[alma-config] alma configuration simulations

[Mark Holdaway]

KEY:  anything followed by "..." is similar to a joke.

> Your point is well taken.  There is no way the simulations we
> propose to conduct in the coming months are any strong indications
> of the true imaging performance of ALMA.  However, the impact of
> pointing error on imaging ability is nearly independent of the
> configuration style -- 

probably incorrect

> or certainly the interplay is non-trivial to understand.  

perhaps; though Cornwell, Holdaway, and Uson 1994 give a clue,
relating the image errors to rms sidelobe level.

Certainly we can investigate this with a toy simulation set: generate a
bunch of arrays randomly, plus some good ones, select N toy configurations
with a good range of rms sidelobe levels, do the pointing error
simulations, and then correlate image quality with some measure of the
array configuration or PSF quality.  Who knows, maybe Leonia's "minimum
peak sidelobe" criteria will do well here.  Thats under a week's worth
of work, and would go far to helping us understand where we are going.
Its time for me to start writing memos again anyway...

> To the same context as all the other errors are
> nearly independent of configuration design.  

Again, they are not independent, just hard to understand.  For example,
phase errors propogate like PSF sidelobes, but it is not the full PSF,
rather something like a part of the PSF, the part of the PSF that is made
by connecting the antenna with the phase error with all other antennas, on
the time-scale over which the error remains correlated.  And then you've
got phase errors on each antenna, so its like you take the full PSF apart
and add the bits up, but out of phase.  So, while it is non-trivial, error
propagation through an image is highly related to the configuration.
It may be that optimizing the full PSF sidelobes is a good approximation
to solving this.

> Given that we have
> no perfect solution to the problem, we should try to do our best
> to isolate the managible effects and try to test things within
> those bounds.  

I am arguing that the effects are non-isolatable.

> In this sense, I see the planned simulations as
> the tests for the competiting configuration designs to various
> source parameters.  A secondary test, perhaps poorly controlled,
> is to evaluate the truth in the doom-and-gloom scenarios of
> "extraplolations and interpolations" in the imaging algorithms.

I don't think any tests we are talking about so far will shed much light
on this.  However, the Kogam and Conway array styles are close enough that
this is not an issue at the moment.  Only if a Keto ring or a circle or
something is seriously being considered do we need to go down that path
for anything besides academic interest.

> The mosaic imaging challenge should most certainly be addressed at
> some point down the line, perhaps as part of the optimization for
> the compact and other smaller configurations.  I don't doubt your
> previous work on this matter, and I am convinced that we will
> need a next major step in software to go beyond 1000:1 imaging,
> somewhat analogous to what the advent of deconvolution algorithms
> have done for synthesis imaging.  I hope you and others in the
> aips++ group will be up to this challenge at some point.
> 

I repeat my main point in my memo:
any image of 1K x 1K will fill the beam for an array of 1.6 km
or smaller.  So, it is not just the 0.1 km array that will be
mosaicing and affacted by pointing errors. 

Now, if you included some very compact sources, say 128 x 128, in
your image gallary, then I would say that they would be minimally affected
by pointing errors for a 1.6 km array.  I think such compact sources
SHOULD be included, by the way, as they will inevitably be observed.

I stand by my assertion that if we go down the road we are proposing to
go down, we will learn almost nothing of relevance to ALMA.

On the contrary, if we go down a modified road, we could actually
learn about how to design array configurations that are minimally
affected by the sorts of errors we are now expecting.

If we don't go down this modified road, my advice would be: don't waste
your time, flip a coin.  (BTW, AIPS++ also has a very nice random number
generator, we can do the job for you...)

The ultimate road, which we are NOT prepared to go down, is to design
array configurations which are optimal with respect to SOLVING for
pointing errors and voltage pattern errors.  Maybe some clever one among
us can come up with some quick ideas about what is important for such
self-cal algorithms without actually writing the algorithms and doing the
simulations.  Then we can use those principles to divine the optimal
array configuration.  But we have to weigh that principle against the
previous principle of finding arrays that produce good images in the
presence of the errors, and choose the balance based upon the expected
signal to noise (ie, if you never have the SNR to do the pointing
self-cal, don't bother;  if you never have the SNR to SEE the effects
of the pointing, forget this whole e-mail...)

	-mark