[evlatests] [Ecsv] Summary of Polarization Meeting

[George Moellenbrock]

What Barry says is correct IF the residual due to the (unknown) constant 
offsets in D, as applied to the parallel hands, is factorable as a 
multiplicative gain AND you bother to re-solve for this incremental gain 
effect (and anything else left over cancels in the formation of I from 
'RR' and 'LL').  Seems to me you still get residual terms that are a 
function of both the offset Ds _and_ the offset itself (and source 
polarization, if any), possibly smaller than the uncorrected (so possibly 
better than nothing), but still non-zero, and non-symmetric.  I think what 
you might manage to achieve here is reconciliation of the range of 
non-ideal polarizations across the array to a single mean non-ideal 
polarization, separately in both hands.  For this to strictly preserve 
Stokes I, these non-ideal states must be precisely orthogonal.  It is not 
clear to me that this is what is achieved.  E.g., what if all of the LCP 
receptors started off less pure than the RCP receptors in a systematic 
way? (such a bias may be unlikely, but this assertion amounts to 
introducing another external constraint, such as that the mean 
polarization in each hand is pure).  I'll think about it some more, as 
Barry suggests.

I think it is very interesting to ask if the R and L systems, as built (by 
virtue of the mechanical processes and testing involved for the polarizing 
elements), tend to be more nearly orthogonal (on each antenna) than pure. 
It seems to me (though I've no shortage of naivete on h/w questions) it 
might be easier to generally arrange orthogonality than absolute purity 
(if you manage purity, of course, you get orthogonality for free).  If the 
receptors are nominally orthogonal, I wonder if this fact could perhaps be 
applied as a constraint in referencing the D solutions that achieves a 
better approximation of the absolute Ds (or at least Ds that behave more 
as Barry suggests)?....

-George


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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