Interferometric array design: Distributions of Fourier samples for imaging

This paper is complementary to (Boone 2001) in which an optimization method was introduced. An analysis is developed in order to define the distributions of uv-plane samples that should be used as targets in the optimization of an array. The aim is to determine how should be distributed the uv-plane samples of a given interferometer array in order to allow imaging with the maximum of sensitivity at a given resolution and with a given level of side-lobes. A general analysis is developed taking into account the levels of interpolation and extrapolation that can be achieved in the uv-plane and the loss of sensitivity implied by an imperfect distribution. For a given number of antennas and a given antenna diameter two characteristic instrument sizes are introduced. They correspond to the largest size allowing single configuration observations and to the largest size allowing imaging with the full sensitivity of the instrument. The shape of the distribution of uv-plane samples minimizing the loss of sensitivity is derived for intermediate sizes and when a Gaussian beam is wanted. In conclusion it is shown that the shape of the distribution of samples and therefore of the array itself is entirely determined by a set of five parameters specifying the work (interpolation and extrapolation) that can be demanded to the imaging process, the level of side-lobes and the resolution at a given wavelength. It is also shown that new generation interferometers such as ALMA and ATA will be able to make clean images without deconvolution algorithms and with the full sensitivity of the instrument provided that the short spacings problem is solved.