[alma-config](no subject)

[Frederic Boone]

Hello,

First, I would like to express my respect for the work
you are doing Dave and John for ALMA configurations
and the enthousiasm of your respective emails.
I am also very grateful for the interest you are
showing concerning the method I developed (now
published in A&A). I would be very glad if this method
could be of any help in the task of designing ALMA.
Also, if any help is required I am ready to spend some
time on the optimizations.

However I would like to make some brief comments. For
conciseness and clarity reasons I write them in a very
direct way. They are only aimed at nourishing the
discussion. Even if controversial, they are never a
critism of your respective works and personal
investments in ALMA project which I sincerely respect.


1. To my point of view (which can be wrong of course)
the best distribution of samples cannot be determined
by considering the level of sidelobes in the dirty
beam only. Unlike what is suggested in Dave's memos,
the problem of image reconstruction (or image
synthesis) encountered in interferometry is
fundamentaly different from the problem of image
restoration related to images obtained with optical
imaging systems. In the first problem the PSF is
perfectly known whereas the Fourier transform of the
brightness distribution is partialy measured and needs
to be estimated everywhere (at least at Nyquist
intervals) in order to allow imaging. On the contrary,
in the image restoration problem the PSF (which
Fourier transform is striclty greater than zero) is
unknown (but can be estimated) and the image convolved
with this PSF is perfectly known within the pixel
noise. 

Thus, in interferometry, a given distribution of
Fourier samples yielding high sidelobes may allow to
reconstruct the brightness distribution with high
precision provided that the uv-plane is sampled with 
the required accuracy. Inversely, a distribution
yielding low side-lobes but insufficiently sampling
the uv-plane might be inadapted to image
reconstruction (some essential information can miss).
It is therefore not possible to assess the imaging
quality of a distribution of samples (i.e. to estimate
the errors that would appear in the reconstructed
image) by studying the level of side-lobes in the
dirty beam: both aspects are not intrinsically
correlated.

Furthermore I think that this point of view is true
whatever the sampling accuracy required to allow
interpolation of the data in uv-plane and not only for
high densities of samples as suggested by John.

2. The problem of resonances or coherent features
across the UV-plane is not a real problem as long as
interpolation of the data is possible everywhere in
uv-plane with a reasonable accuracy. Indeed, if it is
the case, one can consider the estimate of the
visibility function as continuous. Now, what is the
sampling accuracy required for interpolation?
I think that it depends on the prior information
available on the source as well as the performance of
the algorithm used and I am not able to answer to this
question accurately. But I can show that it is
possible with 64 antennas of 12m to achieve Nyquist
sampling (i.e. intervals close to 1/FOV (FOV=Field Of
View)) for baseline lengths up to 5.6 km with 8h
observations. Even if it is shown that Nyquist
sampling is not required it means that interpolation
will be possible up to larger baselines or for shorter
durations of observation. Then, if interpolation is
possible, why should we optimize an array for the case
where interpolation is not possible?

3. The method I developed can be applied to optimize
the distribution of samples at any scale: the scale it
is "looking at" depends on the grid(s) chosen for the
optimization. Thus, if it is considered that one scale
is more important than the others, more grids can be
chosen that have cell sizes close to this scale.

I submitted a paper dedicated to the definition of the
model distribution of samples to be used as target in
the optimization. I am ready to give the preprint to
any one interested.

Best regards,

Frederic

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