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Proceedings Paper

Two Extensions Of Fourier Optical Processors
Author(s): Joseph W. Goodman
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Paper Abstract

We discuss two generalizations of the continuous Fourier transform performed by coherent optical systems. The first concerns the introduction of an appropriate exponential damping factor in the input plane, which leads to a processor that evaluates a two-dimensional slice through the four-dimensional complex Laplace transform domain. By performing Laplace filtering, rather than Fourier filtering, one can in principle trade off dynamic range in the filter plane for dynamic range in the input plane. Using a Laplace transform, it is also possible to find the complex roots of polynomials. The second generalization concerns modification of the continuous Fourier transform to behave as a discrete Fourier transform. With such a modification, it is in principle possible to find (in a single step, without iterations) the eigenvalues of any circulant matrix, or any circulant approximation to a Toeplitz matrix (including correlation matrices) using a coherent optical processor. Furthermore, if a light valve having a suitable nonlinear relation between amplitude transmittance and exposure is available, it is possible to obtain the inverse of any matrix in the class described above in a single pass through a coherent optical processor.

Paper Details

Date Published: 27 February 1984
PDF: 6 pages
Proc. SPIE 0373, Transformations in Optical Signal Processing, (27 February 1984); doi: 10.1117/12.934538
Show Author Affiliations
Joseph W. Goodman, Stanford University (United States)


Published in SPIE Proceedings Vol. 0373:
Transformations in Optical Signal Processing
William T. Rhodes; James R. Fienup; Bahaa Saleh, Editor(s)

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