Abstract

The log-normal Rician probability-density function is based on the following paradigm for the optical field after propagation through atmospheric turbulence: a field with reduced coherence that obeys Rice–Nakagami statistics is modulated by a multiplicative factor that obeys log-normal statistics. The larger eddies in the turbulent medium produce the log-normal statistics, and the smaller ones produce the Gaussian statistics. On the basis of this model all the parameters required by the density function can be calculated by using physical parameters such as turbulence strength, inner scale, and propagation configuration. The heuristic density function is consistent with available data at low and at high turbulence levels.

© 1987 Optical Society of America

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  28. K. Furutsu, “Review of the theory of the irradiance distribution function in a turbulent medium with a particular emphasis on analytical methods,” Radio Sci. 14, 287–299 (1979).
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  29. S. Ito, K. Furutsu, “Theoretical analysis of the high-order irradiance moments of light waves observed in turbulent air,”J. Opt. Soc. Am. 72, 760–764 (1982).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1987 (1)

1985 (2)

1984 (1)

1983 (2)

1982 (4)

1981 (3)

1980 (1)

E. J. Fremouw, R. C. Livingston, D. A. Miller, “On the statistics of scintillating signals,”J. Atmos. Terr. Phys. 42, 717–731 (1980).
[CrossRef]

1979 (4)

L. R. Bissonnette, P. L. Wizinowich, “Probability distribution of turbulent irradiance in a saturation regime,” Appl. Opt. 18, 1590–1599 (1979).
[CrossRef] [PubMed]

K. Furutsu, “Review of the theory of the irradiance distribution function in a turbulent medium with a particular emphasis on analytical methods,” Radio Sci. 14, 287–299 (1979).
[CrossRef]

G. Parry, P. N. Pusey, “K distributions in atmospheric propagation of laser light,”J. Opt. Soc. Am. 69, 796–798 (1979).
[CrossRef]

R. Dashen, “Path integrals for waves in random media,”J. Math. Phys. 20, 894–920 (1979).
[CrossRef]

1978 (3)

E. Jakeman, P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
[CrossRef]

D. L. Knepp, G. C. Valley, “Properties of joint Gaussian statistics,” Radio Sci. 13, 59–68 (1978).
[CrossRef]

R. J. Hill, S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,”J. Opt. Soc. Am. 68, 892–899 (1978).
[CrossRef]

1977 (2)

G. Parry, P. N. Pusey, E. Jakeman, J. G. McWhirter, “Focusing by a random phase screen,” Opt. Commun. 22, 195–201 (1977).
[CrossRef]

A. Consortini, L. Ronchi, “Probability distribution of the sum of N complex random variables,”J. Opt. Soc. Am. 67, 181–185 (1977).
[CrossRef]

1976 (5)

R. Barakat, “Sums of independent lognormally distributed random variables,”J. Opt. Soc. Am. 66, 211–216 (1976).
[CrossRef]

K. Furutsu, “Theory of irradiance distribution function in turbulent media-cluster approximation,”J. Math. Phys. 17, 1252–1263 (1976).
[CrossRef]

E. Jakeman, P. N. Pusey, “A model for non-Rayleigh sea echo,”IEEE Trans. Antennas Propag. AP-24, 806–814 (1976).
[CrossRef]

C. L. Rino, R. C. Livingston, H. E. Whitney, “Some new results on the statistics of radio wave scintillation. I. Empirical evidence for Gaussian statistics,”J. Geophys. Res. 81, 2051–2057 (1976).
[CrossRef]

G. C. Valley, D. L. Knepp, “Application of joint Gaussian statistics to interplanetary scintillation,”J. Geophys. Res. 81, 4723–4730 (1976).
[CrossRef]

1975 (2)

J. W. Strohbehn, T. Wang, J. P. Speck, “On the probability distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

1974 (5)

1972 (1)

1971 (1)

K. Gochelashvili, V. S. Shishov, “Laser beam scintillation beyond a turbulent layer,” Opt. Acta 18, 313–320 (1971).
[CrossRef]

1969 (3)

1968 (4)

