ESA Unclassified - For Official Use

Prepared by nuno miranda Reference ESA-EOPG-CSCOP-TN-0004 Issue 1 Revision 0 Date of Issue 22/07/2015 Status Final Document Type Technical Note Distribution

Sentinel-1 Instrument Processing Facility: Impact of the Elevation Antenna Pattern Phase Compensation on the Interferometric Phase Preservation

ESA Unclassified - For Official Use

Page 2/15

ESA Standard Document ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

Title Sentinel-1 Instrument Processing Facility: Impact of the Elevation Antenna Pattern Phase Compensation on the Interferometric Phase Preservation

Issue 1 Revision 0 Author nuno miranda Date 22/07/2015 Approved by P. Potin Date 22/07/2015

Reason for change Issue Revision Date

First issue 1 0 22/07/2015

Issue Revision Reason for change Date Pages Paragraph(s)

ESA Unclassified - For Official Use

Page 3/15

ESA Standard Document ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

Table of contents:

1   Introduction ....................................................................................................................................... 4  2   Documents ......................................................................................................................................... 4  3   Notations ........................................................................................................................................... 4     Fields used from the manifest file ................................................................................................................................... 4  3.1   Fields used from the main product annotation data set ................................................................................................. 5  3.2   Fields used from the AUX_CAL ...................................................................................................................................... 5  3.3

4   Two-way Elevation Antenna Pattern Phase contribution ................................................................... 5  5   Interferogram correction procedure .................................................................................................. 7     General description ......................................................................................................................................................... 8  5.1   Step 1: retrieving two-way complex EAP term ................................................................................................................ 9  5.2   Step 2: finding the roll steering angle ............................................................................................................................. 9  5.3   Step 3: computing the elevation angle in the geometry of view .................................................................................... 10  5.4   Step 4: re-interpolating the 2-way complex EAP .......................................................................................................... 10  5.5   Step 5: identifying IPF version ....................................................................................................................................... 11  5.6   Step 6: correcting for the phase term ............................................................................................................................ 11  5.7

6   S-1 IPF Auxiliary Calibration File ..................................................................................................... 12  7   Sentinel-1 A Roll Steering Law ......................................................................................................... 13     Roll steering law versus altitude .................................................................................................................................... 13  7.1   Roll Steering Law versus Time ....................................................................................................................................... 14  7.2

ESA Unclassified - For Official Use

Page 4/15

ESA Standard Document ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

1 INTRODUCTION

The Elevation Antenna Patterns (EAPs) used by the S-1 Instrument Processing Facility (IPF) are derived from the S-1 Antenna Model (AM) which is able to predict with great accuracy the gain and phase patterns. The EAP correction by the S-1 IPF was at launch only considering the gain of the EAP, similarly to what was done for ASAR. As an outcome of the S-1A Commissioning Phase, it has been decided to upgrade the S-1 IPF to also correct for the EAP phase, in order to compensate for the induced phase difference between the polarimetric channels. This correction has been introduced in March 2015 with the IPF V243. As a consequence, performing interferograms between products generated with the IPFV243 and the former version V236 leads to range varying phase offset. This technical note explains the nature of the phase offset and provides recommendation towards its correction. 2 DOCUMENTS RD- 1 S-1 *Sentinel-1 Level 1 Detailed Algorithm Definition, S1-TN-MDA-52-7445

RD- 2 S-1 IPF Auxiliary Product Specification, issue 2.9

RD- 3 Sentinel-1 SAR Instrument, Definition of the Roll Steering Law, S1-TN-ASD-PL-0018, issue 2

RD- 4 *S-1 Product Format Specification, S1-RS-MDA-52-7441

3 NOTATIONS

Fields used from the manifest file 3.1name Path ADS

𝜂!"# ascendingNodeTime manifest ipfVersion <software name="Sentinel-1 IPF" version="002.36"/>

manifest

For example: <safe:extension> <s1:orbitProperties> <s1:pass>ASCENDING</s1:pass> <s1:ascendingNodeTime>2015-05-30T17:35:19.722615</s1:ascendingNodeTime> </s1:orbitProperties>

ESA Unclassified - For Official Use

Page 5/15

ESA Standard Document ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

</safe:extension>

Fields used from the main product annotation data set 3.2 name Path Ns /product/imageAnnotation/imageInformation/numberOfSamples fs /product/generalAnnotation/productInformation/rangeSamplingRate 𝜂!"#$" /product/swathTiming/burstList/burst/azimuthTime 𝜏    ! /product/imageAnnotation/imageInformation/slantRangeTime 𝜏!"# /product/antennaPattern/antennaPatternList/antennaPattern/slantRangeTime 𝜃!"# /product/antennaPattern/antennaPatternList/antennaPattern/elevationAngle

