[mmaimcal]Re: [alma-config]Re: comparison of the boone's and kogan's compact configurations

[Bryan Butler]

all,

leonia and i have been discussing this at some length just now.
i had gone off myself and essentially reproduced all of this
independently, and have now been thinking about it quite a bit
(and leonia has clarified some things for me).

it seems clear that simply multiplying the synthesized beam by
the primary beam (which is what dave & frederic did) is too
simple.  the problem is that the synthesized beam is convolved
with the sky brightness, and hence 'moves around' (effectively)
in the PB.  so you have to consider multiplying the synthesized
beam by shifted PBs.  the question is how much is the maximum
shift?  a related question is what is the size of the optimization
region on the sky (for leonia's beam optimizations)?

it also seems clear to me that considering the synthesized beam with
*no* multiplication (what leonia has been doing) is too simple.
this should be considered as the absolute worst case (i.e., a
pathological case where sources on opposites sides of the PB both
happen to fall at locations of peak sidelobes in relation to each
other).  if we were never to deconvolve (always just take the dirty
images), then this would be closer to the right thing to do, but
the fact of the matter is that we will *almost always* deconvolve.

the exact treatment is not clear to me.  maybe a reasonable
compromise might be to calculate the 'worst case shifted peak
sidelobe' - where, instead of downweighting strictly by the PB,
you take a shifted version of the PB instead (so downweight
by less).  the question, again, is 'shifted by *how much*'?  not
clear to me.  i *would* say that making the shift be as much as
the full width between the nulls in the PB seems too much to me
(this is equivalent to having leonia's optimization go over twice
the width between the nulls).  perhaps make the shift be equal to
the FWHM.  i will have a go at this...


	-bryan


On 2002.01.29 09:07 Leonia Kogan wrote:
> Hi David,
> 
> I carried out my calculations at the normalized coordinate:
> 
> Radius = number of the lambda/D = number of resolutions;  D = arrray diameter
> 
> The two side primary beam for the flat illumination is
> 2.4*lambda/d; d is diameter of the dish
> 
> Introduce alpha is a portion of the two side primary beam.
> 
> Then Radius = Alpha*2.4*D/d;
> 
> Subtitude D= 200; d=12 and get
> 
> Radius = alpha*40;
> 
> My calaculations  indicate sidelobes of 9.3% at Radius=20 (alpha=0.5).
> 
> Of cource the multiplication of the PSF by the primary beam will reduce
> the sidelobes. And this explain our difference. But:
> 
> 1. The actual 12 meter dish will have wider primary beam because
>    the illumination will not be flat.
> 
> 2. But I do not think that the multiplication of the PSF by the primary beam
>    is the right operation.
>    You wrote:
> 
> >You are correct that for
> >mosaicing you need to consider a wider area and Mark said that
> >twice the primary beam should be enough.
> 
> I think even for not mosaic observation twice the primary beam should be
> required. Effect of the primary peam on the sidelobes of PSF is not simple
> multiplication ( I think so). The primary beam multiply the sky.
> 
> Consider the PSF pointed at the edge of PM. Then the sky at this point
> will be reduced by the PB. But the sidelobes at the oposite edge of the PB
> (remoted by twice distance) will be reduced by the same factor.
> So the ratio of the sinal and the sidelobe at the oposite edge of the PB
> will be determined by the PSF exclusively.
> 
> Thanks
> 
> Leonia
> 
> 
> ----- Begin Included Message -----
> 
> >From dwoody at ovro.caltech.edu Mon Jan 28 20:21 MST 2002
> Reply-To: "David Woody" <dwoody at ovro.caltech.edu>
> From: "David Woody" <dwoody at ovro.caltech.edu>
> To: "Leonia Kogan" <lkogan at zia.aoc.NRAO.EDU>
> Cc: "douglas bock" <dbock at astron.berkeley.edu>,
>         "Al Wootten" <awootten at cv3.cv.nrao.edu>
> References: <200201271622.JAA00901 at bonito.aoc.nrao.edu>
> Subject: Re: comparison of the boone's and kogan's compact configurations
> Date: Mon, 28 Jan 2002 19:21:58 -0800
> Organization: Caltech
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> 
> Hi Leonia
> My calculations always include the primary beam, i.e. the FT of the
> UV samples multiplied by the primary beam, and hence I do not
> see the far out sidelobes beyond ~15.  You are correct that for
> mosaicing you need to consider a wider area and Mark said that
> twice the primary beam should be enough.  ALMA memo 389
> argues that for a Gaussian primary beam, the correct beam to
> multiple the FT of the UV samples by is only a sqrt(2) larger
> Gaussian beam.  I will run this case soon and send you the
> results for both configurations.  I will also scale Boone's configuration
> down to give the same magnification as your configuration (including
> margin for close packing) so that we are comparing the same capability.
> My guess at this point is that the differences will not be important,
> i.e. very small.
> Cheers
> David
> ----- Original Message -----
> From: "Leonia Kogan" <lkogan at aoc.nrao.edu>
> To: <dwoody at ovro.caltech.edu>; <frederick.boone at obspm.fa>
> Cc: <alma-config at cv3.cv.nrao.edu>
> Sent: Sunday, January 27, 2002 8:22 AM
> Subject: comparison of the boone's and kogan's compact configurations
> 
> 
> 
> 
> 
> ----- End Included Message -----
> 
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