Fourier transform imaging spectroscopy with a multiple-aperture telescope: band-by-band image reconstruction

Fourier transform imaging spectroscopy can be performed with a segmented-aperture telescope or a multiple-telescope array using the subaperture piston control mechanisms. Spectrum recovery from intensity measurements is analyzed for a general aperture configuration. The spatial transfer functions of the recovered spectral images are shown to vanish necessarily at the DC spatial frequency. This poses an interesting image reconstruction problem as the recovered spectral data is missing low spatial-frequency content. Results of a band-by-band reconstruction of simulated data are presented where the low spatial frequency data is reconstructed by maximizing a sharpness metric based on the spatial derivatives of the object estimate.