## Probability-density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulation

JOSA A, Vol. 11, Issue 7, pp. 2080-2092 (1994)

http://dx.doi.org/10.1364/JOSAA.11.002080

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### Abstract

We have carried out numerical simulations of waves traversing a three-dimensional random medium with Gaussian statistics and a power-law spectrum with inner-scale cutoff. The distributions of irradiance on the final observation screen provide the probability-density function (PDF) of irradiance. For both initially plane and initially spherical waves the simulation PDF’s in the strong-fluctuation regime lie between a *K* distribution and a log-normal-convolved-with-exponential distribution. We introduce a plot of the PDF of scaled log-normal irradiance, on which both the exponential and the lognormal PDF’s are universal curves and on which the PDF at both large and small irradiance is shown in detail. We have simulated a spherical-wave experiment, including aperture averaging, and find agreement between the simulated and the observed PDF’s.

© 1994 Optical Society of America

**History**

Original Manuscript: October 4, 1993

Revised Manuscript: January 19, 1994

Manuscript Accepted: January 27, 1994

Published: July 1, 1994

**Citation**

Stanley M. Flatté, Charles Bracher, and Guang-Yu Wang, "Probability-density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulation," J. Opt. Soc. Am. A **11**, 2080-2092 (1994)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-7-2080

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### References

- P. Deitz, N. Wright, “Saturation of scintillation magnitude in near-earth optical propagation,” J. Opt. Soc. Am. 59, 527–535 (1969). [CrossRef]
- A. Gurvich, M. Kallistratova, F. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–714 (1977). [CrossRef]
- J. Martin, S. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988). [CrossRef] [PubMed]
- J. Martin, S. Flatté, “Simulation of point-source scintillation through three-dimensional random media,” J. Opt. Soc. Am. A 7, 838–847 (1990). [CrossRef]
- S. Flatté, C. Bracher, “Simulation of wave propagation in three-dimensional random media,” In Atmospheric, Volume and Surface Scattering and Propagation, A. Consortini, ed. (University of Florence, Florence, Italy, 1991), pp. 27–29.
- S. M. Flatté, G. Y. Wang, J. Martin, “Irradiance variance of optical waves through atmospheric turbulence by numerical simulation and comparison with experiment,” J. Opt. Soc. Am. A 10, 2363–2370 (1993). [CrossRef]
- V. Tatarskii, “Depolarization of light by turbulent atmospheric inhomogeneities,” Radiophys. Quantum Electron. 10, 987–988 (1967). [CrossRef]
- R. Dashen, G. Wang, S. M. Flatté, C. Bracher, “Moments of intensity and log intensity: new asymptotic results for waves in power-law media,” J. Opt. Soc. Am. A 10, 1233–1242 (1993). [CrossRef]
- E. Jakeman, P. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978). [CrossRef]
- E. Jakeman, “On the statistics of K-distributed noise,” J. Phys. A 13, 31–48 (1980). [CrossRef]
- L. Andrews, R. Phillips, “I–K distribution as a universal propagation model of laser beams in atmospheric turbulence,” J. Opt. Soc. Am. A 2, 160–163 (1985). [CrossRef]
- L. Andrews, R. Phillips, “Mathematical genesis of the I–K distribution for random optical fields,” J. Opt. Soc. Am. A 3, 1912–1919 (1986). [CrossRef]
- J. Churnside, R. Hill, “Probability density of irradiance scintillations for strong path-integrated refractive turbulence,” J. Opt. Soc. Am. A 4, 727–733 (1987). [CrossRef]
- K. Furutsu, “Theory of irradiance distribution function in turbulent media—cluster approximation,” J. Math. Phys. 17, 1252–1263 (1976). [CrossRef]
- T. Ewart, “A model of the intensity probability distribution for wave propagation in random media,” J. Acoust. Soc. Am. 86, 1490–1498 (1989). [CrossRef]
- C. Macaskill, T. Ewart, “The probability distribution of intensity for acoustic propagation in a randomly varying ocean,” J. Acoust. Soc. Am. 76, 1466–1473 (1984). [CrossRef]
- T. E. Ewart, D. Percival, “Forward scattered waves in random media—the probability distribution of intensity,” J. Acoust. Soc. Am. 80, 1745–1753 (1986). [CrossRef]
- E. Jakeman, R. Tough, “Generalized K distribution: a statistical model for weak scattering,” J. Opt. Soc. Am. A 4, 1764–1772 (1987). [CrossRef]
- M. Teich, P. Diament, “Multiply stochastic representations for K distributions and their Poisson transforms,” J. Opt. Soc. Am. A 6, 80–91 (1989). [CrossRef]
- E. Rockower, “Quantum derivation of K-distributed noise for finite 〈N〉,” J. Opt. Soc. Am. A 5, 730–734 (1988). [CrossRef]
- R. Barakat, “Weak-scatter generalization of the K-density function with application to laser scattering in atmospheric turbulence,” J. Opt. Soc. Am. A 3, 401–409 (1986). [CrossRef]
- J. H. Churnside, S. F. Clifford, “Log-normal Rician probability-density function of optical scintillations in the turbulent atmosphere,” J. Opt. Soc. Am. A 4, 1923–1930 (1987). [CrossRef]
- N. Ben-Yosef, E. Goldner, “Splitting-source model for the statistics of irradiance scintillations,” J. Opt. Soc. Am. A 5, 126–131 (1988). [CrossRef]
- R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale and surface fluxes,” Waves Random Media 2, 179–201 (1992). [CrossRef]
- M. Gracheva, A. Gurvich, S. Lomadze, V. Pokasov, A. Khrupin, “Probability distribution of strong fluctuation of light intensity in the atmosphere,” Radiophys. Quantum Electron. 17, 83–87 (1974). [CrossRef]
- A. Consortini, F. Cochetti, J. H. Churnside, R. J. Hill, “Inner-scale effect on intensity variance measured for weak to strong atmospheric scintillation,” J. Opt. Soc. Am. A 10, 2354–2362 (1993). [CrossRef]
- V. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (National Technical Information Service, Springfield, Va., 1971).
- A. Giovannini, L. V. Hove, “Negative binomial properties and clan structure in multiplicity distributions,” Acta Phys. Pol. B 19, 495–510 (1988).
- N. Yasuda, “The random-walk model of human migration,” Theor. Popul. Biol. 7, 156–167 (1975). [CrossRef] [PubMed]
- S. Ong, P. Lee, “The non-central negative binomial distribution,” Biomed. J. 21, 611–627 (1979).
- E. Jakeman, “Fresnel scattering by a corrugated random surface with fractal slope,” J. Opt. Soc. Am. 72, 1034–1041 (1982). [CrossRef]
- A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
- K. Goshelashvily, V. Shishov, “Saturated fluctuations in the laser radiation intensity in a turbulent medium,” Sov. Phys. JETP 39, 605–609 (1974).
- R. G. Frehlich, “Intensity covariance of a point source in a random medium with a Kolmogorov spectrum and an inner scale of turbulence,” J. Opt. Soc. Am. A 4, 360–366 (1987). [CrossRef]

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