polarization calibration

21nov01

Polarization calibration measures the phase and amplitude response of the system so that the stokes parameters of the source can be computed from the measured values. A linear matrix (the mueller matrix) is derived that maps the source parameters into the measured stokes parameters. Applying the inverse of this matrix to the measured stokes parameters gives the stokes parameters of the source.

The computation.
Parameter definitions.
The measurement results.
Source list.
lband wide results
lband narrow results.
sband narrow results.
sband wide results.
cband results.

Acquiring the calibration scan data: (top)

Polarization calibration uses 2 cross scans rotated by 45 degrees centered on the expected source position.

Each strip of a cross is 6 beam widths long and takes 60 seconds to traverse. A correlated cal is fired at the beginning of the pattern for calibration purposes (this is done 3 beam widths off source at the start of the first strip). A single pattern takes 5 to 6 minutes to complete. A polarized source is tracked from rise to get good parallactic angle coverage. Sources close to 18 degrees dec (the latitude of the observatory) should be avoided since the azimuth angle changes too rapidly to adequately sample the parallactic angle.

The correlator is run in 3 level stokes mode. Each correlator board is fed both polarizations and computes the two autocorrelations and the two cross correlations. The online system transforms the two autocorrelations and computes the sum and difference to get I and Q. The cross correlation are combined into a complex correlation function and transformed. The real and imaginary parts then give U and V. The spectra are returned normalized to the total power I.

Processing the data:

The processing stage uses the code of carl heiles to "correctly" amplitude and phase calibrate the data and then derive the mueller matrix elements. Let xx, yy be the normalized autocorrelations of the two polarizations and xy, yx be the normalized cross correlations. Px, Py will be the total power in pol A and B respectively. cosft() is the cosine transform and fft() is the complex fourier transform. A complex cross correlation (cacf) is also constructed. Assume there are N channels (a zero lag and n-1 delays) Then cacf is:

cacf[0..2N-1]= yx[0:N-1] ,yx[N-1], xy[N-1:1]

We duplicate the point yx[N-1] since we are 1 point short (there are two 0 delays : xy[0], yx[0] which are the same) and 2*(N-1) lags.

The online datatking computes:

I =(Px*cosft(xx) + Py*cosft(yy))/(Px+Py)
Q=(Px*cosft(xx) - Py*cosft(yy))/(Px+Py)
U= real(fft(cacf))*Px*Py/(Px+Py)
V=-img(fft(cacf))*Px*Py/(Px+Py)

This data is input for the calon/off and the 4 strips. The processing is then:

Recreate the individual polarization data and fixup U,V

XX=(I+Q)*.5*(Px+Py)

YY=(I-Q)*.5*(Px+Py)

U'=U*(Px+Py)

V'=V*(Px+Py)

Intensity calibrate the spectra using the cal. There are 4*60=240 spectra in the 4 strips.

XXcorToK= TcalXXK / (<XXcalOn>-<XXcalOff>)

YYcorToK= TcalYYK / (<YYcalOn>-<YYcalOff>)

XXconv[0:127] = XXcorToK / (XXcalOff[0:127]/<XXcalOff>)

YYconv[0:127]=YYcorToK / (YYcalOff[0:127]/<YYcalOff>)

Ical =(XX * XXconv + YY * YYconv)

Qcal =(XX * XXconv - YY * YYconv)

Ucal =(U ' * sqrt(XXconv * YYconv))

Vcal =(V ' * sqrt(XXconv * YYconv))

Phase calibration.
Fitting the beam and the sidelobes
Computing the matrix elements.

The mueller matrix characterizes the system polarization response. Multiplying the source stokes vector by this matrix gives the measured stokes parameters. Use the inverse of the mueller matrix times the measured stokes parameters to get the source vector.

