The processing of hexagonally sampled signals with standard rectangular techniques: application to 2-D large aperture synthesis interferometric radiometers

In Earth observation programs there is a need of passive low frequency (L-band) measurements to monitor soil moisture and ocean salinity with high spatial resolution 10–20 Km, a radiometric resolution of 1K and a revisit time of 1–3 days [1]. Compared to total power radiometers aperture synthesis interferometric radiometers are technologically attractive because of their reduced mass and hardware requirements. In this field it should be mentioned the one-dimensional (1-D) linear interferometer ESTAR developed by NASA [2] and MIRAS a two-dimensional (2-D) Y-shaped interferometer currently under study by European Space Agency (ESA) [3]. Interferometer radiometers measure the correlation between pairs of nondirective antennas. Each complex correlation is a sample of the “visibility” function which, in the ideal case, is the spatial Fourier transform of the brightness temperature distribution. Since most receiver phase and amplitude errors can be hardware calibrated, Fourier based iterative inversion methods will be useful when antenna errors are small, their radiation voltage patterns are not too different, and mutual coupling is small. In order to minimize on-board hardware requirements—antennas, receivers and correlators—the choice of the interferometer array shape is of great importance since it determines the (u; v) sampling strategy and the minimum number of visibility samples required for a determined aliasing level. In this sense, Y-shaped and triangularshaped arrays with equally spaced antennas are optimal. The main contribution of this paper is a technique that allows us to process the visibility samples over the hexagonal sampling grids given by Y-shaped and triangular-shaped arrays with standard rectangular FFT routines. Since no interpolation processes are involved, the risk of induced artifacts in the recovered brightness temperature over the wide field of view required in Earth observation missions is minimized and signal to noise ratio (SNR) is preserved.