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Published July 1, 1978 | public
Journal Article Open

Spatial convolution and correlation of optical fields via degenerate four-wave mixing


A nonlinear optical technique is described that performs, essentially instantaneously, the functions of spatial correlation and convolution of spatially encoded waves. These real-time operations are accomplished by mixing spatially dependent optical fields in the Fourier-transform plane of a lens system. The use of a degenerate four-wave mixing scheme eliminates (in the Fresnel approximation) phase-matching restrictions and (optical) frequency-scaling factors. Spatial bandwidth-gain considerations and numerical examples, as well as applications to nonlinear microscopy, are presented.

Additional Information

© Copyright 1978 Optical Society of America Received March 13, 1978 This research was supported by the Army Research Office, Durham, North Carolina. D. M. Pepper is a Hughes Research Laboratory Doctoral Fellow. D. Fekete is a Weizmann Institute, Israel, Postdoctoral Fellow. D. M. Pepper acknowledges the support granted by the Hughes Aircraft Company. D. Fekete acknowledges the support granted by the Weizmann Institute of Israel.


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August 22, 2023
October 13, 2023