[I,Q,U,V]measured = MuellerMatrix X [I,Q,U,V] source
[I,Q,U,V]source = MuellerMatrixInverse X [I,Q,U,V] measured

Parameter definitions. (top)

The parameters for the the polarization are described below (at least my attempt at describing them.. I don't claim that it is correct!!!). A more complete (and correct) description can be found in ATOMS 2000-5 (but good luck!!!).

alpha , x

is the coupling between the orthogonal input polarizations by a perfect horn. If Ex,Ey are the signals at the input to the horn, then
Ea= cos(alpha)Ex + e^(ix)*sin(alpha)*Ey
Eb=-e^(ix)*sin(alpha)Ex + cos(alpha)*Ey
are the voltages output by the horn. alpha is the mixing of the amplitudes and x is the phase delay introduced. Alpha projects the X,Y coordinate system of the input onto a coordinate system rotated by alpha. If you took the horn and physically rotated it by 15 degrees relative to the x,y coordinate system, then alpha= 15 degrees. Alpha assumes a perfect feed. The outputs remain orthogonal. For a perfect linear horn alpha=0,and x=0. For a perfect circular horn, equal parts of both linears are mixed with a 90deg phase delay so alpha=45deg, and x=90deg.

epsilon, phi

alpha,x measured the rotation,delay of a perfect feed. An imperfect feed will also have undesired cross coupling and phase delays. These could be caused by the linear probes in the waveguide not being orthogonal. The resulting polarizations will no longer be orthogonal. The input,output would look like:
Eaa= Ea + eps*e^( i*phi)*Eb
Ebb= Eb + eps*e^(-i*phi)*Ea
So a fraction eps of the other voltage gets added in with a phase delay of phi.

psi

A correlated cal is injected before the dewar into both polarizations. The phase difference through the receiver, iflo, cables, correlator.. is then measured by the phase difference of this correlated cal in the two polarizations. This is then removed. The resulting phase difference between the two polarizations of a astronomical source and that measured in the correlator is psi. If the cables from the single diode to the injection point have a different path length, then psi will be non-zero.

deltaG

The amplitude is calibrated using the cal values for each polarization. deltaG is the relative error in these values Err(Ta-Tb)/(Ta+Tb). If you track a source with a linear feed then Q=(Ex^2-Ey^2) will not go to zero for an unpolarized source if deltaG is not zero.

The measurement results: (top)

The results of the polarization calibration are listed below. It is broken down by receiver. For each receiver there are 1 or more frequencies where the mueller matrix was measured. There is a table that contains date, source, pol/mueller, freqDep, and gain/beam. The columns are:

col 1: date. The date when the data was taken

col 2: source. The source name.

col 3: pol/mueller. This contains a plot of the fractional polarization Q, U, and V versus position angle. It also contains the values of the physical parameters and the computed mueller matrix. The plotted value depend on the type of feed. Linear feeds have: X-Y linear, XY linear, YX circular. Circular feeds give: X-Y=V, and XY, YX are Q and U.

col 4: parameter dependence versus frequency

col 5: gain and beam charateristics.

col 6: measured source polarization.

Note: This data is remeasuring the mueller matrix each time. The current (when the data was taken) mueller matrix was not applied before analyzing the data (the mm_xxx routines were not used). The polarization properities of the source have not been corrected by the measured mueller matrix.

Source list: (top)

