[alma-config] Addressing Frederic's Concerns

[Mark Holdaway]

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.
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.
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.

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

(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.)

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.)
     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

>I fully agree with you Mark and I am concerned about
>the uv coverage. Going from 64 to 50 antennas we loose
>40% of the samples and this issue becomes more
>critical.
>
>In the design proposed in the memo draft it seems that
>in a significant part of the uv-region covered by the
>configurations greater than 2 km the sampling is far
>from Nyquist (a least 4 times worse), whereas in
>principle it could be close to Nyquist for
>configurations up to 3.5 km. In other words it seems
>that the sampling could be improved by optimizing the
>configurations for distributions that fall off less
>rapidly. 
>
>Is mosaicing of extended sources with the
>configurations of 3.5 km part of the scientific
>requirements? if yes, does the design presented in the
>draft meet the requirement?
>
>Cheers,
>Frederic.
>
>
>
> 
>
>
>
>	
>
>	
>		
>___________________________________________________________________________ 
>Appel audio GRATUIT partout dans le monde avec le nouveau Yahoo! Messenger 
>Téléchargez cette version sur http://fr.messenger.yahoo.com
>  
>