earth targets (one might say that this is a marginal design).


Table 9.1

Summary of Experiments (Values in Kelvin)

T M

HH T M

CC T M

av T m Difference

NIR#a 295.1 88.2 189.8 191.6 1.9

NIR#b 299.2 91.2 193.2 195.2 2.0

DR#a 298.1 91.0 192.7 194.6 1.9

DR#b 294.1 89.9 190.1 192.0 1.9

TPR#a 294.3 91.0 192.8 192.7 −0.1

TPR#b 294.1 90.7 192.5 192.4 −0.1

Table 9.2

Slope Measurements

Att 2 Cold Point T B

a 0 77K 161.2K

b 0.15 dB 92.9K 161.3K

c 0.3 dB 130.1K 161.1K

d 0.45 dB 182.4K 160.7K



In conclusion, it can be stated that the calibration methods described inthis section are not able to deal with a full calibration of a nonlinear radiometerhaving arbitrary transfer characteristic. However, the methods are well suited for

checking of linearity down to low levels and they may be used to assess the cali-bration curve for a radiometer that is slightly nonlinear in a neat fashion (sec-ond-order curve not deviating much from a linear curve).

The three-point calibration method is the simplest seen from a hardwarepoint of view. All that is needed is a magic tee, two horn antennas, two targets,and a few waveguide sections. On the other hand, it is probably the mostdemanding to handle. One measurement sequence as illustrated in Figure 9.12takes about 20 minutes, and care must be exercised to ensure stability over thattime span.

The slope method requires more advanced hardware as a stable noise diodeis required (if not already built into the radiometer). On the other hand, theexperiments are easier and quicker to carry out, resulting in fewer potential errorsources.

Interesting work on nonlinearity is found in [6–8].

9.5 Calibration of Polarimetric Radiometers

The calibration of polarimetric radiometers represents a special problem. Thetraditional vertically and horizontally polarized channels are calibrated following the procedures outlined earlier in this chapter, but the third and fourth Stokesparameters require other methods, and it is required to generate a pair of knownsignals with a known amount of correlation between them. Figure 9.13 illus-trates a relatively simple yet very useful setup.

As already mentioned, the two linearly polarized channels (normally the

vertical and horizontal channels) are first calibrated as any other radiometer. Thesituation is easy to see referring to the basic correlation radiometer as illustrated


Noise

diode ϕPhase

shifter

Load

Load

Polarimetric

radiometer

In 1

In 2

Figure 9.13 Calibrating a polarimetric radiometer.



in Figure 7.3. Then the two inputs of the now partly calibrated radiometer sys-tem are connected to the input circuitry shown in Figure 9.13. The signal fromthe noise diode is divided equally to the two channels and injected via two cou-

plers. The signals injected are adjusted to a reasonable level, 100K, for example,by proper coupling values and possibly additional attenuators not shown. Thetwo signal paths from the diode to the injection points are of equal electricallength, but one path includes a variable phase changer.

With the noise diode switched off, the loads produce well knownuncorrelated signals to the inputs, and the third and fourth Stokes outputsshould be zero. If they are not, adjustments within the radiometer system arecarried out, or the biases are recorded for later correction purposes. Only smallbiases should be accepted. If large biases are found, further adjustment or even

redesign within the system must be carried out.Switching on the noise diode produces an output from the correlator ide-

ally only in the third Stokes channel (the phase changer is set to zero). If this isnot the case, adjustments to the internal phasing/timing in the radiometer sys-tem are carried out. By means of the already calibrated first and second Stokeschannels, the accurate amount of injected noise in each channel is determined.

At this stage an accurate knowledge of the noise temperature of each channel isalso required. The correlated and uncorrelated signals in each channel are now

known, and by reading the output of the third Stokes channel, this can now becalibrated. By adjusting the external phase changer by 90°, the signal movesfrom the third to the fourth Stokes channel, and this is now calibrated.

Actually, when building a practical polarimetric radiometer system—be itground based, airborne, or spaceborne—it is highly recommended to includethe relatively few microwave calibration components in the radiometer. This

way calibration checks in the field or once spaceborne can be carried out. Thesituation is shown in Figure 9.14 where the basic correlation radiometer from

Figure 7.3 has been augmented with the calibration components. The DTU


ver

hor

LO

REF

REF

RX 1

RX 2

TV

TH

U/2

V/2

Real

Imag∼Noisediode

Complex

corr.

Figure 9.14 Basic correlation radiometer with calibration circuitry.



polarimetric system that was discussed in Section 7.6 are designed this way, butthe components are not shown in Figure 7.5 for clarity at that stage.

Although very useful, the calibration procedure described above has one

deficiency: it does not represent the fundamental calibration method in whichknown signals (known by design) from a primary source/target are presented tothe instrument in question—through its input connector/waveguide or throughits antenna. A simple example of such a fundamental calibration was discussedin Section 9.2 for a single channel radiometer. It is, however, not a simple mat-ter to conceive and design—let alone manufacture—primary targets being ableto generate all four Stokes parameters with great accuracy. The reader is referredto [9, 10] for information about this subject.

References

[1] Trembath, C. L., et al., “A Low-Temperature Microwave Noise Standard,” IEEE Trans.on Microwave Theory and Techniques, Vol. 16, No. 9, 1968, pp. 709–714.

[2] Hardy, W. N., “Precision Temperature Reference for Microwave Radiometry,” IEEE Trans. on Microwave Theory and Techniques, Vol. 21, No. 3, 1973, pp. 149–150.

[3] Randa, J., et al., “Errors Resulting from the Reflectivity of Calibration Targets,” IEEE

Trans. on Geoscience and Remote Sensing, Vol. 43, No. 1, 2005, pp. 50–58.[4] Carver, K. R., Antenna and Radome Loss Measurements for MFMR and PMIS, New Mexico

State University, Report PA 00817, 1975.

[5] Skou, N., “Measurement of Small Antenna Reflector Losses for Radiometer CalibrationBudget,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 35, No. 4, 1997,pp. 967–971.

[6] Walker, D. K., K. J. Coakley, and J. D. Splett, “Nonlinear Modeling of Tunnel DiodeDetectors,” IGARSS’04 Proceedings, 2004, p. 4.

[7] Harrison, R. G., and X. Le Polozec, “Nonsquarelaw Behavior of Diode Detectors Ana-

lyzed by Ritz-Galérkin Method,” IEEE Trans. on Microwave Theory and Techniques,Vol. 42, No. 5, 1994, pp. 840–845.

[8] Reinhardt, V. S., et al., “Methods for Measuring the Power Linearity of Microwave Detec-tors for Radiometer Applications,” IEEE Trans. on Microwave Theory and Techniques, Vol.43, No. 4, 1995, pp. 715–719.

[9] Lahtinen, J., et al., “A Calibration Method for Fully Polarimetric Microwave Radiome-ters,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 41, No. 3, 2003, pp. 588–602.

[10] Lahtinen, J., and M. Hallikainen, “Fabrication and Characterization of Large Free-Stand-ing Polarizer Grids for Millimeter Waves,” Intl. Journal of Infrared and Millimeter Waves,

Vol. 20, No. 1, 1999, pp. 3–20.




10Sensitivity and Stability: Experimentswith Basic Radiometer Receivers

10.1 Background

The sensitivity of a microwave radiometer is generally expressed as

∆T K T T

B

A N

= ⋅ +

⋅ τ

where:

T A = antenna temperature

T N = receiver noise temperature

B = predetection bandwidth

τ = integration time

The value of K is dependent on the radiometer type in question, and thevalue is generally 1 for total power radiometers and 2 for Dicke type switching radiometers. It is clear that the total power radiometers have much better sensi-tivity than the Dicke type of radiometers. However, regarding stability, totalpower radiometers are inferior to the other types. Stability is difficult to predict.

For a spaceborne radiometer, certain constraints affect the choice of parameters and hence the sensitivity achievable: τ is limited by mission require-ments to swath width and footprint size; B is limited due to fear of interferencefrom external sources; and T N is limited by available technology. Hence, there is

99



great interest in the potentially better sensitivity of total power radiometers forcertain applications, where sensitivity requirements are severe.

The total power radiometer is simpler than the other types. It does not

include the Dicke switch and the synchronous detector found in the Dicke typeof receiver, and it certainly does not include the noise-injection circuitry foundonly in the noise-injection radiometer. Hence, a total power radiometer issmaller, lighter, and may consume less power than other radiometer types.

However, this radiometer type can of course only find use for a givenapplication if the accuracy and stability are adequate for that application. Accu-racy is dependent on calibration, so the calibration scheme feasible for a givenapplication must also be considered. However, the basic dark area is the initialstability of the total power receiver itself. Experiments with real radiometer

hardware are required to enlighten the subject.Regarding the choice between Dicke and noise-injection radiometers, for

applications where the total power radiometer fails to meet the requirements, a controversy between researchers seems to exist: Some favor Dicke; others favornoise-injection. In theory, the noise-injection mode of operation is superior tothe Dicke mode, but is it true in real life? Again, experiments with real radiome-ter hardware may answer this question.

The 5-GHz noise-injection radiometer discussed in Chapter 6 has been

modified to operate in three different modes as:

• DR: Dicke radiometer;

• NIR: noise-injection radiometer;

• TPR: total power radiometer.

Also, the 17- and 34-GHz radiometers were included in the experiments

(NIR mode only).Extensive measurements of stability against temperature variations in the

microwave part and in the low-frequency part of the radiometers have been car-ried out to assess the merits of each mode. The temperature variations have beendesigned to resemble those inevitably found in a satellite orbiting the Earth.

Sensitivity measurements have been carried out to confirm the theoreticaldifferences between modes. The 5-GHz radiometer was used for the exercises.

10.2 The Radiometers Used in the Experiments

The 5-GHz noise-injection radiometer is basically designed according to theblock diagram shown as Figure 5.10 but with the addition of a microwavepreamplifier before the mixer. It has for the present task been reconfigured to




operate in the Dicke mode and the total power mode. First, the noise-injectioncircuitry is deactivated. In the Dicke mode the gain of the LF circuit has to bereduced by 56 dB.

The total power mode requires more thorough changes. The Dicke switchis deactivated and the LF circuitry substituted by a stable DC amplifier-integra-tor. The DC amplifier includes a stable offset to compensate for the signalcaused by the receiver noise temperature. Also, the detector is replaced, and a tunnel diode detector is used due to its very low noise close to DC. The latching circulator (normally used as a Dicke switch) is now used as a calibration switch.During the stability measurements, the internal 313-K load was connected tothe radiometer input for 12 seconds each 24 seconds (i.e., the radiometer mea-sures 12-second T A , 12-second T R , 12-second T A , and so on).

The 17- and 34-GHz radiometers were used without modifications (NIR mode only).

10.3 The Experimental Setup

For calibration, sensitivity, and stability measurement purposes, the input of theradiometer must be connected to stable, well-known signal sources. In all mea-

surements to be reported later, the radiometer was connected either to a microwave load in a freezer (see Figure 9.1), or to a commercial, liquid nitrogencooled load (5 GHz only).

The load in the freezer is a termination submerged in a suitable liquid. Thetemperature can be varied down to –30°C, and it is measured by a thermometerand by the digital thermometer of the radiometer. Typically temperaturesaround +20°C (293K) and around –25°C (248K) were used during the mea-surements. In addition, the liquid nitrogen load enabled measurements with a

77-K input to the radiometer (5 GHz only).During sensitivity measurements (5 GHz only), the radiometer was

allowed to reach thermal equilibrium (it takes several hours), and a few minutesof recording were made in each mode (DR, NIR, TPR) and for each input(∼293K, ∼248K, ∼77K).

During stability measurements much longer time series were used—up to8 hours. Again, the radiometer was allowed to reach thermal equilibrium beforethe start of the measurements, in order to reach a well-defined starting point,

but also to ensure that the temperatures in the front end were inside the rathernarrow range of the digital thermometer (38°C to 46°C).Two types of stability measurements were carried out: stability versus

front-end temperature and stability versus the temperature of the LF section of the radiometer. The front-end temperature, being electronically regulated, ischanged simply by adjusting a potentiometer. The back-end temperature was

Sensitivity and Stability: Experiments with Basic Radiometer Receivers 101



raised from its nominal ambient around 23°C to some 35°C by a heater-blowerarrangement.

10.4 5-GHz Sensitivity Measurements

The sensitivity measurements were, as already described, carried out for threedifferent input temperatures: +20°C, −25°C, and 77K. An integration and sam-pling time of 64 ms was used. The results are shown in Table 10.1.

The expected sensitivities (see Chapter 6) are 0.41K for the Dicke typemodes and 0.20–0.21K for the total power mode. A reasonable agreementbetween measured and expected values are found, considering the statisticalnature of the results. The total power mode especially shows good agreement.The DR and the NIR show slightly, but probably statistically significant, largervalues than expected. A possible explanation is given next.

It has been suggested that rapid gain fluctuations in the radiometer (fluc-tuations faster than the integration time) would contribute in a deteriorating fashion to the sensitivity of the radiometer [1, 2]. This mechanism would, how-ever, especially affect the total power mode and thus cannot explain the observeddifferences. The present measurements cannot support the existence of said

fluctuations. Another suggestion shall be brought forward: The fundamental difference

of the factor 2.0 between Dicke and total power mode stems from the square wave modulation of the signal in Dicke radiometers. If, however, the “square wave” signal is limited in bandwidth—which it is in the present radiome-ter—the factor 2 increases, eventually up to a factor of 2.22 in a sinusoidally modulated radiometer (the AF amplifier has a very narrow bandwidth aroundthe Dicke switch frequency). See [2]. In the present radiometer, the AF band-

width has been measured to 100 Hz–13 kHz.The square wave signal before the synchronous detector can be expressed

as follows:


Table 10.1

Measured Sensitivities (5 GHz)

Calibration

Temperature Radiometer Mode

+20°C 0.45K 0.49K 0.22K

−25°C 0.45K 0.48K 0.22K

77K 0.53K 0.47K 0.21K



( ) f t t t t

= ⋅ + + +

4

1

3

3

5

5 π

sin sin sinK

normalized so that the effective value is 1. If only the first harmonic is letthrough the AF amplifier, the effective value of the signal is

E = ⋅ =4 1

20 90

π.

leading to an increase of the factor 2 to 2/0.90 ~ 2.22, as stated before.In the 5-GHz radiometer, where the Dicke frequency is 2.225 kHz and

the AF bandwidth is up to 13 kHz, the three first terms must be considered.Hence, the effective value is calculated from:

E t t t dt 22

2

2

0

21

2

4 1

33

1

55= ⋅ ⋅ + +

∫ π π

π

sin sin sin

which can be evaluated, and the result is E 2 = 0.9331 or E = 0.9659. Having found a measured sensitivity for the TPR of ∼0.22K, the expected sensitivity for

the Dicke type modes is thus 0.22 · 2/0.9659 = 0.46K, which is quite close tothe observed values.

In conclusion, it can be stated that the basic radiometer sensitivity formula gives a good estimate of the performance.

10.5 Stability Measurements

During the stability measurements the 5-GHz radiometer was configured ineither DR or TPR mode, while the NIR mode was represented by the 17- andthe 34-GHz radiometers. Only the 17-GHz results are shown herein, as the34-GHz results are almost identical.

10.5.1 Discussion of the 5-GHz DR Results

An example of the stability measurements is shown by the curves in Figure 10.1.

First, the notation on the curves shall be explained. The abscissa is time in24-second increments; 24 seconds is the update rate of housekeeping data andhence temperatures from the digital thermometer. The graph thus corresponds to254 · 24 seconds ∼1 hour and 42 minutes of recording. The band of eight thin,solid, or broken lines show the temperature of the eight important componentsin the front end, and refer to the left-hand scale in counts. Recall that the physical




temperature is found from: T = counts/32 + 38.0°C. Table 6.1 shows the corre-spondence between component and sensor numbers, which are included on Fig-ure 10.1, but otherwise only when needed in the discussion of the curves. The

curves separate somewhat due to fact that some components are active and gener-ate heat (see curve 7, the noise-injection diode, in Figure 10.1, for example).The temperature of the front end has been forced to oscillate in a fashion

that could resemble the oscillations found in a satellite orbiting the Earth.The enhanced curve named DR shows the output of the radiometer in the

Dicke mode. The output is calculated as follows: Sensor 2 gives the temperatureof the reference load TR . Then the radiometer output is found by subtracting thedigital output multiplied by a calibration constant (actually found during thesensitivity measurements described earlier). The curve is shown on a relative

scale (see the right-hand side of Figure 10.1), as we are only interested in devia-tions from stable levels and not in the absolute level.

Although the results were recorded with 64-ms integration and sampling time, a computer integration to 12-second time slots has been carried out. Thiscorresponds to a sensitivity of:

∆T = ⋅ =041 0064 12 0030. . . K

The standard deviation of a noisy curve can be estimated by using a rule of thumb: The peak-to-peak amplitude on the curve is roughly 0.1K. The standarddeviation for such a signal is roughly:


0

50

100

150

200

250

2541H 42 Min0

1K

DR

5

67

53

0 56

5

4

24

7

1

Figure 10.1 5-GHz DR. T A = −25°C.



σ = ⋅ =01 1

2 20035. . K

which is in good agreement with the expected value.It is immediately observable from Figure 10.1 that the DR shows a large

variation in its output, which correlates very well with the general front-endtemperature—especially with the temperature of the mix-preamp as measuredby sensor number 5. The DR results are very reproducible. This graph repre-sents only one example out of many recorded during the experiments and they all display the same features down to a quite detailed level.

The DR results can be explained by considering gain variations with tem-

perature in microwave amplifiers. In [3], it is stated that the gain of amplifiers,like the ones used here, typically decreases with temperature by 0.013dB/°C/stage at 45°C physical temperature. The present radiometer has twostages in the RF preamplifier and one stage in the mixer-preamplifier. The peak change in front-end temperature during the experimental oscillations is roughly 5°C. Thus, we expect a gain change of:

( )

∆

∆

G

G

= − ⋅ ⋅ =

=

0013 3 5 0 2

0 046 4 6

. .

. . %

dB

In the present case, with T A = −25 °C and T R = 42°C, we find a change inthe output of the radiometer due to gain variation of:

( )δDR = ⋅ + =0 046 42 25 31. . K

which is seen to fit very well with the results in Figure 10.1. It is also clear that

when temperature increases, the gain decreases and hence the difference T R − T A

decreases. As T R is the reference in the radiometer, this means that the output(which is a measure of T A ) increases.

10.5.2 The 5-GHz DR with Correction Algorithm

Figure 10.2 shows the results of the experiment that were originally displayed as

Figure 10.1. As noted before, the DR curve seems quite well correlated with thegeneral temperature level in the front-end. Figure 10.3 shows this correlationmore clearly. Here the radiometer output (vertical relative scale as on Figure10.2) has been plotted versus the front-end temperatures as measured by sensor02 (reference load) and sensor 05 (mixer-preamplifier). It is seen that the corre-lation is best with sensor 05, but certainly not perfect.




As already discussed in Section 10.5.1, the variations in the output of theDR can be explained by considering the gain variation with temperature inmicrowave amplifiers. A typical gain change of δG = 0.013 · 3 dB/°C∼0.009/°C was quoted. In Figure 10.2 the curve marked DRC represents a cor-rected output, using a δG = 0.008 and the reading from sensor 05.

The output of a Dicke radiometer is found as:

( )V b T T G OUT R A = ⋅ − ⋅ where b is a constant. In the present radiometer with A/D conversion the outputis a digital number N . Hence:

( )N c G T T R A = ⋅ ⋅ −

or:

T T N c G A R = − ⋅

which can be expressed as:

DR T N CAL = − ⋅02


00 1H 42 Min 254

50

100

150

200

250

1K

DRCDRC

DR

DR

Figure 10.2 5-GHz DR with correction. T A = −25°C.



DR being the notation on the curves, T 02 is the reference temperature(sensor 02), and CAL is the radiometer calibration constant.

With gain variations present, the output of the radiometer is expressed as

( ) ( )V b T T G G OUT R A = ⋅ − ⋅ ⋅ +1 ∆

where ∆G is the relative change in G (usually a small figure). Again,

( )( )N c G T T G R A = ⋅ ⋅ − +1 ∆


0 Dicke load (02) 255

1K

0 Mix-preamp. (05) 255

1K

Figure 10.3 5-GHz DR scatter plots.



or:

( )T T G N c G A R = − − ⋅ ⋅1 ∆

inserting again CAL for 1/c · G and recalling that ∆G is known as gain changeper centigrade, we get

T T N CAL N G T CAL A R = − ⋅ + ⋅ ⋅ ⋅δ δ

δT is the temperature deviation from normal (steady state) where the cali-bration of the instrument was carried out. In this case we consider the output of sensor 05 having a nominal value of 112 counts = 41.5°C.

Returning to present notation we find

( )DRC T N CAL N T CAL = − ⋅ + ⋅ ⋅ − ⋅02 050 008 415. .

It is seen from Figure 10.2 that this very simple correction algorithmaccounts for a large part of the output fluctuation, but the result is not perfect as

would already be expected from the scatter plots in Figure 10.3. The problem isof course that none of the existing temperature sensors adequately describe thetemperature inside the three microwave amplifier stages. In a future design thiscould easily be accommodated and a better correction would be possible.

Figure 10.4 shows the results from another experiment designed to show the general behavior of the Dicke radiometers subjected to front-end tempera-ture oscillations. This time a very low input temperature of 77K was used, andthis should enhance the problems with DR operation: The low temperaturemeans greater difference T R − T A enhancing changes due to gain variations.Indeed this is observed: note the five times coarser scale necessary to keep the

curves inside the frame.In this case we now expect a change in the output of the radiometer due to

gain variations of:

( )δ

δ

DR

DR

= ⋅ + −=

0 046 42 273 77

11

. K

K

which is seen to fit well with the results. Again the simple correction as discussed earlier has been applied, and the

result (curve DRC) is a suppressed output fluctuation: some 2K as opposed tothe original 12K (apart from the narrow peak at the rapid temperature increaseto the left in Figure 10.4, where the lack of appropriate and intimate tempera-ture sensors is most severe).




