Introduction

Early work in designing the optimal array configurations for the MMA (Cornwell, 1984) and for the SMA (Keto, 1992) assumed that the (u,v) points should be uniformly distributed across the part of the Fourier plane which was to be sampled. This assumption led to ring-like arrays. This is intuitive since the autocorrelation of a ring is a uniform disk with a delta function at the origin. However, the arguments for a uniform Fourier plane distribution have not been on ground as solid as the methods which have been created to give us arrays resulting in uniform coverage.

Radio astronomers, especially in the VLBI community, have struggled for years to get something for next to nothing, reconstructing images from poorly sampled Fourier plane data. Given an arbitrarily complex object, we must have complete (u,v) coverage, sampling the Fourier plane at the Nyquist rate. The MMA's most compact configuration has essentially complete Fourier plane coverage (out to its maximum baseline) in a snapshot, and its a good thing too, since each field of the mosaics it makes will often be filled with complicated structure on all scales. When you don't completely sample the Fourier plane for an arbitrarily complex object, you are trying to solve for more independent resolution elements than you have independent data measurements. Fortunately, most astrophysical sources are not ``arbitrarily complex'', but rather vary in some reasonable manner. Algorithms such as MEM are therefore able to construct reasonably good images even in ill-determined problems due to MEM's bias towards simple images, and image quality degrades gracefully as the imaging problem becomes less well-determined.

On the other hand, there are many objects which are simple enough to permit high quality imaging with relatively poor sampling of the Fourier plane. For example, even without a support constraint explicitly forbidding emission from being reconstructed outside some region of the image, a point source can be imaged well with only a few measured visibilities. Objects of intermediate complexity can be imaged with high quality with moderate Fourier plane coverage, especially if a strong support constraint holds, limiting the emission to a small part of the primary beam.

The desire to design an interferometric array which produces nearly uniform Fourier plane coverage derives from the quest to obtain complete Fourier plane coverage, or as nearly complete Fourier plane coverage as is allowed by the number of antennas in the array. However, this goal does not properly address the kinds of objects which the array will be imaging or the reconstruction algorithms which are currently in use. It may be a dangerous activity to hypothesize how an array will be used based on our current knowledge of the universe, but it may also gain us a great deal if our estimates of the array use are correct. For example:

• If the MMA were only to observe very bright and complicated sources such as the planets, the sun, and nearby continuum sources, at the full natural resolution of each configuration, striving for uniform Fourier plane coverage might be a good strategy.
• If the MMA were to observe mainly sources which were marginally detectable (and indeed, astronomer's optimism will result in many sources not being detected at the full resolution of the configuration in which they were observed), then we would not be so acutely concerned with the ability to achieve extremely high quality images, but with the ability to optimally pull images out of our noisy data.

These two situations place very different demands on the Fourier plane distributions, and because the MMA will often find itself squarely in each of these situations, some compromise between these competing demands is warranted.