[daip] Desired gain normalization scheme.

[Craig Walker]

This message is meant to describe the gain normalization scheme I would 
like to have in BPASS to use for VLBI data.

The data from the correlator are correlation coefficients - the ratio of 
the correlated power to the noise power.  The apriori calibration 
process can be considered to have two major steps.  The first is to 
adjust the data for all of the effects introduced by the various bits of 
hardware in the system, mainly the analog and digital filters.   The 
second step is to multiply by the SEFD - the ratio of Ts/gain which 
converts power to flux density.  That second step might also include 
some corrections for propagation effects like opacity.

The autocorrelations are a measure of the total power in the system. 
For the second step to work properly, the net effect of the various 
corrections for instrumental effects should produce autocorrelations 
that are unity across the portion of the bandpass of interest.  Then, 
after multiplying by the SEFD, the autocorrelation amplitudes will be 
the SEFD, which is the desired situation.  The same scaling of cross 
correlations will produce the calibrated flux density.

One of the first calibration steps for VLBI data is to run ACCOR.  That 
has the effect of making the average of the autocorrelations unity, but 
it does not correct for spectral shape.

With BPASS in its current form, one can get unity calibration results 
for the autocorrelations by normalizing by power over the full band 
using autocorrelation based bandpasses.  Note that one might actually 
not want to normalize at all to force the results to unity, but it 
doesn't really matter because ACCOR has already forced the average to 
unity.  The problem with this method is that the autocorrelations do not 
contain information about the phase bandpass, and one really wants to 
calibrate the phases along with the amplitude.

If one uses strong-source cross correlation data to derive the 
bandpasses, complete with phases, and normalize on power across the full 
band, you get close.  But there are aliasing effects in the edge 
channels that cause the bandpass shape in the autocorrelations to be 
somewhat different, in those channels, from the cross correlation 
bandpass.  The autocorrelations are higher in the edge channels because 
the aliased signals don't correlate.  This effect is stronger for the 
PFB, with soft edge filters, than the DDC or the legacy system with 
harder edged filters.  The result is that, when the cross-correlation 
derived bandpass is applied to the autocorrelations, the values over the 
central channels that you want to keep are slightly suppressed.  In my 
test data, the average value is 0.977 for the PFB and 0.993 for the DDC. 
  One can use CLCOR with the power gain option (new) to correct that and 
get good calibration.  But it would be nice to not have to do the CLCOR 
correction.

In principle, one could run BPASS with autocorrelation based bandpasses, 
apply that, and make an incremental cross-correlation bandpass and it 
should work.  But AIPS is not set up to do that conveniently.  One would 
have to make a new file with the calibration applied after the first 
BPASS.

What would be most convenient, I believe, is for BPASS to make a cross 
correlation based bandpass, apply it to a the autocorrelations, and 
determine the average result over the selected channels, probably not 
including the edge channels.  Then the normalization would be to cause 
those autocorrelation channels to come out 1.00 on average (and 
individually to within the noise).  This would introduce the complexity 
of having to read the crosscorrelations, determine the bandpass shapes, 
read the autocorrelations, apply the bandpass, determine the average in 
the selected channels, then apply to the bandpass the normalization 
required to make that average unity.  The program would thus have to 
deal with both cross and autocorrelations, which it probably does not do 
now.  But the end results, I think, is a proper calibration to do in 
preparation for the scaling by the SEFD to convert correlation 
coefficients to Jy.

Cheers,

Craig





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     R. Craig Walker            Array Operations Center
     cwalker at nrao.edu           National Radio Astronomy Observatory
     Phone  575 835 7247        P. O. Box O
     Fax    575 835 7027        Socorro NM 87801   USA
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