10.5.3 The 17-GHz NIR Results

Figure 10.5 shows the results of a thermal cycle in the 17-GHz NIR. Note thegood correlation with temperature. Figure 10.6 shows the correlation moreclearly.

A good correlation is found between the output and the temperature of the reference load (sensor 01 in this case), but an almost perfect correlationexists between the output and the temperature of the noise diode (sensor 07).This is quite pleasing because the feature is easily explained: A temperaturechange in the noise diode causes a change in output power, which again trans-lates directly into a change in radiometer output. The high degree of correlationensures that a good correction is possible.

The output, N , of the noise-injection radiometer is a direct measure of theinjected noise:

T N CAL I = ⋅

where again CAL is the calibration constant. The input brightness temperatureis found as:

T T N CAL A R = − ⋅

or with the present notation:


0

50

100

150

200

250

0 1H 42 Min

5K

254

DR

DR

DRC

Figure 10.4 5-GHz DR with correction. T A = 77K.



NIR T N CAL = − ⋅01

The injected noise can be expressed more thouroughly as:

( )T N K T T I D D = ⋅ ⋅ +1 ∆

where T D is the output from the noise diode, ∆T D is the relative deviation withtemperature, and K accounts for losses in the noise-injection circuitry. It is seenthat actually CAL = K · ∆T D and we find:

( )T N CAL T I D = ⋅ +1 ∆

and

( )T T N CAL T A R D = − ⋅ +1 ∆

or

T T N CAL N CAL T T A R D = − ⋅ − ⋅ ⋅ ⋅δ δ

where δT D is the relative deviation per centigrade and δT is the temperaturedeviation from nominal value (where the calibration was carried out) concern-ing the noise generator, that is, sensor 07 (nominal value 150 counts corre-sponding to 42.7°C). Returning to the present notation, we find:


00

NIRC

NIR

1H 42 Min 254

50

100

150

200

250

1K

Figure 10.5 17-GHz NIR with corrections. T A = −25°C



( )NIRC T N CAL N CAL T = − ⋅ − ⋅ ⋅ −01 070 007 42 7. .

The value of δT D = 0.007 has been found empirically to give the best cor-rection, and indeed, when observing the curve marked NIRC in Figure 10.5, a very satisfactory correction has been obtained.

10.5.4 Discussion of the TPR Results

Figure 10.7 shows the behavior of the 5-GHz total power radiometer when subjected to temperature oscillations in the RF front end. The input temperature to


0 Noise diode (07) 255

1K

1K

0 Dicke load (01) 255

Figure 10.6 17-GHz NIR scatter plots.



same time receiver noise temperature increases, resulting in a larger out-put. Microwave amplifiers, with noise figures like the one in the present radiom-eter, typically exhibit an increase in noise of 0.014 dB/°C, that is, 0.07 dB or

1.6% for the 5°C temperature change. This results in an output change of 0.016· 527K = 8.4K, and the total change as a result of the temperature variations, isthus expected to be 38.6 − 8.4 ∼ 30K. It is seen from the figure that the varia-tion in INT is roughly 25K, not quite the expected value, but still a satisfactory agreement is noted.

Likewise, the change in EXT is expected to be: 0.046 · 604 − 8.4K ∼ 19K,and the observed value is roughly 13K. Overall, it looks like the typical noisefigure change with temperature used for the calculations is not quite largeenough to fit the present amplifier.

10.5.5 Back-End Stability

In Figure 10.8 we find the response of the DR and the NIR to temperature vari-ations in the low frequency part of the radiometer. The temperature is constant(23°C) until a certain moment, when 35°C warm air is forced into the LF cir-cuitry. After a period, the heating is turned off again. It is seen that the Dicke

mode shows a quite substantial response to the heating. This is the result of a combination of gain changes and drift with temperature in the DC coupled part


0

50

100

150

200

250

0 1H 42 Min 254

NIR

DR

5K

Figure 10.8 5-GHz DR and NIR. LF temperature variations. TA = 77K.



of the LF circuitry. As expected, the NIR is quite invariant to LF temperaturechanges, due to the closed loop operation of this radiometer type.

The total power radiometer’s response, when subjected to temperature

variations in the low-frequency part of the instrument, is also well behaved, andagain the variations are the result of gain changes and drift with temperature.

10.6 Conclusions

For the three investigated radiometer types (DR, TPR, and NIR), measured sen-sitivity agrees well with theoretical predictions, and we note especially that the

TPR exhibits a sensitivity that is superior by a factor of 2 compared with that of the other radiometer types. It is also noted that the simple, well-known formula for radiometer sensitivity is confirmed: No degradation from rapid gainfluctuations was experienced.

Regarding the stability of the DR against thermal variations in the microwave front end, this instrument is well behaved. Variations in output for a con-stant input brightness temperature are noted, they are reproducible fromexperiment to experiment, they show good correlation with the temperature of the microwave amplifiers, and they can be explained (and modeled) by amplifier

gain variation with temperature. A correction algorithm has been implementedbased on the model and a good, but not perfect, correction is possible. An evenbetter correction is expected to be possible if temperature sensors in closecontact with the amplifier stages are available.

The TPR may also be regarded as well behaved. The variations in outputare explainable as in the DR case, and overall the behavior of the TPR in many

ways resembles that of the DR. Stability is good, and single point calibrationevery 24 seconds is adequate to bring the accuracy to the same level as that

found for the DR. As in the Dicke case, a correction for gain variation ispossible.

Regarding the NIR, a very positive conclusion is reached, namely, thateven subjected to relatively large thermal variations in the RF front end, the NIR represents the ultimate design regarding stability. The output variations encoun-tered are simply a result of varying output from the noise diode and can be cor-rected with great accuracy.

Also, the stability of the three radiometer modes against temperature varia-

tions in the low frequency part has been investigated. The NIR is completely invariant to such variations as is to be expected. The DR and the TPR in thepresent design are relatively sensitive to such thermal variations. It is, however, a matter of careful design to alleviate this problem.

In all three cases (DR, NIR, TPR) a calibration each half minute or so(depending on the rise and fall times of possible thermal variations) will ensure




good stability without the need for modeling based on gain or noise generatoroutput variations. However, it is certainly a positive feature that such modeling is possible as a backup, and furthermore, it may reduce the rate at which

calibration is required.The present work can in a certain sense not support the use of the tradi-tional Dicke radiometer for future space systems. If the ultimate in stability andaccuracy is required, the noise-injection concept is the candidate. The penalty iscircuit complexity and loss of sensitivity by a factor of 2, compared with thetotal power radiometer. When the ultimate in sensitivity is required, the totalpower radiometer is the candidate. The penalty is slightly inferior stability andthe requirement for frequent calibration (at least once per minute). Hence, thetotal power radiometer is especially well suited for mechanically scanned imagers

where frequent calibration (once per scan) is easily accommodated without lossof useful data, and the noise-injection radiometer is recommended forpush-broom applications where long periods between calibration are wanted(see Chapter 11).

Further information about stability can be found in [4, 5].

References


[2] Tiuri, M. E., “Radio Astronomy Receivers,” IEEE Trans. on Antennas and Propagation,Vol. 12, No. 7, 1964, pp. 930–938.

[3] Miteq, Miteq Amplifier Handbook, Miteq, 125 Ricefield Lane, Hauppauge, NY 11788,1986.

[4] Hersman, M. S., and G. A. Poe, “Sensitivity of the Total Power Radiometer with Periodic Absolute Calibration,” IEEE Trans. on Microwave Theory and Techniques, Vol. 29, No. 1,

1981, pp. 32–40.

[5] Tanner, A. B., and A. L. Riley, “Design and Performance of a High-Stability Water VaporRadiometer,” Radio Science, Vol. 38, No. 3, 2003, p. 12.




11Radiometer Antennas and Real ApertureImaging Considerations

The purpose of the antenna is to collect the emitted energy from a target andpresent it to the radiometer input.

11.1 Beam Efficiency and LossesThe ideal antenna has a certain gain within its field of view and zero gain out-side. Figure 11.1(a) shows the polar pattern for such an idealized antenna. Themeasurement situation becomes very simple: If an extended target is viewed by the antenna, this collects energy from the target and not from anything else inthe world. However, such an antenna cannot be realized. First, the sharp cutoff of the beam is not possible. Figure 11.1(b) shows a more realistic beam. Todefine the beamwidth, it is now necessary to refer to a certain level on the beam

compared to the peak gain. The −3-dB points are normally used. Actually eventhis pattern is not possible in real life. Sidelobes picking up energy from direc-tions far away from the main beam direction cannot be avoided [see Figure11.1(c)]. By careful design they can be minimized but never avoided.

An important antenna property is the so-called beam efficiency η definedas the ratio between the energy received through the main beam and the totalenergy received by the antenna (main beam + all sidelobes). The antenna in Fig-ure 11.1(a) has a beam efficiency of 100%. To fully describe the beam efficiency

for a realistic pattern, η is often quoted for several levels on the main beam (i.e., η = 90% within the −10-dB points means that 90% of the total energy received

117



by the antenna is received within the −10-dB points of the main beam). Anantenna with η = 95% within the −20-dB points is about the best you can get.

To get a flavor of the problems associated with beam efficiency, let us con-sider an example, where an antenna having η = 95% (total main beam) senses anice floe on the surface of the sea. The ice floe is just the size of the area on the

ground illuminated by the main beam. See Figure 11.2.To simplify the situation, only downward looking sidelobes are assumed

present. In case of a lossless antenna we find:

( )T T T A B SL = ⋅ + − ⋅ η η1

Typical values are T B = 270K (ice) and T SL = 100K (sea), which together with η = 95%, gives:


180 180 180

0 0 0

(a) (b) (c)

Figure 11.1 Antenna polar patterns: (a) idealized sector shape, (b) realistic main beam, and(c) realistic pattern.

Ice

Radiometer

Sea

TB

TSL

Antenna ( , T , ) η 0

Figure 11.2 Antenna measuring an ice floe.



T A = ⋅ + ⋅ =0 95 270 005 100 262. . K

which is quite far from the value of 270K, which we expected to measure. Fortu-

nately, Figure 11.2 displays a situation with extreme contrasts. In general, theice floe may extend for several footprints, and the sea around it will containother ice floes elevating the spurious signal T SL . In total, smaller errors may beexpected. However, it should be noted that imaging near coastlines is in generala problem due to the large radiometric contrast between land (warm ~270K)and sea.

In Figure 11.2 it is noted that the antenna itself may have a loss . This will have to be treated exactly as described in Section 3.3. It is, however, possibleto make antennas with very small losses.

11.2 Antenna Types

Three main types of antennas shall be considered, namely, horns, phased arrays,and reflector antennas.

Figure 11.3 shows a horn, a phased array, and three often-used reflectorantenna types. Horns are low-gain devices, and as such are not used as primary

remote sensing antennas in spaceborne systems. They are often used for

Radiometer Antennas and Real Aperture Imaging Considerations 119

(a)

(b)

(c) (d) (e)

Feed network

Figure 11.3 Antenna types: (a) horn; (b) phased array; (c) front-fed paraboloid; (d)

Cassegrain; and (e) offset paraboloid.



laboratory measurements (calibration), in airborne systems, and as feeds inreflector antennas. Although the horn antenna is illustrated as a square, pyrami-dal horn in Figure 11.3, this is not optimal due to relatively poor patterns. Pot-

ter horns have almost ideal patterns with very low sidelobes and identical in theE and H planes. Also, corrugated horns are well suited and in addition to goodpatterns they feature large bandwidth. Phased arrays are generally not used asradiometer antennas, as they are relatively lossy, one-frequency devices. Figure11.3 shows a slotted waveguide phased array. Microstrip patch antenna arrayscan also be considered. Both are widely used in radar systems. It is possible tomake an electronically steerable antenna by incorporating phase shifters in thefeed network. Due to this feature (and the flatness of the structure), phasedarrays do find use for special purposes.

Regarding the reflector antennas, the simple front-feed paraboloid is notthe best solution due to the losses in the long feed waveguide. The Cassegrainantenna may be used, although it has some problems with sidelobes, due toreflections and refractions in the subreflector and the struts that carry it. Theoffset paraboloid antenna shown in Figure 11.3(e) is the ideal radiometerantenna. The feed can be connected directly to the radiometer (low losses), andno aperture blockage is present. The offset reflector geometry is further evalu-ated in Figure 11.4.


50°

50°30° 30°

Vertical

Vertex

Focal pointFeed

horn

Axis of

parabola

Aperture

Reflector

Drive

assembly

Figure 11.4 Offset paraboloid reflector geometry.



especially unpopular. Therefore, scanning the antenna in a continuous rotating

movement is often used (see Figure 11.7). Measurements are only taken as theantenna looks at the swath in the forward direction. This may seem an awful

waste of measurement time, as the antenna clearly looks away from the usefulswath for the greater part of the rotation period. The situation is, however, thatthe rotating scan should not be compared to an idealized zigzag scan, but to a real life ditto: In real life the zigzag scan cannot take advantage of an antenna that moves across the scan with constant angular velocity, stops immediately atthe scan edge, then moves back again with constant angular velocity. Rather, the

antenna has to come to a gentle stop at the scan limit, and has to be gently accel-erated for the backward scan (sinusoidal variation of scan angle as function of time). Thus, a rather large amount of time is wasted at the scan edges foraccelerating the antenna.

Figure 11.8 illustrates the trade-off between the rotating and the sinusoi-dal scan. The ratio of the resulting sensitivities ∆T REC /∆T ROT for a certain radi-ometer in the reciprocating/rotating case is shown as a function of scanhalf-angle (maximum scan angle in the reciprocating case, equal to the angledefining the useful swath in the rotating case). It is seen that small scanhalf-angles favor the reciprocating scan, while approaching 50° reduces the pen-alty for using a rotating mode. The break-even mark is found at 57°. SMMR used a 25° scan half-angle and a sinusoidal movement, which is clearly justifiedin Figure 11.8, but the scanner to be described in Chapter 13 will use a 60°half-angle and a fully rotating antenna.


Antenna scan

Nadir

path

Swath

Antenna

footprint

Satellite

velocity

vector

Figure 11.6 Conical reciprocating scan.



Note that in some cases it is highly desired to use also the aft look (to have

two different look directions). This may not be a problem for the radiometer,but it may be for the spacecraft designer as it is now required to have unob-structed field of view both fore and aft.

The users in general want small footprints (or better ground resolution, toput it differently). Small footprints mean large antennas or high frequencies.

As technology evolves, high-resolution systems become possible, but a small footprint results in rapid rotation and in very short integration times,

which, through our radiometer sensitivity formula, directly translate into poor

sensitivity. The solution to this fundamental problem is offered by the so-calledpush-broom concept illustrated in Figure 11.9. In the push-broom radiometersystem, a multiple beam antenna covers the swath while the satellite moves for-

ward. A host of radiometer receivers are connected to an equal number of antenna feeds, producing individual beams to sense the Earth simultaneously.The obvious advantages of the push-broom system compared to a scanning system are:

• No moving antenna (makes the satellite builder happy);• Much larger dwell time per footprint, hence better sensitivity (the foot-

prints do not have to time share a single radiometer receiver).

The obvious problems areas are:


Antenna scan

Nadir

path

Useful swath

Antenna

footprint

Satellite

velocity

vector

Figure 11.7 Conical scan by rotating antenna.



• Complicated antenna;

• Many receivers (one per antenna beam).

The problems with the antenna can be solved, and as technology movesforward, cheap and lightweight receivers can be built. So, for future advanced

space-borne radiometer systems, the push-broom concept is to be seriously considered.

A detailed description of the push-broom system is given in [1]. See also[2, 3].

11.4 The Dwell Time Per Footprint Versus the Sampling Time in theRadiometer

In an imaging radiometer system the antenna footprint moves across the sceneto be sensed, and the dwell time per footprint is defined as the time taken by theantenna beam to move a distance of one footprint. When the antenna beamscans a scene with a certain brightness temperature distribution, this results in a certain variation in the input signal to the associated radiometer; hence, there


0

0.1

0.2

0.30.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

0° 10° 20° 30° 40° 50° 60° 70° 80° 90°

Scan half-angle

∆TROT

∆TREC

Figure 11.8 Trade-off between a reciprocating and a rotating scan.



are certain requirements for the sampling in that radiometer. Quite clearly thespectrum associated with these input variations to the radiometer heavily depends on the dwell time per footprint: The faster the scan, the quicker thevariations, or, to put it differently, the wider the spectrum. However, as will beshown next, the actual shape of the antenna pattern plays an important role.

In mathematical terms the sensing of the scene by the moving antenna

corresponds to a convolution of the antenna pattern with the brightness temper-ature distribution of the scene. Hence, to find the transfer function H ( f ) associ-ated with that process, it is assumed that the antenna beam sweeps across a delta function in the scene distribution. Then H ( f ) is simply found as the Fouriertransform of the antenna pattern (transformed to the time domain by means of the scan velocity , or the dwell time per footprint).

Figure 11.10 shows a host of idealized antenna patterns. The patterns havebeen normalized to have an equal 3-dB width, and (without loss of generality)this has been assumed to be 2 seconds (i.e., the footprint dwell time is 2seconds).

Curve A represents a sector shaped pattern (often used for overview consid-erations). B is the main beam of a (sin x )/x pattern. It may seem odd to includethat, as it is a completely unreal antenna having negative sidelobes. (Note that weare dealing with power patterns since the brightness temperature to enter the


Nadir

path

Swath

Antenna

footprints

Satellite

velocity

vector

Figure 11.9 Push-broom imager.



antenna is a power measure.) The reason is purely academic and will emergelater. The next two curves represent far more realistic patterns, namely, a ((sinx )/x )2 having −13-dB sidelobes and ((sin x )/x )4 with −26-dB first sidelobes. Thisstatement is supported by Figure 11.11, which shows normalized patterns of twoactual antennas: one with a 140 λ aperture (e.g., 1.4m at 30 GHz) and one with a

600 λ aperture (e.g., 2m at 90 GHz). When compared with Figure 11.10, the twocurves lie nicely between curves C and D. Finally, curve E is a Gaussian pattern,also sometimes used as a reference for overview considerations.

As previously mentioned, the transfer function of the scanning antenna isfound simply by Fourier transforming these power patterns and the resultsare shown in Figure 11.12. The sector shaped pattern transforms into a |(sinx )/x | with zeros at n · 1/(2 seconds) = n ⋅ 0.5 Hz. Likewise, the (sin x )/x pattern

transforms into a box shape having a total width of 1.9/ π = 0.6 Hz. The trans-

form of the ((sin x )/x )2

pattern can be found by a convolution in the frequency domain of two box patterns and it is a triangle extending out to ±1.4/ π = ±0.45Hz. Again the transform of the ((sin x )/x )4 can be found by a convolution of twotriangles, or by consulting tables of Fourier transforms. The result is:


−20

−10

−3

0

dB

1 2 t(sec)

A B C D E

E:

D:

C:

B:

A:

exp( ( t2

1.43−

( (sin t t

4

sin 1.9 t1.9 t

( (sin 1.4 t1.4 t

2

Sector

Figure 11.10 Antenna power patterns (only one half shown).



If one makes overview considerations using the sector antenna (A), it iscorrect that ∼1 Hz sampling is required; and even with this high rate, somealiasing must be endured due to the large lobe around 0.7 Hz (some filtering could alleviate the problem).

The other extreme is found using the awkward antenna pattern (B): Thisis, from a sampling point of view, the ideal pattern having, in the frequency domain, a sharply limited and quite narrow form. A sampling frequency of 0.6Hz is adequate and no aliasing is present.

Considering the more realistic patterns C, D, and E, we see that a sam-pling frequency around 0.7–0.8 Hz is required, depending on which amount of aliasing can be accepted. Note that in no case is 0.5 Hz (i.e., equal sampling time and dwell time) adequate.

Figure 11.13 displays the total situation H TOT for an antenna transfer func-tion H A corresponding to the realistic patterns D and E (and approximately forC), having selected a sampling frequency f s of 0.7 Hz and including the transferfunction H RAD of the radiometer (from Figure 5.9, scaled to proper frequency).The transfer function of the radiometer slightly modifies the antenna responseand the level of aliasing is very low: maximum −20 dB (and lower near to 0 Hz).


B

C

0

E&

D A

0.5 11

f(Hz)

A

−20

−10

dB H(f)

Figure 11.12 Antenna transfer functions.



Hence, as a rule of thumb, in an imaging radiometer system with a 2-sec-ond dwell time per footprint, a sampling time of 1/0.7 Hz = 1.4 seconds isrequired, or, in general, a sampling time of 0.7 times the dwell time per foot-print is required.

Finally, it shall be stated that finding the upper limit of the sampling timeis interesting in an attempt to keep the data rate from a given radiometer systemas low as possible. This may, however, not be the most important issue as data rates from radiometers are comparatively modest due to generally coarse groundresolution as compared with other sensors. The radiometer integration time is,however, closely related to the necessary sampling time (in the radiometers dis-cussed in this book the sampling time and the integration time are equal).Hence, finding the maximum sampling time is also finding the maximum inte-gration time, thereby an important parameter in the achievable radiometricsensitivity.

11.5 Receiver Considerations for Imagers

The total power receiver exhibits the best obtainable sensitivity properties, givena certain noise figure of the radiometer. Moreover, it is a simple receiver type,


dB H(f)

−20

−10

0

HTOT

HA

HRAD

05 fs 1 f(Hz)

Figure 11.13 Transfer functions of the radiometer system.



not needing a low loss, fast electronic switch (the Dicke switch) in the input cir-cuitry. On the other hand, the total power receiver is inferior to the switching type of radiometers (Dicke radiometer and noise-injection radiometer) regard-

ing stability. The total power receiver has to be calibrated at frequent intervals,at least once per minute.For traditional, mechanically scanned radiometer systems, the require-

ment for receiver sensitivity is severe. At the same time, frequent calibration iseasily achieved: once per scan, while the antenna is looking away from the swathanyway, the receiver is calibrated. Hence, the total power radiometer is an obvi-ous candidate for such systems.

