Tapering the MMA

We will want to taper the MMA's Fourier coverage in at least two common situations:

• we simply don't have the SNR to see what we want to, and tapering will increase the surface brightness sensitivity. (For uniform coverage, doubling the linear beam size increases the beam area by a factor of 4, reduces the number of baselines by a factor of 4, and increases noise by a factor of 2. Hence, noise goes down by 1/2.) Since we have a factor of 4 in size between arrays, this will be done often as people try to observe in the highest resolution configuration just barely possible, and find out that the longest baselines are just a bit too long. Tapering the velocity resolution is an alternative to tapering the spatial resolution, at least for spectral line observations. Tapering the spatial resolution is more effective at increasing the brightness sensitivity, but the tradeoffs between tapering the velocity resolution and the spatial resolution depend upon the scientific objectives of the observations.
• many studies will compare different molecular transitions at different frequencies, and hence, at different resolutions. An accurate comparison requires the same resolution, so N-1 out of N compared images will be tapered to some extent. Since the configuration sizes are quantized in factors of about 4, significant tapering will often be required. Quantities derived from molecular transition comparisons will also be limited by the thermal noise of the input images, so optimal noise behavior upon tapering will buy us lower noise in these derived quantities.

Since the images will often be limited by thermal noise, designing antenna configurations which give good imaging and low noise both at full resolution and when tapered will increase the scientific throughput of the MMA.