Abstract

A coherent optical system for performing continuous Fourier transforms can be modified to perform discrete Fourier transforms. Such a system is capable of diagonalizing circulant matrices presented at its input. The diagonal elements of the new matrix are the eigenvalues of the original matrix. A suitable modification allows the eigenvalues of many different circulant matrices to be found simultaneously. Such a technique can be used for the initial portion of a coherent optical matrix inversion system, which can find the inverses of circulant matrices. The method can also be applied to the problem of inverting Toeplitz matrices in a hybrid digital and optical system.

© 1984 Optical Society of America

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