[evlatests] PDif compression -- definitely false

[Rick Perley]

     I am currently working on establishing the low-frequency flux 
density scale, for frequencies less than 2 GHz.

     This requires use of a standard source -- for these freqencies, the 
only candidate is Cygnus A, whose absolute spectrum is well known.  (Cas 
A and Tau A are both variable, and Virgo A is far too extended to be 
useful).

     Observations were taken last October in C configuration, of Cygnus 
A, plus the usual collection of our standard calibrators, at P, L, and S 
bands.   (Observations were taken at higher frequencies also, but for 
these, Cygnus A is too extended).   The length of the run was 30 hours 
-- a significant investment!

     For these three bands, Ken and/or Vivek modified the SB so that 
*all* observations at P, L, and S bands utilized the requantizer power 
adjustment.  This is absolutely essential for P-band, and is likely 
helpful at the others.   There were over 200 separate observations at 
each band over the length of the run -- that's a lot of RQ adjustments!

     The data are of excellent quality, and provided me a chance to try 
-- for once and for all -- to convince myself that the infamous 'PDif 
compression' is a false digital effect, and not measuring a real 
(analog) gain compression.

     For the impatient, here's the 'bottom line':

     PDif Compression -- where observing a strong source causes a drop 
in the switched power monitor -- is most certainly false.  The amplifier 
gains are not in compression.  Applying the switched power for such 
objects overestimates their flux densities.

     But:  This effect, at L-band, is only visible on Cas A and Cygnus 
A.  For these, the overestimate is at the 4% level.  It is less than 1% 
on Taurus A, and is not measurable on Virgo A.

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     Method:

     I utilized a single, clean SPW, centered at 1488 MHz.  The data 
(both visibilities and switched power) were cleaned up.
     I then applied the monitor data in two ways:

     a) Just the RQ gains.  This is a necessary step to adjust for the 
effects of the RQ adjustment.
     b) Apply both the RQ gains and the PDif values.  Inspection of the 
PDif values clearly demonstrated the presence of 'PDif Compression' -- 
for all observations of Cas A and Cygnus A, the values of PDif were 
lower than all other sources by a few percent for most antennas.  (As 
usual, some showed 'PDif Expansion', and a few showed no compression).

     The visibilities were calibrated in the usual way, using the Baars 
values for 3C286 and 3C295 as standard.

     I then inspected the visibility amplitudes for the stronger 
sources.  It was immediately clear that Cygnus A and Cassiopeia A were 
'stronger' for the data which had the full correction.  For all other 
sources, no differences were visible.

     However -- which one is right?  To determine this, I generated 
images of these sources, and noted the total fluxes.  This required 
removal of 'discrepant' antennas -- antennas whose gains deviated by 
more than 5% from the median.   Only a small number of antennas were 
affected -- the question of what is wrong with these remains unanswered.

     Examination of the total flux in Cygnus A clearly indicates the 
answer.  For the 'RQ-only' adjusted data, the derived flux density of 
Cygnus A is within 1% of the Baars value.  For the 'full adjustment' 
data, the derived flux is 3.3% high.  The observations of 3C286 and 
3C295, for both paths, gave the Baars values exactly. Although this is 
not solid proof (the Baars scale for Cygnus A could be off by this 
amount ...), the simpler explanation is that Baars is right, and our 
digital correction mechanism is wrong.

     We can't use Cas A to make a judgment -- its flux has dropped by 
many tens of percent since the last absolute measurement, in 1970s. But 
the sense of the difference is the same -- the 'full correction' flux 
density is 4.6% higher than the 'RQ only' data.  The effect on Taurus A 
is less than 1%.  No effect can be seen on Virgo A.

     Note that Cas A multiplies the system temperature by about 5, 
Cygnus A by about 4.5.  Observing Taurus A multiplies Tsys by about 2.5, 
and Virgo A by about 1.5

     It is possible -- perhaps likely -- that some analog or digital 
element is just beginning to saturate when the input power is multiplied 
by 5.  The PDif mechanism is a measurement of the power gain *slope* -- 
and does not actually measure the overall non-linearity in the gain.