4.6 Polarization calibration

The calibration of visibility data sensitive to linear polarization involves two distinct operations: (1) determining and correcting the data for the effects of imperfect telescope feeds and (2) removing any systematic phase offsets between the two systems of orthogonal polarization. These two components of polarization calibration will be considered separately.

The effective feed response is parameterized most generally by its polarization ellipticity and the orientation of the major axis of that ellipse. For the VLA, it appears to be adequate to make the simpler assumption that each polarization is corrupted by a small complex gain times the orthogonal polarization.

In general, the polarization of the calibrator(s) to be used to determine the feed parameters will not be known a priori and must be determined along with the feed parameters. Observations of a given source (or sources) over a wide range (≥ 90^∘) of parallactic angles is necessary to separate calibrator polarization from the feed parameters. Task LISTR may be used to determine the parallactic angles at which data have been taken:

Multiple calibrators may be used in determining the feed polarization, but the data from them must be accurately calibrated. In particular, the phase calibration of any calibrator used to determine antenna polarizations should be determined from that calibrator itself (i.e., the source should be self-calibrated). Note that this will normally have occurred for all gain calibrators if the procedure described in the previous sections was followed.

The normal phase calibration technique treats parallel-hand visibilities in the two orthogonal polarizations independently. Thus, there will be a systematic phase difference between the two polarizations systems. This difference may be due to differences in instrumental phase offset for the two systems or due to the propagation medium (i.e., Faraday rotation) or both. Faraday rotation effects are particularly bothersome as they may be time variable and increase rapidly with wavelength. For data at L band or longer wavelengths,  should be given an estimate of the ionospheric Faraday rotation measure using task FARAD. This task computes the ionospheric rotation measure using either total electron content from a nearby ionospheric monitoring station (Boulder Colorado for the VLA) or an empirical model that uses the monthly mean Zurich sunspot number (R1) as a measure of solar activity. If monitoring data are available, they should be used in preference to the model. FARAD enters the ionospheric Faraday rotation measure into the CL table. This is used by PCAL when determining antenna polarization parameters and is used by other calibration tasks to de-rotate the data when polarization corrections are applied. FARAD may be run any number of times with different parameters before PCAL is run; each run of FARAD over-writes the values written previously.

Data from Boulder for the total electron content for year mm is contained in the file TECB.mm in the directory with logical name AIPSIONS. Currently, data are available for 1980 onwards through part of 1992. Some gaps in the TEC data occur, particularly for years 1980 and 1988 and for times when solar activity has been high and no reliable estimate of the total electron content could be made. Unfortunately, we are no longer able to get the TEC data from Boulder. If your VLA data are more recent than early 1992, you can consider using the ionospheric model in FARAD, but you should be aware that the model is crude and should check that it improves matters before using it in your final calibration.

The phase offsets between the right-hand and left-hand polarizations at a given time may be determined using, from a source with a known angle of linear polarization, data which have had the effects of imperfect feeds removed. The phase of the right-left correlations or the conjugate of the left-right correlations indicates the phase difference between the two polarizations.

The (initial) need for ionospheric corrections can be bypassed if either (1) you use unpolarized sources in PCAL, and/or (2) the ionosphere was well behaved during your observations. Typical rotation measures are only a few and therefore affect only L and longer-wavelength bands. The ionosphere is almost always well enough behaved to be ignored at shorter wavelengths and is usually able to be ignored even at L band. Changes of around 10^∘ in the relative phases of R and L polarizations are not enough to disrupt a PCAL solution seriously. And, fortunately, calibrators at long wavelengths, such as P band, tend to be unpolarized. In general, if the ionosphere is well behaved, it can be ignored. If it is bad, no simple model is able to correct it and you may simply have to forget about polarization for that observing run. Note that an apparent position angle variation of 3C286 with time probably indicates that ionospheric rotation is significant. But, if 3C286 shows large rotations, it does not follow that its rotation can be applied to other directions in the sky. All it implies reliably is that a model is needed.

