[alma-config] [Fwd: Re: Memo 538 draft] erratum

[Frederic Boone]

You probably already corrected for the error in my
previous  email about Nyquist sampling: it's
D/(2*lambda) and not the inverse!
so 2*Nyquist=D/lambda and so on.

But this was only a typo error and the values computed
were right.

Regards,
Frederic.

--- Frederic Boone <frederic_boone at yahoo.fr> a écrit :

> Dear Alwyn and John,
> 
> Thanks for the news and the draft.
> 
> > A 50 element ALMA array will not enable the full
> > Level 1 science requirements,
> 
> This is indeed an important change that implies some
> modifications in the design. 
> 
> More quantitatively if we assume (for illustration
> only!)  Nyquist sampling (2*lambda/D) is required
> and
> the observations cannot last more than 8 hours then:
> 
> 1. according to Eq. 24 of A&A 386, 1160, the
> configurations should not exceed 3.5 km. 
> 
> 2. according to Eq. 25 it is possible to have a
> gaussian distribution of samples with a 10dB cutoff
> at
> the edges provided the configurations do not exceed
> 1.2 km.
> 
> The largest configuration (3.5km in this particular
> case) should look like a ring or Reuleaux triangle
> (top of Fig.4 in A&A 386, 1160), the configurations
> in
> case 2 above (<1.3km) should be centrally condensed
> (bottom of Fig.4) and the configurations in the
> range
> 1.3--3.5 km should have an intermediate design (see
> Fig.4, kind of rings with antennas in the center).
> 
> These values are given for illustration (I am not
> claiming we should not have configurations larger
> than
> 3.5 km!), if a sampling at 4*lambda/D (i.e.
> 2*Nyquist)
> is declared to be enough for the sience requirements
> then these values should be multiplied by 2 (and so
> on...).
> 
> Applying these simple considerations to John's
> design,
> a spiral configuration with a maximum baseline of
> 3.5
> km implies a sampling at the edges=
> 3.5/1.3*Nyquist=2.7*Nyquist. But this is assuming a
> 10dB cutoff, and the spiral produces a much lower
> cutoff so that the sampling is most likely
> >4*Nyquist.
> 
> This choice might be justified but it should be
> clear
> that it does not favour imaging of extended complex
> sources (if the source is known a priori to be 4 
> times smaller than the primary beam there is no
> probem). And we are not yet in the highest
> resolution
> regime (these are not the largest configurations). 
> Other choices are possible (e.g. more antennas at
> the
> edges of the configurations) that would give a
> better
> sampling of the uv-plane.
> 
> Some comments about the memo draft.
> ------------------------------------------
> 
> 1. About the re-weighting method mentioned to force
> the beam shape it would be nice to give the
> reference(s). To my knowledge it was first
> introduced
> in the appendix of ALMA memo 400 (also presented at
> the CDR held in Socorro january 2002). 
> 
> 2.  About the sentence in Appendix A:"It is
> certainly
> not the case (as has been claimed in Boone2002) that
> the output of any such deconvolution is always
> equivalent to the noise increase due to a
> re-weighting
> of the data so that the dirty image main lobe equals
> the clean beam.".
> 
> There must be a misunderstanding.
> Indeed, this paper is entirely dedicated to
> estimating
> the effects of deconvolution and minimizing these
> effects with appropriate sample distributions. It is
> clearly written that interpolation between the
> samples
> 
> is part of the deconvolution process and that it
> introduces some noise. This effect is even detailed
> in
> the Appendix B for the case of Shannon
> interpolation.
> In the Section 2 of the paper it is said that,
> although 
> it is difficult to give a universal (i.e. true for
> all
> the deconvolution methods) estimate of the errors it
> can be reasonably expected that the behavior will be
> similar for all methods: the further away the
> samples
> the larger the error.
> Then, as the goal of the paper is to minimize the
> errors with appropriate distribution of samples, it
> is
> proposed that for a given scientific goal there is a
> spacing (more accurately one should talk in terms of
> density of samples) that should not be exceeded
> (which
> depends on the method) to keep the errors close to
> the
> instrumental errors. Then, when we are in this 
> regime, additional errors come from the reweighting.
> Here it should be emphasized that "reweighting" does
> not refer to the deconvolution method actually used:
> "reweighting" refers to a process that is hidden or
> not but present in *all* the deconvolution methods
> *without exception* as long as the output is a clean
> image.
> 
> 3. Then in the next sentence John, you seem to claim
> that deconvolution does not necessarily increase the
> noise like reweighting does (which again I never
> claimed because the interpolation process also
> contributes) and give the example of a point source.
> I don't understand the argument: for a point source
> there is no imaging process and therefore no
> reweighting. For a point source all the samples
> carry
> the same information their distribution does'nt
> matter
> a all!
> The title of my paper is "Distributions of Fourier
> samples for imaging" not for "model fitting"...
> All the point in this reweighting discussion is that
> the distribution of samples matters. By improving
> the
> distribution (even if sampling is already ideal) we
> can improve the image. I guess we agree on that
> point
> (we would probably not care so much about the
> configurations otherwise...).
> 
> 4. Then you seem to associate the "reweighting" with
> the "restoring" process. 
> But again "reweighting" is always there (hidden or
> not) as long as one produces a clean image (not a
> model fit) with a finite resolution. In MEM the beam
> shape can vary acrross the map but the resolution is
> never infinite. 
> There is a beam so there is "reweighting".  
> 
> I would appreciate if these comments can be taken
> into
> account in the memo.
> 
> Best regards,
> Frederic.
> 
> 
> 
> 
> 
> 
> >  but the Executives requested an
> > analysis of this baseline, 
> > based on currently available funding. 
> Accordingly,
> > the JAO asked the 
> > Science IPT for a design for a 50 antenna array
> > which could provide 
> > excellent imaging along with the possibility of
> > extension to 64 antennas.
> > 
> > John Conway has provided this design, which is
> > described in a document 
> > located at the following location (userid and
> > password necessary):
> >
>
http://edm.alma.cl/forums/alma/dispatch.cgi/docapproval/docProfile/103106/d20050829201752/No/t103106.htm
> > or at:
> >
>
http://www.oso.chalmers.se/~jconway/ALMA/OUT/ALMA-90.02.00.00-005-A.SPE.pdf
> > 
> > A separate document in preparation by M.Holdaway
> > defines the positions 
> > and reconfiguration scheme for the approximately
> 35
> > additional pads 
> > which are needed for the outer configurations of
> > ALMA.  This will be 
> > ready by year's end, after some iteration with
> > environmentall concerned 
> > vizcachas and site road and network design.
> > 
> 
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