[evlatests] 3bit PDif Compression -- effects on the visibilities

[Rick Perley]

    It was suggested by Michael at the '3-bit' meeting that I closely 
compare the visibilities, before and after the 3-bit PDif data are 
applied.  I have done this for the B0D0 (8-bit) data, and the two 
parallel AC 3-bit data.  The results are as expected, but as always, 
it's complicated ....
    I did this in the following manner:  I used the flux densities as 
provided by the 8-bit data path -- essentially assuming these are 
correct for all paths.  (I claim that this HAS to be true).  Then, I 
computed the antenna gains for the three sources (strong, medium, weak) 
using these same fluxes for all three data paths, each with and without 
the switched power data applied.  Plots of the gain solutions easily 
tell us if the antenna gains have been correctly adjusted for source 
strength, as seen by that antenna. 
    Note that the data, as loaded, utilized the default antenna gain 
model, and utilized the latest model for opacity.  The only elevation 
gain dependency left should be the gain dependency on temperature. 

    1) In the B0D0 line, all is as is expected.  The PDif data corrected 
quite well the temperature-dependent gains.  There is no 
source-dependent gain differences, either in the raw data, or in the 
PDif corrected data. 

    2) For both the A1C1 and A2C2 data, we get mixed results.  
Application of the PDif values corrects the elevation-dependent gains, 
about as well as in the B0D0 data.  We have nice proof that this is 
working well -- ea14C had a clear 'jump' in gain for about two hours 
(switch?)  -- this was seen by the PDif, and nicely corrected. 
    For most antennas, the *raw* data show no variation of gain with 
source strength.  There are a couple of (small) counter-examples 
however.  For most antennas, application of the PDif values clearly 
worsens the gain dependency upon source strength.  In some cases, there 
is no change.  The few cases where there appeared to be a pre-existing 
variation of gain with source strength were worsened by PDif. 

    So we have an odd situation -- the PDif values *do* correct for the 
gain variations introduced by the temperature dependency of the IF 
system, and by other clear gain variations (like, those caused by bad 
switches).  But they also erroneously adjust the gains by the 'PDif 
Compression' effect.  So this 'compression' is not a real gain 
effect.    It's an artifact. 
    Said another way:  Changes in power caused by a *real* gain change 
are found and corrected by PDif.  But changes in power caused by 
changing source are somehow fooling PDif into thinking they are due to a 
change in gain.    This doesn't happen in the 8-bit path, and tells us 
there is a strong non-linearity in the gain function.