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

[David Woody]

Bryan
I attempted to develop a rigorous solution to this problem
in ALMA memo 389 section II.B equ. 7 and 8.
Cheers
David
----- Original Message -----
From: "Bryan Butler" <bbutler at nrao.edu>
To: "Leonia Kogan" <lkogan at zia.aoc.NRAO.EDU>
Cc: <dwoody at ovro.caltech.edu>; <alma-config at nrao.edu>;
<dbock at astron.berkeley.edu>; <mmaimcal at zia.aoc.NRAO.EDU>
Sent: Tuesday, January 29, 2002 9:22 AM
Subject: Re: [alma-config]Re: comparison of the boone's and kogan's compact
configurations


>
>
> 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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