[mmaimcal]Re: Comment in ALMA memo 489

[Stephane Guilloteau]

Hi everybody (and apologies for those who are on both lists)

    I believe there is a little confusion here. Let me try to remove some of it.

In Pety et al work, the incorporation of single-dish data to ALMA data is done in the UV Plane.  Since an
interferometric observation with ALMA produces visibilities which are the Fourier transform (well, almost) of the
product of the sky brightness with the primary beam at the pointing direction, the only valid single-dish data which can
be added to the interferometric UV table is the total single dish flux in that pointing direction, i.e. the zero
spacing. Strictly speaking, this is consistent with the sampling theorem: the Fourier space can be sampled every antenna
diameter. The way the ensemble of zero spacing flux densities is obtained is irrelevant here: the best way to get then
is most likely to obtain an image to minimize the effects of systematics.

Mark argues that there are better ways to incorporate the single dish information. This may well be true, although it
appears in contradiction with the sampling argument given above.

The MEM approach, which uses a single-dish map as a default image, may well be better than the CLEAN based approach used
in Pety et al.  Note that it cannot be a sampling issue only: the ensemble of zero spacing flux densities in the Pety et
al technique lies on an oversampled grid of points in the sky, so it is possible from this ensemble to produce a
complete single-dish image which contains the same information as any other single-dish map obtained in any other way...

There may be subtle issues about sampling that we don't really understand, and which are related to the shape of the
primary beam.

Any way, the easiest way to check whether better results can be obtained when using ALMA + SD then what was done by Pety
et al. is to make simulations and compare the results. MEM based simulations were done by Morita san et al., and
essentially confirmed the results of the CLEAN based analysis, but I don't remember the details of the simulations.  If
there is any doubt, somebody should perform such simulations again.

Mark says that adding a guard band (in interferometric and single dish mode) around the observed area improve the image
quality. This is understood by everybody, as well as the price that we have to pay for this improved quality.

Mark also says a guard band in Single-Dish mode ONLY also improves the image quality. If I have followed correctly the
discussion, I believe the only demonstration of that (if any) is based on data where there was NO EMISSION outside the
mosaicked area. May be I am mistaken, but in case this is true, I believe it is important to check whether a guard band
also helps when the source is more extended than the mosaicked area, because this is likely to be the actual situation.

Finally, as concerns the observing strategy, it is clear the Single-Dish data and interferometric data cannot be
obtained simultaneously from the same antennas, because of the widely different integration times required in general
for both cases.
What is possible is to devote a small number of antennas to do a Single-Dish On-The-Fly image, while the remaining
antennas are used to do a (pointed or on-the-fly) interferometric mosaic over a generally smaller region. The
single-dish OTF map will  in general cover a  larger area because of the turn-around time overhead.

    I hope this helps, and does not create any additional confusion.

    Best regards,

        Stephane

S. Guilloteau
L3AB
Observatoire Aquitain des Sciences de l'Univers
2 rue de l'Observatoire
BP 89
F-33270 Floirac
  Phone:  (33) 557 77 61 68