[alma-config] more on configuration

[Mark Holdaway]

Dear All,


1) Addressing Ed's comment: I agree.  Working with Multi-Scale Clean, I
recognize that the PSF's at different resolutions can have drastically
different characters -- for example, as you convolve the beam, there are
some very wide negative sidelobes that are coherent, while the largest
sidelobes at high resolution may be next to opposite polarity sidelobes,
and may tend to cancel out.  Furthermore, I recognize that in simulated
observations and imaging, the fractional errors are larger on these bigger
scales.  So, I have long been a proponent of Multi-Scale Sidelobe
Reduction, or MSSR, and have started a non-profit organization,
www.mssr.org, to fight for this urgent need (just kidding).  However, I
would be surprised if this work gets done for ALMA.


2) I've unleashed a monster.  I am NOT advocating just blind optimization
out to twice the primary beam!


Consider this totally made-up example, which will be QUALITATIVELY
correct.  Lets say Leonia optimized PSF's of size X times the Full Width
at Zero Intensity of the PB.  (I earlier argued that we need to optimize
out to X = 2, but NOT BLINDLY.)  Inside X, the PSF will have small peak
sidelobes, and just OUTSIDE X, the PSF will have larg peak sidelobes,
because the Kogan algorithm works by pushing the nasty sidelobes OUTSIDE
the region of optimization.  For argument's sake, lets invent some
plausible sidelobe levels that his optimizations could result in:

X	inner peak	outer peak

0.5	0.04		0.23
1.0	0.07		0.22
1.5	0.10		0.21
2.0	0.13		0.20

(These results are totally made up, but should be qualitatively similar to
actual results in some respects)

First off, we see why we DON'T want to just optimize for X = 0.5: a source
at the half power PB point will have nice sidelobes (max = 0.04), UNTIL WE
GET TO THE FIELD CENTER, where all of a sudden we get hit with a wopping
0.23 sidelobe.  Clearly not a good thing.  Admitedly, its not as bad as it
might sound, as sources at the half power point will be down by 50%, so
the sidelobes will be down by 50% in absolute power.  

OK, IF we optimize all the way out to X = 2, we will have large
sidelobes in the inner PSF (ie, now up to 0.13, even in the inner part of
the PSF. However, because of my arguments last week, we actually don't
NEED to optimize the sidelobes at the PSF edge as much as we need to
optimize them at the PSF CENTER.

IE, we'd really like to get that 0.04 sidelobe level for the inner part of
the PSF without getting hit by 0.23 at the half power point; and we'd like
to push the really nasty sidelobes way out without compromising the inner
PSF optimization.

So, I am advocating optimizing out to 2 times the PB, but a gradated
optimization permitting better optimization where it is most important.
IE, we should be able to have our cake and eat it, too.


3) To address Dave Woody's point that the two factors of the PSF are not
required:

If you DON'T include BOTH factors of the PB (ie, first the physical
multiplication by the PB, and second, the average over where the point
sources are in the beam and multiplication by the PB as in the software
process of mosaicing), you only get something like optimizing the PSF
times the PB.  However, I've demonstrated (hopefully, as Leonia agrees
with this logic) that we need to optimze a PSF which is TWICE the PB in
extent.

 *  Hence, I stand by my statement that we must optimize the PSF times the
* * autocorrelation of the PB, which gets us out to twice the PB in size.

My guess is that, unlike the multiscale optimization (which I think will
never get done for this project in spite of punditry's calls), some sort
of weighted optimization such as this, which puts a more stringent
requirement on sidelobes in the inner PSF, will be done.  It is my
understanding that it does not fit into the Kogan algorithm as it is
currently implemented.

Leonia, what changes are required of your algorithm to permit such a
weighting function?

Also, one of the major problems with the Kogan algorithm was its inability
to treat long track synthesis optimizations, which Conway demonstrated
were required (ie, the snapshot optimization and the long track
optimizations should be different).  HOWEVER, I suggest that the
snapshot optimization should be sufficient for the compact array as it
will often be taking snapshots in the mosaicing process.

	-Mark