[alma-config] reply to mark

[Frederic Boone]

Hi Mark,

> Frederic,
> 
> Well, this Fourier plane coverage and array
> configuration style is
> based on a decision we made several years ago which
> includes
> both image quality measures and operational
> considerations.

I know decisions were taken a few years ago but I
thought the study presented in the memo was done to
adapt the design to the new number of antennas.
That is why I started to discuss the design. But if
the decision is already taken of course this
discussion is useless and I should probably apologize.
On the other hand I was not informed the new design
was already aproved.

> For this discussion, I will not dwell on the
> operational issues
> (incremental reconfiguration and incremental
> resolution).
> 
> The array configuration style that optimizes the
> sampling over
> some range of the (u,v) plane is a ring or Relouex
> triangle.

I don't agree here.
Once the minimum density of samples wanted is decided,
the shape of the distribution of samples (the tapering
if you prefer) is determined by the number of samples
available (ie the number of antennas and the
integration time) and the maximum baseline.
This means that for different values of those
parameters the shape of the distribution of samples
you want to optimize the array for is different, and
consequently the shape of the configuration is
different.

Strongly centrally condensed configurations and rings
are extreme cases, there is a continuous set of
possible configurations inbetween corresponding to
intermediate tapering of the uv-plane.


> HOWEVER, those arrays are markedly inferior in
> producing
> good images, because they produce beams with large
> sidelobes.
> Tapering to reduce the sidelobes results in
> significant sensitivity
> loss and fairly improved images.

Yes if sampling allows it. There is a tradeoff that
can be quantified and the solution can be derived once
the sampling required is fixed.
It reminds me the old discussion rings vs spiral.
I am not saying we should have rings and I agree
tapered distributions are good. But sampling is also
good and in some circumstances this becomes the
limiting parameter.

> 
> We made a conscious decision to build an array which
> produces
> non-optimal (from a Nyquist point of view) (u,v)
> coverage because,
> given the imaging algorithms we have used for the
> last 30 years,
> this coverage produces better images.  

In the last 30 years the imaging algorithms were used
for non-gaussian distributions only, because
interferometers could not afford such distributions.
They were designed to sample as much as possible the
uv-plane.
When sampling is not the limiting parameter then
tapering the distribution improves the image (whatever
the deconvolution method), but when sampling is the
limiting parameter the more tapered the distribution
the worse the image (this qualitative behavior is also
independent of the algorithm used).

> The inner part of the (u,v) plane is sampled pretty
> well, and it is holes
> in the inner part that are the most damaging.  Holes
> in the outer coverage
> get larger and larger as the (u,v) sampling density
> gets less
> and less, but these holes don't matter much. 

My point is that these holes are limiting the image
quality (if this matters a lot or not needs to be
quantified) and this could be improved. 

>  This
> drop off in coverage
> naturally leads to a tapered beam with excellent
> sidelobe properties
> which results in superior images.

Again here I doubt the quality of extended images is
not affected by the poor sampling (for the largest
configs >2km) and I am convinced there is significant
room for improvement. But I am aware I should provide
some simulations to demonstrate this...

> 
> (It is true that next week, you may produce
> an imaging algorithm which produces superior images
> from Nyquist sampled,
> untapered data, but I don't think we can afford to
> design an array that 
> relies
> upon this unproduced algorithm.  That said, I do
> just that below.  I 
> think the
> difference is that I see how the BELOW-mentioned
> algorithm will work,
> and also that algorithm is a second-order effect,
> while the beam sidelobe
> issue is a first order effect.)

This is again where we disagree: for me the poor
sampling in the most extended configs (3.5 km) is the
limiting parameter, and any deconvolution method would
do better on extended sources (let's say with the size
of the primary beam) with better sampling (even if
that is at the expense of tapering).

> 
> ON THE OTHER HAND, we are still left with the
> problem that
> mosaicing, or imaging arbitrarilly complex objects
> which fill the
> field, will gradually break down as we go to higher
> and higher resolution.
> 
> I think the answer to that issue is multi-faceted,
> though this issue has 
> never
> been studied in depth in ALMA:
>     1) At high resolution, most fields will become
> simpler, as the emission
>          that fills  the beam will tend to be low
> brightness features which
>         will drop below the noise level.   This is
> like VLBI, where there
>         may be emission which fills the beam, but
> they can't see it.
>         (On the other hand, there will be some
> sources like 3C48 is
>           in VLBI, with complex structure that
> observers wish they could
>            image better -- so YES, the design
> decision which has been 
> made will
>            have some negative consequences.)

OK, I fully agree, if the requirements on imaging are
relaxed (e.g. the size of the sources to be imaged)
then the sampling required is relaxed accordingly.
Then, I would just note that although this is not
required anymore it would have been possible to design
ALMA with 50 antennas in such a way that imaging of
extended sources with better quality is possible for
the highest resolutions.


>      2) We need to develop a new class of algorithms
> along the line of 
> multi-scale.
>           Lets say we do mosaicing at moderate
> resolution where we have 
> complete
>          coverage (either in a smaller
> configuration, or tapered to the 
> point in the (u,v)
>         plane where we have essentially complete
> coverage).  We make a 
> good image.
>         THEN, we image at full resolution, starting
> with this medium 
> resolution image
>          as a starting model.  Instead of imaging at
> full resolution and 
> full complexity,
>          much of the complexity has already been
> imaged, and we are only 
> imaging
>          increments away from that smooth but
> complex image.   SO, many 
> regions in
>           this image will be consistent with being
> filled with noise, 
> and for the high resolution
>           step, will be consistent with being masked
> -- and the 
> consequence is that we
>           will have fewer pixels to solve for --
> this is similar to 
> imaging a smaller region
>          of the beam, in which case we use larger
> cells in the (u,v) 
> plane, and hence
>         we are closer to Nyquist sampled.   OR, we
> are solving for fewer 
> pixels with
>         the same number of visibilities, and the
> problem becomes better 
> determined.
>         Presumably, this sort of imaging strategy
> for imaging complex 
> structure at high
>         resolution will be explored as ALMA starts
> making wonderful 
> images with
>         a few dozen antennas -- we'll have some
> early Nature article 
> which squeezes
>         a top notch image out of ALMA even though we
> don't have all the 
> antennas.
> 
>             -Mark
> 

These are probably interesting ideas and such an
algorithm may improve the image quality for extended
sources. However, I am convinced a better sampling in
the most extended configuration (3.5 km) would improve
even more the quality (as you said in a previous mail
"there is nothing magical").

Cheers,
Frederic. 


	

	
		
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