For "the general eases (paraxial approximation and non-paraxial ease), the ways of effective design of optical system to be composed of a single mask for the purpose of realizing any given linear transform are presented. Tinder various manners of choice of parameters, the solutions of equations to determine the amplitude-phase distribution of mask are investigated, and the stability of solution is also discussed. Under non-paraxial case, the solutions available in real situation are also found. Applying 4- and 8-dimen-sion Walsh transforms in the three different orders as examples, we investigate the effects of various parameters, such as the spacings between input plane, mask and output plane, and the number of sampling points in mask, on ‘approach distance', which describes the degree of approach of the transform to be performed by the system to any given linear transform. It would provide a realizable way to choose the relevant parameters and an usuful enlightment in the real design of an optical system for realizing a given linear transform.
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