For the push-broom system, requirements for receiver sensitivity aregreatly relaxed due to the much lower data rate per receiver as compared to the

single receiver situation. At the same time, frequent calibration is not attractive,as all receivers are always busy sensing the Earth. A well-designed Dicke radiom-eter, or a noise-injection radiometer, only requires perhaps daily calibration.Hence, the push-broom situation seems to favor a trading of sensitivity for sta-bility and, in conclusion, the Dicke types of switching radiometer is preferred.

References

[1] Künzi, K., N. Skou, and K. Pontoppidan, Study of Push-Broom Radiometer Systems, Final Report, ESTEC Contract No. 5792/84/NL/GM(SC), Electromagnetics Institute, R 298,1984.

[2] Harrington, R. F., and C. P. Hearn, “Microwave Integrated Circuit RadiometerFront-Ends for the Push-Broom Microwave Radiometer,” Government Microcircuit Appli- cation Conference, Orlando, FL, 1982.

[3] Harrington, R. F., and L. S. Keafer, “Push-Broom Radiometry and Its Potential Using Large Space Antennas,” Large Space Antenna Systems Technology, NASA Langley Research

Center, 1982, pp. 81–104.[4] Gloersen, P., and F. T. Barath, “A Scanning Multi-Channel Microwave Radiometer for

Nimbus-G and SEASAT-A,” IEEE Journal on Oceanic Engineering, Vol. 2, No. 4, 1977.

[5] The Nimbus-7 Users’ Guide, NASA Goddard Space Flight Center, Greenbelt, MD, 1978.

[6] Hollinger, J. P., and R. C. Lo, “Low-Frequency Microwave Radiometer for N-ROSS,”Large Space Antenna Systems Technology, NASA Conference Publication 2368, 1984,pp. 87–95.




12Relationships Between Swath Width,Footprint, Integration Time, Sensitivity,Frequency, and Other Parameters forSatellite-Borne, Real Aperture ImagingSystems

The following considerations serve as an illustration of the trade-off betweenimportant parameters as spatial resolution and integration time, hence sensitiv-ity, as well as of the differences between scanning systems and push-broom sys-tems. The satellite case is covered; an analysis of an aircraft imager would follow the same lines yet be simpler due to a simpler geometry (no curved Earth to takeinto account). Only the rotating scan is considered. The angle of incidence atthe ground is 53°, an often-used value (used in well-known systems like SSM/Iand TMI). The satellite altitude is assumed equal to 800 km—a typical figurefor remote sensing satellites.

Note that:

S = swath width

H = satellite height

F = frequency

D = antenna diameter (aperture)

FP = footprint (geometric mean of footprint along track and across track)

T D = dwell time per footprint

τ = radiometer integration time

133



∆T = radiometer sensitivity

N E = number of footprints across the swath

R = Earth radius (6378 km)

V S = satellite velocity

X = radius in the circle on which the footprints are situated

Y = slant range from satellite to footprints

β = half scan angle

12.1 Mechanical Scan

From an inspection of Figure 12.1, and using straightforward geometric consid-erations and inserting known distances, we find:

Y = 1,219 km

α = 45.2°

X = 865 km

The swath width is easily calculated (see Figure 12.2) from:

S X = ⋅ ⋅2 sin β

The maximum useful swath can be reasonably defined by setting β = 60°.This is no sacred value, but it is clear from Figure 12.2 that beyond 60° theincrease in effective swath is very limited, while the number of footprints andhence data rate increase proportionally with β; 60° seems a good compromise.See also discussion in Section 11.3. Thus, we find:

S M = 1498, km (12.1)

The total 360° perimeter of the scan circle is:

C X = ⋅ ⋅ =2 5 435 π , km

The antenna 3-dB beamwidth is found using (11.1):

θ λ= ⋅14. D

where λ is the observational wavelength and D is the antenna diameter(aperture).

Using c = F · λ (c is the speed of light), we find:




( )θ =⋅

=⋅

14 0 42

. .c

F D F D F D in GHz, in m

The 3-dB footprint in the scan direction is now simply:

FPS Y F D

= ⋅ =⋅

θ 512 (km)

The 3-dB footprint in the along track direction is in satellite coordinatesthe same, but when projected onto the ground it is:

Satellite-Borne, Real Aperture Imaging Systems Relationship 135

Velocity

vector

Satellite

α

50°

X

YH

R R

Figure 12.1 Conical scan geometry, side view.



FPL FPS

F D =

°

=

⋅sin 37

851(km)

As a single, representative figure for spatial resolution, the geometricalmean of the footprint dimensions in the along track and across track directionscan be worked out:

FP FPS FPL F D

= ⋅ =⋅

660(km)

so we have:

FPS FP

FPL FP

= ⋅

= ⋅

0 776

129

.

.

Quite often it is really the footprint that is given, and the antenna size that

must be calculated. Hence,

( )( ) ( )

D F FP

mGHz km

=⋅

660(12.2)


Velocity vector

C

Satellite

X X

β β

S

Figure 12.2 The satellite and the swath seen from above.



The number of footprints for contiguous coverage along the scan circle Cis:

N X

FPS FP =

⋅2 π

The number of swaths per second (contiguous coverage) is calculatedfrom:

N V

FPL S

SSP = (12.3)

where V SSP is the velocity of the subsatellite point on the surface of the Earth.These values correspond to just consecutive footprints, which may not be quite

what we require.Hence, the number of footprints to be covered per second is:

N N N

N X V

FPS FPL

F FP S

F SSP

= ⋅

=⋅ ⋅

⋅

2 π

The velocity of the subsatellite point is found from the following set of equations well known from orbital mechanics texts:

V R g

R H R

R H

V V R

R H

S s

SSP S

= ⋅+

= ⋅+

= ⋅

+

000981.

Inserting relevant values in the present case, we find V SSP = 6.625 km/secand the following expression for the number of footprints to be covered persecond:

N FP

F = 36 034

2

,

and the dwell time per footprint is:

T N

FP D

F

= =1

36 034

2

,




Following the discussion in Section 11.4, the sampling and integrationtime τ of the associated radiometer should be equal to the dwell time per foot-print multiplied by 0.7. This corresponds to a 30% footprint overlap in the scan

direction. Requiring also a 30% overlap in the along-track direction, to avoidaliasing also in this case, means that:

τ = ⋅ =T FP

D 0 773 538

22

.,

(sec) (12.4)

Now typical sensitivities can be estimated. For a total power receiver thesensitivity is:

∆T T T

B A N =

+

⋅ τ

T A could, for Earth-oriented sensing, typically be 230K. A current andrealistic spaceborne receiver at middle frequencies around 20 GHz (see Section13.3.4) may have a noise figure of 3 dB (noise figure of the preamplifier: 2 dB;losses of components such as a prefilter, antenna feed, waveguides, all preceding the preamplifier: 1 dB); 3 dB is equivalent to a noise temperature of:

( ) ( )T NF T

N

N

= ⋅ − = ⋅ −=

290 1 290 2 0 1290

.K

Again, at frequencies around 20 GHz, a bandwidth of 200 MHz could betypical for a spaceborne radiometer.

Hence, the sensitivity may be estimated as:

∆T FP

= +

⋅ ⋅

230 290

200 10 73 5386

2

,

( ) ( )∆T FP

FP = 10

K in km (12.5)

At higher frequencies T N will tend to increase, but this is compensated by the larger possible bandwidth of the receiver. At lower frequencies the oppositeis the case: Lower T N is compensated by the fact that lower bandwidths are

required due to interference problems. So the rule-of-thumb figure for sensitiv-ity obtained from (12.5) can be used in the frequency range 5–100 GHz. Below 5 GHz only quite narrow bandwidths are available for passive remote sensing due to many active services, and sensitivities must be assessed individually using the calculated integration time and actual bandwidths.




A single figure of merit for a radiometer receiver is the radiometer constantC defined as the sensitivity corresponding to an integration time of 1 second. Sothe receivers considered here have a radiometer constant of:

C

C

= +

⋅ ⋅

=

230 290

200 10 1

0037

6

. K

The revolution speed of the rotating reflector can be found from the num-ber of swaths per second, N S , divided by 0.7 due to the fact that we require 30%footprint overlap as already discussed:

R N

FPL

V S

S SSP

= = ⋅0 7 0 7. .

(12.6)

or in the present case:

R FP FP S = ⋅0136. ((sec. rev.) in km)

This can also be expressed in revolutions per minute:

ω = =60 441

R FP S

(rpm) (12.7)

12.2 Push-Broom Systems

The maximum useful swath width can be worked out exactly as for the scanning system as S M = 1,498 km.

For a push-broom system there is, however, an important trade-off between swath width on one side and on the other side the number of channelsplus reflector complexity, hence cost. Thus, it is certainly viable to consider a system having a swath smaller than the maximum useful one as quoted earlier.The relationship between actual swath width and the number of footprints(channels) can be estimated as:

S N FPS E = ⋅ ⋅0 7.

The factor 0.7 reflects the usual 30% footprint overlap. As for the scanner:

FPS FP = ⋅0 776.

Satellite-Borne, Real Aperture Imaging Systems Relationships 139



so we find

S N FP S FP E = ⋅ ⋅0 54. ( and in km) (12.8)

The dwell time per footprint is calculated from:

T FPL V D SSP =

However,

FPL FP = ⋅129.

and as before

τ = ⋅0 7. T D

Hence:

τ =

⋅

⋅

129

6625 0 7

.

. .

FP

(sec)

or

τ = ⋅0136. FP (sec) (12.9)

Assuming the same receiver performance and conditions as in the rotating

case, but now with a Dicke type radiometer, the sensitivity will be:

∆

∆

T FP

T FP

= ⋅ +

⋅ ⋅ ⋅

=

2 230 290

200 10 0136

0 20

6 .

.(K) (FP in km)

(12.10)

12.3 Summary and Discussion

Given a representative orbit height of 800 km, the measurement frequency F (GHz), and the ground resolution FP (km), the following formulas have been

worked out for: maximum useful swath width SM (km) (corresponding to a half




scan angle β = 60°), antenna aperture D (m), radiometer integration time τ,typical radiometer sensitivity ∆T (K ), and the revolution time for the rotating antenna R S (seconds)—also expressed as revolutions per minute ω.

For the mechanical scanner it has been assumed that ground coverage witha 30% footprint overlap both across track and along track shall be obtained by a single receiver with one antenna beam by a fully rotating antenna giving a coni-cal scan with an incidence angle on the ground equal to 53°. The receiver has a radiometer constant (sensitivity for 1-second integration time) equal to 0.037K,and it is implemented as a total power radiometer.

For the push-broom system it is assumed that N E footprints (hence N E

receivers) cover the actual swath S simultaneously, the receivers have a radiome-ter constant of 0.074K, and are implemented as Dicke type switching radiome-

ters. Again 53° incidence angle on the ground is assumed.The typical radiometer sensitivity ∆T quoted can only be taken as a

rule-of-thumb figure in the frequency range 5–100 GHz. Outside this range, andif accurate estimates are needed, the sensitivity must be calculated on a case by casebasis using the expression for the integration time τ, and actual radiometer noisefigures and bandwidths. Moreover, the typical sensitivity is given for a typical scenebrightness temperature of 230K. Especially for high-end systems having a low noise figure, the resultant sensitivity will be quite dependent on the actual scene

brightness temperature intended to be measured by the radiometer in question.For both systems, the ground resolution FP is defined as the geomet-

ric mean of the footprint along track and across track: FP FPS FPL = ⋅ mean-ing that FPS = 0.776 · FP and FPL = 1.29 · FP in the present geometry. SeeTable 12.1.

In Figure 12.3 a comparison between mechanically scanned systems (MS)and push-broom systems (PB) is shown. Sensitivities for the two systems are


Table 12.1

Summary of (F in GHz, FP in km)(∆T estimate valid for 5 < F < 100)

Scanner Push-Broom

S M 1,498 km ( β = 60°) 1,498 km ( β = 60°)

D 660

F FP ⋅(m)

660

F FP ⋅(m)

τ FP

2

73 5.(ms) 0.136 · FP (sec)

∆T 10

FP (K)

0 20.

FP (K)

S N E 0.54 · FP (km)

RS 0.136 · FP (sec/rev.)

ω 441/FP (rpm)




0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100

FP (km)

∆T (K) & N/10

MS

N

PB

0.01

0.10

1.00

10.00

100.00

1 10 100

FP (km)

∆T (K) & N

N

MS

PB

Figure 12.3 Comparison (lin and log scales) between ∆T for mechanical scanner (MS) and

for push-broom system (PB). N = ∆T(MS)/∆T(PB). H = 800 km.



shown as functions of desired footprint as well as an improvement factor Ndefined as the ratio between sensitivities for the two systems for a given foot-print. Large N favors push-broom systems.

It is obvious from the curves that for small footprints (a few kilometers),the scanner cannot give reasonable sensitivities, while the push-broom imagercertainly can. N becomes very large as an indication of this.

12.4 Examples

Following the discussions in Sections 12.1 through 12.3, three mission-orientedsystems will be covered as illustrations of the differences between the scanner

and the push-broom system.

12.4.1 General-Purpose Multifrequency Mission

Consider the 18.7-GHz channel of an SSM/I-like multifrequency radiometersystem. A 1-m aperture is assumed (this is a typical size for such a system). Theground resolution will be: FP = 35.3 km.

For the scanner we find:

τ = 16.9 ms∆T = 0.28K

R S = 4.8 seconds/rev. corresponding to 12.5 rpm.

while the push-broom system parameters are:

τ = 4.8 seconds

∆T = 0.03K

N E

= 79 corresponding to the maximum swath S M

A radiometric resolution of 0.28K will satisfy most users and a revolutiontime of 4.8 seconds for a 1-m reflector is not frightening. Surely the push-broomsystem offers better sensitivity but at the expense of complexity (79 receivers anda more complicated antenna system). Hence, the trade-off between scanner andpush-broom in this case favors the first. A scanner will be discussed further inChapter 13.

12.4.2 Coastal Salinity Sensor

A ground resolution of, say, 16 km is compatible with narrow seas and enclosed waters. The generally accepted frequency for the purpose is 1.4 GHz. A radio-metric sensitivity of a fraction of a Kelvin is required.

For a scanning system we find:




D = 30m

τ = 3.35 ms

R S = 2.1 seconds/rev. corresponding to 28 rpm

Only some 20 MHz of bandwidth is available in the L-band protectedband, and a realistic receiver noise temperature is 170K. The ocean brightnesstemperature is typically 130K (vertical polarization around 50° incidence angle).Hence, the sensitivity is:

∆

∆

T

T

= +

⋅ ⋅

=

130 170

20 10 0 00335

12

6 .

. K

Not only are the requirements for sensitivity far from being fulfilled butalso the spacecraft designer is left with the problem of having a 30 m dish rotat-ing with one revolution per 2.1 sec. Clearly not a feasible solution. For a push-broom system we find:

τ = 2.1 seconds

N E = 177 corresponding to the maximum swath S

M

Bearing in mind that for this demanding application, a noise injectionradiometer is probably the candidate radiometer option, the sensitivity can beassessed from (4.7) assuming a reference temperature of 300K:

∆

∆

T

T

= ⋅ +

⋅ ⋅

=

2 300 170

20 10 21

015

6 .

. K

which fulfills the requirements.The cost is receiver and antenna system complexity; 177 identical receivers

are needed, but integrated techniques can be used, thus greatly facilitating massproduction, and at the same time keeping volume and mass to reasonable levels.The antenna system must include 177 individual feeds and have an unusually shaped and sized reflector. There will be more information about such issues inChapter 14.

12.4.3 Realistic Salinity Sensor

The 30-m aperture just discussed is indeed ambitious by all standards, and isprimarily included to illustrate the significant differences between scanners andpush-broom systems. A more realistic salinity sensor could assume a 10-m




aperture, which in turn results in a ground resolution of 47 km. Again, a radio-metric sensitivity of a fraction of a Kelvin is required.

For a scanning system we find:

τ = 30 msR

S = 6.4 seconds/rev. corresponding to 9.4 rpm.

The conditions are as before, and the sensitivity is calculated as:

∆

∆

T

T

= +

⋅ ⋅

=

130 170

20 10 003

0 4

6 .

. K

Even a 10-m reflector is a mighty big antenna to scan with 9.4 rpm, andthe sensitivity is not impressive. Also in this case the scanner is not a feasiblesolution. For a push-broom system we find:

τ = 6.4 seconds

N E = 59 corresponding to the maximum swath S

M

The sensitivity is:

∆

∆

T

T

= ⋅ +

⋅ ⋅

=

2 300 170

20 10 6 4

0 08

6 .

. K

which fulfills all reasonable requirements. A system along these lines is studied in more detail in Chapter 14.




single-frequency horns in a feed cluster and had the feeds (plus the radiometers)rotate with the reflector. This is less elegant but gives a better performance.

Also in the United States, SMMR successors were studied by NASA. Twocandidates, both using a 4-m antenna, have been assessed: the advanced SMMR

for the National Oceanic Satellite System (NOSS) and the Large Antenna Multifrequency Microwave Radiometer (LAMMR). Both employ frequenciesbetween 4 and 37 GHz, and the NOSS system also includes a 91-GHz channel.These systems reflect optimism, as a 4-m antenna was about the largest solidreflector to fit inside launchers, so why not go for the ultimate solution? Theoptimism was not shared by decision-makers, and none of these systems materi-alized. In the meantime, SMMR performed quite well within sea ice studies andthe preferred algorithms used only the 18-GHz and 37-GHz channels. Hence, a

dedicated—and realistic—sea ice sensor, having a 61-cm aperture and featuring the frequencies 19.35 and 37 GHz for classification, 22.235 GHz for atmo-spheric correction, and 85.5 GHz for ice edge detection, was designed and even-tually launched in 1987 [3]. It is called the Special Sensor Microwave/Imager(SSM/I) and is part of the U.S. Defense Meteorological Satellite Program(DMSP). The SSM/I also features a rotating antenna having the feed system andthe radiometers rotate with the antenna. In addition to this, a revolutionary andelegant concept for in-orbit calibration was devised. The system has proven

highly successful, and several instruments have been launched ensuring continuous data availability to the present and beyond.Europe was also caught by the 4-m antenna optimism, and the first ver-

sions of the ESA Multifrequency Imaging Microwave Radiometer (MIMR) fea-tured such a large reflector. MIMR was an ESA program of considerableendurance, and over the years it became more realistic and ended being largely


Table 13.1

SMMR Applications

Ocean parameters Sea surface temperature

Wind speedAtmospheric parameters Water vapor

Liquid water

Rain intensity

Cryopheric parameters Sea ice (fractional ice coverage, ice boundary, ice type classification)

Perennial snow (on ice caps and glaciers)

Seasonal snow (area, water equivalent, water runoff)

Land parameters Permafrost

Soil moisture

Vegetation characteristics



an upgraded and much improved IMR using a 1.6 × 1.4-m reflector. The project was carried to the point where a full instrument was developed and evalu-ated before the program was cancelled.

As an example of how such multifrequency imagers can be designed, a generic system having a 1-m electrical antenna aperture will be worked throughin the following. The starting point of the study is the following requirements:

• Frequencies: 10.65, 18.7, 23.8, 36.5, and 89 GHz;

• Polarizations: vertical and horizontal;

• Sensitivity: corresponding to the receiver model used in Chapter 12,but also evaluated for actual parameters;

• Spatial resolution (footprint): corresponding to 1-m aperture;

• Incidence angle on the Earth: 53° (conical, rotating scan);

• 800-km orbit;

• Radiometric dynamic range: 0–313K.

13.2 System Considerations

13.2.1 General Geometric and Radiometric Characteristics

The instrument to be designed in this chapter utilizes a 1-m aperture antenna.But before focusing on that size, a broader discussion is warranted, and aper-tures ranging between 0.5m and 4m are considered. The background is the setof formulas derived in Chapter 12 and summarized in Table 12.1.

In Table 13.2, calculations based on these formulas are carried out for the

given frequencies and antenna sizes. The notation in the table is self-explanatory when referring to Chapter 12. The table includes instrument options ranging from relatively simple systems with small antennas resulting in benign resourcedemands to the host satellite, to difficult systems with large antennas and indeedsevere resource requirements.

The lowest frequency has the largest footprint; the longest integration timeand hence the best associated sensitivity; and the least severe requirement of antenna rotation rate for contiguous Earth coverage. In a multifrequency sys-

tem, the antenna rotation rate will have to be selected to suit the highest fre-quency. In that case the integration time per instantaneous footprint for thelower frequencies will be shorter than originally calculated. However, simulta -neously the swath is oversampled proportionally, and the original integrationtime (hence, sensitivity) can be restored by suitable integration in the data analysis.

First Example of a Spaceborne Imager: A General-Purpose Mechanical Scanner 149



We can clearly see from the table that a system with a 4-m antenna being illuminated by one 90-GHz feed with one associated receiver leads to an impos-sible situation: Not only is the sensitivity at 90 GHz unsatisfactory (a realistic

receiver performance was assumed for the calculations), but also the spacecraftdesigner is left with the problem of having a very large antenna dish rotating atfour revolutions per second.

There are two possible approaches to this problem: underillumination of the reflector at the higher frequencies, or multiple antenna beams (and receivers)at the higher frequencies. Hybrid solutions are also possible.

13.2.1.1 Underillumination

In this case a certain lower limit is set for the footprint size. To simplify the dis-

cussion a 3-m antenna is considered. Assume, for example, that a footprint of 9.1 × 15.2 km (corresponding to the full illumination of the reflector at 18.7GHz) can satisfy all reasonable user requirements. At the higher frequencies thereflector is suitably underilluminated to obtain the same resolution, and the sen-sitivity and antenna revolution time quoted in Table 13.2 for 18.7 GHz willalso hold for the total multifrequency system—in this case, 0.8K and 37 RPM.The advantage of the principle is that it is easy to implement; the drawback isthat the full resolution capability of the antenna is not utilized.

