[alma-config]low sidelobes vs correct sampling

[Frederic Boone]

Hi,

The discussion about the sampling rate required and
the connection with the level of sidelobes seems
really interesting and essential. Also, if I can
afford, I would like to come back to this point (sorry
for this long email).

First, I would like to precise the point I made in my
last email. 
It was probably too concise and too caricatured.
I have to insist on the fact that I don't intend to
demonstrate that the analysis developed by Dave is
wrong.  I am also very impressed by this work and I
think that everything is right in it. 
The only point I am wondering about is:
Can one assess the quality of a configuration by the
level of sidelobes only?

More precisely:

1. Is there a minimum density of samples required
around a point (u,v) to allow estimation the
visibility function with a reasonable uncertainty at
this point and whatever the algorithm used?

2. If not, why do we build interferometer arrays (this
is a joke of course but it hides a serious question)?

3. If yes, can the errors  in the map arising from
defficient sampling of some regions of the uv-disc be
more important than the errors coming from the
sidelobes (when the algorithm used is susceptable to
sidelobes)?

4. Are these two types of errors related to each
other?

5. If they are not related to each other shouldn't we
care about the sampling?

6. If they are related then, what is the difference
between ensuring a correct sampling and lowering the
level of sidelobes?

My opinion is:

1. yes
3. yes 
4. no
5. yes

I would like to add that I don't mean that Nyquist
sampling is required. I cannot even say which sampling
is required. As Melvyn said it  depends on the prior
knowledge of the source. It may also depend on the
algorithm used.
But again for ALMA we are quite sure that whatever the
sampling required (it is probably poorer than Nyquist)
we can make it (we can make Nyquist). Then, shouldn't
we try to evaluate the sampling rate required for the
science we want to make and optimize the
configurations in such a way that they ensure this
sampling?
It seems to me that it is something like a cultural
revolution in interferometry: it will be possible to
estimate the visibility function with a good precision
everywhere in the sampled uv-disc (I don't mean that
current interferometers are bad but ALMA will be much
better). Mark said that our algorithms are not
designed for such a situation. But isn't it worth 
developing new algorithms? (Note that in the
particular and ideal case of Nyquist sampling least
square fit -including the noise of course- is
sufficient).

In the ps file attached I try to illustrate the fact
that the sidelobes are not related to the sampling
rate. This document does not pretend to be a rigorous
demonstration. It rizes some questions which are open
to discussion.

Thank you for your attention and sorry again for the
length of this email.
Best regards,

Frederic

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