[evlatests] [Ecsv] Summary of Polarization Meeting

[Walter Brisken]

Hi all,

Perhaps I didn't get the whole story as I did not attend this meeting, but 
I suspect Barry's response here is limited in applicability to the portion 
of the primary beam that can be well approximated as having no 
instrumental polarization.  Absolute polarization calibration does start 
to matter when observing near the edges of the beam, perhaps even at the 
half power point.  This is because the natural basis polarization states 
become chosen for you (and are no longer arbitrary), and thus you can no 
longer rely on a polarization basis that fits your needs.  Since the 
natural polarization basis states will change over the primary beam, only 
properly calibrated data should produce wide-field images without 
artifacts.

I propose a simple observation to test this proposition.  Measure and 
calibrate a database on a bright source observed on bore sight.  Then 
attempt to apply the resultant polarization calibration to observations of 
the same source observed at a few -6dB points around the center of the 
beam while incorporating the full-beam polarization corrections in the 
form of the models Sanjay has in his imaging code.  I suspect that 
artifacts will appear.

This concept forms the ground layer of an idea I've had (but have yet to 
test) for polarization calibration for the VLBA.  One can use the 
instrumental polarization of the off-axis antenna beams to produce an 
effective source of known polarization angle from an unpolarized source. 
When I get enough time I plan to try this.

-Walter

On Fri, 16 Jul 2010, Barry Clark wrote:

> I slightly disagree about the usefulness of the absolute D terms.
> For purposes of estimating I (necessary for very high dynamic ranges),
> the ordinary, relative ones are adequate.  The use of any sort of
> D terms suffices to move the observation to two orthogonal
> polarizations, and I is the sum of the powers in the two.
>
> An interesting way of looking at D term application is that the
> linear form moves the vectors along the tangent plane to the
> Poincare sphere, and the higher order terms convert this motion
> to a rotation preserving the radius (that is, the power).
>
> As George pointed out, you can add arbitrary constants to the D terms,
> which shoves you to a different polarization reference, but I believe
> that if it is done right, it will preserve I.  (This is much easier
> to see if you first think about calibrating on an unpolarized source,
> and once you convince yourself that works, thinking about a polarized
> one.)
>
> The usefulness of the absolute D terms is in measuring the polarized
> flux.  If our orthogonal polarizations differ from true circular by,
> say, 1 dB, the naively estimated linear polarizations will be wrong
> by about 1% of their values.
>
> Rick Perley wrote:
> [snip]
>>
>>     B) Status of polarization calibration in CASA, including
>> implementation of full matrix corrections.
>>
>>     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).  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)
>>        George reports that he is nearly ready to do tests of the full
>> corrections.  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).  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.
>>     Other methods to determine absolute Ds were briefly discussed.   If
>> time permits, I may test these.
>>     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.
>>
> [snip]
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