D. A. DeWolf, “Saturation of irradiance fluctuations due to turbulent atmosphere,”J. Opt. Soc. Am. 58, 461–466 (1968).
[CrossRef]

R. L. Mitchell, “Permanence of the log-normal distribution,”J. Opt. Soc. Am. 58, 1267–1272 (1968).
[CrossRef]

A. S. Gurvich, M. A. Kallistratova, N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 1360–1370 (1968).

A. S. Gurvich, M. A. Kallistratova, N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 1360–1370 (1968).

1967 (2)

M. E. Gracheva, “Investigation of the statistical properties of strong fluctuations in the intensity of light propagated through the atmosphere near the earth,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 10, 775–778 (1967).

D. L. Fried, G. E. Mevers, M. P. Keister, “Measurements of laser-beam scintillation in the atmosphere,”J. Opt. Soc. Am. 57, 787–797 (1967).
[CrossRef]

1965 (1)

M. E. Gracheva, A. S. Gurvich, “Strong fluctuations in the intensity of light propagated through the atmosphere close to the earth,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 8, 717–724 (1965).

Andrews, L. C.

Barakat, R.

Bissonnette, L. R.

Bunkin, F. V.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Churnside, J. H.

Clifford, S. F.

Coles, W. A.

Consortini, A.

Dashen, R.

R. Dashen, “Distribution of intensity in a multiply scattering medium,” Opt. Lett. 9, 110–112 (1984).
[CrossRef] [PubMed]

R. Dashen, “Path integrals for waves in random media,”J. Math. Phys. 20, 894–920 (1979).
[CrossRef]

Deitz, P. H.

DeWolf, D. A.

Fante, R. L.

Frehlich, R. G.

Fremouw, E. J.

E. J. Fremouw, R. C. Livingston, D. A. Miller, “On the statistics of scintillating signals,”J. Atmos. Terr. Phys. 42, 717–731 (1980).
[CrossRef]

Fried, D. L.

Furutsu, K.

S. Ito, K. Furutsu, “Theoretical analysis of the high-order irradiance moments of light waves observed in turbulent air,”J. Opt. Soc. Am. 72, 760–764 (1982).
[CrossRef]

K. Furutsu, “Review of the theory of the irradiance distribution function in a turbulent medium with a particular emphasis on analytical methods,” Radio Sci. 14, 287–299 (1979).
[CrossRef]

K. Furutsu, “Theory of irradiance distribution function in turbulent media-cluster approximation,”J. Math. Phys. 17, 1252–1263 (1976).
[CrossRef]

K. Furutsu, “Statistical theory of wave propagation in a random medium and the irradiance distribution function,”J. Opt. Soc. Am. 62, 240–254 (1972).
[CrossRef]

Gochelashvili, K.

K. Gochelashvili, V. S. Shishov, “Laser beam scintillation beyond a turbulent layer,” Opt. Acta 18, 313–320 (1971).
[CrossRef]

Gochelashvily, K. S.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Gracheva, M. E.

M. E. Gracheva, “Investigation of the statistical properties of strong fluctuations in the intensity of light propagated through the atmosphere near the earth,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 10, 775–778 (1967).

M. E. Gracheva, A. S. Gurvich, “Strong fluctuations in the intensity of light propagated through the atmosphere close to the earth,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 8, 717–724 (1965).

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. I. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuation of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), pp. 107–127.
[CrossRef]

Gurvich, A. S.

A. S. Gurvich, M. A. Kallistratova, N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 1360–1370 (1968).

A. S. Gurvich, M. A. Kallistratova, N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 1360–1370 (1968).

M. E. Gracheva, A. S. Gurvich, “Strong fluctuations in the intensity of light propagated through the atmosphere close to the earth,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 8, 717–724 (1965).

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. I. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuation of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), pp. 107–127.
[CrossRef]

Hill, R. J.

Ito, S.

Jakeman, E.

E. Jakeman, P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
[CrossRef]

G. Parry, P. N. Pusey, E. Jakeman, J. G. McWhirter, “Focusing by a random phase screen,” Opt. Commun. 22, 195–201 (1977).
[CrossRef]

E. Jakeman, P. N. Pusey, “A model for non-Rayleigh sea echo,”IEEE Trans. Antennas Propag. AP-24, 806–814 (1976).
[CrossRef]

Kallistratova, M. A.

