Interferometric array layout design by tomographic projection

TL;DR: A new method is demonstrated that can move antenna positions to achieve an ideal density distribution for the UV samples without the need for gridding and is applicable to very few as well as a large number of antennas.

Abstract: Context. This study pertains to the optimization of the layout of a single configuration interferometric array to achieve a desired natural tapering for the density distribution of its UV plane coverage. Existing techniques that seek this goal determine a two dimensional density gradient that acts on the UV samples and in turn on the antenna positions. This gradient is commonly computed by gridding the UV plane, and is sometimes averaged over a number of different scales due to the sparseness of the UV samples. Aims. The goal of this study is to demonstrate a new method that can move antenna positions to achieve an ideal density distribution for the UV samples without the need for gridding. Methods. An approach is described where the UV samples are projected into a one dimensional vector. If an equivalent projection is done for an ideal model distribution, the difference between these vectors yields correction terms which can be mapped to new antenna positions. Such modifications are made in all directions until a close match is achieved to the desired UV plane coverage and equivalently, by the Fourier transform, the ideal point spread function. Results. Results are provided that relate achievable resolution (for Gaussian UV coverage) to the number of antennas available to the algorithm, for a few different observation modes. Preliminary layouts are shown for the Square Kilometer Array pathfinder project, the Karoo Array Telescope. Conclusions. The proposed method is applicable to very few as well as a large number of antennas. Multiple objective optimization is not considered.