A second advantage deserves to be mentioned. Several channels will haveequally sized footprints, simplifying subsequent data analysis; oftentimes, geo-physical retrievals are based on data from several channels, including several fre-quencies. Basically this requires all channels be processed to have identicalfootprints before retrieval algorithms are applied. But again: since a variety of applications normally are to be served by any one mission, and these applica-tions use different frequency combinations, it is not very satisfactory to excludethe use of the full resolution power of the antenna system.

13.2.1.2 Multiple Beams

In this case more than one feed horn, each with its individual receiver, produceseveral antenna beams to sense the swath simultaneously. The antenna rotationrate can be lowered proportionally with the number of beams at a given fre-quency. For example the use of five beams at 89 GHz reduces the rotation rateto that required by the 18.7-GHz channel. Two receivers at 36.5 GHz can easily do the job at this frequency. The 23.8-GHz channel cannot give contiguousground coverage with one receiver, but, as it does not sense the ground anyway (but rather the atmosphere), this may be acceptable. Otherwise, two receiversare needed, or a slight underillumination can be an attractive solution. Theadvantage of this concept is that full use of the reflector is made at all frequen-cies. The disadvantage is complexity.





Table 13.2

Using the Information in Table 12.1 for an Imager with Certain Frequencies

and a Range of Antenna Sizes

D (m ) FPS (km) FPL (km) (msec) RPM T (K) F (GHz)

0.5

0.7

1

1.2

1.5

2

3

4

96.2

68.7

48.1

40.1

32.1

24.1

16.0

12.0

159.9

114.2

79.9

66.6

53.3

40.0

26.6

20.0

209.1

106.7

52.3

36.3

23.2

13.1

5.8

3.3

3.6

5.0

7.0

8.5

10.7

14.2

21.3

28.4

0.08

0.11

0.16

0.19

0.24

0.32

0.48

0.65

10.65

0.5

0.7

1

1.2

1.5

2

3

4

54.8

39.1

27.4

22.8

18.3

13.7

9.1

6.9

91.0

65.0

45.5

37.9

30.4

22.8

15.2

11.4

67.8

34.6

17.0

11.8

7.5

4.2

1.9

1.1

6.2

8.7

12.5

15.0

18.7

24.9

37.4

49.9

0.14

0.20

0.28

0.34

0.42

0.57

0.85

1.13

18.7

0.5

0.71

1.2

1.5

2

3

4

43.0

30.721.5

17.9

14.4

10.8

7.2

5.4

71.5

51.135.8

29.8

23.8

17.9

11.9

8.9

41.9

21.410.5

7.3

4.7

2.6

1.2

0.7

7.9

11.115.9

19.0

23.8

31.7

47.6

63.5

0.18

0.250.36

0.43

0.54

0.72

1.08

1.44

23.8

0.5

0.7

11.2

1.5

2

3

4

28.1

20.1

14.011.7

9.4

7.0

4.7

3.5

46.6

33.3

23.319.4

15.6

11.7

7.8

5.8

17.8

9.1

4.53.1

2.0

1.1

0.5

0.3

12.2

17.0

24.329.2

36.5

48.7

73.0

97.4

0.28

0.39

0.550.66

0.83

1.11

1.66

2.21

36.5

0.5

0.7

1

1.2

1.5

2

3

4

11.5

8.2

5.8

4.8

3.8

2.9

1.9

1.4

19.1

13.7

9.6

8.0

6.4

4.8

3.2

2.4

3.0

1.5

0.7

0.5

0.3

0.2

0.1

0.0

29.7

41.6

59.4

71.2

89.0

118.7

178.1

237.5

0.67

0.94

1.35

1.62

2.02

2.70

4.05

5.39

89.0



13.2.2 Instrument Options

Let us now return to the 1-m aperture system to be covered in this chapter. For thissize of antenna, a rotation rate around 40 RPM is deemed practical. A radiometric

resolution around 0.5K can serve most applications adequately (around 1K accept-able at 89 GHz). A range of options having different combinations of under-illumination and multiple beams can be devised as illustrated in the following.

13.2.2.1 Option 1

This is just the straightforward, basic option as assumed in Table 13.2 for a 1-mantenna. The spatial resolutions, sensitivities, and other salient features arerepeated in Table 13.3.

The sensitivity requirements are not quite fulfilled for the two higher-fre-quency channels, and even worse, the antenna rotation rate is unacceptably high. Each frequency has one dual polarized feed horn and basically two receiv-ers. As indicated, the two polarizations at the lower frequencies may be mea-sured by just one receiver, due to the rather high oversampling of the Earth: Theantenna rotation rate is determined by the highest-frequency channel. A multi-plex switch must be inserted between the two antenna ports (H and V polariza-tion) and the receiver input, but for redundancy and system reliability reasons,

two individual receivers may very well be preferred anyway. Likewise, it is indi-cated that in fact two receivers may not be needed at 23.8 GHz as this channelsenses the atmosphere where two polarizations may not be needed, but againsystem reliability may dictate the use of two receivers. Therefore, in total there

will probably be 5 × 2 = 10 receivers.

13.2.2.2 Option 2

The reflector is underilluminated at 89 GHz so that this channel will feature the

same ground resolution as the 36.5-GHz channel. This solution is illustrated inTable 13.4.


Table 13.3

Key Figures for the Basic Option

F (GHz)

Footprint

(km) T (K)

Number

of Feeds

Number of

Receivers

Antenna

RPM

10.65 48 × 80 0.16 1 2 (1) 59

18.7 27 × 46 0.28 1 2 (1)

23.8 22 × 36 0.36 1 2 (1)

36.5 14 × 23 0.55 1 2

89.0 5.8 × 9.6 1.4 1 2



The sensitivities as well as the antenna revolution rate are satisfactory. Thesolution is simple, but as already argued it may not be satisfactory not to utilizethe full resolution potential of the antenna. As before, each frequency has onedual polarized feed horn and two receivers, in total 5 × 2 = 10 receivers.

13.2.2.3 Option 3

Again the reflector revolution time is fixed at 24 RPM (i.e., to suit the36.5-GHz channel), but now the 89-GHz channel must use more than one feedhorn to cover the swath. It is clear from Table 13.2 that two channels at 89 GHz

will not quite assure the required 30% footprint overlap along track, as 2 · 9.56km (the 89-GHz FPL) = 19.12 km, that is, somewhat less than the 23.32 km(the 36.5-GHz FPL) just fulfilling overlap requirements. The actual overlap is:(19.12 − 23.32 · 0.7)/19.12 = 0.15, that is, 15%. This may well be consideredacceptable in view of the high cost of implementing a third 89-GHz channelthat would be required if requirements should be strictly adhered to. The impli-cation of having only 15% overlap will, in most cases, be small. The aliasing

errors can in general not be quantified, as they are scene-dependent. For many natural scenes (or brightness temperature distributions), even poorer overlapcauses low aliasing errors: It depends of the contents of high frequencies in thespatial frequency domain, and this is often moderate for natural scenes. How-ever, it can be stated—based on experience with system simulators—that the30% overlap requirement ensures alias free operation in all practical cases.

It should be noted that a slight underillumination at 89 GHz of theantenna reflector, in order to yield a footprint of 11.66 × 7.02 km (i.e., half of

that at 36.5 GHz), will bring us back in line with the 30% overlap requirementand completely alias free operation. This must be a user choice in each individ-ual case.

The option is illustrated in Table 13.5. The numbers in the table arelargely as in the previous two tables, apart from the important fact that


Table 13.4

Key Figures for the Underillumination Option

F (GHz)

Footprint

(km) T (K)

Number

of Feeds

Number of

Receivers

Antenna

RPM

10.65 48 × 80 0.16 1 2 24

18.7 27 × 46 0.28 1 2

23.8 22 × 36 0.36 1 2

36.5 14 × 23 0.55 1 2

89.0 14 × 23 0.55 1 2



acceptable rotation rate and sensitivity at 89 GHz are achieved by having twofeed horns, hence antenna beams at this frequency. The 89-GHz sensitivity isfound by taking the value from Table 13.2 (1.35K) and realize that it isimproved by the square root of the ratio between the 59.4 RPM (what would beneeded using one single channel) and 24.3 RPM (actually employed). (Notethat the integration time is directly enlarged by this ratio, meaning that the sen-sitivity is divided by the square root of the ratio.)

The sensitivities as well as the antenna revolution rate are satisfactory. The

solution is still relatively simple: The price to pay is a doubling of the feed andthe receivers at the highest frequency, but these are of modest size and weight, sothe penalty is moderate. As before, most frequencies have one dual polarizedfeed horn and two receivers, while the 89-GHz channel employs the double of that, in total 6 × 2 = 12 receivers.

13.2.2.4 Option 4

This option is included to show that it is possible to obtain a slower antenna

rotation rate and improved radiometric sensitivity at the higher frequencies atthe expense of system complexity. The reflector revolution time is fixed at 12.5RPM to suit the 18.7-GHz channel. Five feeds are required at 89 GHz to ensurecomplete Earth coverage. Two feeds at 36.5 GHz are adequate, while onereceiver at 23.8 GHz is probably acceptable, as some undersampling may be allright for this atmospheric channel (also, a slight underillumination is a possibil-ity). See Table 13.6.

Again, the sensitivities at the channels beyond 18.7 GHz are found by tak-

ing the appropriate values from Table 13.2 and divide them by the square rootof the ratio between the original RPM (what would be needed using one singlechannel) and the 12.5 RPM actually employed. The number of receivers hasnow increased to 10 × 2 = 20. It is seen that good sensitivities and low rotationrate is indeed a possibility, but at the expense of a great many receivers and many feeds possibly leading to severe real estate problems in the feed area.


Table 13.5

Key Figures for the Multiple Beam Option

F (GHz)

Footprint

(km) T (K)

Number

of Feeds

Number of

Receivers

Antenna

RPM

10.65 48 × 80 0.16 1 2 24

18.7 27 × 46 0.28 1 2

23.8 22 × 36 0.36 1 2

36.5 14 × 23 0.55 1 2

89.0 5.8 × 9.6 0.86 2 4



13.2.2.5 Summary

Option 1 is relatively simple. It has a limited number of feed horns and receiv-ers. Each feed is dual polarized, so, in general, two receivers (a dual receiver unit)are required per feed horn. However, at the lowest frequencies the oversampling of the Earth is such that both polarizations may be multiplexed into onereceiver. For redundancy reasons two receivers are still desired. At 23.8 GHztwo polarizations are not really required as this channel only senses the atmo-sphere. Again, for redundancy reasons, a dual receiver unit is preferred. Theradiometric sensitivity at 89 GHz leaves something to be desired, but, worse, theantenna rotation rate is unacceptably high.

Option 2 is also simple. It solves the problem with a marginal radiometricresolution and with a high antenna rotation rate. Option 2 will fulfill many geo-physical requirements, but certainly not all. For example, sea ice boundary map-ping requires the best possible spatial resolution while requirements toradiometric resolution are less stringent. It is thus quite unsatisfactory not to aimat ultimate spatial resolution (not make full use of reflector) at all frequencies.

Option 3 is a good compromise between requirements and complexity.The option will serve many geophysical requirements concerning both spatialresolution and radiometric sensitivity. It makes full use of the antenna resolutioncapability, and it must be recalled that the user can always trade spatial resolu-tion for sensitivity in the data analysis by proper integration, and thus at thesame time achieve equal footprints at different frequencies. The implementationof the option is relatively straightforward as it only requires one extra feed hornand two extra receivers.

Option 4 is included only to show that it is possible to obtain slowerantenna rotation and better radiometric sensitivity at the expense of hardwarecomplexity. The slow rotation time found for option 4 can probably not war-rant the extra hardware complexity. The horn area will especially suffer from realestate problems.


Table 13.6

Key Figures for Enhanced Multiple Beam Option

F (GHz)

Footprint

(km) T (K)

Number

of Feeds

Number of

Receivers

Antenna

RPM

10.65 48 × 80 0.16 1 2 12.5

18.7 27 × 46 0.28 1 2

23.8 22 × 36 0.32 1 2

36.5 14 × 23 0.40 2 4

89.0 5.8 × 9.6 0.62 5 10



Only option 3 will be considered in the following.

13.2.3 Baseline Instrument Specifications

Table 13.7 summarizes the key parameters for the multifrequency, conically scanning imager to be discussed in the subsequent sections. Horizontal and ver-tical polarization is sensed at each frequency, and two simultaneous beams areemployed at 89 GHz to achieve a reasonable antenna rotation rate as well asacceptable radiometric sensitivities at all frequencies. Each frequency is served by one dual polarized feed horn and two receivers, apart from the 89-GHz channel

where twice that is needed—in total 6 feeds and 12 receivers. The incidenceangle on the Earth is 53°, and the orbit altitude is 800 km.

13.2.4 Instrument Layout and Receiver Type

The multifrequency conically scanning radiometer system is illustrated inFigure 13.1.

The offset parabolic reflector antenna and the drum holding the radiome-ters and the cluster of feed horns rotate around a vertical axis, thus ensuring constant incidence angle on the ground.

Following the discussions in Section 11.5, total power receivers areassumed. The superior sensitivity of the total power radiometer, as compared

with other radiometer types, is certainly needed for this application as evidentfrom the ∆T figures in Table 13.7. At the same time frequent calibration—once per antenna revolution—is readily achieved. The total power radiometerrequires two calibration points: one cold and one hot. The cold calibrationpoint is actually the cold space brightness temperature, and each time the feedcluster is passing under the tilted mirror indicated in Figure 13.1, the beam is

diverted towards cold sky. A little later the feed cluster passes under a bucketholding an ambient temperature absorber, thus providing the hot calibration


Table 13.7

Key Figures for the Baseline Instrument

F (GHz)

Footprint

(km) T (K)

Number

of Feeds

Number of

Receivers

Antenna

RPM

10.65 48 × 80 0.16 1 2 2418.7 27 × 46 0.28 1 2

23.8 22 × 36 0.36 1 2

36.5 14 × 23 0.55 1 2

89.0 5.8 × 9.6 0.86 2 4



point. This elegant solution ensures a very satisfactory calibration where only the reflector is outside the calibration loop—and reflectors can be made withvery low losses that will not deteriorate calibration fidelity [4]. This is in contrastto early systems like the SMMR, which used calibration switches, calibrationloads, and dedicated sky-looking horns in front of the receivers. Thus, losses andreflections were different when imaging and when calibrating, and minuteaccounting for those was a necessity (and a difficulty).

13.3 Receiver Design

The radiometers of the system are used in pairs: H and V polarization, fre-quency for frequency (two pairs at 89 GHz). Hence, it is practical to constructthem as dual receiver units: a pair of receivers for one given frequency.

Following the discussion in Section 5.1.1, the receivers operating at 10.65to 36.5 GHz will be designed as direct receivers: Microwave amplifiers covering the frequency range are readily available, as well as good quality tunnel diodedetectors; requirements to filter selectivity are not overwhelming for these

broadband applications (which would otherwise favor the superheterodyneprinciple with its IF filter possibilities); and finally, for spaceborne applications,it is a strong argument to get rid of the power consuming local oscillator. Thesituation is not quite so favorable for the 89-GHz channel, and it will bedesigned as a DSB superheterodyne receiver without preamplifier.

13.3.1 The Direct Receivers (10.65–36.5 GHz)

The design and layout of the direct total power receiver is very close to that of the SSB receiver as discussed in Section 5.4.2, and it is illustrated in Figure 13.2.The input calibration switch is not present in this design where the calibrationswitching process is taken care of as part of the antenna scan. The mix-preampand the local oscillator are not present and the IF filter is omitted. This has theconsequence that all filtering takes place at the RF level, and thus the


Figure 13.1 Scanner. (Courtesy of the European Space Agency.)



requirements to the RF filter may well be tighter than normally found in super-heterodyne designs. In general, this is no problem due to the rather wide fre-quency bands normally used in radiometers. The IF amplifier is substituted by an RF amplifier. With these changes, the design is just as before: RF amplifica-tion is determined so that proper signal levels are achieved at the detector, theDC amplification is determined so the proper signal levels are present on the

A/D converter, the offset is determined so that proper use of the A/D converters’range is achieved.

The A/D converter is a 12-bit converter, giving a digital resolution of the0–313-K input signal of below 0.1K.

13.3.2 The 89-GHz DSB Receivers

The design and layout of this DSB total power receiver is as discussed in Section5.4.1 and illustrated in Figure 5.11. As earlier, the input calibration switch isnot present in this design where the calibration switching process is taken care of as part of the antenna scan.

The local oscillator architecture warrants some discussion. As already described, the receivers are arranged two by two as dual receiver units. It is anobvious idea to use one LO to drive both mixers in a dual receiver unit, but thisresults in a potential single point failure: loss of the oscillator incapacitates both

receivers. Moreover, the local oscillator is deemed one of the components in a radiometer most likely to fail. Hence, an arrangement with two oscillators driv-ing the two mixers through a quadrature hybrid (magic tee at this high fre-quency) is proposed (see Figure 13.3).

Only one oscillator is operating, and if this stops working, DC power isremoved and switched to the other oscillator. Whenever possible, dielectric


∆ Σ / DC

DCRFTA

∼∼∼RF-x.xmV

Data ck

Filter

Isolator

Square law

detector

Offset

Integrator

Analog to

digital

converter

RF

∫

Figure 13.2 Direct receiver layout.



resonator oscillators should be used. They have adequate frequency stability forradiometer use, and they are far more power-efficient than other oscillator types.

13.3.3 Integrated Receivers: Weight and Power

For three decades now, we have seen a variety of imaging microwave radiometersystems in space, and technology has developed over the years resulting insmaller, lighter, and more power-efficient microwave systems. For spacebornesystems this is very important.

The famous SMMR launched in 1978 represents the technology of the1970s. It had 10 radiometers spanning a frequency range from 6.6 GHz to 37GHz. The receivers had a weight of 30 kg and consumed 65W of power (i.e., 3kg and 6.5W per receiver on average). The radiometers were constructed using individual waveguide components joined together using sections of waveguide.The 1980s saw the development of the SSM/I series of multifrequency, imaging radiometers. The same technology was used, now featuring 3 kg and 5W perreceiver. A dramatic change happened during the 1990s where MMIC technol-

ogy became practical even at higher microwave frequencies. The JASON radi-ometer system serves the frequencies 18.2, 23.8, and 34 GHz, and featuresindividual receiver units about 9 × 6 × 3 cm in size, with a weight of 400g and a power consumption of 2W. A unit includes everything from a Dicke switch toan A/D converter. TRW has designed and built these MMIC radiometers.Recent developments for a next generation JASON-like instrument saves addi-tional resources by combining several receivers into one package: A three-radi-ometer Dicke system (18.7, 21, and 34 GHz) is integrated into one unit about 8×

10 ×

2.5 cm with a weight of 550g and consuming 4W. This breadboard unit was developed by Quinstar Technologies under a JPL contract. Again,everything from Dicke switches to A/D converters is included (Table 13.8).

Based on the Quinstar specifications, it is safe to assume that for the fre-quencies 10.65 GHz to 36.5 GHz radiometers, dual receiver units having a

weight of 500g and a power consumption of 2.6W can be developed for the


∼

∼

Ant. V

Ant. H

RX 1

RX 2

LO 1

LO 2

Out

Out

QH

2

3

∆

Σ

Figure 13.3 Dual receiver unit.



present purpose. This is actually a conservative assumption, as no Dicke

switches and no input multiplexing, as implemented in the Quinstar unit, arerequired.

Also, at 89 GHz it is safe to assume the weight of 500g for a dual receiverunit, but the power requirement is increased by 1W to a total of 3.6W for a dualreceiver unit in order to reflect the presence of a local oscillator.

13.3.4 Performance of the Receivers

Until now, the radiometric performance of the system has been based on thetypical bandwidths and noise figures as assumed in Chapter 12 for overview cal-culations. In each actual case, proper calculations of the resulting sensitivity must of course be carried out based on the actual bandwidths and noise figures.In the following it is assumed that the bandwidths as indicated in Table 13.9have been established.

The stated bandwidths are, as throughout this book, the predetectionbandwidth (i.e., the bandwidth that is used in the radiometer sensitivity for-

mula). For direct receivers and single-sideband (SSB) receivers, this is also theinput RF bandwidth. However, for double-sideband (DSB) receivers, the input


Table 13.8

Weight and Power History

Year Name

Number of

Receivers

Weight

(kg) Power (W)

Weight and Power

Per Receiver

1978 SMMR 10 30 65 3 kg and 6.5W

1987 SSM/I 7 24 35 3 kg and 5W

1999 JASON 3 1.2 6 400g and 2W

2001 Quinstar 3 0.55 4 180g and 1.3W

Table 13.9

Actual Sensitivity Issues

F (GHz)

Bandwidth

(MHz)

Noise

Figure (dB)

Integration

Time (ms) T (K)

10.65 100 2.5 52.3 0.2018.7 200 2.8 17.0 0.27

23.8 200 3.0 10.5 0.36

36.5 300 3.1 4.5 0.46

89.0 500 5.0 1.8 0.90



RF bandwidth is twice the predetection bandwidth. Thus, in the present case,the input bandwidths are as quoted in Table 13.9 for all channels but the 89GHz channel, where it is 1 GHz.