A. S. Gurvich, M. A. Kallistratova, N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 1360–1370 (1968).

A. S. Gurvich, M. A. Kallistratova, N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 1360–1370 (1968).

Kashkarov, S. S.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. I. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuation of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), pp. 107–127.
[CrossRef]

Keister, M. P.

Knepp, D. L.

D. L. Knepp, G. C. Valley, “Properties of joint Gaussian statistics,” Radio Sci. 13, 59–68 (1978).
[CrossRef]

G. C. Valley, D. L. Knepp, “Application of joint Gaussian statistics to interplanetary scintillation,”J. Geophys. Res. 81, 4723–4730 (1976).
[CrossRef]

Lawrence, R. S.

Livingston, R. C.

E. J. Fremouw, R. C. Livingston, D. A. Miller, “On the statistics of scintillating signals,”J. Atmos. Terr. Phys. 42, 717–731 (1980).
[CrossRef]

C. L. Rino, R. C. Livingston, H. E. Whitney, “Some new results on the statistics of radio wave scintillation. I. Empirical evidence for Gaussian statistics,”J. Geophys. Res. 81, 2051–2057 (1976).
[CrossRef]

McWhirter, J. G.

G. Parry, P. N. Pusey, E. Jakeman, J. G. McWhirter, “Focusing by a random phase screen,” Opt. Commun. 22, 195–201 (1977).
[CrossRef]

Mevers, G. E.

Miller, D. A.

E. J. Fremouw, R. C. Livingston, D. A. Miller, “On the statistics of scintillating signals,”J. Atmos. Terr. Phys. 42, 717–731 (1980).
[CrossRef]

Mitchell, R. L.

Newman, D.

Ochs, G. R.

Parry, G.

G. Parry, “Measurement of atmospheric turbulence induced intensity fluctuations in a laser beam,” Opt. Acta 28, 715–728 (1981).
[CrossRef]

G. Parry, P. N. Pusey, “K distributions in atmospheric propagation of laser light,”J. Opt. Soc. Am. 69, 796–798 (1979).
[CrossRef]

G. Parry, P. N. Pusey, E. Jakeman, J. G. McWhirter, “Focusing by a random phase screen,” Opt. Commun. 22, 195–201 (1977).
[CrossRef]

Phillips, R. L.

Pokasov, V. I. V.

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. I. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuation of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), pp. 107–127.
[CrossRef]

Prokhorov, A. M.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Pusey, P. N.

G. Parry, P. N. Pusey, “K distributions in atmospheric propagation of laser light,”J. Opt. Soc. Am. 69, 796–798 (1979).
[CrossRef]

E. Jakeman, P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
[CrossRef]

G. Parry, P. N. Pusey, E. Jakeman, J. G. McWhirter, “Focusing by a random phase screen,” Opt. Commun. 22, 195–201 (1977).
[CrossRef]

E. Jakeman, P. N. Pusey, “A model for non-Rayleigh sea echo,”IEEE Trans. Antennas Propag. AP-24, 806–814 (1976).
[CrossRef]

Rino, C. L.

C. L. Rino, R. C. Livingston, H. E. Whitney, “Some new results on the statistics of radio wave scintillation. I. Empirical evidence for Gaussian statistics,”J. Geophys. Res. 81, 2051–2057 (1976).
[CrossRef]

Ronchi, L.

Shishov, V. I.

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Shishov, V. S.

K. Gochelashvili, V. S. Shishov, “Laser beam scintillation beyond a turbulent layer,” Opt. Acta 18, 313–320 (1971).
[CrossRef]

Speck, J. P.

J. W. Strohbehn, T. Wang, J. P. Speck, “On the probability distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

Strohbehn, J. W.

