[evlatests] PDif, R-L Phase, and Polarimetry

[Rick Perley]

     I presented last Thursday evidence from the 'BD' side of Ku-band 
that changes in the R-L phases (whose stability on at least one antenna 
is critical for accurate polarimetry) are highly correlated with changes 
in the measured 'PDif' in the switched power monitor. It was also noted 
that the 'AC' side of  Ku-band was much more stable than the 'BD', in 
both parameters.   At the time, I did not have the data from the other 
bands.  These data are now in, and I can summarize the situation.

     I'll note here that Eric has greatly assisted in the 
characterization of this issue by generating a special AIPS program 
(`CENTR') which moves the phase reference channel from the edge to the 
center of each subband (aka 'spectral window').  This has the beneficial 
effect of removing the rocking phase ramp which accompanies the delay 
tracking.  The magnitude of the delay effect on the phase, at the edge 
of the subband, is compariable to the R-L phase differences we are finding.

     I emphasize here that these conclusions come from a script which 
made well over 1000 band changes (and almost as many correlator 
configuration changes) in one day.  There is no evidence that 
single-band scripts will suffer any of the issues noted below.

     *Top-Level Summary*

     1) Antennas which demonstrate large (10 degrees or more) changes in 
R-L phase between scans also have large changes in the switched power in 
one or both of the two polarization channels.  This is true at *all 
bands*.  However, there does not appear to be a perfect one-to-one 
correspondence between a deviant PDif and a bad R-L phase.  There are 
some (few) cases where a change in switched power was seen without a 
corresponding phase change.
     The magnitude of the R-L phase is typically 10 to 50 degrees. Some 
(but very few) reach 90 degrees.

     2) The converse to the above seems to be always true:  Antennas 
whose two polarizations show no scan-based changes in PDif always have 
steady R-L phases.  *Hence, when searching for a good phase reference 
antenna (especially for doing polarimetry), pick one whose PDif values 
show only smooth variations which are the same on both polarizations.*  
(See #3, below).

     3) The relation between changes in PDif and R-L phases extends to 
slow changes as well.  There are numerous examples of antennas with slow 
changes in PDif on one polarization and not the other, which also show 
slow changes in R-L phase with identical timescale. (This is not 
necessarily a surprise -- the change in PDif indicates a change in gain, 
which is accompanied by a change in phase).

     Unfortunately, it is not at all clear (and is probably unlikely) 
that there is any predictive power in the changes in PDif.  That is, 
there is likely no algorithm which will accurately convert a change in 
PDif into a change in phase.

     4) The low frequency bands are much less affected by this issue.  
Indeed, L, S, and C bands have no, or nearly no, R-L phase changes.  
(It's harder to make a similar statement about PDif, as RFI introduces 
PDif changes unrelated to system parameter changes).

     5) The R-L/PDif variation problem is most severe in the four 
highest frequency bands.  Ku and K bands appear to be the most affected 
-- but this conclusion may well be due to the much higher SNR of these 
two bands, compared to Ka and Q.   For Ku and K bands, the 'BD' IFs are 
much more strongly affected than the 'AC'.

     6) X-band is a transitional case -- not nearly as bad as Ku, but 
much worse than C.

     7) There is good evidence for a diurnal change in R-L phase on many 
antennas.  The shape of this change is an excellent match to the outside 
temperature change -- the obvious conclusion is that the two analog 
polarization channels have different temperature coefficients, or have 
different temperatures through the day. Fortunately, this magnitude of 
this effect is small -- 5 degrees or less, in most cases.

    * Why is this important?*

     An (R-L) phase change is equivalent to a rotation of the 
polarization frame on the sky.  That is, if the (R-L) phase on the array 
changes by 20 degrees for a scan, then a polarization image make from 
that scan will show the polarization vectors rotated by half this -- 10 
degrees.  (Stokes 'I' is not affected).  For a weak source, it may be 
argued this is not a significant problem -- and perhaps it isn't.  But 
for a strongly polarized source, the resulting images (in Q and U) will 
not deconvolve properly, with high residuals clearly evident in the image.

     When calibrating polarimetry, it is critical that a reference 
antenna with 'rock-steady' R-L phase be utilized.  The effect of phase 
calibration is to impose the reference antenna's R-L phase on *all other 
antennas*.  (There are other schemes -- such as using a global mean over 
all antennas as the reference.  But I disagree with this 'safety in 
numbers' approach.  Far better to find, and repair, that which is 
causing the problem in the first place).

     Fortunately -- there is an easy fix for R-L phase changes available 
in the post-processing software, provided a polarization model is 
available.  The AIPS task 'RLCAL' uses the model to calculate the change 
in L-channel phase for each scan (or record, if desired).  These 
corrections can be applied to the data, in a process similar to phase 
self-calibration.