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Applied Optics

Applied Optics


  • Vol. 18, Iss. 10 — May. 15, 1979
  • pp: 1590–1599

Probability distribution of turbulent irradiance in a saturation regime

L. R. Bissonnette and P. L. Wizinowich  »View Author Affiliations

Applied Optics, Vol. 18, Issue 10, pp. 1590-1599 (1979)

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Application of the central limit theorem to the stochastic equation of propagation suggests that the probability distribution of the complex wave amplitude defined on the geometrical phase front is approximately normal. The resulting irradiance probability density function, valid in the strong scintillation regime, is an exponential multiplied by the modified Bessel function I0 both of argument proportional to the irradiance; it is not the Rice-Nakagami density function. Quantitative tests show that this exponential-Bessel function constitutes as good a fit as the log-normal to the irradiance probability data reported in this paper. Since the normal distribution hypothesis is consistent with the stochastic wave equation, the model proposed here should be a simple substitute to the often used but theoretically incorrect log-normal irradiance probability distribution model.

© 1979 Optical Society of America

Original Manuscript: November 1, 1978
Published: May 15, 1979

L. R. Bissonnette and P. L. Wizinowich, "Probability distribution of turbulent irradiance in a saturation regime," Appl. Opt. 18, 1590-1599 (1979)

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  1. T.-i. Wang, J. W. Strohbehn, J. Opt. Soc. Am. 64, 583 (1974). [CrossRef]
  2. L. R. Bissonnette, “Log-Normal Probability Distribution of Strong Irradiance Fluctuations: an Asymptotic Analysis,” NATO-AGARD Conference Proceedings 183 on Optical Propagation in the Atmosphere (National Technical Information Service, Springfield, Va., 1975), paper 19.
  3. L. R. Bissonnette, “Modelling of Laser Beam Propagation in Atmospheric Turbulence,” presented at the Second International Symposium on Gas-Flow and Chemical Lasers, von Karman Institute, Rhode-Saint-Genèse, Belgium, 11–15 September 1978; Proceedings to appear in 1979. (Hemisphere Publishing Corporation, Washington, D.C.)
  4. J. W. Strohbehn, T.-i. Wang, J. P. Speck, Radio Sci. 10, 59 (1975). [CrossRef]
  5. R. A. Elliot, J. R. Dunphy, J. R. Kerr, in Digest of Topical Meeting on Optical Propagation Through Turbulence, Rain and Fog (Optical Society of America, Washington, D.C., 1977), paper WA5.
  6. L. R. Bissonnette, Appl. Opt. 16, 2242 (1977). [CrossRef] [PubMed]
  7. B. W. Lindgren, G. W. McElrath, Introduction to Probability and Statistics (Macmillan, New York, 1963).
  8. T.-i. Wang, J. W. Strohbehn, J. Opt. Soc. Am. 64, 994 (1974). [CrossRef]
  9. F. Davidson, A. Gonzalez-del-Valle, J. Opt. Soc. Am. 65, 655 (1975). [CrossRef]

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