source	receivers(# measurements)	%pol
B0017+154	lbn,(0),lbw(4),sbn(0),cb(1)	6.3 lb
B0035+130	lbn(1)
B0106+013		9.7% nvss lb
B0124+189	lbw(1)	5.0% nvss lb
B0134+329 3C48	lbn(0),sbn(2),sbw(1)cb(4)	.4% nvss lb
B0340+048	lbw(1)(pending)	7.2% lb
B0518+165 3C138	lbw(7),sbn(2),sbw(2),cb(1)	7.2% nvss lb
B0534+342	lbw(2),sbw(1)	1.9% nvss lb
J0603+219	lbn(1)
B0633+045	lbn(1)
J0725+144	lbw(1)	7% nvss
B0824+294	lbw(1),lbn(3),sbn(0),cb(1)	3.7% nvss lb
B0831+171	sbw(1)	.6% nvss lb
B0838+133	lbw(3),lbn(6),sbn(1),cb(1)	1.9% nvss lb
J0935+086	lbn(1)
J0943+027	lbn(1)
J1017+275	lbn(1)
B1040+123	lbn(4),lbw(2),sbn(1),sbw(2),cb(1)	5.6% nvss lb
B1140+123	lbw(2) pendig	1.0 lb
B1328+254	cb(1),
B1328+307 3C286	lbw(5),sbw(1)	6.7% nvss lb
B1317+179	lbn(1),lbw(1)	6.8% nvss lb
B1442+101	lbw(1),lbn(0),sbn(1),sbw(1)	1.3% nvss lb
B1535+139	lbw(1)	2.0% nvss lb
B1602+014	cb(1)
B1634+269	lbw(2)	3.9% nvss lb
B1641+173	cb(1)
B1756+134	cb(1)
B1857+129	lbn(0),sbn(0),cb(1)	.6% nvss lb
B2041+170	lbw(1),lbn(0),sbn(1),cb(1)	6.3% nvss lb
B2121+248	lbw(1)
B2209+080	lbw(1),lbn(1),sbn(1),cb(1)	4.4% nvss lb
B2314+038	lbw(2),lbn(0),sbn(0),cb(1)	2.2% nvss lb
B2230+114	lbn(1)
J2225+213	lbn(0),sbn(1)
B2247+140	lbn(0),sbn(1)	.9% nvss lb
B2249+185	sbn(1)	3.6% nvss lb

lband wide results. (top)

Lband wide is a native linear feed. The receiver has a correlated cal to use for phase calibration. Data is taken in two frequency bands:

lbwlo 1175,1300,1375, and 1415 Mhz

lbwhi 1415, 1550, 1666, and 1610 Mhz

updated through 01jun07.


col 1 date	col 2 source	col 3 fracPol Mueller	col4 vs frq	col 5 gain, beam	freqBand
11aug01	B0518+165	fig	fig	fig	lbwlo
11aug01	B0838+133	fig	fig	fig	lbwlo
11aug01	B2314+038	fig	fig	fig	lbwlo
12aug01	B0518+165	fig	fig	fig	lbwhi
12aug01	B0838+133	fig	fig	fig	lbwhi
12aug01	B1634+269	fig	fig	fig	lbwhi
12aug01	B2041+170	fig	fig	fig	lbwhi
12aug01	B2314+038	fig	fig	fig	lbwhi
13aug01	B0124+189	fig	fig	fig	lbwhi
13aug01	B1634+269	fig	fig	fig	lbwlo
25sep01	B2209+080	fig	fig	fig	lbwlo
19nov01	B0838+133	fig	fig	fig	lbwlo
24dec01	B0824+294	fig	fig	fig	lbwlo
13apr02	B1535+139	fig	fig	fig	lbwlo
11oct02	B1328+307	fig	fig	fig	lbwhi
17feb03	NewLbw
03mar03	B1040+123	fig	fig	fig	lbwlo (1)
03mar03	B1328+307	fig	fig	fig	lbwlo (1)
14may03	B2121+248	fig	fig	fig	lbwhi
10jul04	B0518+165	fig	fig		lbwlo
16sep04	B1442+101	fig	fig		lbwlo
20oct04	J0725+144	fig	fig		lbwhi
27apr05	B1040+123	fig	fig		lbwhi
14jul05	B1328+307	fig	fig		lbwlo
11dec05	B0534+342	fig	fig		lbwlo
23dec05	B0518+165	fig	fig		lbwhi
04jan06	B0518+165	fig	fig		lbwlo
26jan06	B0534+342	fig	fig		lbwhi
04aug06	B0017+154	fig	fig		lbwlo
14oct06	B0824+294	fig	fig		lbwlo
14oct06	B1040+123	fig	fig		lbwhi
27oct06	B0824+294	fig	fig		lbwhi
15nov06	B0340+048	fig	fig		lbwlo
26nov06	B1317+179	fig	fig		lbwlo
02dec06	B1140+223	fig	fig		lbwlo
02dec06	B1328+307	fig	fig		lbwlo
03dec06	B1140+223	fig	fig		lbwlo
10dec06	B1328+307	fig	fig		lbwlo
06jan07	B0017+154	fig	fig		lbwhi
07jan07	B0017+154	fig	fig		lbwlo
02feb07	B0017+154	fig	fig		lbwlo
02feb07	B0518+165	fig	fig		lbwlo
04feb07	B0518+165	fig	fig		lbwhi

