Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Means, variances, and covariances for laser beam propagation through a random medium

Author: Robert A. Schmeltzer
Journal: Quart. Appl. Math. 24 (1967), 339-354
DOI: https://doi.org/10.1090/qam/99911
MathSciNet review: QAM99911
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Abstract | References | Additional Information

Abstract: Wave propagation in a random continuous medium is studied by solving the stochastic wave equation with a random function for the refractive index coefficient. By the application of the Rytov transformation, an equivalent spatial form of the nonlinear Riccati equation is obtained which is then solved by means of an iteration scheme. The statistical properties of the propagated wave are then computed for the case of a coherent focused source with a Gaussian amplitude distribution. These formulas contain, as limiting sub-cases, the results of previous analyses for the spherical and plane wave. More generally, they describe the propagation of a laser beam.

References [Enhancements On Off] (What's this?)

  • [1] V. I. Tatarskii, Wave propagation in a turbulent medium, Translated from the Russian by R. A. Silverman, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1961. MR 0127671
  • [2] D. L. Fried, Statistics of a geometric representation of wavefront distortion, J. Opt. Soc. Amer. 55 (1965), 1427–1435. MR 0184540, https://doi.org/10.1364/JOSA.55.001427
  • [3] D. L. Fried, The effect of wavefront distortion on the performance of an ideal optical heterodyne receiver and an ideal camera, Conference on Atmospheric Limitations to Optical Propagation, Central Radio Propagation Lab., National Bureau of Standards, and National Center for Atmospheric Research, Boulder, Colorado, March 1965
  • [4] L. A. Chernov, Wave propagation in a random medium, English transl, McGraw-Hill, New York, 1960
  • [5] W. C. Hoffman, Wave propagation in a general random continuous medium, Proc. Sympos. Appl. Math., Vol. XVI, Amer. Math. Soc., Providence, R.I., 1964, pp. 117–144. MR 0162487

Additional Information

DOI: https://doi.org/10.1090/qam/99911
Article copyright: © Copyright 1967 American Mathematical Society

American Mathematical Society