Hi everybody, Here are my comments on Darrel message, as well as the promised draft on compact array issues. The draft can be found at http://iram.fr/~guillote/alma/short-spacing.ps or if you prefer PDF http://iram.fr/~guillote/alma/short-spacing.pdf Stephane Comments on Darrel's message: >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. I completely agree with Darrel in that respect. Taken at face value, his argument would imply 6-m antennas. Unfortunately, it seems that only larger antennas (8-m) can provide the required sensitivity (both for calibration and image weighting) without severe number/feasibility problems. > >(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. Indeed, there is already so much overweight on the 15 meter baselines that adding the mixed diameter baselines make things even worse. >(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.] Sounds OK for me (even the numbers...). > > Finally, getting to your questions: > >1. Stand-alone imager. I believe the answer will depend very much on what deconvolution technique is required to make the proper merging between the ACA and the "Enhanced ALMA". My prejudice is that ACA should have some decent imaging capabilities per-se. However, as described in my draft, I believe the sensitivity for calibration actually drives the antenna number and size. > >2. How much consideration should we give to the cross- >> correlation between the smaller antennas and the 12m >> antennas? I support Darrel's viewpoint. Making the cross-correlation prevents from using the ACA and ALMA with different integration times, suppressing an important degree of freedom in the re-weighting scheme. It seems (to be confirmed) that calibration is still possible with the stand-alone ACA, so I do not see any compelling reason to have the cross-correlation.