[alma-config]low sidelobes vs correct sampling

[Leonia Kogan]

David,

I completely agree with you and like your statements which make the 
problem more clear.

You wrote:

>Although I have not seen a proof, I believe that configurations
>with "good" PSFs, i.e. well defined central peak and low sidelobes
>(and now we should probably add zero average sidelobes) will
>produce better images using current algorithms and also using
>as yet undeveloped algorithms than configurations with "poor"
>PSFs.

It has been proved for current algorithms by simulation and published at 
several ALMA memos.

Leonia
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>From alma-config-admin at donar.cv.nrao.edu Thu Oct  4 19:23 MDT 2001
Reply-To: "David Woody" <dwoody at ovro.caltech.edu>
From: "David Woody" <dwoody at ovro.caltech.edu>
To: "Frederic Boone" <frederic_boone at yahoo.fr>,
        <alma-config at donar.cv.nrao.edu>
References: <20011004193822.10594.qmail at web12705.mail.yahoo.com>
Subject: Re: [alma-config]low sidelobes vs correct sampling
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Date: Thu, 4 Oct 2001 18:16:03 -0700
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Here is a short summary of my view on interferometry.
This will be a boring rehash to many but may be useful anyway to see
if we can't come to understand the differences in the various
approaches to the configuration issue. 

What the astronomers (other than the odd cosmologist) want
is an accurate image of the sky.   What radio astronomers
discovered long ago is that they can get images of the sky
measuring the visibilities and taking the FT of the data.
They are not really interested at all in the visibilities themselves.
What you actually get if you just FT the data
you do have is the true image convolved with the PSF or
dirty beam.  Thus the PSF describes "perfectly" the effect
of the missing, poorly sampled and uneven sampling of the
UV-plane.  Thus if this is all you did, then the PSF and its
sidelobes tell you directly what kinds of errors and artifacts
your approximate image will have.  The reason I did the work
leading up to ALMA memo #389 was to quantify the effect
of the missing UV data, etc.

But radio astronomers found that excellent, and presumably 
correct, images could be made using very sparse UV coverage
with very poor PSFs by applying clever imaging algorithms.
Although I have not seen a proof, I believe that configurations
with "good" PSFs, i.e. well defined central peak and low sidelobes
(and now we should probably add zero average sidelobes) will
produce better images using current algorithms and also using
as yet undeveloped algorithms than configurations with "poor"
PSFs.

It is clear that if you sample all of the UV-plane at the Nyquist
rate you recover all of the visibilities.  But if you simply FT this
data, again you get the true image convolved with the PSF for
the distribution of UV samples you have.  Thus if you end up
with a UV distribution with a sharp edge, the near sidelobes
will be large and your FT image will reflect this.  Of course you
can reweight your data to produce a very smooth UV distribution
and the FT of this data will produce a beautiful near perfect
rendition of the true image convolved with a nice Gaussian
like beam.  But this comes at the cost of poorer signal-to-noise,
especially for the point sources.

It is also well known that better UV coverage, i.e. more data,
produces better images.  But this is also reflected in the PSF
and the size of the peaks, more antennas and baselines produce
better PSFs.  Again memo #389 quantifies this.

Thus it comes down to whether you want to 
1. fully sample the UV-plane so that you can produce 
nearly ideal PSFs after reweighting the data and lose S/N 
or 
2. produce the best possible PSFs at a given resolution
without requiring reweighting and apply modern imaging 
techniques that will hopefully reduce the effect of the PSF 
imperfections to a negligible level.

Having worked with a small low sensitivity array, I always
favor maximizing the S/N, i.e. option 2.
  
****************************************
| David Woody
| 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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