[Almasci] Re: [mmaimcal]Re: Comment in ALMA memo 489

[Mark Holdaway]

> > The way I look at it:
> >
> > If you had just a single pointing of interferometric data plus a single
> > total power point, that total power point will only raise or lower the
> > entire map like a piston -- it isn't making the image any more realistic.
> > In this case, it is just the (0,0) point. In order to get out the higher
> > spatial frequencies in the single dish data, you need multiple pointings,
> > and knowledge of the beam.  So, instead of just that one pointing, lets
> > make a 3 x 3 map of single dish pointings.  Now, the adjacent pointings
> > also have their (0,0) measurements, and those measurements, combined with
> > the beam, tell the image how the extended emission must "bend". So, those
> > adjacent pointings are telling the total power data in the central
> > pointing how better to distribute itself (ie, higher spatial frequencies
> > than (0,0), but information you could never get if you didn't have more
> > pointings, so it isn't just doing a piston thing.
> 
>     Sounds a priori reasonable, but when short spacing is missing, what
> you see is not a negative offset, but a negative bowl... I never found
> any decent explanation for that. Any idea ?

The bowl:  this is when you have no total power.
Another thought experiemnt to understand the bowl:
Assume you have uniform (u,v) coverage, you get a SINC function
(actually J1 Bessle function?) for a beam.  Now, cut a hole in
the middle of the (u,v) coverage, 

   Beam = 
   FT ( Uniform - Inner.Hole ) = FT( Uniform) - FT ( inner.hole )

   (( where Inner.Hole is itself a uniform coverage of the same
      amplitude as "Uniform", but smaller extent, so when you subtract
      from Uniform, you get zero for the short spacing coverage ))

    FT(uniform) = narrow SINC function
    FT( inner hole) = broad SINC function, lower amplitude (due to
                      the smaller size of the hole)

   SO, the inner hole gives you a low level, broad SINC-type function --
   as you subtract that from the first term, it gives you a
   PSF with a broad negative bowl, the inverse size of the 
   inner (u,v) hole.

   Now, if you are imaging objects which are smaller than the
   bowl in the PSF, there is no confusion, deconvolution works
   fine.   If you are imaging objects which are larger, you
   see the bowl around those objects, I'm not exactly sure why
   you can't deconvolve it away (maybe its all SNR), but it doesn't work.
   So, I think the bowl is always there in the Dirty Map, but
   it isn't so obvious unless you have something extended to
   convolve that bowly-PSF with to actually see it coming in coherently.

   If you just add a single total power point, it raises everything, it
might get rid of the bowl, but in a somewhat artificial manner (ie, not
high fidelity).  Often the negative bowl has a positive "lip"  around it
(expecially if you use MEM), and that will still be there.


> 
> >
> > The interferometer data has all the multiple spacings (down to the
> > shortest baseline) already, so it KNOWS how to distribute the flux inside
> > a given pointing without recourse to additional neighboring pointings.
> >
>     But what is done in the joint deconvolution of ALMA+SD DOES take
> that into account !. The knowledge of the location of the more "compact"
> sources found by CLEAN directly tells where to locate the single dish
> flux. Remember, we are deconvolving the mosaic all at once, and NOT
> making a linear mosaicing after deconvolution.
> 

Yes, CLEAN tells you where to place the more compact flux --
but it can't tell you where to put the less compact flux, ie,
structure that is smaller than (0,0), but larger than the
shortest interferometer baselines.  Which is the whole crux of the matter.

> 
> 
> >
> > Now, the observation described above is sort of a 1 pointing mosaic with a
> > guard band of total power data about it.

>     We never discussed the case of a single-field in this way.
> Comparisons were made on Mosaics only...

Come on, man, its a THOUGHT EXPERIMENT.  If you can see the
problem for a single pointing, you can extend that thinking to
a mosaic, which will have the same problems at the edges.


> > Generalize it in your mind to a
> > multi-pointing mosaic with a guard band in total power around that.
> >
> > In the simulations, the ALMA+ACA+SD case benefits from this guard band in
> > that an OTF map was used (though that case doesn't need it as much, as the
> > shortest ACA baselines also have some of the same information) --

>     Actually, not really. The OTF map was used as an intermediate step,
> but I don't believe we take any information from a guard band around the
> ACA data. Need to go back to details to check that.

Details.  Details which perhaps haven't been spelled out?
At any rate, I expect the ACA's coverage on the sky to extend beyond the
ALMA sky coverage, which will be similar to a guard band.
Oops -- you jusy made this point below.  Agreed!

>     I agree however that no guard band for ACA still implies SOME guard
> band for the ALMA fields, since the ACA beam is larger. But the ALMA
> antennas did not observe that guard band in interferometry.
> 

I think the total power guard band is more important that the
interferometer guard band.

> > but the
> > ALMA+SD simulation case didn't benefit from this guard band since it was
> > never included.  I originally made this point to Pety in 2001, but it
> > apparently wasn't properly understood.

>     I remember quite well you made this point, but the fact is that
> there is no way to implement such a guard band in the CLEAN algorithm we
> used.
> 
> > That was during the rush to the ACA, which seemed unstoppable.

>     I disagree both with "rush" and with "unstoppable", which to me seem
> to imply we expected a pre-definite answer.
>     There was a clear demand from the ASAC to make simulation to ASSESS
> the usefulness of the ACA, not to PROVE it. Time was short, and the
> available software too. Simulations were made with MEM which showed ACA
> improve things, we (Pety et al) made simulations with other techniques
> based on CLEAN which show a similar result.
> 
>     It was in particular the convergence of the two approaches which
> convince the ASAC. As I remember, somebody (can't figure out who)
> finally said "anyhow, it is certainly better to measure these spacings
> than to entirely rely on software to recover them".
> 
> 
> > It seems that we are currently able to be more thoughtful about all of this.
> >
>     Algorithms which use the "guard band" along the lines you propose
> remain to invent, or at least to be used for this application. I still
> believe you (or somebody else charged of that job) must make simulations
> proving the assertion. 

Fair enough.

  -Mark

> Remember that one of the problems in ALL
> deconvolution techniques is the amplification of errors. You argue that
> you can use the information better (and I tend to agree with the
> rationale, although there are some contradiction with the sampling
> arguments), but I believe it remains to be seen whether this improved
> information is sufficient in realistic cases, i.e. cases with
> observational errors.
> 
> In short, we have some good reasons to believe that
>     - perhaps the CLEAN based method is not optimal
>     - and perhaps other methods can do better 
> but both assertions remain to be proven. The second one also includes
> the first, anyhow, so working on the second is best for every body...
> 
>         Stephane
>