Review of concepts in Lecture1

Review of conceptsReview of conceptsinin

Lecture1Lecture1

By Tom Wilson

Lecture 2 page 1Lecture 2 page 1

1972: TMIXER = 3000 K (SSB) LMIXER = 2 (3 dB loss)

TLNA = 20 K GLNA = 103 (30 dB gain)

So TRX = 3000 K + 40 K + (1/500)T2

T T L TL

GTR X M IX E R M IX E R L N A

M IX E R

L N A

2 . . .

2005: TMIXER = 50 K (SSB) LMIXER = 1.2 for =100 GHz

TLNA = 5 K GLNA = 103

So TRX = 50 K + 1.2*5 K + (1.2/(1000))

In addition to the receiver, the atmosphere will add perhaps 20 K extra. In cm wavelength range, less improvement in noise temperatures with time, but most receivers are HEMTs, and we now can build MULTI-BEAM SYSTEMS

Lecture2 page 2Lecture2 page 2

RECEIVERS

Fundamental Relation:

TimeTime 1 sec1 sec 1 hour1 hour 16 hours16 hours 64 hours64 hours

TT

R M SSY S

T

TR M S

SY S

1

0 0 1 6.

0 0 0 4.

0 0 0 2.

• For broadband measurements, try to keep TSYS small, but also good to have large (bolometers)

• For very narrow spectral lines, coherent receivers have as small as you want. for example one can have = 10-9 0

•Note that from Doppler relation, V= c/

•At 100 GHz, 1 km s-1=333 kHz

Factor of500 improvement


• Coherent receivers preserve phase, but TRX > h/k ( at 115 GHz, h/k = 5.5 K ) from the uncertainty principle Et=h

• TSYS includes noise from Rx, atmosphere and source

• In coherent systems, noise from first stage is most important

•Mixer is a non-linear device with signal (s) and local oscillator (l) input:

sinltsinstcos(lt+st) + cos(st-lt……………

t t

F.T.

F.T.

R A t B t d t( ) ( ) ( ) ( )2

(Must be careful with limits in integral of periodic functions)

Lecture 2, page 3bArrows here show sampling at twice the frequency

Lecture 2: Antennas and Lecture 2: Antennas and CalibrationsCalibrations

Single dishes in simple termsSingle dishes in simple terms

CalibrationsCalibrations

ExamplesExamples

Single dishes in more formal termsSingle dishes in more formal terms

Lecture 2 page

Simple Diffraction Simple Diffraction First Null First Sidelobe

Diameter, D

Wavelength,

Can use example of waves passing through an aperture

Lecture 2 page 5

Rectangular ApertureRectangular Aperture

SilverMIT RadiationLabSeries

Lecture 2, page 6

sin

Du


FILLED APERTURES: Simple Approach

From diffraction = k / D=200k (mm)/D(m), where k is about 1, but can have larger values, but then need a more complex antenna theory

Reciprocity: Parameters of transmitting antennas same as those for receiving antennas

Usually “Filled apertures” means “paraboloids”

The ALMA 12 meter millimeter/sub-mm prototype radio telescopesin Socorro New Mexico


2

2

)(3520

8

2

1

meterD

KTSor

k

DwhereST

dTkdSAdWPower

A

A

AA

Ae

BA

M B

T

T

S: Flux density

TA: This is assuming that the atmosphere of earth has little effect

(0 is in units of arc min and the beam and source are gaussian. Wavelength in cm and TA is corrected for absorption in earth’s atmosphere)


Show that these are equivalent

Descriptive Parameters to characterize antennas:

: Full width to half power beam size

MB: Main beam solid angle

: Antenna efficiency

: Beam efficiency



Measure B using intense point sources, assume B is a gaussian. Then

MB = 1.133 B2 (Gaussians)

COMPACT SOURCES:

Ag: Geometric area of antenna

Effective area

Aeff = Ae =A Ag A : Antenna efficiency

0 : Observed beam size relation for gaussians

B : Beam

S : Source

02 2 2 B S

IkT kT

S I dkT

M B

M B

2 2

2

2 2

2

22

2

222

22

Beams

ssMB

sBeamobs

ssobsMB

TT

TT

Call TMB

the ‘Main Beam

Temperature’

Integrating over the beam

Could also integrate over The source

MB

ST

cmM B

2 6 5 02

2.( )0 is in units of

arc min and the beam and source are gaussian. Wavelength in cm)

Rayleigh-JeansFrom Lecture 1:

Lecture2 page12Lecture2 page12

(Problem for you: Given the previous relations between T(Problem for you: Given the previous relations between TMBMB , T , TAA and Sand S , determine a relation for the ratio of , determine a relation for the ratio of AA to to in terms of in terms of antenna diameter, antenna diameter, and and


APPLICATION OF THESE CONCEPTS

NGC7027 (a PNe) has SS = 5.4 Jy at 1.3 cm. What is the T= 5.4 Jy at 1.3 cm. What is the TMBMB (main beam (main beam

brightness temperature) if the 100-m FWHP beam size is 43”?brightness temperature) if the 100-m FWHP beam size is 43”?

