[alma-config] Near-in sidelobes

[Leonia Kogan]

John,

Your comparison of the two arrays (spiral and donut) sidelobes based on
the the one dimension slice of the beam patterns. At least this is the
case shown in
http://www.oso.chalmers.se/~jconway/ALMA/SIMULATIONS/SIM3/.

It is quite possible that the two dimension beams will give another result.


Leonia



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>From owner-alma-config at kochab.cv.nrao.edu Thu Jun  8 02:16 MDT 2000
Date: Thu, 8 Jun 2000 11:29:46 +0200 (CEST)
From: John Conway <jconway at ebur.oso.chalmers.se>
To: Min Yun <myun at zia.aoc.NRAO.EDU>
cc: alma-config at zia.aoc.NRAO.EDU, jconway at oso.chalmers.se
Subject: [alma-config] Near-in sidelobes
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Hi,


> My point is that the strawperson donut arrays have SMALLER near-in 
> sidelobes than the spiral array Morita-san used for his study -- because
> donut arrays also have tapered uv coverage and the particular sprial
> array used was not optimized -- and it will make an interesting
> comparison.  I would like to shatter this incorrect notion some people
> have that the donut arrays have a much worse near-in sidelobe problem.
> The near-in sidelobe problem is a general one and is not inherent to 
> any particular style of array.
> 

1) I would like to unshatter the myth!
I don't understand much of the  above paragraph. 
I did a comparison of 6hr beams for a self-similar spiral and 
a Kogan donut array (one of the versions
preseneted at URSI) in 

http://www.oso.chalmers.se/~jconway/ALMA/SIMULATIONS/SIM3/

The peak  near-in sidelobes (within 10 beams) for the spiral were about a
factor of two less. In fact within about 3 beams the 
spiral doesn't have any coherent ring-like  near-in sidelobes at all
while the donut has a series of rings.

The reason for this is obvious - the amount of taper is larger for the
spiral pattern - it is very close to gaussian while the Kogan array 
has a similar  internal taper but a sharper cutoff at the edge
(see figures 1 and 2 in above web page). 
Obviously the level of the near-in sidelobe IS 'inherent in the
particular style of array'

I would contend that The spiral array is a close as can be to being
optimised for NEAR-IN sidelobes, since the uv density distribution is 
very  close to gaussian (see figure). It is however 
true that the spiral beam has not been optimised to reduce  FAR-OUT 
sidelobes - but thats another matter. 

To summarise on near-in sidelobes. For snapshots and natural weighting 
the first positive sidelobes are something like 

Ring                          10%-15%
Double ring (Kogan)            5%-7%
Spiral                          2.5%

For long tracks the near-in sidelobes do not reduce significantly
but far-out sielobes do. From my imaging simulations of complex objects
(my m51 and Cygnus A tests) I find that image quality does depend
significantly on the near in sidelobe level. 





2) Is a gaussain beam desirable? Re Mins worry about 'wings' and
'pedestals' in synthesised beams. 

Now all maps I know use 
a gaussian restoring beam - the final answer from CLEAN is not
'what does the sky looks like' (which is ill posed, since what resulotion
are we talking about, picoarcesconds?), but what would the sky look
like if we first convolved it with a beam. 
Clean (and MEM if we pre or post convolves) indirectly answers this
question. Perhaps in some cases it might be worth using something other 
than a gaussian for a restoring beam - but so far I've not heard  about  
anybody using this - and there are imaging problems, - anything with a
sharper cutoff has a  fourier transform with larger values at 
high spatial frequencies and therefore lets in more of the badly
extrapolated data beyond the edge of the uv coverage. Gaussians
are a good compromise between having compact support and no sidelobes
in both domains. The prolate speroidals are also compact but have
some sidelobes.

Anyway my main point is that a 
gaussian beam seems to be what the punters want, and the 
eye/brain is good at interpresting such maps.  The gaussian beam does
after all decrease exponentially and there are no sidelobes.
The only case where there is a problem is when you want to look at 
a weak feature about 0.5 beam from a bright feature, and the weaker 
featyre is  obscured by the gaussian wings- but then you can just choose a 
smaller gaussian restoing beam!
 - given all the above a uv coverage  which naturally gives 
a gaussian mainlobe would seem a reasobale target.

I would argue that the  problem with the VLA that MIn alludes 
to is that it is actually more centrally condensed than gaussian - 
hence there are often indeed wide wings and pedestals which
can cause problems.

      John



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