[asac] ACA design and imaging study

[Darrel Emerson]

Hi Min,
   For what they're worth, here are my prejudices.

First, some general remarks, mostly obvious and well known:

(a) The #1 purpose of the ACA is to give more faithful coverage of the
short spacings, between about 6m baseline or a little less, up to 12m or
a little more.  6 meters is a little beyond the half-intensity cut-off
of a 12 meter dish in single dish mode, while the 12 meter spacing is a
little below the half-intensity cut-off of an 18-m baseline of two 12
meter dishes operating as an interferometer (i.e. packing density
=1.5D).
   The issue here is not on equalizing signal-to-noise ratio, but on
improving dynamic range by avoiding such a large deconvolution factor,
so in some sense equalizing dynamic range as a function of spatial
frequency.  By this I mean: If you try to use spatial frequencies that
are attenuated by the antenna response by a factor of 2, then systematic
errors such as calibration errors, pointing errors and so on become
twice as critical.  I'd like to see us avoid having deconvolution
factors greater than 2 (I'm an idealist!).  This will give us more
faithful imaging;  it's particularly important at these short spacings
because the visibility function of most sources we'll be needing to
mosaic goes roaring up at shorter baselines, so consequently a slight
calibration error on the very short baselines would easily dominate the
errors on the overall synthesized map.
   Conclusion:  the ACA should be optimized to give best response in the
baseline range 6m to 12m. Other considerations are secondary.

(b)  Remember that in combining big dishes with small dishes, you only
get the field of view of the smaller dish, rather than the (perhaps at
first sight intuitive) geometric mean of the antenna half-power
beamwidths.  This would not be true if the antenna patterns were true
gaussians, but beyond the half-power point REAL antenna patterns usually
have deep nulls; the nulls of the narrowest antenna pattern of a pair of
antennas used as an interferometer define the field of view, not the
geometric mean of the radius to the nulls.  So, to first order, the
mixed-size antenna pair only has a usable field of view of the larger
antenna, with the sensitivity of course equivalent to an anterferometer
using the geometric mean of the antenna areas.  This is a (perhaps
minor) limitation on the usefulness of mixed-diameter baselines.
   Assuming a packing density of 1.5, an (e.g.) 8-meter antenna combined
with a 12-meter antenna will have a minimum baseline of about 15
meters.  (There are some reasonable assumptions here.)  That's too big a
baseline to be optimum at helping the short spacing problem, where the
range 6m to 12m is most badly needed.  This is a more major limitation
on the utility of mixed-diameter baselines, although admittedly there
could be some small supplement to the S/N on 15 meter baselines and
higher. 

(c) Remember, the effective sensitivity of the mixed baseline
interferometer is significantly worse, by a factor GREATER than the
reduced total collecting area. E.g. a 12-m dish with a 12-m dish has the
effective collecting area of (pi/4)*(12^2 + 12^2) = 226 m^2.  A 12-m
dish with an 8-m dish has an effective collecting area of two 9.8-m
dishes, (pi/4)*(12*8+12*8) = 150 m^2, although the physical collecting
area is (pi/4)*(12^2+8^2)= 163 m^2.  [Someone should check I got that
sum right.]


   Finally, getting to your questions:

1. Stand-alone imager.  Remember, the ACA will still need single (12-m)
dish observations to fill in ITS short spacings; WITH THAT, I suspect
that the imaging quality of even a relatively small number of antennas, 
adding the 12-m single dish data but not the 12-meter
interferometer-pair data, will be quite good.  For some projects, it may
be that minimum baselines between two 12 m dishes may already be too
great.  So, my prejudice is that the ACA should be usable as a
stand-alone imager, but still INCLUDING single dish data from 12-meter
dishes, and stand-alone in the sense that JUST MAYBE it won't always be
necessary to add data from 12-meter-to-12-meter antenna baselines.

2. Because of the limited help with the short spacing problem, the
reduced sensitivity, and the limited field of view - not to mention the
computational problems - I would vote for NOT considering the
cross-correlation of smaller with bigger antennas for any imaging. 
HOWEVER, it may be that for calibration the cross-correlation would be
advantageous.  So, I'd suggest making the separation of the ACA from the
main array fairly small, so it's easier to calibrate the ACA using mixed
dish diameter baselines, but not bothering with any optimization of UV
coverage with a mixed dish diameter baselines array.

   My overall prejudice: design the ACA just to optimize the short
spacing coverage in the region where ALMA would otherwise be deficient,
from about 6m to 12m.  All other considerations are secondary. 

             Cheers,
                   Darrel.

Min Yun wrote:
> 
> I would like to hear from the ASAC a little more feedback
> on what considerations should go into the ACA design and
> the evaluation of its imaging performance.  As I mentioned
> during the telecon, having the problem better defined is
> really the first step.  And the consideration that providing
> the short spacing data is the primary purpose is a significant
> first step.  To help guide this work further, could you voice
> your opinion on the following questions?
> 
> 1. How much consideration should be give the ACA as a
> stand-alone imager?  We will no longer emphasize its
> possible function as a TeraHz array, but should we try
> to preserve any future possibilities?
> 
> 2. How much consideration should we give to the cross-
> correlation between the smaller antennas and the 12m
> antennas?  If the cross-calibration using the cross-
> correlation is important, this needs to be designed
> into the layout of the ACA but possibly at some cost
> to maximizing the sampling of the shortest spacings.
> 
> These two consideration will drive the ACA design to two
> distinct and competiting ideas, and there will be some
> impact favoring 7 x 8m array versus 16 x 6m array as well.
> I can already tell you that we will not have an all-singing,
> all-dancing array even with 16 antennas.  So, my question
> really is what the priorities should be at what weight,
> with respect to providing the maximum short-spacing sampling
> (i.e. a separate filled configuration).
> 
> Thank you for your thoughts on these points in advance.
> 
>                                 Min S. Yun