[evlatests] Summary of Polarization Meeting

[George Moellenbrock]

All-

>    B) Status of polarization calibration in CASA, including
> implementation of full matrix corrections.

I'm afraid much of Rick's summary here requires correction.

>    This refers to the implementation of the full 4 x 4 'Mueller' matrix
> which relates the observed cross products (RR, RL, LR, LL) to the
> desired Stokes visibilites (I, Q, U, V).

None of this has to do with mere conversions (the 'Mueller' matrix) from 
"observed cross products (RR, RL, LR, LL) to the desired Stokes 
visiblities (I, Q, U, V)".  This, of course, is trivial, and we are 
already doing it, e.g., to form images in the Stokes paramters from data 
in correlations.  The role of instrumental polarization solutions in 
realizing the Stokes parameters _correctly_ is, in fact, done via 'Jones' 
matrix algebra, and done separately from the conversion to formal
Stokes parameters.

> The implemented software in
> both CASA and AIPS utilizes the first-order approximation, which drops
> all products between D terms and Stokes Q, U, V and other Ds.  (That is,
> it retains only the product between D and I)

Regarding the instrumental polarization calibration solve, CASA currently 
supports (and, for now, compells) essentially the same standard linear 
approximation as AIPS (terms containing the product of 2 more Ds, Qs, or 
Us and all terms containing V are ignored, leaving only linear terms in D 
multiplying Stokes I in the crosshands along with the intended terms). 
There are a few additional explicit modes also supported 
(channel-dependence within spec windows, asserted source polarization, 
etc.), cf AIPS (though I'll confess some ignorance about exactly what PCAL 
can do).  I'll clarify (for CASA) all of this separately.

>       George reports that he is nearly ready to do tests of the full
> corrections.

The code required to _apply_ an instrumental polarization solution in the 
full matrix (non-linearized) formalism mostly exists (it was there first, 
actually), and can be turned on again with a very small effort, but has 
been disabled (to avoid misleading users) because:

> An importance point is that, for the VLA, it is very
> unlikely that the *absolute* Ds can be derived as a matter of course
> from ordinary observations -- by construction, all antennas view the
> sources at the same parallactic angle, making impossible, or at least
> highly unlikely, a robust method for extracting the absolute Ds.  By
> necessity, all 'Ds' determined from standard interferometry are
> referenced to a standard -- either a global mean (CASA, MIRIAD), or a
> particular antenna (AIPS).

Well, I'd hope to say "tricky" rather than "unlikely".  _Polarized_ 
calibrators are required (unpolarized calibrators provide only the 
additional DDI term in the parallel hands, which cannot be 
completely decoupled from the gain calibration if the mean departure from 
polarization purity is non-zero), and quite probably some iteration with 
the ordinary gain calibration (a la linear feed heuristics) will also be 
necessary.  I believe most of the solving code for the non-linearized 
solution also already exists, but it will require a bit more work to 
re-energize it (cf the apply-only case).

In the linear approximation solve, CASA refers its D solutions to a single 
refant (like AIPS), if requested (it sets the refant's Dr to (0+0j) and 
offsets all of the other Dr and Dl accordingly).  We plan to support 
other referencing modes (e.g., a global mean), mainly to handle inadequate 
poln cal observations (e.g., no parallactic angle coverage), as well as no 
referencing at all for the properly constrained non-linearized solve.

> The full matrix correction requires
> absolute, not relative Ds (which are sufficient for the linearized
> treatment).   It was agreed that a good test of the code will be to
> utilize the 'absolute' Ds determined by receiver rotation, from which we
> hope an interative process can be developed.   There is reasonable hope
> for this procedure, given the stability of the D terms.  Note that in
> general, these higher order corrections may only be needed for imaging
> in the multi-hundred thousand to one regime.

This 'receiver rotation trick' enables decoupling the R and L instr pol 
systems from each other (and hence, 'absolute' Ds)  via differential 
parallactic rotation of the sort achieved naturally in VLBI, all while 
using the linear approximation (introducing higher order terms is not 
required).  CASA can probably be tricked into recognizing the rotated
antenna's parallactic angle offset, and solve the whole system
jointly....

>    Other methods to determine absolute Ds were briefly discussed.   If
> time permits, I may test these.

I took some data many years ago that involves 3 different VLA antennas 
alternately co-observing with both the VLA and VLBA.  The co-observing VLA 
antennas can be solved absolutely in the VLBI observation, and then used 
to refer the internal VLA D-term solution.  Because of the structure of 
the observation (switching the VLA's reference antenna repeatedly to 
follow the VLBI-participating VLA antenna), there were some bookkeeping 
issues in the resulting datasets, and I never quite completed the 
analysis.  It could be resurrected, if deemed desirable, but the answer we 
get will no longer apply, of course.

>    George is currently busy with development of polarimetry for ALMA,
> but should soon be available for these trials.  He will report
> separately on these issues in more detail.

Yes, the linear approximation treatment for linear feeds is nearly done 
(linears-specific source pol estimation and XY-phase compensation, 
mainly), and a number of peripheral developments implemented in that 
effort will be useful for the EVLA case (e.g., cross-hand delay 
solve/apply, some streamlined calibration model specification).  Also, the 
"<1 GHz" EVLA/NRL system will use linear feeds, and so will require the 
linears treatment.  For both polarization bases, the existing fundamental 
instr pol solver is exactly the same, in fact.  I will shortly embark upon 
the generalization to the non-linearized solve with both instruments in 
mind.  Alas, the EVLA polarization heuristics will evolve to look more 
like the linears case in general (rather than vice-versa), as noted above.

Yes, I already have started a summary of "CASA Polarization Status and 
Plans" (based on my statements in the meeting on Wed), and I will try to 
distribute it by early next week.  It will also include some info about 
the expected (and pretty much standard) gain/bandpass calibration that 
should occur prior to attempting polarization calibration in CASA.

-George











>
>    C) Status of off-axis polarimetry.
>
>    Sanjay reports that the necessary code is available for testing
> within CASA, but that higher priority items are taking up his time.
>    Frazer has suggested that the beam polarization models (derived by
> Walter using Penticton's GRASP8 software) would be sufficient for
> testing the code.  Others opined that the beam holography observations
> made by Rick last December, and reduced by Bill Cotton, (and reported by
> Bill in an OBIT memo) would be more appropriate.  Bill offered to
> provide suitable tables for this purpose.   Bill also offered to use
> these models with his OBIT environment, to calibrate some of Frazer's
> wide-field data.
>
>    Time ran out before a discussion of observational methodologies
> suitable for our EVLA users (both 'internal' RSRO/ECSO, and external
> 'OSRO') could be held.  We will need another meeting, perhaps in a
> couple of weeks, to review the status.
>
>
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