[mmaimcal] Re: mathematics of calculating the PSF (fwd)

[Leonia Kogan]

Mark,

I can not work at the language of a presciption, even if it is supported by
D. Woody. I have to have my mutual aggreement.

1. My analysis shows that the effective PSF with taking into account PB is

   PSF_ef(p,dp) = PSF(p+dp) x PB(p);   x stands here for multiplication
 
   Of course I can be wrong.

   The following is the way I got this result:

In the case of the very wide primary beam the dirty map DM is the convolution 
of the SKY with the PSF:

DM(dp) = INT [PSF(dp+p) x SKY(p) xdp]

The effect of the primary beam is in multiplication of the SKY by PB.
Therefore the DM is becoming:

DM(dp) = INT [PSF(dp+p) x SKY(p) x PB(p) x dp]

So   PSF_ef(p,dp) = PSF(dp+p) x PB(p)

2. I think we are speaking about something different.
   And it is difficult to continue the argue at the level of e-mails.
   It would be nice if you publish the memo about this with the text 
   and math. Then it will be simpler to understand the point at least for me.


Thanks

Leonia

 
   

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Date: Wed, 25 Apr 2001 11:25:14 -0700 (MST)
From: Mark Holdaway <mholdawa at cv3.cv.nrao.edu>
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Subject: [mmaimcal] Re: mathematics of calculating the PSF (fwd)
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Prescription:  take the primary beam, convolve it with itself,
multiply that by the PSF, optimize the effective PSF you've just
created.


---------- Forwarded message ----------
Date: Wed, 18 Apr 2001 09:59:07 -0700
From: David Woody <dwoody at ovro.caltech.edu>
To: Mark Holdaway <mholdawa at nrao.edu>
Subject: Re: mathematics of calculating the PSF

Hi Mark

I have come up with a formulation for the off-axis PSF
based upon the concept of measurement orthogonality.
It does not rely on the usual image processing steps,
but produces an PSF like what you described, i.e.
the raw FT of the delta function UV samples multiplied by
PB(p)*PB(p+dp)
where p is the position of the point source and dp is the
offset from this position and also the sky coordinate for the
raw FT.

So I think we have a common result and can proceed.

Cheers
David
****************************************
| David Woody
| Assistant Director of Instrumentation
| Owens Valley Radio Observatory
| P.O. Box 968, 100 Leighton Lane
| Big Pine, CA 93513, USA
| Phone 760-938-2075ext111, FAX 760-938-2075
|dwoody at caltech.edu
****************************************




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