Imaging Through Atmospheric Turbulence Using Modified Log Gradients

Herbert W. Swan; Joseph W. Goodman

doi:10.1117/12.934061

7 December 1982 Imaging Through Atmospheric Turbulence Using Modified Log Gradients

Herbert W. Swan, Joseph W. Goodman

Proceedings Volume 0358, Applications of Mathematics in Modern Optics; (1982) https://doi.org/10.1117/12.934061
Event: 26th Annual Technical Symposium, 1982, San Diego, United States

Abstract

A new approach to the problem of imaging through a time-varying randomly inhomogeneous medium is presented. This method assumes that an ensemble of short exposure images of a single fixed scene or object is available. It also assumes that knowledge of the average short-term optical transfer function is either known or estimated empirically from a point reference source. Restoration is performed by averaging a modified log gradient of the observed image spectra. This log gradient operator is an exact, mapping of discrete convolution into finite-field addi-tion, and is closely related to the complex "cepstrum," popularized by Oppenheim, It is shown to be invertible to within a constant multiplicative factor by a series of eigenvector computations. The mathematics of this gradient operator are developed, and two-dimensional simulations are presented.

Citation Download Citation

Herbert W. Swan and Joseph W. Goodman "Imaging Through Atmospheric Turbulence Using Modified Log Gradients", Proc. SPIE 0358, Applications of Mathematics in Modern Optics, (7 December 1982); https://doi.org/10.1117/12.934061

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