J. W. Strohbehn, T. Wang, J. P. Speck, “On the probability distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

T. Wang, J. W. Strohbehn, “Log-normal paradox in atmospheric scintillations,”J. Opt. Soc. Am. 64, 583–591 (1974).
[CrossRef]

T. Wang, J. W. Strohbehn, “Perturbed log-normal distribution of irradiance fluctuations,”J. Opt. Soc. Am. 64, 994–999 (1974).
[CrossRef]

J. W. Strohbehn, “Modern theories in the propagation of optical waves in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), pp. 45–106.
[CrossRef]

Tatarskii, V. I.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971).

Time, N. S.

A. S. Gurvich, M. A. Kallistratova, N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 1360–1370 (1968).

A. S. Gurvich, M. A. Kallistratova, N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 1360–1370 (1968).

Valley, G. C.

D. L. Knepp, G. C. Valley, “Properties of joint Gaussian statistics,” Radio Sci. 13, 59–68 (1978).
[CrossRef]

G. C. Valley, D. L. Knepp, “Application of joint Gaussian statistics to interplanetary scintillation,”J. Geophys. Res. 81, 4723–4730 (1976).
[CrossRef]

Wang, T.

Whitney, H. E.

C. L. Rino, R. C. Livingston, H. E. Whitney, “Some new results on the statistics of radio wave scintillation. I. Empirical evidence for Gaussian statistics,”J. Geophys. Res. 81, 2051–2057 (1976).
[CrossRef]

Wizinowich, P. L.

Wright, N. J.

Yura, H. T.

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (1)

E. Jakeman, P. N. Pusey, “A model for non-Rayleigh sea echo,”IEEE Trans. Antennas Propag. AP-24, 806–814 (1976).
[CrossRef]

Izv. Vyssh. Uchebn. Zaved. Radiofiz. (4)

M. E. Gracheva, A. S. Gurvich, “Strong fluctuations in the intensity of light propagated through the atmosphere close to the earth,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 8, 717–724 (1965).

M. E. Gracheva, “Investigation of the statistical properties of strong fluctuations in the intensity of light propagated through the atmosphere near the earth,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 10, 775–778 (1967).

A. S. Gurvich, M. A. Kallistratova, N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 1360–1370 (1968).

A. S. Gurvich, M. A. Kallistratova, N. S. Time, “Fluctuations in the parameters of a light wave from a laser during propagation in the atmosphere,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 1360–1370 (1968).

J. Atmos. Terr. Phys. (1)

E. J. Fremouw, R. C. Livingston, D. A. Miller, “On the statistics of scintillating signals,”J. Atmos. Terr. Phys. 42, 717–731 (1980).
[CrossRef]

J. Geophys. Res. (2)

C. L. Rino, R. C. Livingston, H. E. Whitney, “Some new results on the statistics of radio wave scintillation. I. Empirical evidence for Gaussian statistics,”J. Geophys. Res. 81, 2051–2057 (1976).
[CrossRef]

G. C. Valley, D. L. Knepp, “Application of joint Gaussian statistics to interplanetary scintillation,”J. Geophys. Res. 81, 4723–4730 (1976).
[CrossRef]

J. Math. Phys. (2)

K. Furutsu, “Theory of irradiance distribution function in turbulent media-cluster approximation,”J. Math. Phys. 17, 1252–1263 (1976).
[CrossRef]

R. Dashen, “Path integrals for waves in random media,”J. Math. Phys. 20, 894–920 (1979).
[CrossRef]

J. Opt. Soc. Am. (23)

R. L. Mitchell, “Permanence of the log-normal distribution,”J. Opt. Soc. Am. 58, 1267–1272 (1968).
[CrossRef]

R. Barakat, “Sums of independent lognormally distributed random variables,”J. Opt. Soc. Am. 66, 211–216 (1976).
[CrossRef]

A. Consortini, L. Ronchi, “Probability distribution of the sum of N complex random variables,”J. Opt. Soc. Am. 67, 181–185 (1977).
[CrossRef]

T. Wang, J. W. Strohbehn, “Perturbed log-normal distribution of irradiance fluctuations,”J. Opt. Soc. Am. 64, 994–999 (1974).
[CrossRef]

D. A. DeWolf, “Are strong irradiance fluctuations log normal or Rayleigh distributed?”J. Opt. Soc. Am. 59, 1455–1460 (1969).
[CrossRef]