Fields used from the AUX_CAL 3.3name Path

Geap /auxiliaryCalibration/calibrationParamsList/calibrationParams/elevationAntennaPattern/values

Δθ /auxiliaryCalibration/calibrationParamsList/calibrationParams/elevationAntennaPattern/elevationAngleIncrement

4 TWO-WAY ELEVATION ANTENNA PATTERN PHASE

CONTRIBUTION

The S-1 Antenna Model (AM) provides 1-way elevation (and also azimuth) antenna patterns. These patterns are further processed to generate 2-way EAP. These 2-way EAP are made available to the S-1 Instrument Processing Facility (IPF) in a dedicated auxiliary product from now on referred as AUX_CAL. These AUX_CAL are also available to the users in a dedicated site, see section 6. Figure 1 shows for all the interferometric modes, beams and polarisations the 2-way EAP phase around the main lobe. Taken the example of IW (Figure 1.a), it can be seen that the 2-way EAP phase introduces:

! Smooth fluctuation of the phase in elevation ! Offset from a sub-swath to another. In the case of IW, it can be measured an offset

~70deg fromIW1 toIW2

ESA Unclassified - For Official Use

Page 6/15

ESA Standard Document ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

When forming interferograms between data processed by the IPFV236 (no EAP phase correction) and IPFV243 (EAP phase correction introduced), the interferometric phase also contains the EAP phase contribution. This is illustrated in Figure 2.(a) where the phase offset between IW1 and IW2 is clearly visible. The smooth range variation is also present although not visible.

(a)IW (b)EW

(c) SM

Figure 1: Elevation Antenna Pattern (2-way) phase as provided by the Sentinel-1 Antenna Model and stored in the AUX_CAL file.

ESA Unclassified - For Official Use

Page 7/15

ESA Standard Document ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

Using the EAP phase provided in the AUX_CAL, it is possible to correct for these effects as shown in Figure 2.(a)

(a) Before correction (b) after correction is applied

Figure 2: Intergerogram between IPF V236 and V243 products. (a) represents the interfegrom that is obtained without correction while b) represents the interferogram performed after the phase correction described in this

document

5 INTERFEROGRAM CORRECTION PROCEDURE

This chapter describes the approach to correct for the EAP phase screen. The correction can be done in different ways e.g. correcting the SLC product or correcting the interferogram.

ESA Unclassified - For Official Use

Page 8/15

ESA Standard Document ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

In this section, it is assumed that the phase correction is done at SLC product level. The IPF V236 product is corrected to bring it at the same level of correction as the IPFV243 product.

General description 5.1The IPF performs the two-way EAP correction as defined in [RD- 1]. The EAP correction performed is applied at complex pixel level as following:

𝑠!"## =𝑠

𝐺!"# . 𝑒!∅!"#

where: ! s is the uncorrected SLC data ! scorr is the corrected SLC data ! Geap is the complex 2 way antenna pattern than can be divided in two terms:

! |Geap| : gain term ! Φeap : phase term represented in Figure 1. It is the argument of the complex EAP

provided in the AUX_CAL. In the case of IPF V243 and higher version the full correction is performed while in the case of IPFV236 only the gain term is corrected. Consequently, the IPF V236 SLC products need to be corrected for the missing phase term:

𝑠!"#!"#_!"## =𝑠!"#!"#𝑒!!!"#

This correction is implemented by the following steps:

! Retrieving the 2-way EAP phase term using the information provided in the AUX_CAL.

! Finding the roll steering angle using the nominal roll steering law. ! Converting the off-boresight angle to elevation angle in the geometry of view

using the roll steering angle. ! Interpolating the 2-way EAP phase term to the burst (or block) dimension ! Correcting the burst.

ESA Unclassified - For Official Use

Page 9/15

ESA Standard Document ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

Step 1: retrieving two-way complex EAP term 5.2 The 2-way EAP is provided in the AUX_CAL per (sub-)swath and polarisation. It is a vector of complex values (I,Q) provided as function of the elevation angle in the antenna model frame. The vector is sampled at a step, Δθ, of typically 0.05deg. Δθ is defined in section section 3.3. Retrieve from the AUX_CAL the complex EAP (Geap) for the desired swath and polarisation (see section 3.3). Geap is a complex vector composed by Nelt complex values. Note that by construction, the number of complex elements, Nelt, is an odd number. Compute the vector of elevation angle in antenna frame, θAM, as defined in the auxiliary file specification document [RD- 2]

𝜃!" =−(N!"# − 1)

2 ,+ N!"# − 1

2 ∗ Δ!    

θAM contains Nelt elements separa/ted by Δθ.