The TRW MMIC radiometers used in JASON exhibit 2.8 dB noise figureat 18.2 GHz, 3.0 dB at 23.8 GHz, and 3.1 dB at 34 GHz. For the present pur-pose, these are still realistic figures, bearing in mind that the JASON radiome-ters include a lossy Dicke switch that is not present here, while, on the otherhand, a small loss (hence noise figure degradation) accounting for a small sectionof input waveguide and the feed horn should be added. A 2.5 dB is assumed rea-sonable at the lower 10.7 GHz. Using the prescribed bandwidth (300 MHz)and integration time (4.5 ms) from Table 13.9, we find for the 36.5-GHz chan-nel: T = 0.46K. For the lower frequencies we can also assess the sensitivity

using the bandwidths and integration times from the table, but then it must berecalled that the calculated sensitivity will be the sensitivity after proper groundpreprocessing, in which integration is carried out both across track and along track to reflect the larger footprint compared with the one (36.5 GHz) on whichthe actual sampling is based. This results in the following figures: ∆T = 0.36K at23.8 GHz, ∆T = 0.27K at 18.7 GHz, and ∆T = 0.20K at 10.65 GHz.

A state-of-the-art, but realistic, noise figure for an 89-GHz spaceborneradiometer is 5 dB corresponding to a 626-K noise temperature. The integra-

tion time is the 0.75 ms from Table 13.2, modified to reflect the lower antenna rotation rate: τ = 0.75 · 59.4/24.3 ms = 1.8 ms. As a result, ∆T = 0.90K.

It is seen that the actual sensitivities as shown in Table 13.9 compare quite well with the typical sensitivities derived in Chapter 12, and displayed in Table13.7. However, it must be emphasized that, especially at the higher frequencies,there is some freedom to adjust the bandwidth and thus obtain other sensitivi-ties. At the lower frequencies there are so many active services that relatively nar-row protected bands must be adhered to, but at the higher frequencies,

especially in the 90-GHz range, there are possibilities for an input bandwidth of several gigahertz without severe radio interference threats from active services.

13.3.5 Critical Design Features

Overall, it is fair to state that microwave radiometers, of the type and in the fre-quency range discussed here, employ mature technology and design features.However, a few critical areas shall be pointed out in the following.

Microwave radiometers are very sensitive to front-end losses and reflectioncoefficients. As these cannot generally be avoided (although they can be mini-mized), they must be known and stable with time so that corrections are possi-ble. Hence, careful waveguide design has been the dominant technology until




recently. As stated earlier, MMIC technology is now a viable option, generally characterized by good stability in addition to the other virtues to which wealready alluded.

Stability is greatly enhanced by a stable thermal environment. Hence, it isrequired that the dual receiver units are thermally stabilized to some given meantemperature ±1°C or so. This stabilization is easier the smaller the receiver, soonce again the MMIC technology offers clear advantages. The mean tempera-ture need not be the same for all receivers, the absolute level does not matter (aslong as it is within reasonable operating levels for electronics), and the stability isto be understood as short-term stability (typically orbital variations). A long-term drift over weeks and years is of no concern. The temperatures in thedual receiver units must be carefully monitored and form part of the housekeep-

ing data. The only lossy components outside the temperature-stabilized enclo-sures are the antenna waveguides and feeds. All possible effort must be put intothe mechanical design to keep waveguide lengths as short as possible. Theirlosses must be known, and their temperature monitored carefully at severalpoints along each waveguide run. The reflection coefficients of the antenna ports must be kept to very low values, but this is generally no problem for offsetreflector antennas with feed horn illumination. The mechanical layout musttake into consideration thermal expansion and contraction of the relatively rigid

antenna waveguides. Flex-guides cannot be recommended due to poor stability.The LF section of total power radiometers is very sensitive to low fre-

quency noise (from DC up to, and somewhat above, 1/τ). The smallest integra-tion time in question here is 1.8 ms, corresponding to 560 Hz. Hence, powersupply noise and ripple should be avoided below about 5 kHz. Switch modepower converters should generally be avoided, but, as they exhibit superior effi-ciency as compared with linear supplies, they will have to be used in space sys-tems. They must be carefully designed for low noise and carefully evaluated with

the radiometers.The local oscillators in radiometer receivers generate harmonics that may be emitted through the feed horns and find their way to other radiometers athigher frequencies. Hence, local oscillator frequencies must be arranged in sucha fashion that no radiometer input band include harmonics of any local oscilla-tor. This is not a problem in the present system where only the 89-GHz radiom-eters employ local oscillators, but generally it should be remembered.

Apart from the above-mentioned internal EMC problem, compatibility with other sensors and services of the carrying satellite must be ensured. Surely no radio transmission can be allowed in any of the radiometer input bands. Also,harmonics from any transmitter must be considered. The frequency of majortransmitters should be selected so that harmonics do not intercept any radiome-ter input band, or they must be reduced to very low levels at the source




13.4 Antenna Design

Only a few comments shall be brought forward for the sake of completeness, thesubject being outside the scope of this book. The general antenna geometry isshown in Figure 13.4. The geometry is equivalent to the one shown in Figure11.4, with a 50° offset angle.

The reflector has a 100-cm circular aperture and the focal length is 75 cm.The antenna term: “F/D ratio” is 0.30 (note that in this context D is not theaperture but the total diameter of the paraboloid from which the offset sectionmay be cut out). The total dimensions of the reflector are 100 × 112 cm. Thefeed axis is tilted 50° with respect to the parabola axis.

Typical Potter horns are assumed at the lower frequencies, and multiflare

horns at 89 GHz. The Potter and the multiflare horns are light, compact designs with very thin walls (hence little difference between inner and outer diameter of the horn aperture). Table 13.10 shows the outer diameter of the horn aperturesfor a set of Potter/multiflare horns.


F=75 cm

30°

ApertureD=100cm

cm

cm

30°

ApertureD=100cm

cm

cm

F 75 cm=

20

40

60

80

100

120

140

−20 20 40 60 80 100 120 140 160

Figure 13.4 Antenna geometry.



The offset reflector is scaled for an illumination angle of 30°. At this anglethe typical horn patterns are down by 20–21 dB. Adding roughly a 1-dB spaceattenuation results in an edge illumination of the reflector in the −21- to –22-dBrange, meaning that the factor 1.4 in the beamwidth equation (11.1) is justified(ensuring low sidelobes and good beam efficiency).

Figure 13.5 shows a possible horn layout. The relative horn dimensionsare as shown in Table 13.10. The X between the 89-GHz horns marks the focalpoint of the reflector. Note that no angular orientation is given. This must bedetermined so that the antenna beams from the two 89-GHz horns give contig-uous coverage (with 15% overlap).

All horns should be as close to the focal point (measured in wavelength atthe individual frequency) as possible. This means that the highest frequency horns should be placed near the focal point first.


Table 13.10

Horn Dimensions

F (GHz) d (mm)

10.65 88

18.7 50

23.8 40

36.5 27

89.0 11

10.7

18.7

23.8

36.5

89 89

Figure 13.5 Antenna feed layout.



Due to the fact that the feeds are not all at the prime focus of the reflector,the footprints on the ground will be displaced from one another. As long as thedisplacements are known (which they are), this is no problem, but some geo-

metrical corrections will have to be carried out as part of data processing afterthe instrument is operating.The feed positions are not critical as seen from an antenna performance

point of view (although they are for determining the footprint positions). It isclear that displacements in the focal plane of several wavelengths are required toenable the cluster. Still, good performance can be achieved.

In order to ensure the required 53° incidence angle on the ground fromthe satellite altitude, the whole antenna system (reflector plus feeds) must betilted forwards by 4.8° (the line in Figure 13.4 from the focal point to the center

of the reflector, equal to the feed axis, is not vertical but tilted by 4.8°) according to the scan geometry as shown in Figure 12.1. Alternatively, the antenna designcould directly have used a 45.2° offset angle and no additional tilt. This may notbe so practical, however, as it would—in real life—imply that a whole range of antenna designs would be required to serve different satellite altitudes (the 800km selected here is only a typical example). In all cases rotation is around a vertical axis.

13.5 Calibration and Linearity

13.5.1 Prelaunch Radiometric Calibration

The basic calibration is carried out to find the calibration curve of the radiome-ter receivers, that is, the relationship between known input levels and corre-sponding digital output counts. Primarily, this is done with the receiverssubjected to their nominal environment. During such exercises, the linearity of

the receivers must be verified and the sensitivity (defined as the standard devia-tion of the output signal for a constant input level) checked. Having calibratedthe receivers, these, together with proper calibration sources, can be used tomeasure the losses in antenna reflectors, feeds, and waveguides.

However, the receivers cannot be expected to operate under a nominal,constant temperature when in orbit. First, a thermal analysis might show thatthe temperature within the radiometer instrument will oscillate by typically upto several degrees during an orbit cycle. Second, unforeseen thermal gradients

may be experienced in orbit. So it is necessary to investigate radiometer perfor-mance under nonideal thermal conditions.The results from the experiments in Chapter 10 show that it is possible to

find the true brightness temperature at the antenna when the radiometer tem-perature is different from its nominal value. To do this, each receiver must becalibrated subject to different temperature levels and temperature oscillations.




These oscillations shall be planned to resemble as much as possible the oscilla-tions that may occur in orbit. Many temperature sensors must be embedded ineach receiver and their output recorded during calibration exercises, and

included in the housekeeping data transmitted from the satellite. Sensors mustalso measure the temperature of the antenna horns, antenna waveguides, andhot loads. Adequate sensors must be employed to ensure a reasonable picture of the thermal conditions within the instrument. Having the calibration data forthe receivers, the losses of waveguides and horns, and the housekeeping data, it ispossible to calculate the brightness temperatures as viewed by the antenna.

A different calibration approach is also possible. After the manufactureand integration are done, the total instrument is subjected to representative ther-mal oscillations and levels, with different, known radiometric input signals. A

multiple regression is performed on the input and output signals (the outputsignals being the radiometer counts and the housekeeping data) and calibrationequations will emerge.

It can be useful to perform both calibration techniques and it will increasethe correction possibilities in case of unforeseen thermal or other problems inspace.

One may ask: Why bother about the prelaunch calibration (apart from theinitial calibration and linearity check of the individual receivers), because we

have both a hot point and a cold point available for frequent calibration once inorbit?

The reason is that for space instruments fallback solutions should alwaysbe implemented as far as possible. In case of unforeseen problems, it is of greatvalue to be able to calculate corrected brightness temperatures based on modelsand prelaunch exercises (as was discussed in Chapter 10). Here the fallback solu-tion does not require extra hardware or resources in the satellite (apart fromtemperature sensors which do not contribute to weight, power, and data rate by

any significant amount). Only some thermal exercises before launch are needed(which may, however, be expensive and time-consuming).

13.5.2 On-Board Calibration

The present scanner with fully rotating antenna/feed/receiver assembly willemploy the hot load/cold sky reflector calibration layout as mentioned in Sec-tion 13.2, and as also found in well-known systems like the SSM/I and the

MIMR. The principle is illustrated in Figure 13.6. While the antenna rotates, at a certain time while the antenna beam wouldlook away from the useful swath anyway, the ray path between the feed and themain reflector is interrupted by the hot load, and likewise for the sky reflector.Thus, the switch indicated in Figure 13.6 is actually not physically present, andan almost perfect two-point calibration is carried out; only reflectors are outside




the calibration loop. As already mentioned, the loss of present-day, high-perfor-mance reflectors is so low that it can be neglected, and, if this for some reason is

not the case, the loss can be measured extremely accurately by radiometricmeans, and corrected.

The calibration method as described earlier assumes that the radiometerreceiver’s transfer function is linear. This is generally the case for a well-designedradiometer when we discuss relatively standard requirements as in the presentcase: Linearity must be viewed upon relative to the required sensitivity and abso-lute accuracy (which are typically of the same size), here around 0.5K. Linearity has been a matter of discussion for future high-accuracy systems requiring a frac-

tion of Kelvin accuracy, but in the present case adequate linearity fidelity isobtainable by careful design—especially concerning the detector circuit. Theseissues were discussed in Section 9.4. Experiments with real hardware show thatpresent-day, well-designed radiometers are indeed linear to within a fraction of a Kelvin. Also, it is well known that often the major contributor to nonlinearitiesis the detector (not very surprising), and by proper detector design (tunnel diode

with correct loading) these can be held at a very low level.

13.6 System Issues

13.6.1 System Weight and Power

The weight and power of the radiometers have already been discussed in Section13.3.3. Another important resource driver is the antenna reflector. Low-weightstructures have been built, and it is known that a 2-m carbon fiber compositedish weighing 12 kg has been launched into space. Similarly, a 3-m dish for a

future ocean salinity mission has been designed with a weight of 21 kg. So, a present rule of thumb states an antenna reflector weight around 3 to 4 kg persquare meter with proven technology. Hence, the present reflector would weigharound 3 kg. With this low reflector weight, the struts and other structure tocarry the reflector and the associated feeds become a significant part of the totalantenna weight, in the present case around 5 kg.


*

*

TH

TC

Out

In

OutTB

Radiometer

Figure 13.6 Calibration schematics.



Finally, a complete radiometer system of course includes several otherunits than what have been discussed above, and a total power and weight budgetcould look as it does in Table 13.11.

13.6.2 Data Rate

The data rate can be estimated by assuming 16-bit data words from the receivers(4 bits for label, 12 bits for radiometric data). The rate per receiver is determinedby the integration time, which is equal to the sampling time. To simplify the sit-uation, the sampling rate of the 10.65- to 23.8-GHz channels is assumed to beequal to the sampling rate of a 36.5-GHz channel (the frequency that deter-

mined the antenna rotation rate). As the footprint is larger at these lower fre-quency channels compared with the 36.5-GHz channel, some on-boardintegration could be carried out to lower the data rate. The estimates are thusconservative.

It must be recalled that the useful swath, where the receivers are sampled atnominal speed, only corresponds to 120° out of the full 360° rotation. In addi-tion, the radiometers are sampled while the feeds pass under the cold sky reflec-tor and the hot load, let us assume 2 × 30° of rotation. Thus, the receivers are

sampled at nominal rate during 180° out of the 360° rotation.For the 10.65- to the 36.5-GHz channels (4 × 2 = 8 receivers in total), thedata rate is:


Table 13.11

Power and Weight Budget

Power: Receivers 18W

Data handling 5W

Scan 10W

Power supply 6W

Total power 39W

Weight: Antenna including struts 8 kg

Receivers 3 kg

Feeds 2 kg

Data handling 2 kg

Power supply 2 kgCalibration 6 kg

Scan motor 5 kg

Deployment 6 kg

Total weight 34 kg



References

[1] Gloersen, P., and F. T. Barath, “A Scanning Multi-Channel Microwave Radiometer forNimbus-G and SEASAT-A,” IEEE Journal on Oceanic Engineering, Vol. 2, No. 4, 1977.

[2] “IMR, Imaging Microwave Radiometer—Phase A Study,” ESA Document Ref. ESS/SS1006, 1980.

[3] Hollinger, J. P., and R. C. Lo, SSM/I Project Summary Report, NRL Memorandum Report5055, Naval Research Lab., 1983.

[4] Skou, N., “Measurement of Small Antenna Reflector Losses for Radiometer CalibrationBudget,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 35, No. 4, 1997,pp. 967–971.


Table 13.12

Summary of Specifications

F (GHz)

Footprint

(km)

Bandwidth

(MHz)

Noise

Figure (dB)

Integration

Time (ms) T (K) Feeds Receivers

10.65 48 × 80 100 2.5 52.3 0.20 1 2

18.7 27 × 46 200 2.8 17.0 0.27 1 2

23.8 22 × 36 200 3.0 10.5 0.36 1 2

36.5 14 × 23 300 3.1 4.5 0.46 1 2

89.0 5.8 × 9.6 500 5.0 1.8 0.90 2 4



14Second Example of a Spaceborne Imager:A Sea Salinity/Soil Moisture Push-BroomRadiometer System

This chapter will show how to arrive at the design of a system, the aim of whichis to measure certain geophysical parameters with certain accuracies and resolu-tions by using the guidelines set forth in the previous chapters.

14.1 Background

A frequency of 1.4 GHz is generally accepted for measuring sea salinity and a ground resolution around 50 km is acceptable. From Table 12.1 it is seen thatthis results in an antenna aperture of some 10m. It is clear that a mechanicalscanner with this size of antenna would be very demanding concerning satellite

resources, as already discussed in Section 12.4.3. The push-broom conceptoffers a much more viable possibility, and high capacity spacecraft can carry structures of the size in question.

The technical specifications for the design to be carried out in the follow-ing are:

• A frequency around 1.4 GHz;

• An antenna aperture of 10m;

• A satellite altitude of 800 km;• Incidence angle on ground: 53°.

171



Using the formulas in Section 12.3, we find:

• Maximum swath width: 1,500 km;

• Footprint: 47 km (FPS = 36 km, FPL = 60 km);• Integration time: 6.4 seconds;

• Number of receivers: 59.

A trade-off between swath width and the number of receivers is possible.In the present design it is decided to opt for 21 receivers, giving a swath of 530km. Such a decision reflects a compromise: A wide swath provides better (more

frequent) ground coverage, but requires more resources (many receivers, largeantenna). This is a quite frequent situation when planning a spaceborne sensorsystem: There is a delicate balance between user wishes or requirements and theavailable resources (in the end often boiling down to financial resources).

14.2 The Brightness Temperature of the Sea

The brightness temperature of the sea depends on several parameters: frequency,

incidence angle, polarization, sea surface temperature, wind speed (actually sur-face roughness), and salinity. Disregarding surface roughness, the brightnesstemperature can in fact be calculated in a relatively straight forward mannerassuming the sea surface to be a plane boundary between two media, water andair, and then evaluate the Fresnell reflection coefficients knowing the dielectricconstant of water. The Klein & Swift computerized model for the brightnesstemperature of the sea [1] does that, and it has been run for a range of theseparameters, keeping the incidence angle fixed at 53°. Based on the output from

the model, the following can be concluded.Only at rather low frequencies is a response to salinity present, especially at

low sea surface temperatures. The sensitivity to salinity increases with decreasing frequency well into the UHF range. As the crowded UHF band is approached,however, insurmountable problems with interference from active radio servicesarise, and it is generally accepted that the lowest possible frequency band forradiometer work is the protected radio astronomy band 1.400–1.427 GHz.

At 1.4 GHz the vertical brightness temperature depends on sea surface

temperature (SST ) and salinity (S ) as illustrated in Figure 14.1.It is noted that the sensitivity to salinity is best at warm temperatures. It isalso noted that some dependence on temperature is evident especially for low salinity water. Fortunately, we are in the situation that a large part of the Earth’soceans are in the best possible category: moderate-to-warm temperatures andhigh salinity around 35 practical salinity unit (psu) (1 psu is in effect equal to 1




pool experiment specifically set up to test the Klein & Swift model confirmed itsaccuracy [7]. The RMS difference between measured and modeled brightnesstemperatures was found to be around 0.1K.

The wind speed sensitivities are slightly less well founded. A recent experi-ment [8] has largely confirmed the Hollinger figures used here, but error barsassociated with the data of both experiments are quite big, so the quoted sensi-tivity of 0.1K per meters per second can only be regarded as a guideline for sys-tem considerations.

14.3 The Brightness Temperature of Moist Soil

Laboratory measurements of the dielectric constant of moist soil show a very large change with varying water content, as seen from Figure 14.3 [9]. This isnot very surprising when considering that dry soil typically has a dielectric con-stant of around 3 for the real part with a low imaginary part. Water, on the otherhand, has at 1.4 GHz a very high dielectric constant of around 80 (real) with animaginary part strongly dependent on the contents of salts. When mixing soiland water, the resulting dielectric constant exhibits a very large variation with

water contents (i.e., soil moisture). Assuming the soil surface as a flat interface

between soil and air, the brightness temperature as sensed by a downwards look-ing radiometer can be calculated just as was explained for the calm sea surface,and it will show a large variation with soil moisture.

Of course, the surface of the Earth is not a smooth, flat interface, and fur-thermore it is normally not bare. Thus, many experiments have been carried outover the years to investigate the merits of radiometers in a realistic context. It canbe concluded that a frequency below 2–3 GHz is required for soil moisture mea-surements. This is primarily due to the masking effect of the vegetation cover at

higher frequencies. However, there is a lower limit to the usable frequency set by interference (as was discussed in the previous section) and a generally acceptedcompromise is 1.4 GHz. Horizontal polarization is preferred over vertical. Thisstems from the fact that vegetation has predominant vertical structures andtherefore affects the vertical polarization most, but at 1.4 GHz vertical polariza-tion is certainly also usable. Even at 1.4 GHz dense vegetation is nottransparable, and brightness temperature corrections based on models with bio-mass input is required. The biomass may be estimated by other spaceborne

measurements for example in the optical region.The brightness temperature of soil is also dependent on surface roughness,and this parameter cannot easily be measured independently. However, the timescale for roughness changes is very different from the time scale for soil moisturechanges. Concerning farmland, for example, the roughness changes dramatically only a few times each year, when the farmer prepares the fields. Hence, the time

Second Example of a Spaceborne Imager 175



type. The design follows the guidelines set forth in Chapter 5, and assuming a realistic receiver noise temperature of 170K as already mentioned in Section12.4, the values indicated in Figure 14.4 are found.

Compared with the generic noise-injection radiometer design shown inFigure 5.10, the major differences are that the receiver, being a direct detectreceiver, has no mixer and LO and hence no IF circuitry. The consequence ismore RF amplification and more stringent requirements to the RF filter. Also, itis indicated that the Dicke switch for this low microwave frequency design is nota latching circulator but rather a PIN diode switch. Latching circulators are toobig at this frequency, so the slightly larger loss of a semiconductor switch mustbe accepted.

A completely different design option is a very viable candidate at this rela-

tively low frequency, namely, the digital radiometer (see Figure 14.5).The digital radiometer uses no detection but sampling and A/D conver-

sion directly at the RF frequency, here around 1.4 GHz. This does not imply that the sampling frequency has to be twice this RF frequency, bearing in mindthat according to Nyquist the sampling frequency has to be twice the band-

width—which in this case is only 19 MHz. So allowing for some overhead, thesampling in this example is chosen to be 63.5 MHz as also indicated in Figure14.5. Actually, the sampling frequency cannot be chosen freely above twice the

bandwidth: A thorough frequency planning, taking all sideband products intoaccount and avoiding aliasing, must be carried out.


