A Hexagonal Pseudo-polar FFT for Formation-Flying Interferometric Radiometry

A novel mission concept applying satellite formation flight to passive microwave interferometry was recently proposed to significantly improve the interferometer’s spatial resolution. This concept was shown to sample the visibility in a hexagonal tile of polar grids, and to recover the brightness map, this visibility must be inverted via a discrete polar inverse Fourier transform. For a fast and accurate solution, this letter develops a modified hexagonal variant of the pseudo-polar fast Fourier transform (PPFFT) and its inverse and explores its performance when applied to the proposed formation-flight radiometer. Compared to the conventional rectangular PPFFT, we find approximately a fivefold improvement in the recovered radiometric accuracy, where the rms radiometric error is in the order of $10^{-2}$ K. The impact of visibility interpolation method is also explored, showing that an FFT-based interpolation technique leads to the most accurate final image recovery.