Apodization filtering applied to a bandlimited optical Fourier transformer

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The basic Fourier optical transform operation that exists between the front and rear focal planes of a coherently illuminated lens is examined from the viewpoint of spatial bandlimiting. It is common to regard this relationship as exact in its application to optical data processors, but in reality, finite size lens and pupil functions impose spatial bandlimiting that smooths or broadens the fields in the transform domain. To reduce these effects, shaded apertures or apodizing filters are placed in the lens plane. Experimental data are presented to demonstrate that a noticeable improvement in resolution can be obtained by use of these filters.