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Optical systems, which inherently possess two degrees of freedom rather than the single degree of freedom available in a single electronic channel, appear to offer some advantages over their electronic counterparts for certain applications. Coherent optical systems have the added property that one may easily obtain many successive two-dimensional Fourier transforms of any given light amplitude distribution, or, by use of astigmatic optics, one-dimensional transforms can be obtained. Therefore, most linear operations of an integral transform nature are easily implemented. The optical implementation of integral transforms which are of importance to communication theory is discussed; the general problems of optical filter synthesis and multichannel computation and data processing are introduced, followed by a discussion of potential applications. Astigmatic systems, which permit multichannel operation in lieu of two-dimensional processing, are treated as a special case of general two-dimensional processors. Complex input functions are discussed with relation to their role in coherent optical systems.