Optical spatial frequency filtering using interferences

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Abstract
Several recent publications describe optical image-processing experiments in which the spatial-filtering operation is performed by an interference phenomenon. In this paper we derive the general conditions allowing interferences to play the role of a spatial filter. It is shown that, although a spatially coherent illumination is necessary, the interferometer must be able to produce localized fringes, and that the localization locus must coincide with the Fourier spectra formed through the two (or more) arms of the interferometer. The filtering operation may be understood either as an interference between these Fourier spectra or as an interference between the images of the object formed by each of the arms of the interferometer. In the case of most usual interferometers, these images are simply geometrical images of the object that are shifted with respect to each other, and the shift is responsible for the filtering effect. Two classes of interferometric setups can be distinguished, depending on whether the shift is perpendicular or parallel to the image plane. Examples are given, and experimental results are presented.