Dealiased spectral images from aliased Fizeau Fourier transform spectroscopy measurements

Fizeau Fourier transform imaging spectroscopy (FTIS) is a technique for collecting both spatial and spectral information about an object with a Fizeau imaging interferometer and postprocessing. The technique possesses unconventional imaging properties due to the fact that the system transfer functions, including the imaging and spectral postprocessing operations, are given by cross correlations between subapertures of the optical system, in comparison with the conventional optical transfer function, which is given by the autocorrelation of the entire aperture of the system. The unconventional imaging properties of Fizeau FTIS can be exploited to form spatially dealiased spectral images from undersampled intensity measurements (obtain superresolution relative to the detector pixel spacing). We demonstrate this dealiasing technique through computer simulations and discuss the associated design and operational trade-offs.