[evlatests] Some Thoughts on Polarizer-Induced 'closure' errors

[Sanjay Bhatnagar]

On Thu, Nov 5, 2009 at 3:17 PM, Rick Perley <rperley at nrao.edu> wrote:
>
>    Although it might be thought that we can 'fix' this problem by
> simply incorporating the results of a standard 'PCAL' analysis, it's not
> so.  The outputs from the standard polarization analyses have to be
> referenced to some assumed standard, as the first-order responses in the
> (RL) and (LR) correlations are proportional to *differences* in the D
> terms.  So the 'D' terms we usually see are not the 'real' ones -- they
> are all referenced to some (unknown) standard value.  It doesn't matter
> in polarization imaging, since the assumed offsets cancel out, but it
> *does* matter in the corrections needed to the parallel-hand
> responses.   To do this in a more complete way (than simply running the
> BLCAL route), we need to measure the absolute (non-referenced) values of
> the antenna polarizations.    There are various ways to do this -- but I
> think the easiest is to use the 'rotate the receiver trick'.  The
> trouble here is that this is labor intensive -- o.k. for a one-off
> experiment.  But if these terms do vary significantly in time, and we
> need to track them to do high-fidelity imaging, a more automated
> approach will be needed.

There are (at least) two relevant papers on this issue (of "closure"
noise due to polarization leakage and attempts to automate its
calibration):

Massi et. al., 1997, A&A, 318, L32
http://adsabs.harvard.edu/abs/1997A%26A...318L..32M

This discusses the exact same issue of large antenna based
polarization leakage terms in EVN masquerading as "closure" noise.
EVN has upto 20% polarization leakages!

GMRT had similar issues (~5% leakage at 327 MHz with upto 10% for bad
antennas).  Assuming the source in the sky to be unpolarized (or with
a known polarization vector), one can write a solver to
*simultaneously* solve for the complex gains and leakages using the
parallel-hand data.  The solution are the sum of gains and leakage per
antenna (G_i + D_i). With some reasonable assumptions about the
statistical distribution of the polarization properties of the
antennas in the array, the solutions can be separated into G_i and
D_i.  However for calibration purposes this separation is not
required.

The relevant paper for this is:

Bhatnagar & Nityananda, 2001, A&A, 375, 344-350
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2001A%26A...375..344B&db_key=AST&high=3cd1ba40a617297

This paper also has a plot of simulation of RMS noise limit vs.
percentage polarization leakage.



I have pulled out the solver from the GMRT software and stuck it in as
a solver in CASA calibration framework.  Some tests are required to
make sure that all is well (data is flowing to the solver routine in
the correct format, etc.).  We can then apply it on 3C147 field and
see what happens.  If this is the source of closure noise
(D_i)*conj(D_j) * (Stokes-I amplitude) should be close to the BLCAL
solutions for the various baselines.

Regards,
sanjay

-- 
संजय