[evlatests] More on R-L phases

Sun Apr 17 15:12:41 EDT 2022

The parallactic angle calculated for a target, geographical location and time is only realized for polarization and applicable to an observation in an ideal situation, where the orientation of the feed polarization aligns with the

vertical circle. I think of cross-hairs tied to the pupil with a misalignment to the vertical, rotated with respect to the vertical. For me, it is easier to visualize in terms of linear polarization, and as already noted, this rotation

becomes a phase difference for circulars.

The applicable rotation is about the boresight optical axis and the feeds might have been installed aligned to a mechanical azimuth vertical circle. Telescope mount errors, modeled by the pointing model, connect the mechanical

orientation and optical orientation.

Rick has already zeroed in on one component of the mount error viz., the azimuth  axis tilt. The key aspect of the azimuth axis tilt in the current context is that the required pointing correction in azimuth is a function of elevation, with a tan(el) dependence. The resulting azimuth corrections result in a rotation of the polarization orientation (pupil cross-hair), or a phase difference for circulars, which blows up with elevation. The aztilt also

causes elevation errors, but the azimuth pointing corrections are more important than elevation corrections due to the tan(el) elevation dependence. The impact of elevation corrections remain at the same level as their actual (small) error values, whereas the azimuth corrections scale up several fold as tan(el), leading to a large effect.

Now, there are two other mount errors that have a similar character – the azimuth collimation error which has a 1/cos(el) dependence, and the elevation axis tilt which has a tan(el) dependence, same as the aztilt. A full accounting of the phase errors that Rick has observed should consider these parameters of the mount error model (the pointing model) as well. I expect that these parameters are of larger magnitude (the azcoll in particular, from experience with other telescopes) and may resolve the current poor detailed matching of the observed phases to the actual known antenna parameters - only aztilt has been considered so far, where there was not a match in magnitude

or correlation with actual values. This can also solve the other issue that bothered me - of the width of the patterns seen with hour angle, which appear to be wider than the aztilt-only interpretation: 1/cos(el) is wider than

tan(el). I think there is nothing fundamentally special about aztilt, except that it is equivalent to placing an antenna at a different location, which allowed Rick to calculate the expected errors relatively easily. These

are all mount errors which impact the realized polarization position angle relative to the feeds. A proper analysis should consider the actual antenna locations and their respective mount errors which lead to different rotations of the polarization position angle. Field rotation for the just the (ideal) parallactic angle alone when calibrating is not sufficient (in addition to the geocentric/geodetic question George pointed out, except that this does not change from antenna to antenna).

George has already provided an explanation for the results on R-L phases, which makes sense to me.

In summary, I think that the geometrical interpretation appears to be alive and well and looking at additional mount errors may provide a path for detailed matching. I intended to make some plots to show the expected patterns, but

haven't gotten to a point where I can present something sensible, but wanted to share the thought, nevertheless, for whatever it is worth.

Hopefully, this is helpful.

Cheers,

TK.

The expressions for mount errors, if someone would like to look at this more closely before I get to it, are:

(e.g. N. Patel & T. K. Sridharan, 2004, SPIE, "Pointing calibration of the SMA antennas", Proc. SPIE 5496, Advanced Software, Control, and Communication Systems for Astronomy, (15 September 2004); https://doi.org/10.1117/12.549655))

dAz = AzDC + AzC/cos(El) +TEl*tan(El) + TAz*(sin(Az-Azt)*tan(El)

dEl = ElDC + ElSag + TAz*cos(Az-Azt)

dAz, dEl: az and el pointing errors from mount errors.

AzDC : Encoder offset

AzC  : Azimuth Collimation error

TEl  : Tilt, Elevation axis

TAz  : Tilt, Azimuth axis

Azt  : Direction of Azimuth axis tilt

ElDC : Elevation encoder offset + Elevation collimation error

ElSag: Sag function in elevation

Only the dAz expression and the last three terms there would be important contributors.

From: evlatests <evlatests-bounces at listmgr.nrao.edu> on behalf of George Moellenbrock via evlatests <evlatests at listmgr.nrao.edu>
Reply-To: George Moellenbrock <gmoellen at nrao.edu>
Date: Tuesday, April 12, 2022 at 4:44 AM
To: "evlatests at listmgr.nrao.edu" <evlatests at listmgr.nrao.edu>
Subject: Re: [evlatests] More on R-L phases

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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