[evlatests] D*P contributions to total intensity

[George Moellenbrock]

Bill-

Yes indeed, I was assuming sufficient per-channel SNR for
the channelized solution.   Also (for Barry), that the external
reference for the per-channel position angle (R-L phase)
calibration is known a priori _per_channel_.   We already claim
to  know this angle is ~constant for 3C286 over the whole of the VLA's
frequency coverage---perhaps the story is a bit more interesting
in detail....

The 10-20 degrees of R-L 'phase bandpass' I mentioned is
_after_ correcting the cross-hands for the channelized D-terms.
You see it in every baseline's cross-hands, and it has opposite
sign in RL and LR.  It is just the channel-dep R-L calibration,
and one should expect something interesting there, based just
on what you see in ordinary (parallel-hand) bandpass phases.
I.e., it was strictly not a statement about the freq-dep of the D-terms
themselves.    (This is not what I intended to suggest, if I
understand your reply.  In fact, the D-term spectra are rather
more interesting than the R-L phase, I think.)

Whether there is a significant net slope in the R-L bandpass
(an R-L delay) depends on whether or not you removed
it ahead of time or not, but (with sufficient SNR) you needn't
bother if you remain consistent and do _both_ a channelized
D and a channelized R-L calibration.   It is like letting an
ordinary sampled bandpass correct for delay---if you are
going to do a channelized bandpass anyway, you need not first
remove a delay (unless there are other issues to contend
with, like time-dependence in the delay, for which you want to
leverage sensitivity).   It is correct that this
approach does _not_ isolate the D-term phase spectrum from
the R-L bandpass [delay or no]---each channel's D-term
is in the R-L frame delivered by the refant used in the
gain/bandpass calibration.  That this R-L phase frame
may include a significant delay just doesn't matter to
the instr pol calibration, at least for the unpolarized calibrator
case.  If one is interested in unwinding the D-term phase
according to the R-L bandpass phase (a channelized version
of CLCOR's 'PANG' mode, I think), one could, but we
aren't bothering to do so in CASA (the R-L phase bandpass
is applied as a separate cal table, after the D table is applied).

I'll rustle up some plots of this and distribute, as soon
as I have a chance.

I agree that parameterizing the D-term spectrum---specific
standing waves we know should be there, etc.---would be
desirable for cases where SNR is lacking.  I don't think
this changes the strategy, so long as the phase part of
this parameterization can cope with as arbitrary an R-L
delay (e.g., cycles slips) as might remain after standard
gain/bandpass/(delay) calibration.  But so far, SNR/channel
hasn't been found wanting in the sorts of polarization
observations we've embarked on so far, as least for
commissioning purposes.

-George


On Tue, Jul 27, 2010 at 2:25 PM, Bill Cotton <bcotton at nrao.edu> wrote:
> George,
>
>   Certainly solving for the D terms per channel allows for an
> arbitrary function of frequency but can suffer from low SNR.
> If the instrumental polarization is a relatively slow function of
> frequency as you suggest, then it can be parameterized.  This can
> result in better SNR while including the frequency dependence.
> I wonder from your description if a R-L phase bandpass for the
> reference antenna would leave a more nearly constant instrumental
> polarization.  If what you describe is, in fact, merely the R-L phase
> spectrum of the reference antenna that would greatly simplify
> calibration.
>
> -Bill
>
> "GM" == George Moellenbrock <gmoellen at aoc.nrao.edu> writes:
>
> GM> Actually, for an unpolarized calibrator (at least, see below),
> GM> the best solution is to solve for the D-terms per _channel_,
> GM> each in its own R-L phase frame, then solve for R-L also
> GM> per channel to get the positional angle calibrated.   This
> GM> is essentially just the traditional approach invoked per channel
> GM> rather than per "IF".   We support this in CASA, and it is what
> GM> we did for the summer school tutorial using 3C84.  Note that
> GM> the R-L phase residual (post gain calibration) is not just a pure
> GM> delay---there is an interesting R-L phase bandpass at the
> GM> level of a few 10s of degrees variation on top
> GM> of any R-L delay slope (across 128 MHz), as well (look
> GM> at any bandpass phase in the parallel hands, and expect
> GM> as much for the refant's cross-hand phase bandpass).
>
> GM> Currently, CASA does the source polarization estimate
> GM> per spw (not per channel), so large coherence problems
> GM> (e.g., delays) need to be removed for a sensible
> GM> source polarization estimate.  To this end (and as part
> GM> of adding support for linear feeds), I've added
> GM> a rudimentary R-L delay solving option to gaincal in CASA
> GM> (checked in yesterday).  This should permit improving
> GM> spectral coherence sufficiently for a decent source pol
> GM> estimate, followed by channel-dep (or not) D-term
> GM> estimation.
>
> GM> -George
>
> GM> On Tue, Jul 27, 2010 at 7:41 AM,  <bcotton at nrao.edu> wrote:
>>>
>>>   I've been working on the wideband C band polarization test data and
>>> have run into a problem which has long been an issue for VLBI
>>> polarimetry, namely the interaction between the R-L delay and the
>>> instrumental polarization.
>>>   After the parallel hand calibration there is ideally a single delay
>>> and phase offset between the R and L gain systems.  This should be
>>> easy to determine from looking at a known polarized signal.  However,
>>> the instrumental polarization also contributes and for the high
>>> instrumental polarization for the EVLA this is a serious contribution
>>> even for strongly polarized sources like 3C286.
>>>   The R-L delay term needs to be removed before fitting D terms but
>>> the D terms corrupt estimation of the R-L delay.  The frequency
>>> structure of the D terms is one of the issues that needs to be better
>>> understood but it's is hard to separate from the R-L delay.
>>>   The optimum solution might be a joint estimation of the R and L
>>> gains, R-L phase and delay, bandpass and the frequency dependent D
>>> terms.  That's alot of data to shove into a least squares solver.
>>>
>>> -Bill
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>
>