[mmaimcal] Re: Polarization Teleconference

[Mark Holdaway]

Larry wrote:
> 
>     The biggest problem with wide-field polarization imaging is
> something that you did not address: even if the polarization of each
> antenna's beam is perfectly known (calibrated), it is not
> straightforward to apply this information to the raw visibilities so
> as to produce accurate images of the polarized radiation.  Only under
> the assumptions that the polarization state is constant across the
> beams and identical among the antennas does this become tractable.
> 

I would say there are five regimes of correction:

1) Do nothing: 
differences in the polarization pattern among antennas
and as the parallactic angle turns will result in partial cancelation
of the spurious polarization signal in the image plane.  We can quantify
this reduction in error with simulations, some software needs to be
written.  Alternatively, we know enough about this to estimate the
magnitude of the effect, but the detailed answer will depend a lot on
the details of the observing (ie, parallactic angle range, source
brightness distribution).

2) Bulk image plane correction:
Given measurements of the polarization pattern of each antenna, or
of the array as a whole (ie, the average of all antennas), the mean
polarization pattern for the entire observation can be calculated.
Given a model of the total intensity distribution, we can calculate the
spurious polarization in the image plane, and correct for it.  Quick,
simple, and better than doing nothing.  How much better? Simulations
required, or we could estimate.  Should work perfectly for a snapshot
observation when all antennas have identical patterns.

3) Many snapshot Fourier plane correction:
Given a model of the total intensity distribution, and a model or
measurement of the mean polarization pattern for the array, we can
estimate the spurious polarization in the image plane, with very high
accuracy, for each snapshot.  Fourier transform the spurious image
plane polarization for each snapshot and subtract from the visibilities.
This works better than the Bulk image plane correction, and is
still fairly cheap.

4) Differences among antennas, Fourier plane correction:
If each antenna has a different pattern, we can still do a procedure
like the Fourier plane correction, but we need to use each antenna-pair's
polarization patterns.  This is bloody slow, and is basically similar
to imaging with known pointing errors.  We need to be able to do this
anyway to simulate the effects of the polarization pattern on the data.

5) Deal with even more details:
What if the polarization patterns are time or elevation dependent?
I'll say no more!

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(1) is done all the time: we can make VLA mosaics of linear polarization
at better than 1% accuracy (though worse than 0.1%; I'd say its 0.5% 
peak error in fractional polarization -- which is comparable to the
on-axis D term calibration -- with good parallactic angle
coverage, unless there is a very bright source nearby).  The linear
polarization problem at the VLA is not strictly analagous to the beam
squint the linears will have on ALMA.  For one, the positive-negative
lobes in the pattern switch every 90 degrees rather than 180 degrees,
so you get better cancelation faster.
(2) was implemented by Cotton for the NVSS, and is similar to the
mean correction which the Zeeman people fit to at the VLA.    
(3) is a simple extension of (2) (dead reckoning ala Cotton, not fitting
the spurious image plane signal as the Zeeman people do).  
(4) is a step beyond, and 
(5) is further out.