±1

∆/Σ DC

AFRF

46 dB

1 mV/ µW100 dB

0.5 VDC/1 Vpp

1.50 sec

29 dB

10 V 100%=

300 K

Noise switch

−3.7 dB

−3 dB

TA

Noise diode

ENR 28 dB=DATA CK FS

1404 MHz

1423 MHz

∼∼∼

−1 dB

−20 dB0.66Vpp

6.6 V µ pp

0.33 V9.5 V

95%

0K

299 K 1 K

29900K

RF

30 dB

Figure 14.4 The noise-injection direct receiver.



The digital radiometer as described here actually carries out the down-

conversion in the sampling process, and it is also named: radiometer withsubharmonic sampling. The system relies on the fact that fast A/D converters,having an analog input bandwidth encompassing L-band frequencies and a time

jitter low enough to suit sampling of the same frequencies, are available,for example, the Maxim MAX104. For more information about digitalradiometers, see [12, 13].

The output from the A/D converter is immediately integrated suitably in a fast field programmable gate array (FPGA), thus slowing down the data rate to

more common radiometer data rates. This FPGA is named “processor” in Fig-ure 14.5 as it also includes algorithms controlling the noise switch. The proces-sor can actually also carry out other important tasks. Provided some furtheroversampling is done, digital filtering becomes an option. This would make itpossible to relax on the analog RF filter (which can become clumsy at L-band)and at the same time ensure very good out-of-band suppression, which is impor-tant at L-band where many active services are close by. In addition to this attrac-tive feature, the advantage of the digital radiometer is that it represents theultimate reduction in analog hardware. On the other hand, it must not be for-gotten that the stability of the A/D converter (sampling circuitry and referencevoltage especially) becomes a very important issue, and fast converters are powerconsuming. Nothing is free.

Based on the considerations in Chapter 13, where it was found that a dualreceiver unit at middle microwave frequencies might have a weight of 500g and


RFRF

30 dB

26 dB

300 K

Noise switch

−3.7 dB

−3 dB

TA

Noise diode

ENR 28 dB=CK: 63.5 MHz FS

1404 MHz

1423 MHz

∼∼∼

−1 dB

−20 dB

95%

0K

299 K 1 K

29900K

RF

30 dB

Processor Fast A/D

DATA

Figure 14.5 The digital receiver with noise-injection.




Rotation axis =

vertical axis

W 18.6 m=

f 13.2 m=

45.2°

D

1 0

m

=

Figure 14.6 Push-broom torus antenna with 21 feeds.

Figure 14.7 The push-broom radiometer demo system.



An alternative to the horns is microstrip patch antennas. In general, these will have higher losses than horns do, but considering the considerable bulk of the horns, it may well be an option worth investigating. The losses in patch

antennas are largely associated with the feed network, so every effort towards a low-loss design must be pursued, for example, using air suspended stripline.

14.6 Calibration

Calibration, in this section, means checks while the radiometer instrument isflying in space. In addition to this, a fundamental calibration is carried out

before launch, using the principles described in Chapter 9 and further discussedin Section 13.5. As mentioned several times, it is reasonable for push-broom radiometer

receivers to trade sensitivity for stability to ease calibration. Hence, Dicke-typeswitching radiometers are selected. Such radiometers only need one, low tem-perature calibration point, and, equally important, may only need calibrationdaily (given proper electrical, mechanical, and thermal design).

The cold calibration point is for ground-based (and airborne) radiometersachieved by cooling a load to a low temperature, often by liquid nitrogen. This

is not at all practical in a spacecraft (today, at least). However, other cooling methods are available: Peltier cooling and radiation cooling. Temperaturesaround 200K are possible with both methods. For applications where the mea-sured brightness temperatures are comparatively high (e.g., sea ice measure-ments), this could be fine. For others involving low brightness temperatures(oceanography), it is not quite satisfactory. Each of the two cooling methods hasits more serious technical drawback: The Peltier elements are power-consuming;the passive radiator is large and requires unobstructed view to free space (away

from the Sun). However, the methods may play a role for very high-frequency radiometers, where hardware is small (i.e., little weight and volume to cool).

Another promising possibility for a low temperature calibration point isthe so-called active cold load. This is, in fact, an FET transistor amplifier wherethe input acts as a matched load having a noise temperature much lower thanthe physical temperature (actually comparable with the noise of the circuit whenused as an amplifier). In [16, 17] such devices having noise temperatures in the60–70-K range are discussed. In [18] the performance of a 120-K active cold

load is presented.For satellite radiometers an antenna pointing toward free space is a very attractive cold calibration point. The cold space temperature can be launchedinto the radiometer input in two different manners: by switching the input away from the main antenna to some smaller antenna (sky horn) pointing toward freespace, or by diverting the main antenna beam away from the Earth’s surface




(including the limb of the atmosphere) through the use of some steerable mir-ror. The sky horn method is a possible and proven technique for single receiversystems. In the push-broom case, with a host of receivers, this solution is not

quite as attractive. The many sky horns would have to be mounted on the sur-face of the satellite to pick up radiation from free space and require a substantialamount of waveguide and switch hardware.

The method of diverting the main beam toward free space involves a mir-ror being moved slowly along the front of the feed horns, diverting the beamsone by one.

• Problem 1: Moving parts. However, the movement is slow, the moving

mass is small, and the action is not very frequent.• Problem 2: Architectural constraints for the spacecraft designer. Both

the normal antenna beam and the sky beam must be unobstructed by other sensors (equivalent to the sky horn situation described earlier).

• Great advantage: A very satisfactory calibration is carried out. The cali-bration includes the total sensor (apart from the main reflector) and noextra loss and complexity is introduced in the signal path through theuse of calibration switches.

Until now schemes have been discussed in which all radiometer receiversare individually calibrated to absolute accuracy. If this is deemed impossible, dueto some of the problems already mentioned, another fundamentally differentcalibration scheme can be proposed, namely, a two-step process: (1) relativeintercalibration of all sensors, and (2) absolute calibration of one (or a few) of the sensors.

1. Relative intercalibration. This is done entirely in the data analysis pro-cess after the radiometer system is operating in space. Incorrectintercalibration will result in banding in the radiometer imagery. By along-track integration, channel for channel, of long passes over openocean, a calibration vector arises. This integrated information is usedto adjust the calibration constants of the different receivers relative toeach other.

2. Absolute calibration of one or a few sensors. A small mirror beneaththe ray path to direct the beam toward free space, or a calibrationswitch leads the signal from a sky horn into the receiver input. In thiscase the sky horn solution is attractive, as it employs no moving partsand only requires a single sky horn and one switch. Care must beexercised when selecting this switch with regard to loss. Possibly a




A more in-depth consideration of the Faraday rotation is found in [20].From this, Figure 14.9 is taken. It shows the worst-case average rotation on12.00 UTC March equinox. The average over one month of the daytime maxi-

mum rotation is estimated to 28°, whereas monthly maximum averages at 6a.m. are around 5°. In addition, day-to-day variations can reach values within+100% to −50% of the averaged values due to the unpredictable nature of theionosphere.

Proposed missions generally have a 6 a.m. orbit, so from these consider-ations it is clear that the radiometer system has to cope with at least 5°, possibly up to 10°, Faraday rotation.

The polarization rotation will result in a slight mixing of the true vertical(T BV ) and horizontal (T BH ) brightness temperatures. A dual polarized radiometer

will thus measure:

′ = ⋅ + ⋅

′ = ⋅ + ⋅

T T T

T T T

BV BV BH

BH BV BH

cos sin

sin cos

2 2

2 2

θ θ

θ θ(14.1)

Typical values are T BV = 132K and T BH = 66K. Assuming θ = 10°, we find:

′ = ′ =T T BV BH 130 0 68 0. .K and K

The 2-K error in T BV translates into an error in retrieved salinity of about2–4 psu (depending on sea temperature), which is totally unacceptable.

14.7.2 Correction Based on Knowing the Rotation Angle

The set of equations (14.1) can be solved with respect to T BV , for example. Aftersome reductions, the following expression is found:

T T T tg

tg BV

BV BH =

′ − ′ ⋅

−

2

21

θ

θ(14.2)

Hence, if both the local vertical ( ′

T BV ) and horizontal ( ′

T BH ) brightnesstemperatures are measured, and θ is known, the true vertical brightness temper-ature can be found. The rotation angle can be calculated from the total electroncontents (TEC) maps available from a variety of sources. However, a self-stand-ing mission not dependent on the availability and accuracy of such externalsources can also be conceived as will be done in the following sections.




14.7.3 Correction Based on the Polarization Ratio

The true and the local polarization ratios are defined as:

R T T

R T

T

BV

BH

BV

BH

=

′ = ′

′

(14.3)

Inserting the expressions for the local brightness temperatures into theexpression for the local polarization ratio leads after some reductions to the fol-

lowing expression for the angle of rotation:

tg R R

R R 2

1θ =

− ′

⋅ ′ −(14.4)

Hence, if the true polarization ratio is known, the Faraday rotation can befound from measurements of the local polarization ratio.

Figures 14.10 and 14.11 have been generated from the model for the

brightness temperature emitted from the sea already discussed in connection with Figure 14.1, including the wind responses shown in Figure 14.2 (0.1K perm/s at V pol and 0.3K per m/s at H pol). From Figure 14.10 it is seen that the


1.900

1.920

1.940

1.960

1.980

2.000

2.020

2.040

2.060

2.080

2.100

0 5 10 15 20 25 30 35

SST (°C)

R0 psu

14 psu

22 psu

30 psu

38 psu

Figure 14.10 Polarization ratio (R) as a function of sea surface temperature (SST) with salin-

ity as parameter. Wind speed is zero.



true polarization only exhibits a marginal dependence on salinity and tempera-ture: R varies between 2.00 and 2.09 for SST ranging from 0–30° and salinity ranging from 0–38 psu.

The variations are typically much less for realistic conditions whereapproximate temperature and salinity values for a given area are known (fromclimatology and from other measurements). For example, for SST = 21 ± 1°Cand for S = 35 ± 1 psu, R varies between 2.061 and 2.068 corresponding to a 0.3% variation.

Figure 14.11 shows a much stronger dependence on wind speed with R variations from 2.06 down to 1.94 for wind speeds between 0 and 20 m/s (20°Cand 34 psu), that is, a 6% variation.

Hence, if the wind speed is known, the true polarization ratio (R ) can beestimated with good fidelity. By measuring the local ratio ( )′R , θ can then befound, and finally having this, the true vertical brightness temperature is foundusing the formulas shown earlier. Similarly, the true horizontal brightness tem-perature may be found.

Simple Example with No Measurement Errors Consider the following example:

• S = 34 psu;

• SST = 20°C;


1.900

1.920

1.940

1.960

1.980

2.000

2.020

2.040

2.060

2.080

2.100

0 5 10 15 20 25

WS (m/sec)

R

0 °C

10 °C

20 °C

Figure 14.11 Polarization ratio (R) as a function of wind speed (WS) with sea surface tem-

perature as parameter. Salinity is 34 psu.



• WS = 10 m/s.

From the ocean model is then found:

• T BV = 132.65K;

• T BH = 66.40K;

• R = 1.998.

Assuming a 10° Faraday rotation, the measured (local) brightness temper-ature values are found to be:

• ′T BV =130.65K;

• ′T BH = 68.40K.

If these values are used without correcting for the Faraday rotation, theretrieval would be incorrect. The H-pol value points towards lower salinity

while the V-pol value points towards higher salinity (bearing in mind that it issteadily assumed that the wind speed is known from other sources).

The measured local polarization ratio is R ′ = 1.910, the true polarizationratio R is known as the wind speed is known, so the Faraday rotation is foundfrom (14.4) to be θ = 10.02°, and from (14.2): T BV = 132.65K, meaning thatthe correct value of the 1.4-GHz vertical brightness temperature is recovered,and good quality geophysical parameters may be found.

14.7.4 Consequences for Instrument Design

Note that in order to correct for Faraday rotation, the radiometer system mustmeasure both vertical and horizontal polarizations. This doubles the number of receivers (weight and power consequences) and requires the feeds to be dualpolarized (design complexity but marginal influence on weight and power). Theantenna reflector serves both polarizations without problems.

It is noteworthy that a dual polarized system actually is optimum for thecombined sea salinity/soil moisture mission as this solves the problem that basi-cally sea salinity is primarily dependent on vertical polarized measurements

while the optimum polarization for soil moisture is horizontal.

14.7.5 Circumventing the Problem by Using the First Stokes Parameter

As it is obvious from the previous discussion, the radiometer needs to measureboth the vertical and the horizontal polarizations and by the addition of those




we have the first Stokes parameter [see (7.4)]. This parameter represents thetotal power in the electrical field, and it is totally invariant to Faraday rotation.Hence, if the geophysical parameters in question (here salinity) can be retrieved

as well from the first Stokes parameter as from the vertical polarization, the Fara-day problem is solved and need no further concern. This is largely the case:Salinity is found from the first Stokes parameter with good sensitivity, but theinfluence of wind is slightly larger. Thus we are faced with a choice: having tocorrect for both wind and Faraday each with their uncertainties (see Sections14.7.2 and 14.7.3), or just correcting for the wind with a slightly larger uncer-tainty (first Stokes). There is more information about this in [21].

14.8 Other Disturbing Factors: Space and Atmosphere

As already mentioned in Section 14.7, which deals with Faraday rotation insome detail since this effect has important consequences for instrument design,there are other disturbing factors that must be taken into account in order toobtain correct measurements of the radiated brightness temperature: space radi-ation and atmospheric effects. They will only be mentioned briefly here as theeffects and the way to correct for them has no consequences for the design of the

L-band radiometer—which is the subject of this chapter—although there may be important consequences for the data processing once the instrument is flying in space. More detailed information can be found in [22–24].

14.8.1 Space Radiation

Microwave power emitted from space will generally enter the antenna mainbeam through reflection in the sea surface. Three contributions must beconsidered:

1. The cosmic radiation is isotropic at a constant level of 2.8K, and thisbias does not affect measurement accuracy.

2. The galactic noise exhibits a great variation, depending on whether theantenna beam reflected in the sea surface looks toward the galactic poleor the galactic center (0.8K and 16K, respectively, at 1.4 GHz). Thiseffect must certainly be taken into consideration. Corrections must becarried out on the measured data, which is possible as the galactic noiseis well mapped.

3. Sun glint. The Sun is a very intense microwave emitter, with a bright-ness temperature dependent on solar activity, but always on the orderof 100,000K or more at the frequencies in question here. Direct Sunreflection in the sea surface must be avoided, which is best done by




choosing an early morning, Sun-synchronous, near polar orbit, forexample, a 6 a.m. orbit. This, in short, means that the equatorialascending passing takes place at sunrise, and the Sun will be almost

90° away from the look direction of the radiometer (forward-looking assumed). However, this is only a crude assessment, and at high lati-tudes—additionally bearing in mind that the radiometer has a certainswath width, and that under rough sea surface conditions, scatteredsolar radiation will be received from directions away from the speculardirection—some pixels will probably be contaminated by reflectedSun radiation. This requires detailed analysis and pixel flagging aspart of the data processing once the instrument is flying.

14.8.2 Atmospheric Effects

Absorption by water vapor is generally of great concern within microwave radiom-etry. However, for the low frequencies considered here, this effect can be neglected.

Also oxygen contributes to the atmospheric effects. The loss and reradiation due tooxygen contributes around 4.5K to the received brightness temperature, and mustbe corrected for. Moreover, the contribution is dependent on surface pressure andtemperature, but with a low sensitivity, which makes it easy to correct. Typical

clouds and rain rates give very low contributions and can be neglected (see [25].

14.9 Summary

A sea salinity/soil moisture sensor with a 1.4-GHz push-broom radiometer sys-tem as the core instrument has been described. The major characteristics of thesystem are:

• Antenna aperture: 10m;

• Polarization: vertical and horizontal;

• “Scan” angle: ±18°;

• Swath width: 530 km;

• Footprint: 36 × 60 km (47 km average);

• Number of channels: 21;

• Integration time: 6.4 seconds.

The system senses the Earth from an early (6 a.m.) morning Sun-synchro-nous 800-km orbit, and 2 × 21 = 42 noise-injection radiometers are used. Thedetailed characteristics are:




• Frequency: 1,404–1,423 MHz

• Noise temperature: 170K

• Sensitivity: 0.08K (for 6.4-second integration)

The radiometer system will consume 112W of prime power (84W forreceivers, 10W for data handling, and 18W for power supply).

The main antenna dimensions are:

• Reflector size: 10 × 18.6m;

• Focal length: 13.2m.

The total system weight is assumed to be 392 kg (150 kg for antenna,210 kg for feeds, 21 kg for receivers, 11 kg for miscellaneous electronics +

calibration).The 1.4-GHz radiometer system can measure sea salinity (S ) to better

than 0.3 psu, provided that sea surface temperature (SST ) is known to within0.3°C and wind speed (WS ) to within 1 m/s. This resolution in the salinity measurement corresponds to a snapshot measurement over the 47-km footprint.

Spatial or time averaging is possible in order to improve radiometric resolutionas sea salinity in the open ocean is generally a slowly varying parameter both intime and space. Averaging to 100-km ground resolution enables close to a 0.1-psu resolution in salinity measurements.

The 1.4-GHz radiometer system is well equipped for soil moisture mea-surements over land. The radiometric resolution is ample, and the 50-kmground resolution respectable—fitting well the resolution of present climatology and meteorology models, for which the L-band data will be an important input.

References

[1] Klein, L. A., and C. T. Swift, “An Improved Model for the Dielectric Constant of Sea Water at Microwave Frequencies,” IEEE Trans. on Antennas and Propagation, Vol. 25,No. 1, 1977, pp. 104–111.

[2] Hollinger, J. P., “Passive Microwave Measurements of Sea Surface Roughness,” IEEE Geoscience Electronics, Vol. 25, No. 2, 1971, pp. 165–169.

[3] Sasaki, Y., et al., “The Dependence of Sea-Surface Microwave Emission on Wind Speed,Frequency, Incidence Angle, and Polarization over the Frequency Range from 1–40GHz,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 25, No. 2, 1987, pp. 138–146.

[4] Blume, H. -J. C., and B. M. Kendal, “Passive Microwave Measurements of Temperatureand Salinity in Coastal Zones,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 20,No. 3, 1982, pp. 394–404.




[5] Blume, H. -J. C., B. M. Kendall, and J. C. Fedors, “Measurement of Ocean Temperatureand Salinity Via Microwave Radiometry,” Boundary-Layer Meteorology, Vol. 13, 1978,pp. 295–308.

[6] Blume, H. -J. C., et al., “Radiometric Observations of Sea Temperature at 2.65 GHz over

the Chesapeake Bay,” IEEE Trans. on Antennas and Propagation, Vol. 25, No. 1, 1977,pp. 121–128.

[7] Wilson, W. J., et al., “L/S-Band Radiometer Measurements of a Saltwater Pond,” IEEE Proc. of IGARSS’02, 2002, pp. 1120–1122.

[8] Champs, A., et al., “Sea Surface Emissivity at L-Band: Derived Dependence with Inci-dence and Azimuth Angles,” Proc. of EuroSTARRS, WISE, and LOSAC Workshop, ESA SP-525, 2003, pp. 105–116.

[9] Schmugge, T. J., “Remote Sensing of Soil Moisture: Recent Advances,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 21, No. 3, 1983, pp. 336–344.

[10] Gudmandsen, P., N. Skou, and B. Wolff, (eds.), Spaceborne Microwave Radiometers, FinalReport, ESTEC Contract No. 4964/81/NL/MS/(SC), Electromagnetics Institute, Tech.University of Denmark, R 267, 1983.

[11] Ruf, C. S., “Vicarious Calibration of an Ocean Salinity Radiometer from Low EarthOrbit,” American Meteorological Society, J. of Atmospheric and Ocean Technology, Vol. 20,No. 11, 2003, pp. 1656-1670.

[12] Fischman, M. A., and A. W. England, “Sensitivity of a 1.4 GHz Direct-Sampling DigitalRadiometer,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 37, No. 5, 1999,pp. 2172–2180.

[13] Rotbøll, J., S.S. Søbjærg, and N. Skou, “A Novel L-Band Polarimetric Radiometer Featur-ing Subharmonic Sampling,” Radio Science, Vol. 38, No. 3, 2003, pp. 11-1–11-7.

[14] Pontoppidan, K., and N. Skou, Microwave Radiometry Study Concerning Push-Broom Sys- tems, Final Report, ESTEC Contract NO. 6374/85/NL/GM(SC), Vol. 1:Electromagnetics Institute, R 332, Vol. 2: TICRA A/S, 1986.

[15] Skou, N., and S. S. Kristensen, “Comparison of Imagery from a Scanning and a Pushbroom Microwave Radiometer,” IEEE Proc. of IGARSS´91, 1991, pp. 2107–2110.

[16] Frater, R. H., and D. R. Williams, “An Active ‘Cold’ Noise Source,” IEEE Trans. on

Microwave Theory and Techniques, Vol. 29, No. 4, 1981, pp. 344–347.[17] Forward, R. L., and T. C. Cisco, “Electronically Cold Microwave Artificial Resistors,”

Trans. on Microwave Theory and Techniques, Vol. 31, No. 1, 1983, pp. 45–50.

[18] Randa, J., L. P. Dunleavy, and L. A. Terrell, “Stability Measurements on Noise Sources,”IEEE Trans. on Information and Measurement, Vol. 50, No. 2, 2001, pp. 368–372.

[19] Hollinger, J. P., and R. C. Lo, Low-Frequency Microwave Radiometer for N-ROSS, Large Space Antenna Systems Technology, NASA Conference Publication 2368, 1984, pp. 87-95.

[20] Svedhem, H., Ionospheric Delay and Faraday Rotation at Microwave Radiometer Frequen- cies, ESTEC Report TRI/075/HS/mt, 1986.

[21] Skou, N., “Faraday Rotation and L-Band Oceanographic Measurements,” Radio Science,Vol. 38, No. 4, 2003, pp. 24-1–24-8.

