[evlatests] More on R-L phases
George Moellenbrock
gmoellen at nrao.edu
Tue Apr 12 04:44:07 EDT 2022
Rick-
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:
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
/differences/ 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, /and any absolute effects common to all antennas will be
entirely invisible./ 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 /external/ 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 /electronics/). 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 /geometry/), unless we
are lucky enough to pick a refant without significant geometric errors.
Maybe there is such an antenna, but there is more....
We are additionally subject to any mismatch between the real /absolute/
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, /the whole
array (and thus any refant) is systematically leaning NORTH by ~10.7
arcmin within the coordinate system used for the parang calculation/,
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).
(*As before, I'd welcome Eric's correction on this point, if I'm wrong
about AIPS here.)
Regarding the BLCHN (==BLCAL bandpass, per p-hand, I presume?)
corrections, two thoughts occur:
1. What does BLCHN/BLCAL do with the crosshands? Doesn't touch them,
presumably? (I hope)
2. I recall a rather cute demo of relative "BLCAL" effectiveness from
early EVLA commissioning wherein /constant/ 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 /constant/ ~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?
-George
On 4/11/22 20:11, Rick Perley via evlatests wrote:
>
> Previous circulars described the curious phase differences between the
> RCP and LCP correlations. A plausible connection with differential
> antenna tilts was suggested.
>
> 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.
>
> 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.
>
> As will be described below, all of these expectations, *except one*
> are met.
>
> 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).
>
> 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.
>
> 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.
>
> 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:
>
> (1) BLCHN, which does a correlator-based solution using the RR and LL
> data, and
>
> (2) RLCAL, which solves for the R-L phase difference, based on the
> temporal change in position angle of the polarized emission.
>
> Details are described below.
>
> *A) Stokes I images. *
>
> 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.
>
> 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.
>
> 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).
>
> Attached are 'before' and 'after' image pairs, for each source, in
> Stokes 'I'. Things to note:
>
> 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.
>
> 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.
>
> 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.
>
>
> *B) Polarization Images.
> *
>
> 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.
>
> 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.
>
> 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.
>
> This program was run on the observed images for 3C286, 3C287 and 3C273
> data. A very clear signature was seen with the following characteristics:
>
> a) A phase signature of a few degrees (maximum 4.0 for 3C286), with
> 'odd' symmetry about meridian transit.
>
> b) Far stronger on 3C286 than the others, almost no signature at all
> on 3C273.
>
> c) Sharply dependent on parallactic angle.
>
> d) *Independent of the reference antenna. (!!!) *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.
>
> 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.
>
> 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.
>
> To show the correlation with parallactic angle, here are the generated
> RL solutions for 3C286 (in degrees) , along with the actual
> parallactic angle:
>
> RL Phase Par Angle
>
> 0.4 -74
>
> 0.5 -74
>
> 0.5 -74
>
> 0.9 -74
>
> 0.8 -74
>
> 1.1 -72
>
> 1.6 -69
>
> 2.6 -62
>
> 4.0 -45
>
> 0.7 3
>
> -2.8 48
>
> -2.8 64
>
> -2.8 64
>
> -2.4 70
>
> -2.0 72
>
> -1.8 74
>
> -1.7 74
>
> -1.6 74
>
> ---------------------------------
>
> 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?
>
> C) Bottom Line:
>
> 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.
>
> All suggestion will be seriously considered!
>
> Rick
>
>
>
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