Step 2: finding the roll steering angle 5.3The vector of elevation angles, 𝜃!", is provided in the antenna frame as shown in Figure 1 (x-axis). It requires to be converted into elevation angles in the geometry of view (angle between the earth center-satellite and satellite-target). The two are related by the roll steering angle, 𝜃!""#$%&'. The roll steering angle can be retrieved using the nominal roll steering law using defined in [RD- 3]. This document provides “easy to use” nominal laws giving the roll steering as function of:

1. the elapsed seconds from the Ascending Node Crossing (ANX). The ascending node crossing time is annotated in the manifest.safe file e.g.:

<s1:ascendingNodeTime>2015-05-19T13:20:13.696694</s1:ascendingNodeTime>

2. the satellite height that can be derived from the annotated state vector: /product/generalAnnotation/orbitList/orbit/position/[x,y,z]

ESA Unclassified - For Official Use

Page 10/15

ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

In this technical note it is decided to use the first definition. The computation of the roll steering is then simply dependent on the elapsed seconds from the ANX. The nominal roll steering laws are describe in section 7. Compute the elapsed seconds between the ANX and the block or burst start time ηanx:

∆!"#= 𝜂!"#$" − 𝜂!"# Use the roll steering law defined in [RD- 3], to compute the roll steering at the desired time:

𝜃!""#$%&'   = 𝑎𝑛𝑥2𝑟𝑜𝑙𝑙(∆!"#) The anx2roll function is the successive call of the functions given in section 7.2 and 7.1

Step 3: computing the elevation angle in the geometry of view 5.4

𝜃!"# = 𝜃!" +  𝜃!""#$%&' 𝜃!"# is a vector of Nelt elements separated by 𝛥!.

Step 4: re-interpolating the 2-way complex EAP 5.5In order to correct the data with ∅!"#, it is necessary to interpolate this vector at each range samples. The interpolation needs to be done in the complex domain in order to avoid phase discontinuities Compute the slant range time vector, τ, at every range sample:

𝜏 = 𝜏! +   0,𝑁! − 1 ∗  1𝑓!

τ is composed of Ns elements starting at τ0 separated by 1/fs. Retrieve the elevation antenna pattern record closest to the start time of the burst (or block) to be processed:

𝑐𝑙𝑜𝑠𝑒𝑠𝑡𝐸𝑎𝑝𝑅𝑒𝑐𝑜𝑟𝑑 = 𝑔𝑒𝑡𝐶𝑙𝑜𝑠𝑒𝑠𝑡𝐸𝑎𝑝𝑅𝑒𝑐𝑜𝑟𝑑(𝜂!"#$") From the closest EAP record get the sub-sampled vector of elevation angles and slant range times:

𝜏!"# = 𝑐𝑙𝑜𝑠𝑒𝑠𝑡𝐸𝑎𝑝𝑅𝑒𝑐𝑜𝑟𝑑. 𝑠𝑙𝑎𝑛𝑡𝑅𝑎𝑛𝑔𝑒𝑡𝑖𝑚𝑒 𝜃!"# = 𝑐𝑙𝑜𝑠𝑒𝑠𝑡𝐸𝑎𝑝𝑅𝑒𝑐𝑜𝑟𝑑. 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛𝐴𝑛𝑔𝑙𝑒

ESA Unclassified - For Official Use

Page 11/15

ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

Interpolate 𝜃!"# to have one value per range sample:

𝜃 = 𝑖𝑛𝑡𝑒𝑟𝑝𝑜𝑙(𝜃!"# , 𝜏!"# , 𝜏) θ is a vector composed of Ns elements. Finally interpolate, in the complex domain, the complex EAP to have one value per range sample:

𝐺!"#_!"#$%&'()#$* =  𝑖𝑛𝑡𝑒𝑟𝑝𝑜𝑙(𝐺!"#,𝜃!"# ,𝜃)

Step 5: identifying IPF version 5.6The S-1 IPF version annotated in the manifest.safe file provided in the root of the product folder tree … <facility country="Italy" name="ESRIN headquarters" organisation="ESRIN" site="Rome">

<software name="Sentinel-1 IPF" version="002.36"/> </facility> …

Step 6: correcting for the phase term 5.7This step consists in correcting the IPF V236 data using the interpolated complex Elevation Antenna Pattern vomputed at step 4.

Φeap_interpolated = arg(Geap_interpolated) The correction is done for each line of a processing burst (or block) if the data has been processed with the IPFV236

𝑠!"##(𝜂, 𝜏) =𝑠 𝜂, 𝜏

𝑒!!"#_!"#$%&'()#$*(!)