[22] Yueh, S. H., et al., “Error Sources and Feasibility for Microwave Remote Sensing of OceanSurface Salinity,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 39, No. 5, 2001,pp. 1049–1059.




[23] Le Vine, D. M., and S. Abraham, S., “The Effect of the Ionosphere on Remote Sensing of Sea Surface Salinity from Space: Absorption and Emission at L Band,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 40, 2002, pp. 771–782.

[24] Le Vine, D. M., and S. Abraham, “Galactic Noise and Passive Microwave Remote Sensing

from Space at L Band,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 42, 2004,pp. 119–129.

[25] Skou, N., and Hoffmann-Bang, “L-Band Radiometeres Measuring Salinity from Space: Atmospheric Propagation Effects,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 43,No. 10, 2005, pp. 2210–2217.




15Examples of Synthetic ApertureRadiometers

15.1 Introduction

This chapter gives a brief discussion of the trades involved in designing a syn-thetic aperture radiometer for Earth remote sensing and then illustrates the con-cepts with two synthetic aperture radiometers. The first is an existing aircraftsensor called, ESTAR. ESTAR played an important role in the development of this technology for remote sensing and provided data to demonstrate the poten-tial for remote sensing of soil moisture from space. A brief overview is given of the hardware and the techniques employed for image reconstruction and cali-bration. An image is shown from the soil moisture experiment at the WalnutGulch Watershed an experiment that was critical in demonstrating the viability of this technology. The second example is a sensor called HYDROSTAR. Thisis an instrument that was proposed for remote sensing from space. Although

HYDROSTAR was never actually flown, it does illustrate the potential of aper-ture synthesis for remote sensing from space. Design parameters are giventogether with expected performance. This instrument is similar in principle tothe aircraft instrument, ESTAR; however there are many ways in which aperturesynthesis could be implimented in space. In fact, at the time of this writing, a mission called SMOS that uses synthesis with small antennas arranged in theform of a Y is being built by the European Space Agency (ESA) for remotesensing of soil moisture and ocean salinity from space.

197



15.2 Implementation of Synthesis

The primary penalty paid for employing aperture synthesis is a decrease in signal

to noise for each measurement (baseline) compared to a filled aperture. Thisoccurs because each measurement in the synthesis array is presumably made

with antennas much smaller than a single antenna with resolution equivalent tothat of the synthesized array (e.g., to take advantage of array thinning that ispossible with synthesis). The result is a potential worsening of radiometric sensi-tivity (RMS noise) in the image [e.g., see (8.7)]. However, since no scanning isnecessary in aperture synthesis, the time per measurement can be increased,

which improves the time-bandwidth product. Also, the image is comprised of

many measurements (baselines). Because of these two factors, it is possible even with minimum redundancy configurations (configurations with a minimum of repeated baselines) to approach the radiometric sensitivity of an equivalent realaperture radiometer [1, 2].

The art in applying aperture synthesis is finding configurations that permitsubstantial thinning of the array (e.g., to save mass in remote sensing fromspace) and at the same time achieving radiometric sensitivity commensurate

with the science requirements for the observable. In practical remote-sensing sit-uations observation, time is limited by the motion of the spacecraft (about 7

km/sec in low Earth orbit) or by the time constant of the observable. Figure 8.3illustrated a concept suitable for remote sensing from geosynchronous orbit

where, because there is no relative motion of the spacecraft, the time to form animage and the size of the synthesis array (number of baselines) is limited by thetime constant of the geophysical observable. On the other hand, Figure 15.1illustrates two configurations that are practical when the spacecraft is moving rapidly with respect to the surface as, for example, in remote sensing from low Earth orbit. The example in Figure 15.1(a) is a combination of a real and a syn-

thetic aperture antenna. The real antennas are “stick” antennas oriented withtheir long axis in the direction of motion. The stick antennas produce a narrow fan beam with good resolution along track and essentially no resolution in theacross track dimension. Resolution across track is obtained using aperture syn-thesis. A configuration of this type can reduce the antenna aperture needed inspace by about 80% and still obtain radiometric sensitivity comparable to a realaperture [1–3]. This is the configuration used in the aircraft prototype ESTAR and proposed for HYDROSTAR, the instrument proposed for measuring soil

moisture from space. The example in Figure 15.1(b) is a concept for employing aperture synthesis in both dimensions. In this example small antennas arearranged along the arms of a cross and the necessary baselines are obtained by making measurements between all independent pairs of antennas. This configu-ration can have spatial resolution comparable to a filled aperture with thedimensions similar to those of the arms. The compromise one makes in using




aperture synthesis in a configuration such as this is a potential loss of radiometricsensitivity because the array is so highly thinned. There is also increased process-ing complexity because the number of products that must be measured growsrapidly as the array is thinned. However, the advantage in terms of weight andmechanical simplicity of such a senor can be very important. Many variations onthis theme are possible. Aircraft instruments with antennas arranged in “Y” and“U” configurations are being built [4, 5] and an instrument in space is being built using the “Y” configuration [6]. The “Y” is an important configurationbecause it minimizes the number of redundant baselines, although it is not

Examples of Synthetic Aperture Radiometers 199

Small antennas

(a)

(b)

Figure 15.1 Two configurations showing how aperture synthesis might be implemented for

remote sensing from space. (a) A hybrid that uses aperture synthesis only in the

across-track dimension. (b) A configuration employing small antennas along thearms of a “cross” that uses aperture synthesis in both dimensions.



necessarily the most efficient in terms of the number of antennas needed for a given resolution.

15.3 Airborne Example: ESTAR

15.3.1 Hardware

To illustrate how aperture synthesis can be implemented in practice, the air-borne sensor called ESTAR will be used as an example. This is an existing instrument that is important because it helped to demonstrate that aperture syn-thesis was practical for passive microwave remote sensing and in particular for

sensing soil moisture and ocean salinity.ESTAR was developed at NASA’s Goddard Space Flight Center inGreenbelt, Maryland, and at the University of Massachusetts in Amherst, Mas-sachusetts [7, 8]. It is an L-band radiometer in the hybrid configuration shownin Figure 15.1(a). It was designed for remote sensing of soil moisture where theneed for large apertures is greatest because the measurement of soil moisture isbest done at long wavelengths. (Long wavelengths are needed to penetrate intothe soil and through the vegetation canopy.) The hybrid configuration wasadopted because it is practical for application in space and because it involves

relatively simple processing compared to configurations that employ thinning inboth dimensions.

The real antennas that comprise the thinned array in ESTAR are lineararrays of horizontally polarized dipoles. In operation, these antennas are oriented

with their long axis in the direction of motion [Figure 15.2(a)]. The stick anten-nas produce a narrow fan beam with good resolution along track but essentially no resolution in the across track dimension. The resolution across the track isobtained using aperture synthesis. ESTAR has five stick antennas that are spaced

at integer multiples of a half-wavelength (about 10.6 cm at the center frequency of 1.413 GHz). Each stick antenna consists of a row of eight dipoles [Figure15.2(b)]. With this configuration of sticks employed in ESTAR, it is possible toobtain seven unique baselines plus one at the zero spacing. The result is a synthe-sized beam with a width of about ±4° at nadir in the cross track dimension. Theresolution in the along track dimension is determined by the real aperture and isabout ±8°. An image is formed by placing the across-track images edge to edgeduring successive integration periods. This is similar to a raster scan in a conven-

tional cross-track scanner except that in the synthesis radiometer the cross-track image is created in software and there is no mechanical motion of the sensor.The actual antenna hardware is shown in Figure 15.3. The instrument is

shown in Figure 15.3(a) as it was installed on an Orion P-3 aircraft in prepara-tion for test flights. The white structure at the bottom of the instrumentationbox is a radome covering the stick antennas. The RF circuitry is housed inside




The dimensions of this particular instrument were determined by the sizeof a radiometer it replaced on the aircraft because it had to fit into the samespace. It was not intended to be an optimum structure. In fact, among the inter-esting problems in aperture synthesis are issues of optimization such as: (1)determining the configuration that gives the maximum baseline with a givennumber of antennas; or, conversely, (2) determining the minimum number of antennas needed for a given maximum baseline. In each of these problems, thespacing is a multiple of a fixed minimum and it is required that all baselines aremeasured at least once. For example, if size were not a problem what would be

the optimum configuration for ESTAR if it had six antennas and wanted maxi-mum resolution? Solutions to these problems can be found by trial and error,and there tend to be many solutions. Unique solutions have been found only fora few very simple special cases. Hence, there is a lot of variability possible even inoptimum designs.


(a)

(b)

Figure 15.3 (a) The ESTAR antenna array. (b) The ESTAR array with the radome removed so

that the stick antennas can be seen. At the top is the box mounted in the bomb

bay of an Orion P-3 ready to fly.



The raw data output in ESTAR consists of seven complex voltages (thein-phase and quadrature output from the correlators at each of the seven inde-pendent, nonzero baselines), plus a total power measurement at the zero spac-

ing. These can be expressed analytically using (8.3) specialized to the case of synthesis in one-dimension. Denoting the measurements with the integer m(i.e., m = 0, 1, 2, …, 7) corresponding to the length of the baseline in multiplesof λ/2, and substituting into (8.3), the correlator output, V (m ), can be written inthe form:

( ) ( ) ( ) ( )V m C T P m e d D m jm

m = +−

+

∫ θ θ θ π θ

π

π

, sin

2

2

(15.1)

where θ is the incidence angle in the across-track dimension measured fromnadir, T (θ) is the microwave “brightness” temperature of the scene, and P (m , θ)is the product of the “voltage” patterns of the two antennas employed in thisbaseline. When the antennas are identical, P (m , θ) reduces to the conventional“power” pattern of the antenna and is proportional to its gain. The constant C m

is a scale factor which includes the gain of the RF system and must be deter-mined as part of the calibration procedure. The coefficients D m are constants

which were added in the analysis of ESTAR to accommodate the circuitry usedfor the zero spacing channel (a noise injection radiometer) and to account forbiases (offsets) present in the early versions of the correlator circuitry. Anotherreason for including the offsets is the possibility of coupling between receivers asexplained by Corbella et al [9]. The D m are small except in the case of thezero-spacing and are determined during calibration. Equation (15.1) is complex and the coefficients C and D are in general complex (representing phase differ-ences in the signal paths for each receiver).

In the ideal case when P

(m

, θ) and C m

are independent of m, a change of variables such as employed to write (8.5) permits (15.1) to be written in theform of a Fourier transform. In this case it is possible, at least in principle, toinvert the transform to find T (θ) in terms of the correlator outputs V (m ) andbiases, D m . This is the theoretical basis for aperture synthesis. However, in theactual case, several obstacles must be overcome to achieve the inversion. First,V (m ) is not known at a continuum of points spanning the desired spectraldomain. For example, in ESTAR V (m ) is known only at a relatively small subsetof discrete points corresponding to the seven baselines. Second, the unknown

scale factors, C m , are not known a priori and may be different for each baseline(because the gains and phase paths are different) and may change (because gainsdrift). Third, the individual antenna patterns are not truly identical (e.g.,because of mutual coupling and coupling to the structure). In ESTAR the P (m ,θ) are different for each antenna pair [10]. Finally, the offsets D m may not be




zero and must be determined for each baseline. One procedure to account forthese deviations from the ideal is to perform a numerical inversion of (15.1)using parameters of the instrument measured in the laboratory. This procedure

is outlined in the following sections.

15.3.2 Image Reconstruction

In the case of ESTAR an inversion was obtained by replacing the integral in(15.1) by its approximating sum and, thereby, reducing (15.1) to a matrix of algebraic equations. In this procedure, the scale factors, C m , are written C m = C o

αm , where C o is a constant, independent of m , which converts the ESTAR out-put to units of brightness temperature. The αm represent differences in gain and

phase among channels (baselines). Absorbing the unknowns αm into the matrix,G, (15.1) becomes:

V C G T D k i

ki i k = +∑0 (15.2)

where the symbol Σ i means that the sum is over the index “i”. The odd values of k (i.e., k = 2m + 1) correspond to the in-phase output of the correlator [real partof (15.1)] in which case

( ) ( )[ ]G P m m ki k i i = α θ π θ θ, cos sin ∆ (15.3a)

and the even values of k (i.e., k = 2m) correspond to the quadrature output of the correlator, in which case

( ) ( )[ ]G P m m ki k i i = α θ π θ θ, sin sin ∆ (15.3b)

In the case of the zero spacing radiometer, m = 0, k = 1 and (15.3a) applies.In ESTAR there are 15 values V k (one for the zero spacing and two each

for the seven nonzero baselines). In this case, G ki is a matrix with 15 rows (K =15) and N columns where N is the number of terms in the approximating sumfor the integral in (15.1). The number, N , is somewhat arbitrary. In ESTAR, N = 91 which corresponds to ∆θ = 2° in the approximating sum. Compare this

with the synthesized beam which has a beam width (distance between zeros) of about 8° and is an indication of the resolution of the instrument (see Section

8.3). The feature that makes (15.2) useful is that the G ki are measurable parame-ters of the instrument. They are the impulse response of the sensor and can bemeasured in a conventional antenna chamber by looking at a point source. Insuch a situation, N is determined by the number of positions at which the pointsource is observed.




Assuming that the G ki have been measured, an image is formed by solving (15.2) for the N values of T i . The data are the K measurements, V k . This systemof equations is underdetermined (N > K ); however, a solution can be found by

imposing a secondary condition (e.g., minimizing the square error when com-pared to the ideal solution). In particular, the matrix equation, V = GT where G is N × K with N > K , has a minimum least square solution T ′ of the following form [11]:

[ ]{ }′ = −

T G GG V t t 1(15.4)

where G t [GG t ]−1 is called the “pseudo” inverse (and the superscript “t” denotesthe transpose of the matrix). In most of the work done with ESTAR, imagereconstruction in the form of Equation 15.4 has been employed. The image is:

[ ]{ }[ ]T G GG V D C t t = −−1

0 (15.5)

In (15.5), V is a vector of measured “visibilities,” G is a characteristic of the instrument (and measured in the laboratory), and D and C o are unknowns

that are determined by looking at known sources during “calibration.”

15.3.3 Calibration

In an ideal system (C o = 1 and D k = 0) the rows of G are just the instrument out-put, V , when the input, T , is a point source (a vector with zeros everywhereexcept at one position, θ

i

= θi =

n

). Hence, the elements, G ki

, can be measured inthe laboratory by letting the instrument view a point source and then moving the point source sequentially to positions from −90o < θ < 90o so as to movethrough the columns of G . In practice this is done in an antenna chamber by putting a source at one end, and rotating the antenna array at the other end

while continuously monitoring the output, V k , from each of the channels.One must also account for system biases, D , and the background radiation

emanating from the chamber. One way of doing this is to take the difference of measurements, first with the source on and again with the source off. For exam-

ple, assume that the background is constant (a good assumption if the measure-ments are made in an antenna chamber). Letting this constant be T BB , oneobtains the following with the source off:

( )V Off C T G D k o BB i

ki k = +∑ (15.6a)




When the source is on, the instrument also receives radiation from thesource T s . Thus:

( ) [ ]V On C T G T G D k o BB i

ki s kn k = + +∑ (15.6b)

where it is assumed the source is in position, n . Taking the difference, oneobtains

( ) ( ) ( ){ }G C T V On V Off kn o s k k = −1 (15.7)

By changing the position “n” of the source relative to the antenna array,one can determine all the columns of G ki . For example, ESTAR uses 91 posi-tions of the point source, corresponding to source positions from +90o to –90°in two-degree increments.

The ESTAR instrument records the output from all the baselines simulta-neously. Hence, in the anechoic chamber measurements are actually made of allthe k -rows of G ki at the same time. This is important because it means that rela-tive differences between channels are correctly represented even though the con-

stants, C o and T s , may not be known. Phase and gain introduced in the RF pathare removed using an internal reference (calibration) source. One possibility is a stable noise source with a switch at the antenna terminals that periodically switches from the antennas to the noise source. While in the “calibrate” modethe instrument output, V k , is proportional to the complex gain of each correlatorchannel [in effect proportional to the αk in (15.3)]. By dividing the raw ESTAR data by the output signal when in the calibrate mode, the αk are in effect can-celed and only one gain constant, C o , remains to be determined. A similar proce-dure, although with a more complex distribution network has been adopted forthe spacecraft sensor being developed for the SMOS mission [4, 12].

The remaining step is to determine the constants C o and D k in (15.2). Thiscan be achieved by viewing two scenes with known brightness temperature. Theconstants are determined by comparing the measured output V k with the theo-retical output of the test scene. This is analogous to calibration in a conventionaltotal power radiometer, except that “calibration” constants must be determinedfor several channels (one for each V k ). In practice, a linear regression is used in

which values of C o and D k are chosen which give an optimum fit of the measured

visibilities to the theoretical values. For example, test scenes used for ESTAR have been scenes such as a blackbody (e.g., the antenna chamber) and water(e.g., a large lake). The former is warm (300K) and the later cool (around 100K)at L-band.




15.3.4 Discussion

Let G ′ = G i t [GG t ]−1 denote the pseudo-inverse and let V k ′ be a set of visibilitiesnormalized by subtracting D k and dividing by C o as in (15.5). Then, the solution

of (15.1) is:

′= ′ ′∑T G V i k

ki k (15.8a)

[ ]= ′∑ j

ij j G G T (15.8b)

where T j is the matrix of brightness temperatures representing the actual scene.In the ideal case (identical antennas and receivers), the rows of [G ′G ] are iden-tical but shifted and (15.8b) has the form of a discrete-valued convolution: theconvolution of the i th row of the matrix [G ′G ] with the scene T j . In this case(15.8b) is the discrete analog of the conventional expression for the response of an antenna with power pattern P (θ) to a thermal source (incoherent radiation)

with effective temperature T (θ) [13]:

( ) ( ) ( )′ = − ′ ′ ′∫ T P T d θ θ θ θ θ (15.9)

Writing (15.9) as a sum (i.e., replacing the integral by its approximating sum) and comparing with (15.8b), one sees that each row of [G ′G ] correspondsto P (θ – θ′) at a particular value of θ. In other words, the rows of [G ′G ] repre-sent the power pattern of the “synthesized” antenna.

Figures 15.4 through 15.6 show examples for an ideal ESTAR. Figure15.4 is a plot as function of θ of the numbers in the rows of the matrix G corre-sponding to a baseline with spacings of 2 λ and 7 λ/2 (m = 4 and 7). The solidcurve is the even term (in phase) and the dashed curve is the odd term (quadra-ture). Examples of the synthesized antenna pattern are shown in Figure 15.5.These are examples of the rows of [G ′G ]. Curves are shown for the rows corre-sponding to viewing angles of 0°, ±20°, and ±30°. For comparison the ideal pat-tern of one of the stick antennas (a linear array of eight dipoles) is shown inFigure 15.6 plotted with the synthesized beam at nadir (0°). The two have beennormalized to have the same peak value. The pattern (power pattern) of the stick is approximately ±8° wide at the half-power points (a linear array of eightdipoles spaced λ/2 apart). The pattern of the nadir pointing beam synthesized

by ESTAR is narrower at half-power by about a factor of two (±4°). This is a characteristic of interferometers that is possible because of the complex conju-gate baselines. Notice the large sidelobes of the synthesized pattern. This is also a characteristic of aperture synthesis. The sidelobes can be reduced at the expenseof resolution (broadening of the main beam) by weighting the visibilities during




image reconstruction [11]. Also notice (see Figure 15.5) that not all of the syn-thesized beams are identical.

Noticeable broadening occurs at large viewing angles. Examples for theactual ESTAR instrument are shown in [8]. If one limits the field of view of the

synthesized image to angles for which the synthesized beams are essentially iden-tical, then one can think of the image reconstruction described above as a scan of an effective antenna beam (e.g., the solid line shown in Figure 15.6) across thescene. The important point is that this scan takes place in software (i.e., instan-taneously) and one does not have to account for scan time as in a conventionalcross-track scanning radiometer.

