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<p>Rick-</p>
<p>I think the failed expectation you bemoan is that you now see
only/mostly the odd symmetry effect, and largely independent of
refant, and of the varied R-L effects observed (indirectly) for
them. I have a likely explanation:<br>
</p>
<p>As has been emphasized ad nauseum (and correctly) in discussions
so far, examination of R-L phases from (p-hand) gain solutions can
only show <i>differences</i> in antenna-based systematic field
rotation due to the effective geometry (e.g., relative tilts,
etc.) of the antennas, such that everything is always w.r.t. the
unrecovered geometrical facts of the refant, <i>and any absolute
effects common to all antennas will be entirely invisible.</i>
On the other hand, examination of realized linear polarization
position angle (i.e., phases of the RL and LR* correlations)
connects the observation to an <i>external</i> truth (the source
polarization, assumed constant), against which we typically
calibrate, nominally on the assumption that the remaining
uncalibrated residual--i.e., the cross-hand phase of the
refant--is stable in time (a statement about <i>electronics</i>).
In fact, we can correctly surmise from the R-L evidence that this
last assumption is likely not particularly true for sources that
transit near zenith (due to <i>geometry</i>), unless we are lucky
enough to pick a refant without significant geometric errors.
Maybe there is such an antenna, but there is more....</p>
<p>We are additionally subject to any mismatch between the real <i>absolute</i>
geometry of the refant and the geometric model for field rotation
built into the parallactic angle correction performed when
calibration is applied. As I tried to point out in the earlier
thread (3/28, among other things, responding to--indeed, warning
about--musings on examining crosshands), this is where the details
of coordinate systems matter, and it is my suspicion that the
AIPS* (like CASA) parallactic angle calculation is likely using
geocentric latitude (spherical earth), rather than geodetic
(oblate spheroid). In other words, <i>the whole array (and thus
any refant) is systematically leaning NORTH by ~10.7 arcmin
within the coordinate system used for the parang calculation</i>,
and so (unless there are E-W tilts of similar magnitude in the
refant), we'll be dominated by a net N-S tilt (mostly) regardless
of refant choice, and therefore observe (mainly) the odd symmetry
in measured time-dep linear polarization position angle. I think
that is what you are describing (without a plot, alas). </p>
<p>(*As before, I'd welcome Eric's correction on this point, if I'm
wrong about AIPS here.)</p>
<p><br>
</p>
<p>Regarding the BLCHN (==BLCAL bandpass, per p-hand, I presume?)
corrections, two thoughts occur:</p>
<p>1. What does BLCHN/BLCAL do with the crosshands? Doesn't touch
them, presumably? (I hope)<br>
</p>
<p>2. I recall a rather cute demo of relative "BLCAL" effectiveness
from early EVLA commissioning wherein <i>constant</i> BLCAL
worked better (in Stokes I) for an unpolarized source (probably
OQ208) than it did for a strongly polarized one (probably 3C286),
which only yielded to a time-dep BLCAL. As we were realizing
that EVLA instrumental pol was significantly worse than old VLA
(and one or two bands were especially bad due to non-cryo
polarizers), this was attributed to the fact that the closure
errors were mainly caused by the instrumental polarization terms
in the parallel hands. For the unpolarized source, there is only
the <i>constant</i> ~DiDj*I term so constant BLCAL can model it
successfully. For the polarized source, there are also
(parang-rotating) D*(Q+iU) terms which don't get corrected in
detail unless the BLCAL is time-dependent. It is not quite clear
from your description if this explanation works for you current
data. That OQ208 approaches expected thermal and 3C286 remains
higher is consistent, but I'm not sure how to interpret your
improvement factors in this context. Factors in excess of
thermal noise and as a function of fractional polarization would
be clearer.... Thoughts? <br>
</p>
<p>-George</p>
<p><br>
</p>
<p><br>
</p>
<div class="moz-cite-prefix">On 4/11/22 20:11, Rick Perley via
evlatests wrote:<br>
</div>
<blockquote type="cite"
cite="mid:f38e680f-ca5c-c8f4-b973-9ed76492be5c@nrao.edu">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<p>Previous circulars described the curious phase differences
