[evlatests] D*P contributions to total intensity

[bcotton at nrao.edu]

Rick,

   Interesting.  One thing to try is the full nonlinear SOLTYPE='ORI-"
solution in AIPS/PCAL.  The solutions use all RR,LL,RL and LR.
As I remember, the corrections put all the terms including those
affecting RR and LL into the Muller matrix.  The issue then becomes
whether or not the relative terms (ellipticity and orientation rather
than D terms) are good enough.  (Note: using this mode of PCAL
requires using CLCOR to make the parallactic angle corrections before
any phase calibration.)  If this is the DR limitation, then even an
approximate correction should produce a visible improvement. 
   I would try this but I can no longer get AIPS/PCAL to run at all
on EVLA data and it will take me a while to replace the functionality.

-Bill

Rick Perley writes:
 >     Plots of the cross-power visibility spectrum of Cygnus A, in all 
 > Stokes parameters have shown the remarkable fact that the Q and U 
 > visibilities are often a substantial fraction of -- and can even exceed 
 > -- the I visibility.  This situation has long been known for 
 > observations of distributed galactic emission.  What I want to emphasize 
 > here is that it will be a common situation for observations of highly 
 > polarized emission in general. 
 > 
 >     There's no surprise in this.  But what I want to emphasize here is 
 > that this provides another explanation (and a good one!) for our 
 > troubles in deriving high-fidelity images of objects like Cygnus A.  The 
 > reason is the leakage between Q and U into I.  It works like this:
 > 
 >     The observed correlation in (say) RR is written (ignoring issues of 
 > parallel hand calibration, and assuming that V = 0):
 > 
 >        Vrr = (1 + Dr1Dr2*)I + Dr1(Q-iU) + Dr2*(Q+iU). 
 > 
 >     where I, Q and U are the visibilities for Stokes' I, Q, and U, and 
 > Dr1 is (for example) the complex coupling from LCP into RCP for antenna 
 > 1.  We normally argue that since the D's are a few percent, and both Q 
 > and U are a few percent of I, that the cross products between Ds, and 
 > between D and Q (or U) are of order 0.1% or less, and hence negligible.  
 > 
 >     But for highly polarized extended objects, the argument that the Q 
 > or U visibilities are negligible is incorrect -- they are often 
 > compariable to, and can on occasion exceed the I visibility.  Take the 
 > case where the I visibility hits a null (I = 0), while the Q and U 
 > visibilities do not.  (This is a common situation).   The measured Vrr, 
 > rather than being zero, becomes a scrambled version of the  polarized 
 > flux visibility.   Unless a correction is made, the derived 'I' 
 > visibilities will be in error, sometimes by significant amounts.   This 
 > is a non-self-calibrateable error, which will lead to image degradation 
 > in the regime where dynamic ranges of thousands - to - one are desired. 
 > 
 >     So far as I know, the inversion from the 'RR' and 'LL' visibilities 
 > to derive the 'I' visibility takes no account of this leakage.   
 > Clearly, for precise imaging of objects like Cygnus A, a fuller 
 > inversion will be needed.
 > 
 >     It is still unclear to me whether the 'relative' Ds that are 
 > determined as a matter of course via standard techniques are sufficient 
 > for this application, or whether the true Ds are needed.   I think 
 > 'true' Ds are needed, but others are invited to argue otherwise!
 > 
 > 
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