UseUse

Where Where 0 is the telescope beam size in are min.

Suppose the “true” gaussian source size is 10”, what is TB (true brightness temperature). Could use

ST

cm

T

T K

M B

M B

M B

2 6 5

5 4 2 6 5

4 36 0

1 3

6 7

02

2

2

2

.( )

. ..

.

STM B

5 4 2 6 5

1 06 0

1 3

2

2. ..

(Problem: Repeat for the (Problem: Repeat for the

30-m, with beam 30-m, with beam

27’’, wavelength 27’’, wavelength

3.5 mm, flux density3.5 mm, flux density

4.7 Jy)4.7 Jy)


Or

And get

We know from optical spectroscopy that the electron temperature of NGC7027 is Te = 14000 K. Use equation of radiative transfer:

To get 0 0 0 9.

This is a source which is thermal, so the radiation is free-free or Bremsstrahlung (will discuss in Lecture 3)

2

22

10

1043MBB TT

KTB 124

eTT eB 1


VenusVenus, at closest approach, has a size of 62”. If we measure an antenna temperature, TA, of 4.2 K with an 8.7’ beam, and a beam efficiency of B = 0.5, what is the surface temperature of Venus?

T K T T so T K

T T

T K

A B M B M B M B

S S M B B S

S

4 2 0 5 8 6

8 68 7

6 26 0

6 26 0

6 6 0

2 2 2

22

2

. . .

..

Jansky used a telescope with a 30° beam at = 14.6 m. The maximum intensity was 1.5 .106 Jy in a beam(this was calibrated in the 1970’s; see Lecture 1). What is the TMB?

1 5 1 0 2 6 53 0 6 0

1 4 6 0

4 1 0

6

2

2

5

. .

T

K T

M B

M B

If B = 0.5, then TA = 2 .105 K >> TRX

At 14.6 meters, the whole sky shines brightly, night and day!!

Jansky did not detect the Sun, WHY?

(see Lecture 1 page 2)

(Repeat for 3 mm(Repeat for 3 mm

with a 27” beam)with a 27” beam)


SURVEYS: THE SKY HAS 41,252 SQUARE DEGREES

Suppose you survey the whole sky with a 30’ beam at 408 MHz. Need 3 samples per beam. (try to characterize a cosine with fewer points).

Need 36 samples per square degree, or 1.5 .106 samples in all.

Receiver has = 10 MHz. Use = 10 MHz. Use = 10s /point and assume TSKY >> TRX

TT T

TR M SSY S SY S

SK Y

1 01 0

8

4

In all measurement time = 1.5 ..107 sec = ½ year

Now: Try = 5 GHz, = 5 GHz, = 2.4’, TRX = 50 K with integration = 50 K with integration time = 10s

and and = 500 MHz= 500 MHz

T

KKR M S

5 07 1 0 4

Really more since need to switch to reduce atmospheric noise fluctuation, so TTRMSRMS =10 =10-3-3 K. If K. If A = 0.5, on a 100-m telescope, get 1.3 K, TA per Jy, so SSrmsrms = 0.7 = 0.7 . .1010-4-4 Jy. Detect at 4 Jy. Detect at 4 TTRMSRMS =3 =3 ..1010-4-4 Jy = 0.3 mJy. Jy = 0.3 mJy.

But need 2.3But need 2.3 . .101088 samples, or 6.5 samples, or 6.5 ..101055 hours = 74 years. hours = 74 years.

Need Need MULTIBEAMINGMULTIBEAMING

isintegral overentire power pattern

12b

More details of antennasMore details of antennas


Define A as integral over whole Power Pattern, PN:

A NP d d ( , ) s in

00

2

M B NM A INB E A M

P d BM B

A

B: Fraction of power in main beam used for sources which are extended to about size of main beam.

For point sources, use A

A Ae A g

Example: Why need mm calibration Example: Why need mm calibration

From Lecture 1: The Moon is measured at 3mm wavelength with a 12m telescope. The antenna beamsize is =50”, less than Moon size of 30’. So the source fills the main beam and we know that the temperature of the Moon is 220K. This should be the main beam brightness temperature, TMB = 220 K. The beam efficiency is =80%, so the measured antenna temperature should be TA=0.80*220K=176K. We find it is more since the sidelobes also receive power from the Moon. This is like the situation for CO lines in the This is like the situation for CO lines in the millimeters. We need to take this into account.millimeters. We need to take this into account.

