[daip] BPCOR: spectral index correction

[Eric Greisen]

Olaf Wucknitz wrote:
> Hi,
> 
> I tried BPCOR for the first time to correct for the spectral index of the 
> calibrator or tilt spectral slopes in general.
> 
> There seem to be some problems with it, even though I am not entirely sure 
> if I understand everything correctly.
> 
> 1. BIF and EIF don't seem to be used.
> 
> 2. All gains are corrected with freq**APARM(1). I think only the sqrt of
>     that factor should be applied to each antenna.
> 
> 3. The scaling with frequency uses the reference frequency etc. but not
>     the offsets for all IFs. In the case of large separations between IFs,
>     this is not entirely accurate.
> 
> 4. The pivot channel APARM(4) is not properly applied, and the frequency
>     calculations don't seem to be plausible generally.
>     IF CHNOFQ is meant to be the frequency at the pivot channel, it should
>     be
> 
>        CHNOFQ = REFFRQ - (REFPIX - CHNPIV) * CHNINC
> 
>     rather than
> 
>        CHNOFQ = REFFRQ + (REFPIX - CHNPIV) * CHNINC
> 
> 
>     And the correction factor should be
> 
>                 ACOR = (1.0 - ((CHNINC/CHNOFQ)*(CHNPIV-ICHAN)))
>       *            ** (0.5*APARM(1))
> 
>     instead of
> 
>                 ACOR = (1.0 - ((CHNINC/CHNOFQ)*(REFPIX-ICHAN)))
>       *            ** APARM(1)
> 
>     to make it unity at ICHAN=CHNPIV.
> 
> 
> As said, my interpretation may not be entirely correct, but in any case 
> the result seems to be wrong.
> 
> This does not have the highest priority for me at the moment, because I 
> can use parseltongue instead to make the corrections.

Looking at the authors of this task I am not surprised that there are 
misunderstandings of things.  I had forgotten that the task existed.
The correct formulae involve computing the freq at the fiducial channel 
and at each of the other channels and doing (Freq/Freq0) ** (aparm(1)/2)
and dividing by that.  The normalization of the BP also involved all 
channels so I added an option to set the channels used with inner 3/4 as 
default.  Tomorrow's MNJ will improve matters.

BPASS has a much better spectral index option and has default values for 
a few known sources (VLA ones of course).

Eric Greisen