ESA Unclassified - For Official Use

Page 12/15

ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

where s(η ,τ ) is the block/burst of SLC data processed with the IPF V236. Once corrected for the phase term corrected scorr(η ,τ ) can be used to form the interferogram with products processed with the IPF V243 and higher versions leading to the corrected interferogram shown in in Figure 2.(b). 6 S-1 IPF AUXILIARY CALIBRATION FILE

The Elevation Antenna Patterns are provided in the AUX_CAL products that can be found at the following URL: https://qc.sentinel1.eo.esa.int/aux_cal/ This page provides access to the full list of AUX_CAL that have been generated. There are multiple files which only few are active. The active ones are represented by a tick mark ✔. For data processed with the IPFV236 the following link can be used. https://qc.sentinel1.eo.esa.int/aux_cal/?active=True&instrument_configuration_id=3&validity_start_time=2014-09-15 It will allow retrieving a suitable AUX_CAL file containing a complex EAP valid for all products processed with the IPFV236. Clicking on the above link will allow retrieving an AUX_CAL that is tar gzipped (Thus needing to be uncompressed). The format of the AUX_CAL is defined in RD- 2. As an example the section of IW1/HH is provided here below. In red are marked the field needed and described in section 3.3 <calibrationParams> <swath>IW1</swath> <polarisation>HH</polarisation> <elevationAntennaPattern> <beamNominalNearRange>26.72</beamNominalNearRange> <beamNominalFarRange>31.67</beamNominalFarRange> <elevationAngleIncrement>0.05</elevationAngleIncrement> <values count="601">-3.053e+09 -…</values> </elevationAntennaPattern> <azimuthAntennaPattern> <azimuthAngleIncrement>0.005</azimuthAngleIncrement> <values count="401">-54.017 … </values> </azimuthAntennaPattern> <azimuthAntennaElementPattern> <azimuthAngleIncrement>0.03</azimuthAngleIncrement> <values count="201">-18.0399 … </values> </azimuthAntennaElementPattern> <absoluteCalibrationConstant>1.0</absoluteCalibrationConstant>

ESA Unclassified - For Official Use

Page 13/15

ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

<noiseCalibrationFactor>1</noiseCalibrationFactor> </calibrationParams>

7 SENTINEL-1 A ROLL STEERING LAW

Roll steering law versus altitude 7.1The SAR mode design and the SAR performance Analysis are based on a linear roll steering versus satellite altitude. The roll steering law defines the off nadir pointing of the antenna mechanical bore sight versus time. The law for the roll steering is:

𝜃!""#$%&' =  𝜃!"# −  𝛼!"##  . (𝐻 − 𝐻!"#)

Parameter Value Remarks

θoffNadir Antenna bore sight off nadir angle as function of altitude. θref 29.450 deg Antenna bore sight off nadir angle at reference altitude Href 711.700 km Reference altitude αroll 0.05660deg/km roll steering sensitivity versus altitude H input in meters The actual satellite altitude in meters given as input ;+ ; :Description: ; Returns the Platform nominal roll as function of satellite altitude ; as per Sentinel-1 SAR Instrument, Definition of the Roll Steering Law, ; S1-TN-ASD-PL-0018, issue 2 ; ; :Params: ; altitude : Sat. altitude in meters ; ;- function s1_height2roll, altitude href=711.700D ;km boresight_ref= 29.450D ; deg alpha_roll = 0.0566D ;deg/km return, boresight_ref - alpha_roll* (altitude/1000D - href) end

ESA Unclassified - For Official Use

Page 14/15

ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

Roll Steering Law versus Time 7.2Satellite altitude versus time may be derived from a look up table providing e.g. the altitude round the orbit as function of time within the orbit tanx. Satellite altitudes round the orbit can be well approximated by a function:

𝐻 𝑡 = ℎ! + ℎ!  . sin  (𝑛  .𝜔!"# . 𝑡 − 𝑡!"# + 𝜑!!

!!!

Parameter Value Remarks h0

707714.8 m

h1 8351.5 m

h2 8947.0 m

h3 23.32 m

h4 11.74 m

𝝋1 3.1495 rad

𝝋2 -1.5655 rad 𝝋3 -3.1297 rad

𝝋4 4.7222 rad

Torb

5924.57 s 175 orbits / 12 days

;+ ; :Description: ; Returns the Platform nominal roll as function of elapsed time from ascending node crossing time (ANX) ; as per Sentinel-1 SAR Instrument, Definition of the Roll Steering Law, ; S1-TN-ASD-PL-0018, issue 2 ; ; :Params: ; anxTime : Elapsed time since the ANX [seconds] ; ;- function s1_anx2Height, anxTime h0 = 707714.8;m h = [8351.5, 8947.0, 23.32, 11.74] ;m

ESA Unclassified - For Official Use

Page 15/15

ESA Standard Document

Date 22/07/2015 Issue 1 Rev 0

phi = [3.1495, -1.5655 , -3.1297, 4.7222] ;radians Torb = (12D*24D*60D*60D)/175D worb = 2D*!pi / Torb sum=0 for i=0,n_elements(h) -1 do begin sum += h(i) * sin((i+1) * worb * anxTime + phi[i]) endfor Height = h0 + sum return, height end