notes:

Data taken after shimming but before new model installed. It had large pointing errors (up to 1Amin).
jun07: reran jul04-> feb07 data to use new fixup_param routine in mmlsfit to get rid of jumps in alpha,psi.
aug07: reran jul04->feb07 data to use nominal_linear param to fix jumps in alpha,psi.

procesing: x101/x102/allcal/lbw/, x101/x102/newcall/lbw

lband narrow results. (top)

lband narrow is a native circular feed. The polarization properties change rapidly as you move away from the center of the OMT. The receiver does not have a correlated cal for calibration purposes. The last column is the expected fractional polarizations. The values in () are the polarization angles on the sky. The analysis is deriving the mueller matrix. The measured polarization values have not been corrected by the computed mueller matrix.
Updated through 01oct02.

lband narrow at 1300,1375,1415,1500 Mhz. Native circular.
date	source	fracPol Mueller	vs frq	gain, beam	%pol 1400 expected
20apr01	B0838+133	fig	fig	fig	1.8
21apr01	B0838+133	fig	fig	fig	1.8
22apr01	B0035+130	fig	fig	fig	5.3
22apr01	B0838+133	fig	fig	fig	1.8
22apr01	B1040+123	fig	fig	fig	6.1 (meas)
22apr01	B2230+114	fig	fig	fig	4.5
23apr01	B1040+123	fig	fig	fig	5.6 (5.8 meas)
09may01	J0935+086	fig	fig	fig	1.5 (nvss)
10may01	J0943+027	fig	fig	fig	1.5(nvss)
24may01	J1017+275	fig	fig	fig	4.9 (-77.5)
05jun01	J0603+219	fig	fig	fig	.8(-59)
05jun01	B0838+133	fig	fig	fig	1.8
05jun01	B1040+123	fig	fig	fig	5.6
24sep01	B2209+080	fig	fig	fig	5.7 (meas)
03nov01	B0838+133	fig	fig	fig	1.8
26dec01	B0824+294	fig	fig	fig	5.1 (meas)
13feb02	B0824+294	fig	fig	fig	4.0 (meas)
13feb02	B1040+123	fig	fig	fig	7. 1 (meas)
22feb02	B0824+294	fig	fig	fig	4.0 (meas)
25feb02	B0633+045	fig	fig	fig	4.4 (meas)
11jul02					(1*)
13sep02	B1317+179	fig	fig	fig	6.9 (meas)
20sep02	B0838+133	fig	fig	fig	2.4 (meas)

11jul02: cal values recomputed. new values backdated to 01sep02. Recomputed all the data.

processing: x101/x102/allcal/lbn/

sband narrow results at 2380 Mhz. (top)

