Processing recipe: Linear Polarisation
Author: R.G. Strom
For obtaining polarization maps from standard continuum observations (all four dipole combinations must be present). See also the description of the program NCALIB, part 3.
In a normal WSRT continuum observation, four dipole combinations (XX, XY, etc.) are measured for each fixed-movable (numbered-lettered telescope) baseline. Since mid-1983, the standard configuration is for the X-dipoles in all telescopes to be set parallel (hence the Y-dipoles are also). A polarization code is recorded for each observation, which gives the X-dipole position angle in the fixed and movable telescopes, in steps of 
. The usual setting for the X-dipoles is 
(i.e., directed toward increasing RA), which gives a polarization code of 22. This results in the following definition of the Stokes parameters: 
(where 
). In the remainder of this description it will be assumed that the observation being corrected has code 22, and of course that all four dipole combinations have good data.
Most continuum observations made before mid-1983 were done with the dipoles in the movable telescopes rotated by to the fixed ones, usually with polarization code 21 [or in any event with the digits differing by an odd number]. For analyzing such observations, the user should consult with the WSRT User Service in Dwingeloo. From time to time, calibration sources are still observed in code 21 [generally indicated by `
' appended to the source name]. In almost all line observations, only one or two of the dipole combinations (XX, YY) are measured; they are of course unsuitable for determining source polarization.
The determination of the (observed) Stokes 
depends, as shown by the first two equations above, upon how well the gains of the XX and YY channels can be ascertained (since usually, 
). For the 
and 
determinations, the critical parameters are the dipole setting or orthogonality, and the ellipticity. Moreover, since is usually small (i.e., 
) its determination will also depend upon the quality of the XY and YX gains. The other parameter required to correct the XY and YX combinations is the 
phase difference. The correction is usually small (since it should have been determined and applied online in Westerbork) and has to be determined from an observation of a polarized source, or a special `crossed' (code 21) calibration source measurement. Finally, it may be necessary to correct for Faraday rotation in the ionosphere (this is usually only necessary at 49 and 92 cm), and for variations in the instrumental polarization if there is significant emission beyond the central part of the primary beam.
The following is a step-by-step summary of the processing recipe. For some of these steps, more detail is provided below.
for the calibrator (optional): (NMAP, followed by NPLOT or NGIDS.)
images of field: (NMAP, followed by NPLOT or NGIDS)
) and INPOL* (where * = 
for the other three Stokes parameters).)
Before determining the instrumental polarization using a calibrator, redundancy and selfcal solutions must be applied (use SELFCAL and ALIGN in the NCALIB option REDUN). This will also provide a useful check of the data quality. Note that at 92 cm (and in some cases 49 cm) there are background sources which may have to be included in the model used for ALIGN. Having run the ALIGN solution, NCALIB can be used to calculate the instrumental polarization (POLAR_OPTION: CALC) and examine the result (POLAR_OPTION: SHOW). Under normal conditions, the orthogonalities and positions of most dipoles should be under 
,
and the ellipticities generally under 1%. Large values (more than a few
degrees or percent) probably indicate an instrumental problem (bad data) and require further investigation. Run a solution on a different calibrator as a check. Deviant points can be changed by hand (POLAR_OPTION: EDIT). Tables of instrumental polarization are also generated from time to time in Westerbork, and the values can be entered by hand (POLAR_OPTION: SET), or used to cross-check the solution from NCALIB.
As a check on the instrumental polarization thus generated, it may be useful to make a map of an unpolarized calibrator if one has been observed for a few hours or more during the same period (a shorter observation could also be used, but the map might prove difficult to interpret). Make sure that SELFCAL and ALIGN corrections have been successfully applied, and then look at the Q, U and V maps (made with NMAP). Ideally, they should be zero; the residual as a fraction of the flux density is an indication of the error which will be present in the polarization map of your observation. (If your source is very extended, however, the polarization error pattern generated by a point source may be misleading).
Finally, we have to determine (or at least check) the phase difference. This is best done using a linearly polarized calibrator (strictly speaking, a source with strong U signal). The method assumes that V is much smaller than U (since 
, a nonnegligible V affects the phase), which is usually the case. The correction can be calculated (VZERO_OPTION: CALC, ASK, etc.) and applied to the data in several ways. Usually, the XY and YX phase zeroes have been determined and applied on-line to sufficient accuracy for most polarization maps, so the correction should be a few degrees or so. However, there have been instances where the difference was as much as 
, so it is advisable to check. If various frequency channels are used, the phase difference should be calculated for each one separately, as the correction is usually frequency dependent.
The instrumental polarization determined from a calibrator is, strictly speaking, only correct for a source at the beam center, though at most frequencies the variation within the half-power primary beam is small. For polarization mapping over large fields, there is a separate correction for off-axis instrumental polarization (NCALIB: NMODEL - BEAM).
Errors; some error patterns; effect of source extent.
Ionospheric effects and the I map.
What can be done if a polarization combination is missing?
Etc.
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