Lecture 2 page 15

Rectangular ApertureRectangular Aperture

Silver, MIT RadiationLabSeries


First Sidelobe(for a 12mantenna at =3 mm,at 75” from axis)

Half width To half power

Historical Introduction to CalibrationHistorical Introduction to Calibration

In centimeters, atmosphere has little effect, and In centimeters, atmosphere has little effect, and can use flux density transfer from standard can use flux density transfer from standard sources for calibrationsources for calibrationThis is by means of a pulsed calibration, injected This is by means of a pulsed calibration, injected periodically together with the signalperiodically together with the signalThis was to transfer scale from a known source to This was to transfer scale from a known source to the source of interestthe source of interestAtmosphere had little or no influenceAtmosphere had little or no influenceThis is This is notnot so in the millimeter wavelength range so in the millimeter wavelength range Water vapor is the larger problem: this has a scale Water vapor is the larger problem: this has a scale

height of 2 kmheight of 2 km Oxygen has a scale height of 8 kmOxygen has a scale height of 8 km



T T T T eB B 0

Calibration for MillimetersFROM LECTURE 1:

Equation of radiative transfer and Rayleigh-Jeans approximation gave

on source off source

If use

for “on-source

minus off-source” get

TB: Measured

T: Atmosphere

T0: Astronomical source

T T e T e T T eB A A( ) 1 10

Must correct for thisloss in the atmosphere


3 4 5 2 2 5

4 6 0 2 2 5

8 0 6 2 2 5

3

6

2 0

Carbon monoxide, CO, line frequencies

Fine structureLines of neutralCarbon (C I)

GHz is not close to any water lines, butThe opacity is representative

Thisplot for

Thus the source intensity is reduced. In the millimeters, historically the measurements concentrated on spectral lines, especially carbon monoxideCO. To calibrate the very extended emission from molecular clouds, one used the ‘chopper cal’ method. This made use of measurements of a warm absorber, the atmosphere and then (often) a cold absorber.


)( rxHH TTGV

1

y

yTTT LH

rx

)( rxLL TTGV

rxL

rxH

L

H

TT

TT

V

V


y

AeTFGTTFGVVV atmeffskyHeffskyHcal )(

AeTGVVV Aoffsourcesig ´

eff

A

cal

sigA F

T

V

VT ´

´

eff

effMB B

FT

])1([ rxHeffskyeffsky TTFTFGV


Beff isthe same as

Tsky=Tatme

Details: Error Beam Details: Error Beam

Lecture2 page23Lecture2 page23(At 1.3 mm, the power in the error beam is about 20% of that in the main beam)

30-m Error Beam (Greve et al. 1998 A&A Suppl 133, 271) Lecture2 page24Lecture2 page24

214.2 FB

The Effect of Feed Legs on the Telescope Beam Pattern


Effelsberg 100-mtelescope: a classic case of ‘fat feed legs’’

Reflections in the TelescopeReflections in the TelescopeLecture2 page27Lecture2 page27

Reflection is at the feed horn

Instrumental Baseline RipplesInstrumental Baseline Ripples


Both spectra are ‘signal minus reference over reference’, at different axial focus settings

Observing StrategiesObserving Strategies

Position SwitchingPosition Switching

Beam SwitchingBeam Switching

On the Fly MappingOn the Fly Mapping

Frequency SwitchingFrequency Switching


Beam Switch/Position SwitchBeam Switch/Position Switch(Also ‘wobble Switching’)(Also ‘wobble Switching’)

Noise is factor of two larger than in total power spectrum

Lecture2 Lecture2 page30page30

On-the –Fly MappingOn-the –Fly Mapping

For n on’s, spend more time on off source

Have ‘n’ on’s for each off

Total integration time, t, for each on-source spectrum is the sum of ton & toff


Frequency SwitchingFrequency Switching

more noise in this spectrum, compared to a total power spectrum


Telescope Pointing Telescope Pointing

Must have fairly intense sources with Must have fairly intense sources with known positionsknown positions

These must be small compared to the These must be small compared to the telescope beamtelescope beam

Could be spectral line or continuum Could be spectral line or continuum sources, planets, moons of planets, some sources, planets, moons of planets, some asteroidsasteroids


Full Width to Half Power points: The position of the source is most accurately

found by determining these locations

Could also use a Gaussian fit to the scan, if the signal to noiseRatio is sufficient. This is usually done for continuum measurements.For spectral line pointing, one usually measures at the source peak and 4 points around the peak, usually at the half power points.


Calibration SourcesCalibration Sources

Even though the chopper calibration gives a Even though the chopper calibration gives a value for Tvalue for TAA* or T* or TMBMB, may be additional factors, , may be additional factors, such as mixer sideband ratio, telescope gain vs such as mixer sideband ratio, telescope gain vs elevation effects, pointing errors…elevation effects, pointing errors… With fixed tuned SSB mixers this is less true, but one With fixed tuned SSB mixers this is less true, but one

may still want to have a system check using a may still want to have a system check using a ‘standard’ source. ‘standard’ source.

Not as large a problem with continuum measurementsNot as large a problem with continuum measurements But using measurements of standard sources allows But using measurements of standard sources allows

one to determine an intensity scale that others can one to determine an intensity scale that others can relate their measurements to. relate their measurements to.

Lecture2 Lecture2 page35page35

Review of concepts in Lecture1

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