Polarization calibration may be performed on amplitude- and phase-calibrated VLA data using the following five-step procedure:

Step 1: Run PCAL on one or more phase calibrator sources observed with a wide range of parallactic angles:

PCAL will list the fitted values of the antenna polarization parameters and the source polarizations with estimates of the uncertainties. If these results do not appear reasonable (e.g., large errors or large corrections or inconsistent solutions for the calibrator polarizations at neighboring frequencies), more editing and a rerun of PCAL may be necessary. PCAL puts the derived source polarizations in the SU table and the antenna feed values in the AN table. These values may be examined later with PRTAN and PRTAB.

Step 2:. Use RLDIF to determine the apparent right minus left phase angle of the polarization calibrator source, e.g., 3C286 or 3C138:

The matrix of scan-averaged right minus left phase angles (actually RL and conjugate of LR polarizations) will be printed. Check that none of the phases differ from the mean by more than a few degrees. If any do, then use UVFLG to edit these data and go back to step 1. After the matrix of phases, the average over the matrix of the right minus left phases is displayed. This is the number to be used in step 4. RLDIF returns these, one for each IF, in the CLCORPRM adverb array. It even averages over multiple calibrator scans, getting a reliable estimate of the average by iteratively discarding outliers. To see the results, type

LISTR may also be used with OPTYPE ’MATX’ ; STOKES ’POLC’ to make the printer display, one IF at a time. But you will have to do any averaging and placing of the results in CLCORPRM yourself.

This method will fail if the calibrator source (3C286 or 3C138, usually) is heavily resolved and the atmospheric phase stability is poor. (These two are frequently coupled!) Under these conditions, the self-calibration of the calibrator will have failed and will have to be done especially for the polarization calibration. In the steps below, you may safely relax the uv limits by about 20%, but should solve only for phases using SOLMODE = ’P’. The process consists of:

1. Apply CALIB to the inner (short-baseline) antennas on the calibrator source using the rules in the table found in §4.3.3 but relaxed a bit. Set DOCALIB = 1 ; GAINUSE = 2 ; SOLMODE = ’P’.
2. Use CLCAL to apply these solutions to the calibrator source using GAINVER = 2 ; GAINUSE = 3.
3. Run LISTR for cross-hand phases using only the antennas used with CALIB.
4. Use EXTDEST to delete CL table 3, a most important step.

After correcting the calibration, repeat steps 2.1 and 2.2 and the special calibration until satisfactory results are obtained.

Step 3: Use TASAV to copy all your table files to a dummy uv data set, saving in particular the CL table with the results of the amplitude and phase calibration. This step is not essential, but it reduces the magnitude of the disaster if the the next step is done incorrectly. (Note - this may be a good idea at several stages of the calibration process!)

The task TACOP may be used to recover any tables that get trashed during later steps. CLCOR will make a new CL table now, so a TACOP step is not needed.

Step 4: The right minus left phase offset corrections are made using task CLCOR. The phase offset correction is the expected value (twice the source polarization angle) minus the observed phases from step 2. The expected value is 66 degrees for 3C286, -18 for 3C138 (at L band, perhaps -24 at higher frequencies), and -140 for 3C48 (at 6-cm or shorter wavelengths). Thus, having used RLDIF and 3C286 in step 2 above

Then

This will cause CLCOR to apply appropriate corrections to the CL and AN tables. If the CL table becomes hopelessly corrupted, delete it and return to Step 3. If the AN table is corrupted, then PCAL must be re-run. If more than one CL table needs to be corrected, use the OPCODE=’POLR’ option only once; other CL tables must be corrected using OPCODE=’PHAS’ and correcting 1 IF at a time. CLCOR (with OPCODE = ’POLR’) may be applied multiple times to the same CL table, in order to get the R-L phases “right.” But you must not apply CLCOR in succession to different CL tables of the same database. If there is any doubt, rerun PCAL. The best way to judge if all is well in the final polarization solution is to look at the spread in the cross-hand phases for 3C286 or 3C138 (step 5 below). If the spread (“eyeball rms”) is less than 3 degrees, then all is well. If more than ten, then there is definitely something wrong.

Step 5: Use RLDIF to verify the polarization corrections:

Note well: all of this calibration process must be done with only one FQ at a time. PCAL with FQID = 2 will over-write solutions done for any other FQID.

The phases produced should be consistent. Significant deviations of the phase may indicate that further editing is needed or that residual atmospheric phase errors are still present. If this display appears okay, then the polarization corrections may be applied in SPLIT (see below) by specifying DOPOL = 1 when applying the calibration to produce single-source files.