[evlatests] D*P contributions to total intensity

[Rick Perley]

    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!