[alma-config] BOUNCE alma-config at majordomo.cv.nrao.edu: Non-member submission from ["David Woody" <dwoody at caltech.edu>]

[Min Yun]

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From: "David Woody" <dwoody at caltech.edu>
To: "ALMA config" <alma-config at zia.aoc.NRAO.EDU>
Subject: Re: earth rotation and more on UV coverage
Date: Tue, 8 Feb 2000 11:41:27 -0800
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Mark is correct, as usual.  If the snap shot coverage is uniform, it remains
uniform even with earth rotation.  But is does help tapered UV coverage
cover more UV cells at long baselines.  This is what you really want.
Ideally you want your integration time/cell to mimic the FT of your
desired PSF to maximize sensitivity.  Achieving this tapered integration 
time/cell by moving the longer baselines quickly between cells accomplishes
this while also giving more complete coverage.  

_______________________________________________________
Attempt to figure out where we are in UV vs image metrics.

One way to look at the imaging algorithms that are being
used is to treat them as complex model fitting programs
that fit images to the measured UV data 
plus whatever other constraints,
such as positivity and maximum smoothness, etc., you choose to
apply.  This paradigm allows us to skip over 
troublesome words such as "interpolation", "extrapolation", 
"missing data" and "non-linear".

The simulation results seem to show that short baselines
are more important than long baselines.  That is, 
given a fixed number of UV measurements, you are better
off not measuring some of the longer baseline UV cells
and instead making more measurements of the short 
baselines to improve their S/N.  The longer baselines
have less "signal" and hence
you should spend less time measuring them even if
you might miss some new or unique information.
The FT of the test images will probably show that the 
information content or S/N decreases with UV distance.
This implies that it is more important to get
the flux and shape of the larger extended objects than
it is to get the point sources correct.  This is what
the current millimeter interferometers see, but is
not what you often see in optical or IR images.  A field of
stars or unresolved objects is imaged better with 
more long baselines.  Measurements anywhere in the UV plane
add equally to the S/N of a point source but the longer
baselines are required for accurate location and separation
of binary sources, etc.

It seems to me that the question at this point becomes:  
What taper do we want in the raw UV-coverage?
Uniform (no taper), linear, 1/UV, gaussian, cosine....
Clearly we want to maximize Ed Fomalont's smoothness
metric.  All of these tapers will yield "complete"
coverage out to some maximum configuration diameter with
uniform giving the largest diameter configuration with
complete coverage.  As noted above, earth rotation
can be effective in increasing the long BL coverage. 
Combining several configurations also gives tapering.

It may be more important to have configurations that
cover the two approaches of uniform and tapered UV 
coverage than it is to have many different scale sizes.

It is possible that images produced using uniform UV data
will have resolution function (FT of disk = J1(r)/r )
 artifacts that degrade the image, 
but this is not the same as saying the science information
is degraded.  A close call science conclusion should be
tested against the raw UV measurements and not against
a heavily processed image.  Of course we all live and 
die by the visual image on the cover of Nature, so it
is important that we present a nice picture that backs
up our conclusions.  This will probably require some
tapering of the UV data to remove resolution function
artifacts.  

The algorithms being used for image simulation may
not be dealing with uniform or edge weighted UV data 
very well.  As I understand them, they try to produce
models that fit all of the UV data to within the quoted
noise of each cell while keeping the image as "smooth"
as possible or some similar criteria.  Taper coverage
implicitly assumes that the image is smooth, i.e. that
there is not much action at the long baselines, and is
a good match to the algorithms and test images.
Uniform coverage implies that the information content
is evenly spread across the UV plane and the algorithms
don't deal well with the sudden loss of data at the edge 
of the coverage.  The simulations that Kogan did in
memo 247 are particularly disturbing.  It is hard understand
why the uniform circular array image in fig. 6 b did not 
find the three small sources to the right of the field center.  
It is hard to believe that this is fundamental in the 
circular array UV coverage.

I think we all agree that pure circular arrays are not
optimum.  I used circular arrays in memo 270 only to
simplify the calculations.  Keto rings or possibly
Keto donuts will be much better, especially wrt
the accentuation at the edge of the UV coverage.

 *****************************************************
| David Woody                                             
| dwoody at caltech.edu                             
*****************************************************


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