between the RCP and LCP correlations. A plausible connection
with differential antenna tilts was suggested. <br>
</p>
<p>If this is indeed the case, we should see the effects of the
R-L phase differentials in the cross-hand data for highly
polarized sources. Three of the four objects observed in this
study are indeed strongly polarized, so I have looked closely
for the expected signature. <br>
</p>
<p>Since we have circularly polarized systems, the expected
signature is a change in the apparent position angle of the
linearly polarized flux of the polarized sources. The magnitude
should be about the same as the observed R-L phase, and it
should be greatest for those sources which transit nearest the
zenith (i.e., largest for 3C286, and least for 3C273). Finally,
it should change with difference reference antennas, as the
effect of calibration is to put all antennas into the phase
frame of the reference antenna. <br>
</p>
<p>As will be described below, all of these expectations, *except
one* are met. <br>
</p>
<p>To do these tests, I extracted a single spectral window from
the data (to speed up the rather laborious processing). I chose
a frequency (4936) for which there was both a 3-bit SPW and an
identical 8-bit SPW (identical means the same center frequency,
wiodth, resolution, and observation time). <br>
</p>
<p>To check on the effect of changing reference antennas, I
calibrated, and imaged, with three different reference antennas,
chosen for having very different R-L profiles in the prior
work: ea01, ea02, and ea19. <br>
</p>
<p>Data were calibrated with standard techniques, and self-cal,
using an excellent model, performed on each. R-L phase plots
were made, and confirmed what has been reported before. <br>
</p>
<p>Images in I, Q, and U were then generated (to be shown below).
I have two special tricks which were performed to improve the
images: <br>
</p>
<p>(1) BLCHN, which does a correlator-based solution using the RR
and LL data, and <br>
</p>
<p>(2) RLCAL, which solves for the R-L phase difference, based on
the temporal change in position angle of the polarized
emission. <br>
</p>
<p>Details are described below. <br>
</p>
<p><b>A) Stokes I images. </b><br>
</p>
<p>The observing duration for each source in this run was about
the same for each: about 15 minutes (a bit more on OQ208).
Hence, each should have about the same noise limit. The
initial 'dynamic range' for all four sources was about the same
-- about 25,000:1 (peak to rms) -- somewhat less for 3C273
(which will be explained below). The expected rms noise is
about 35 microJy/beam -- the observed limits were much higher:
76, 133, 275 and 1440 microJy/beam for OQ208, 3C287, 3C286 and
3C273, respective. <br>
</p>
<p>No amount of self-cal can improve on these results. The source
of the problem lies in the failure of the correlator gains to be
described in terms of product as antenna gain fluctuations. The
effect on the imaging is easily seen in the images themselves.
See below. <br>
</p>
<p>AIPS has a couple of nifty programs to solve for and utilize
correlator-based gains. BLCHN solves for these on a
channel-by-channel basis. I used the program to find and apply
these gains. BLCHN uses a model (clean components) and the
self-calibrated data. For this application, I solved for a
single solution, for each baseline, averaging over the entire
observation duration. (BLCHN is a very dangerous program --
were we to use a short time interval, it will happily make the
data match the model *exactly* -- no matter how far the model is
from reality). <br>
</p>
<p>Attached are 'before' and 'after' image pairs, for each source,
in Stokes 'I'. Things to note:</p>
<p>a) For OQ208, 3C286 and 3C287, the application of this constant
correlator-based correction has greatly improved the images.
The grey scales in each change in proportion to the peak
brightness: -0.1 to 1 mJy for OQ208, -0.2 to 2 mJy for 3C287,
-0.4 to 4 mJy for 3C286, and -1.4 to 14 mJy for 3C273. </p>
<p>b) The 'closure perturbations' for 3C273 are much more
prominent than the other sources -- this is because this object
is at +2 declination, so the u-v tracks are nearly perfectly
horizontal, which results, in the transform, with the error
effect primarily seen in the N-S bar. <br>
</p>
<p>c) The factor of improvement is quite large: a factor of 4.5
for 3C286, 3.5 for 3C286, 2.0 for OQ208, and 2.5 for 3C273. The
noise in OQ 208 is near thermal (it is the weakest source) --
all the others are still well above thermal, especially 3C273.