15.3.5 Example of Imagery

The ESTAR instrument was an important step in demonstrating the potentialof aperture synthesis for passive microwave remote sensing at long wavelengths,and it played an important role in the development of remote sensing of soilmoisture. It provided data to support development of algorithms to retrieve soilmoisture in experiments such as at the Little Washita Watershed in 1992 [8, 14]


−50

−50

−0.5

−0.5

0

0

−1

−1

0.5

0.5

1 A

m p

l i t u d

e ( r

e l a t i v e

)

1

−40

−40

−30

−30

−20

−20

−10

−10

0

0

10

10

20

20

30

30

40

40

50

50Angle (degrees)

Figure 15.4 Rows of the matrix G for a spacing of (a) 2 λ and (b) 7 λ /2 corresponding to m = 4,7 respectively in (15.1). The solid line is the inphase term and the dashed line is

the quadrature term.



and the Southern Great Plains experiments in 1997 and 1999 [15, 16]. It alsoplayed an important role in demonstrating the potential for remote sensing of

sea surface salinity in experiments such as the Delaware Coastal CurrentExperiment [17].Figure 15.7 is an image made by ESTAR in Viginia, south of the border

with Maryland. The Chesapeake Bay is to the left and the Atlantic Ocean is tothe right and the land area is called the “Delmarva” Penninsula. The axes arelabelled in latitude (abscissa) and longitude (ordinate). As a reference, 37.5°Nlatitude is approximately due east of Richmond, Virgina. Images such as this

were made as part of calibration and instrument checks prior to major cam-paigns such as the Southern Great Plains experiments mentioned earlier. This isa good region to test an imaging L-band radiometer because of the high radio-metric contrast between land and water and the abundance of detail to testimage quality. This image is a composite of data collected on five different occa-sions from September 1995 to August 1999. The regions can be distinguishedby the slightly different mean brightness temperatures. (See [18] for a color


−0.4

−0.2

−50 −40Angle (degrees)

A m p

l i t u d

e ( r

e l a t i v e

)

−30 −20 −10 0 10 20 30 40 50

0

0.2

0.4

0.6

0.8

1

Figure 15.5 Examples of the synthesized antenna pattern. Patterns are shown with pointing

angles (boresite) of 0, ±20 and ±30 degrees. The units on the ordinate are rela-

tive amplitude.



image.) Each subimage consists of about four lines flown East-West at an alti-tude of 2,000 feet. The ESTAR brightness temperature map has been superim-posed on the geographical map indicating the peninsula boundaries and

streams. Another example is shown in Figure 15.8. This is an example from mea-surements made at the USDA’s Walnut Gulch watershed near Tombstone, Ari-zona, during soil moisture measuring experiments in 1991 [8, 14]. This was animportant experiment because it demonstrated that images of scientific quality could be obtained with this technique. ESTAR made two flights during thisexperiment, one on August 1 and again on August 3. Prior to August 1, a smalllocalized rainfall event occurred at the watershed very near the center of thestudy area. On the afternoon preceding the second flight (August 3), a largethunderstorm occurred over the watershed centered near the western edge of thestudy area (left-hand side of Figure 15.8). This storm was localized to the west-ern two-thirds of the watershed. The eastern edge of the watershed received very little rainfall during this storm. The rainfall patterns are evident in the image.The effect of the small, isolated rainfall event prior to the flight on August 1 is


−0.4

−0.2

−50 −40Angle (degrees)

A m p

l i t u d

e ( r

e l a t i v e

)

−30 −20 −10 0 10 20 30 40 50

0

0.2

0.4

0.6

0.8

1

Figure 15.6 Comparison of the synthesized beam (solid line) with the power pattern of a lin-

ear array (dashed line) of similar size (7 half-wavelengths).



clearly evident near the center of the image for August 1 (top). Similarly, the leftside of the image for August 3 clearly shows the effects of the thunderstorm inthe western portion of the watershed. Comparison of the two images shows a dramatic decrease in brightness temperature on the western edge of the water-shed (left) due to the rainfall and an increase in brightness temperature on the

eastern side of the watershed (right) indicative of the drying which took placeover this portion of the watershed between the two flights. For a quantitativecomparison of the ESTAR data with ground truth, see [8, 16], and for a colorversion of this image, see [8].

15.4 Spaceborne Examples

15.4.1 HYDROSTAR

A synthetic aperture radiometer designed to obtain global maps of soil moistureand sea surface salinity from space was proposed to NASA in the late 1990s inresponse to a call for Earth System Science Pathfinder missions. The instrument

was called HYDROSTAR and was patterned after ESTAR. It employed


Longitude

L a

t i t

u d

e

−75.90 −75.80 −75.70 −75.60

37.50

37.55

37.60

37.65

37.70

Brightness [K]

71 103 131 145 159 173 187 201 215 229 243 257 271 285 299 313

Figure 15.7 ESTAR images of the Delmarva Peninsula. This is a composite from five differ-ent flights conducted from 1995 to 1999.



aperture synthesis in the across track dimension, operated at L-band with hori-zontal polarization, and employed electronics and calibration schemes validatedby ESTAR. By employing aperture synthesis in the cross-track dimension, theaperture needed in space was reduced to less than 20% of that needed for a filled

aperture of the same resolution, and the need for mechanical or electricalmotion (scanning) was eliminated.

The salient features of HYDROSTAR are summarized in Table 15.1. Thescience objectives of the HYDROSTAR mission were primarily driven by therequirements for the measurement of soil moisture. Hence, the mission calledfor observations at a constant local time (Sun synchronous orbit) with a revisittime with global coverage of 3 days or less. The HYDROSTAR mission calledfor a 670-km orbit with a 6 a.m. equatorial crossing and it achieved the desired

revisit time by processing in the cross track dimension to ±35°.HYDROSTAR is shown in its deployed configuration in Figure 15.9. The

instrument was composed of three major subsystems: the antenna system, whichincludes the stick antennas and the deployment structure, the RF system, whichincludes the front end and other radiometer RF electronics, and the signal


195 285

Brightness [K]

August 3

August 1

Figure 15.8 ESTAR images of the Walnut Gulch Watershed during flights on August 1 and

August 3, 1991. The cool temperatures are an indication of an increase in the

moisture in the soil following a thunderstorm prior to the flight on August 3.



processing system, which includes the A/D conversion and digital correlators. All of the radiometer electronics with the exception of the RF front ends are

located together near the spacecraft. The RF front ends are located at the anten-nas and are connected to the radiometer electronics at the spacecraft withlow-loss coaxial cable. In its normal operating mode, the integration time perimage is 0.5 second and a noise diode is used for internal calibration as inESTAR. Absolute calibration is accomplished using reference scenes in a manner similar to that described above for ESTAR.

HYDROSTAR employed 16 antennas arranged in a minimum redun-dancy. The minimum spacing is a half-wavelength and the antenna array has 90

independent baselines at integer multiples of a half-wavelength. The array spans9.5m in the across-track dimension. Each antenna in the array is a rectangular

waveguide stick 5.8m long. The waveguide has 36 slots inclined to produce hor-izontal polarization and cut in the narrow wall of the guide. Each stick has analong track beamwidth of 2.3° at band center corresponding to a resolution of about 30 km at nadir from the 670-km orbit. Because wave guides arenarrowband devices, operation over the desired bandwidth is obtained by subdi-viding each stick into four resonant subarrays of nine slots, each coupled

together with a flexible combining network. The antennas are fabricated incomposite to minimize weight and maximize rigidity and thermal stability. Theresolution across-track matches the along-track resolution at the swath edge(±35o). At nadir, the across-track resolution of the synthesized beam has a peak-to-null beamwidth of 1.2° corresponding to about 15-km resolution.


Table 15.1

Parameters of the Proposed HYDROSTAR Mission

Mission Instrument

Coverage Global Frequency L-band (1.413 GHz)

Revisit 3 days Polarization Horizontal

Orbit 670 km FOV ±450 km

Sunsynchronous Pointing Nadir

6 a.m. ascending Dimensions 5.8 × 9.5m

Antennas 16 waveguide sticks

Resolution 30 km (15 km across track)

Sensitivity 1K

Accuracy 3K (or better)

Mass 500 kg

Power 350W



For launch, the antennas are folded and the array compressed. The deploy-ment sequence on orbit is shown in Figure 15.10. For launch, the waveguidesare collapsed into two wings of eight waveguides each. Each antenna consists of four subantennas and, in the stowed position, the outer segments of each wave-guide are folded 180° and rest on the inner segments. To deploy the antenna array, three separate steps are required. First, the spring-loaded waveguide outersegments immediately rotate 180° and latch to their full extension. Next, each

wing is rotated into the observing plane (rotated 90°). Finally, the waveguidesare extended on the hinged truss to the required position.

15.4.2 SMOS

Although HYDROSTAR was a viable sensor and development proceeded to thepoint of testing a full-sized scale model of the antenna array, it was never built.

However, a synthetic aperture radiometer has been selected by the EuropeanSpace Agency (ESA) and is under development as the second Earth ExplorerOpportunity Mission within ESA’s Living Planet Program. This is also anL-band instrument designed for remote sensing of soil moisture and ocean salin-ity. It employs aperture synthesis in two dimensions and is dual-polarized [6,12]. The instrument in its original design, called MIRAS (Microwave Imaging


Figure 15.9 HYDROSTAR in its deployed configuration. The synthesis array consists of 19

waveguide antennas. Each antenna is comprised of four subelements.



Radiometer using Aperture Synthesis), was also dual frequency (L-band andC-band); however, in the final design, only the L-band channel was kept. Themission is called SMOS (Soil Moisture and Ocean Salinity) and is scheduled forlaunch in 2007.

Figure 15.11 is an artist’s concept of the SMOS spacecraft showing the

instrument and the deployment sequence. The sensor employs an array of antennas arranged in a “Y” configuration. Each row in the “Y” consists of 21contiguous antenna elements uniformly spaced at 0.875 wavelength. There are a total of 69 antenna elements in the array. The remaining six antenna elementsare arranged in pairs between the arms in the central “hub.” The innermost ele-ment in each pair is connected to a noise injection radiometer and provides thedc value of the image (that is, the zero-space baseline). The outer element ineach pair is a correlation radiometer and is also used in the image reconstruction.

In the deployed position the plane of the Y is tilted with respect to nadir.The plane of the Y is tilted forward at about 32.5°. This was done in order toincrease the incidence angles at the surface and thereby enhance the differencebetween the two polarizations. The antennas are dual-polarized and the instru-ment can operate in two modes: dual polarization in which it measures both


4.

1. 2.

3.

Figure 15.10 The deployment sequence for HYDROSTAR. Deployment starts at the top left

(1). The sticks unfold (2), rotate (3) and the spread to their final positions (4).



vertical and horizontal polarization and fully polarimetric in which the crossterm is also measured. Internal calibration is provided by a distributed noisesignal.

Mechanically the instrument consists of the central hub and three deploy-able arms. Each arm consists of three sections that are folded at launch. Figure15.11 shows the solar panels and arms as they deploy after launch and also thefinal configuration when fully deployed. The length of each arm is 4.0m. The

effective resolution on the ground varies across the footprint because of the largerange of incidence angles. On average the resolution is on the order of 43 kmand the useful swath across-track is about 1,060 km.

The antenna spacing and forward-looking geometry present some interest-ing issues for SMOS. In particular, the antenna spacing admits grating lobes inthe reconstructed image so that only a portion of the field of view is useful [12].Because of the large amount of thinning, the RMS noise in each snap shot (oneintegration period) is relatively large. However, because many pixels appear in

more than one snap shot, averaging is possible to reduce the noise. Another interesting feature of this instrument is the use of 1-bit digitalcorrelators for each of the baselines. This introduces additional noise, butreduces the complexity and power requirements of the correlator circuitry. Italso requires a different type of radiometer for the zero spacing to provide the dcsignal. As mentioned earlier, a noise injection radiometer (see Chapter 4) has


Figure 15.11 The SMOS mission showing the deployment sequence and the MIRAS instru-

ment in its deployed configuration. The small circles along the arms of the “Y”

are the individual antennas in the synthesis array. [Courtesy of EADS (Euro-

pean Aeronautic Defense and Space)–CASA Espacio and ESA.]



been chosen for this application. Finally, in its deployed configuration, the sen-sor is very big. This makes direct measurement of its impulse response (the

G-matrix discussed in Section 15.3.2) in an antenna chamber very difficult. Alternatives such as modeling from measurements of the instrument subsystems with verification by observing reference targets on orbit are being considered.

The characteristics of the instrument and mission are summarized inTable 15.2. Monolithic microwave integrated circuits (MMICs) are employedfor the receivers, which amplify and downconvert. The baseband signals are dig-itized at 1 bit and routed via optical fiber to a central processor. Approximately 3,500 complex correlations are required. The antennas are dual-polarized

dipoles implemented with multilayer microstrip circuitry. They are about 16.5cm in diameter. The estimated overall mass of the instrument is 370 kg and thepower consumption is 525W. The sensor will be launched into a sunsynchronous orbit at an altitude of 763 km and is scheduled for 3 years of operation with an option to extend the mission for an additional 2 years.

References

[1] Le Vine, D. M., “The Sensitivity of Synthetic Aperture Radiometers for Remote Sensing Applications from Space,” Radio Science, Vol. 25, No. 4, 1990, pp. 441–453.

[2] Ruf, C. S., et al., “Interferometric Synthetic Aperture Radiometery for Remote Sensing of the Earth,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 26, 1988, pp. 597–611.


Table 15.2

Characteristics of SMOS

Mission Instrument

Coverage Global Frequency L-band (1.413 GHz)

Revisit 3 days Polarization H & V with an option for polarimetric

Orbit 763 km FOV ±450 km

Sunsynchronous Pointing 32° (forward)

6 a.m. ascending Dimensions 4.3m per arm

Antennas 21 per arm (69 total; 0.875 λ spacing)

Resolution 30–90 km

Sensitivity 0.8–2.2K

Accuracy 3K (or better)

Mass 370 kg

Power 525W



[3] Le Vine, D. M., “A Multifrequency Microwave Radiometer of the Future,” IEEE Trans.on Geoscience and Remote Sensing, Vol. 27, No. 2, March 1989, pp. 193–199.

[4] Le Vine, D. M., “Synthetic Aperture Radiometer Systems,” IEEE Trans. on Microwave Theory and Technique, Vol. 47, No. 12, December 1999, pp. 2228–2236.

[5] Le Vine, D. M., M. Haken, and C.T. Swift, “Development of the Synthetic ApertureRadiometer ESTAR and the Next Generation,” Proc. Internat. Geosci and Remote Sens.Sympos. (IGARSS), Anchorage, AK, September 2004.

[6] Kerr, Y., et al., “Soil Moisture Retrieval from Space: The Soil Moisture and Ocean Salinity (SMOS) Mission,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 39, No. 8, August2001.

[7] Le Vine, D. M., et al., “Initial Results in the Development of a Synthetic Aperture Micro- wave Radiometer,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 28, No. 4, 1990,pp. 614–619.

[8] Le Vine, D. M., et al., “ESTAR: A Synthetic Aperture Microwave Radiometer for RemoteSensing Applications,” Proc. IEEE, Vol. 82, No. 12, December 1994, pp. 1787–1801.

[9] Corbella, I., et al., “The Visibility Function in Interferometric Aperture Synthesis Radi-ometry,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 42, No. 8, 2004,pp. 1667–1682.

[10] Griffis, A., “Earth Remote Sensing with an Electronically Scanned Thinned Array Radi-ometer,” Ph.D. dissertation, Dept. of Elec. Engin., Univ. of Mass., February 1993.

[11] Tanner, A. B., “Aperture Synthesis for Passive Microwave Remote Sensing: The Electroni-

cally Scanned Thinned Array Radiometer,” Ph.D. dissertation, Dept. of Elec. Engin.,Univ. of Mass., February 1990.

[12] Kerr, Y. H., et al., “The Soil Moisture and Ocean Salinity Mission: An Overview” inMicrowave Radiometry and Remote Sensing of the Earth’s Surface and Atmosphere, P.Pampaloni and S. Paloscia, (eds.), Zeist, the Netherlands: VSP, 2000, pp. 467–475.

[13] Kraus, J. D., Radio Astronomy, New York: McGraw-Hill, Ch. 6, 1966.

[14] Jackson, T. J., et al., “Large Area Mapping of Soil Moisture Using the ESTAR PassiveMicrowave Radiometer in Washita-92,” Remote Sens. Environ., Vol. 53, 1995, pp. 27–37.

[15] Jackson, T. J., et al., “Soil Moisture Mapping at Regional Scales Using Microwave Radi-

ometry: The Southern Great Plains Hydrology Experiment,” IEEE Trans. on Geoscience and Remote Sensing, Vol 37, No. 5, September 1999, pp. 2136–2151.

[16] Le Vine, D. M., et al., “ESTAR Measurements During the Southern Great Plains Experi-ment (SGP99),” IEEE Trans. on Geoscience and Remote Sensing, Vol. 39, No. 8, 2001,pp. 1680–1685.

[17] Le Vine, D. M., et al., “Remote Sensing of Ocean Salinity: Results from the DelawareCoastal Current Experiment,” J. Atmos. and Oceanic Tech., Vol. 15, 1998,pp. 1478–1484.

[18] Le Vine, D. M., C. T. Swift, and M. Haken, “Development of the Synthetic Aperture

Microwave Radiometer, ESTAR,” IEEE Trans. on Geoscience and Remote Sensing, Vol. 39,No. 1, 2001, pp. 119–202.




Acronyms

AC Alternating Current

AF Audio Frequency

CORRAD Correlation Radiometer

DC Direct Current

DR Dicke Radiometer

DRO Dielectric Resonator Oscillator

DSB Double Sideband

DTU Technical University of Denmark

EMC Electro Magnetic Compatibility

ENR Excess Noise RatioESA European Space Agency

ESTAR Electronically Scanned Thinned Aperture Radiometer

FPGA Field Programmable Gate Array

IF Intermediate Frequency

IMR Imaging Microwave Radiometer

INS Inertial Navigation System

IR Infrared

219



LAMMR Large Aperture Multifrequency Microwave Radiometer

LF Low frequency

LO Local OscillatorMIMR Multifrequency Imaging Microwave Radiometer

MIRAS Microwave Imaging Radiometer with Aperture Synthesis

MMIC Monolithic Microwave Integrated Circuit

NASA National Aeronautical and Space Administration

NIR Noise-Injection Radiometer

NOSS National Oceanic Satellite System

psu practical salinity unit (= parts per thousand)

RF Radio Frequency

S Salinity

SMMR Scanning Multichannel Microwave Radiometer

SMOS Soil Moisture and Ocean Salinity

SSB Single Sideband

SSM/I Special Sensor Microwave / Imager

SST Sea Surface Temperature

TEC Total Electron Contents

TPR Total Power Radiometer

UHF Ultra High Frequency

WS Wind Speed




Index

Absolute accuracy, 9–11 Active cold load, 184 AF amplifier, 33 Aliasing, 37, 128 Antenna, 117–21, 163–65, 181 Antenna beamwidth, 121 Antenna geometry, 120, 163, 181

Antenna rpm, 134–39, 152–53 Antenna target calibration, 82–83 Antenna temperature, 7 Aperture synthesis, 69, 72–73, 75–76,

198–200, 200–4, 208–11, 214–17

Baseline, 69–71, 74, 75, 76–78,200–4,204–5, 205–6, 213

Beam efficiency, 117–19Brightness temperature, 7, 75, 203, 207,

209–11Calibration, 81, 96–98, 165–67, 184–86,

205–06Calibration load, 82–84Calibration target, 82–85Complex correlator, 19, 57–62, 65Conical scanner, 122–23, 134–35, 143, 147Correlation radiometer, 18–20, 60–62,

64–68, 69

Data rate, 168–69Detector, 30–31, 40–42Dicke radiometer, 14–16, 27–37, 104, 131

Digital radiometer, 178Digital thermometer, 50Direct receiver, 25–26, 157–58DSB receiver, 26–27, 40–42Dual receiver unit, 158–59Dwell time, 125–30, 137

Faraday rotation, 186–92Footprint, 121, 134, 152–53Fringe washing, 74

IF circuitry, 31–31Image reconstruction, 197, 204–5, 207–8Integrated receiver, 159–60Integration time, 9, 34, 138, 140–41Integrator, 33–34

LF circuitry, 33–34

Linearity, 87–96, 165–67Line scanner, 121–25

MMIC technology, 159–60, 217Multiple beams, 150

Noise diode, 39, 92–93, 97, 109–11Noise-injection radiometer, 16, 38–40,

47–53, 109–11, 178–81Noise temperature, 9, 29–30

Offset paraboloid, 119–21, 163–65

Polarimetric radiometer,55–68, 96–98Polarimetry, 55–57

221



Polarization, 55–57, 173, 189–91Polarization combining radiometer, 57–60Preamplifier, 25–27, 40–42, 42–43Pseudo inverse, 204–5

Push-broom imager, 121–25, 139–40,177–84

Radiometer receiver, 7Receiver noise figure, 29–30, 134–39,

160–61Receivers for imagers, 130–31

Sampling, 37, 38, 125–30Sea salinity, 172–75, 209, 214–15Sea surface temperature, 172–75Sensitivity, 7–9, 14–16, 17–18, 62–64, 73,

75–76, 102–3, 141, 198–200,212–13, 217

Sensitivity measurements, 102–3Sky calibration, 85–86, 156–57, 166–67,

184–86Sky horn, 157, 184–86Soil moisture, 69, 175–76, 200–4, 208–11,

211–14, 214Space radiation, 192–93Spatial frequency, 71, 73–74

SSB receiver, 26–27, 42–43Stability, 9–11, 43–44, 47–53, 103–14Stability measurements, 103–14Stokes parameters, 55–57

Superheterodyne receiver, 25–27Swath width, 121–25,134–36, 140–41Synchronous detector, 33–34Synthesized beam (antenna pattern), 76–78,

200–4,204–5, 207–8Synthetic aperture radiometer, 197, 211–14,

214–217

Temperature stabilized enclosure, 49Torus reflector, 181

Total power radiometer, 13–14, 40–43,111–13, 130–31, 157–58

Weight and power, 159–60, 167–68,178–81, 183, 194, 211–14,214–17

Wind speed, 172

Visibility, 70, 75, 205, 207–8Visibility function, 75

∆/Σ converter, 34–37




The Artech House Remote Sensing Library

Fawwaz T. Ulaby, Series Editor

Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation, Ian G. Cumming and Frank H. Wong

Digital Terrain Modeling: Acquisitions, Manipulation, and Applications, Naser El-Sheimy, Caterina Valeo, and Ayman Habib

Handbook of Radar Scattering Statistics for Terrain, F. T. Ulaby and

M. C. DobsonHandbook of Radar Scattering Statistics for Terrain: Software and

User’s Manual , F. T. Ulaby and M. C. Dobson

Magnetic Sensors and Magnetometers, Pavel Ripka, editor

Microwave Radiometer Systems: Design and Analysis, Second Edition,Niels Skou and David Le Vine

Microwave Remote Sensing: Fundamentals and Radiometry,

Volume I, F. T. Ulaby, R. K. Moore, and A. K. Fung

Microwave Remote Sensing: Radar Remote Sensing and SurfaceScattering and Emission Theory, Volume II , F. T. Ulaby,R. K. Moore, and A. K. Fung

Microwave Remote Sensing: From Theory to Applications, VolumeIII , F. T. Ulaby, R. K. Moore, and A. K. Fung

Radargrammetric Image Processing, F. W. Leberl

Radar Polarimetry for Geoscience Applications, C. Elachi andF. T. Ulaby

Understanding Synthetic Aperture Radar Images, Chris Oliverand Shaun Quegan

Wavelets for Sensing Technologies, Andrew K. Chan andCheng Peng



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Microwave Radiometer Systems - Design and Analysis 2nd Ed. by Niels Skou

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