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

Tue Jan 29 15:11:29 EST 2002

i should realize that smarter folks have always dealt with things
before i get to them :)...

but, seriously, i'm not sure you've got eqns 7 & 8 right.  they are simply
stated, not proven.

let me develop a counter-example which i think shows that these equations
aren't quite right.  consider a point source at the half-power point of
the PB.  now, consider the sidelobe response to this point source at the
PB center.  your equation would have that sidelobe reponse downweighted
by ~0.71 (the value of a PB with sqrt{2} wider FWHM).  but, in fact,
the sidelobe response here *shouldn't be downweighted at all* by the
PB response - it's at the center of the PB.  you could argue that it
should even be 'upweighted' in a strict SNR sense - the signal from
the point source at the HWHM is only half what it should be, while
the 'confusing' source at the pointing center is at full value (multiplied
by the sidelobe level).

so, i think heuristically you got the argument right - that you take
the upper envelope of the family of PSF's, and that this then is equivalent
to taking a modified primary beam - but i am not convinced that you got
the mathematics right.

my crude treatment of the problem (which i described in the earlier email)
takes the modified PB as:
   PB'[s] = PB[max(0.0,s-FWHM)]
which is similar to yours, but a bit different (it's flat-topped at 1.0
out to roughly the FWHM [in radius])...

this is relatively easy to see and argue about in 1D, but gets
more complicated in 2D, and, i think most of the argument goes away
when you start talking about deconvolution.

	-bryan

On 2002.01.29 11:31 David Woody wrote:
> 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
> > > MIME-Version: 1.0
> > > Content-Transfer-Encoding: 7bit
> > > X-Priority: 3
> > > X-MSMail-Priority: Normal
> > > X-Mailer: Microsoft Outlook Express 5.50.4522.1200
> > > X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4522.1200
> > > X-Lines: 25
> > > Status: RO
> > >
> > > 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 -----
> > >
> > > _______________________________________________
> > > Alma-config mailing list
> > > Alma-config at listmgr.cv.nrao.edu
> > > http://listmgr.cv.nrao.edu/mailman/listinfo/alma-config
> > >
> > _______________________________________________
> > Alma-config mailing list
> > Alma-config at listmgr.cv.nrao.edu
> > http://listmgr.cv.nrao.edu/mailman/listinfo/alma-config
> >
> 
> 