Apparently, a (constant) closure correction is not enough to
remove all the errors. the noise in 3C273, in particular,
remains a factor of about 20 higher than thermal. <br>
</p>
<p><br>
</p>
<p><b>B) Polarization Images. <br>
</b></p>
<p>Stokes Q and U images were made for all sources. OQ208 is
nearly completely unpolarized -- the images have what appears to
be noise-limited appearance. <br>
</p>
<p>For the other sources, there is significant polarized
emission: 3.5% for 3C287, 11,.5% for 3C286, and nearly 10% for
3C273. Examination of the Q and U images for 3C286 in
particular, clearly showed the effect of a change in R-L phase
for some of the scans. <br>
</p>
<p>Some years ago, I asked Eric to generate a program to solve for
R-L phase changes -- RLCAL. This is essentially a polarization
positional angle self-calibration program: It compares the
observed RL and LR phases to that predicted by a model, and
finds the changes in the RL and LR phases which best matches the
model. <br>
</p>
<p>This program was run on the observed images for 3C286, 3C287
and 3C273 data. A very clear signature was seen with the
following characteristics:</p>
<p>a) A phase signature of a few degrees (maximum 4.0 for 3C286),
with 'odd' symmetry about meridian transit. <br>
</p>
<p>b) Far stronger on 3C286 than the others, almost no signature
at all on 3C273. <br>
</p>
<p>c) Sharply dependent on parallactic angle. <br>
</p>
<p>d) <b>Independent of the reference antenna. (!!!) </b>I
repeated this full operation (calibration, imaging,
self-calibration) with three different reference antennas,
chosen because they have starkly different R-L phases as seen by
the earlier work. They all gave the same signatures to the
RLCAL program. <br>
</p>
<p>Attached are three figures, showing the effect of applying the
RL and LR phase changes to the data. OQ 208 has no
polarization, so is omitted. These are in Stokes 'Q' only --
the 'U' images show the same effects. <br>
</p>
<p>The 3C286 and 3C287 images are greatly improved, although clear
residuals remain. However 3C273 is hardly improved at all -- no
surprise as the observed RL and LR phase solutions from RLCAL
are nearly constant. <br>
</p>
<p>To show the correlation with parallactic angle, here are the
generated RL solutions for 3C286 (in degrees) , along with the
actual parallactic angle:</p>
<p>RL Phase Par Angle</p>
<p>0.4 -74</p>
<p>0.5 -74 <br>
</p>
<p>0.5 -74</p>
<p>0.9 -74</p>
<p>0.8 -74</p>
<p>1.1 -72</p>
<p>1.6 -69</p>
<p>2.6 -62</p>
<p>4.0 -45</p>
<p>0.7 3</p>
<p>-2.8 48</p>
<p>-2.8 64</p>
<p>-2.8 64</p>
<p>-2.4 70</p>
<p>-2.0 72</p>
<p>-1.8 74</p>
<p>-1.7 74</p>
<p>-1.6 74</p>
<p>---------------------------------</p>
<p>A similar, but much smaller range in phase correction, is seen
in 3C287. For 3C273, the range in parallactic angle is 79
degrees (-31 to +48 degrees), but the range in RL phase
correction is only 1.4 degrees. So the correlation of phase
correction with parallactic angle is far from perfect. Perhaps
the correlation is better with elevation? but then, why do the
profiles have very clear odd symmetry w.r.t. transit? <br>
</p>
<p>C) Bottom Line:</p>
<p>I'm puzzled, perplexed, and completely devoid of a proposed
solution which matches both the R-L and the RL phase effects.
They are similar, yet different. <br>
</p>
<p>All suggestion will be seriously considered! <br>
</p>
<p>Rick<br>
</p>
<p><br>
</p>
<br>
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