Sband narrow at 2380 Mhz. Native circular.
date	source	fracPol mueller	vs freq	gain/ beam	measured % Pol
05jan01	B1442+101	fig	fig	fig	1.0
06jan01	B2247+140	fig	fig	fig	1.8
08jan01	J2225+213	fig	fig	fig	9.2
13jan01	B0134+329 (3C48)	fig	fig	fig	1.3
13jun01	B0838+133	fig	fig	fig	3.2
13jun01	B1040+123	fig	fig	fig	9.2
25sep01	B0134+329(3C48)	fig	fig	fig	1.3
25sep01	B0518+165(3C138)	fig	fig	fig	9.6
27nov01	B2209+080	fig	fig	fig	6.4
30nov01	B2249+185	fig	fig	fig	5.2
01dec01	B2041+170	fig	fig	fig	10.7
17feb06	B0518+165(3C138)	fig	fig		9.5

10apr06 installed new sbn cal values (hadn't been measured in years). backdated to be valid from 14oct03. The 17feb06 has the new cal value.

processing: x101/x102/newcal/sbn

sband wide results at 2212, 2380, 2690, 2850 Mhz (top)

Sband wide is a native linear receiver with a correlated cal.


date	source	fracPol mueller	vs freq	gain/ beam	measured %Pol
19sep01	B1442+101	fig	fig	fig	1.1,1.4,1.8,1.8
24sep01	B0518+165 3C138	fig	fig	fig	4.9,3.8,2.0,1.2
23dec01	B0134+329 3C48	fig	fig	fig	1.2,2.0,1.8,1.6
24dec01	B0518+165 3C138	fig	fig	fig	5.8,4.3,2.8,2.0
24dec01	B1040+123	fig	fig	fig	4.4,3.7,2.9,1.9
19feb02	B0534+342	fig	fig	fig	1.2,2.5,1.6,1.8
20feb02	B0831+171	fig	fig	fig	1.2,2.1,1.3,1.2
20feb02	B1040+123	fig	fig	fig	4.3,4.1,2.3,1.6
20feb02	B1328+307 3C286	fig	fig	fig	9-10%

processing: x101/x102/allca//sbw

cband results. (top)

Cband is a native linear receiver with a correlated cal. The calibration routines are run in a high or low mode. The frequencies for the two modes are:

Low 4500, 4860, 5000, and 5400 Mhz

High 5000,5400,5690, and 5900 Mhz

The H, or L in the dat column signifies a high or low frequency run.

cband results
date	source	fracPol mueller	vs freq	gain/ beam	source Pol %
31jan01L	B2209+080	fig	fig	fig	7.0/10.1/7.1/8.9
01feb01L	B0017+154	fig	fig	fig	15.7/15.6/15.9/16.2
02feb01L	B0134+329(3C48)	fig	fig	fig	5.1/5.6/5.7/6.1
28jun01L	B0134+329(3C48)	fig	fig	fig	3.1/3.9/3.6/4.2
03aug01L	B1857+129	fig	fig	fig	4.9/5.1/5.2/5.7
03aug01L	B2041+170	fig	fig	fig	11.7/11.3/11.6/11.5
03aug01L	B2314+038	fig	fig	fig	2.1/2.2/2.2/2.7
05aug01L	B1641+173	fig	fig	fig	.9/.5/.7/.8
04nov01L	B0824+294	fig	fig	fig	5.8/5.7/5.6/5.6
17nov01L	B0838+133	fig	fig	fig	2.3/2.0/2.0/1.6
22dec01L	B0134+329(3C48)	fig	fig	fig	4.5/4.9/4.9/5.3
23dec01L	B0518+165(3C138)	fig	fig	fig	11.7/11.3/11.4/11.1
26dec01L	B1040+123	fig	fig	fig	9.3/9.0/9.1/9.0
31jan02L	B0134+329(3C48)	fig	fig	fig	3.9/4.4/4.4/4.9
10apr02H	B1328+254	fig	fig	fig	5.1/5.0/4.9/4.4
10apr02H	B1602+014	fig	fig	fig	1.3/1.8/2.5/3.2
10apr02H	B1756+134	fig	fig	fig	3.2/3.5/3.9/3.9
06feb08L	B0518+165	fig	fig		10.9/11.2/11.0/10.5

processing: x101/x102/newcal/cband

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