D. L. Fried, G. E. Mevers, M. P. Keister, “Measurements of laser-beam scintillation in the atmosphere,”J. Opt. Soc. Am. 57, 787–797 (1967).
[CrossRef]

G. R. Ochs, R. S. Lawrence, “Saturation of laser-beam scintillation under conditions of strong atmospheric turbulence,”J. Opt. Soc. Am. 59, 226–227 (1969).
[CrossRef]

P. H. Deitz, N. J. Wright, “Saturation of scintillation magnitude in near-earth optical propagation,”J. Opt. Soc. Am. 59, 527–535 (1969).
[CrossRef]

T. Wang, J. W. Strohbehn, “Log-normal paradox in atmospheric scintillations,”J. Opt. Soc. Am. 64, 583–591 (1974).
[CrossRef]

D. A. DeWolf, “Saturation of irradiance fluctuations due to turbulent atmosphere,”J. Opt. Soc. Am. 58, 461–466 (1968).
[CrossRef]

K. Furutsu, “Statistical theory of wave propagation in a random medium and the irradiance distribution function,”J. Opt. Soc. Am. 62, 240–254 (1972).
[CrossRef]

L. R. Bissonnette, “Propagation model of laser beams in turbulence,”J. Opt. Soc. Am. 73, 262–268 (1983).
[CrossRef]

S. Ito, K. Furutsu, “Theoretical analysis of the high-order irradiance moments of light waves observed in turbulent air,”J. Opt. Soc. Am. 72, 760–764 (1982).
[CrossRef]

G. Parry, P. N. Pusey, “K distributions in atmospheric propagation of laser light,”J. Opt. Soc. Am. 69, 796–798 (1979).
[CrossRef]

R. L. Fante, “Inner-scale size effect on the scintillations of light in the turbulent atmosphere,”J. Opt. Soc. Am. 73, 277–281 (1983).
[CrossRef]

S. F. Clifford, G. R. Ochs, R. S. Lawrence, “Saturation of optical scintillation by strong turbulence,”J. Opt. Soc. Am. 64, 148–154 (1974).
[CrossRef]

R. J. Hill, S. F. Clifford, “Theory of saturation of optical scintillation by strong turbulence for arbitrary refractive-index spectra,”J. Opt. Soc. Am. 71, 675–686 (1981).
[CrossRef]

R. J. Hill, “Theory of saturation by strong turbulence: plane-wave variance and covariance and spherical-wave covariance,”J. Opt. Soc. Am. 72, 212–222 (1982).
[CrossRef]

H. T. Yura, “Physical model for strong optical-amplitude fluctuations in a turbulent medium,”J. Opt. Soc. Am. 64, 59–67 (1974).
[CrossRef]

R. L. Phillips, L. C. Andrews, “Measured statistics of laser-light scattering in atmospheric turbulence,”J. Opt. Soc. Am. 71, 1440–1445 (1981).
[CrossRef]

R. L. Phillips, L. C. Andrews, “Universal statistical model for irradiance fluctuations in a turbulent medium,”J. Opt. Soc. Am. 72, 864–870 (1982).
[CrossRef]

R. J. Hill, S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,”J. Opt. Soc. Am. 68, 892–899 (1978).
[CrossRef]

W. A. Coles, R. G. Frehlich, “Simultaneous measurements of angular scattering and intensity scintillation in the atmosphere,”J. Opt. Soc. Am. 72, 1042–1048 (1982).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Acta (2)

K. Gochelashvili, V. S. Shishov, “Laser beam scintillation beyond a turbulent layer,” Opt. Acta 18, 313–320 (1971).
[CrossRef]

G. Parry, “Measurement of atmospheric turbulence induced intensity fluctuations in a laser beam,” Opt. Acta 28, 715–728 (1981).
[CrossRef]

Opt. Commun. (1)

G. Parry, P. N. Pusey, E. Jakeman, J. G. McWhirter, “Focusing by a random phase screen,” Opt. Commun. 22, 195–201 (1977).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

E. Jakeman, P. N. Pusey, “Significance of K distributions in scattering experiments,” Phys. Rev. Lett. 40, 546–550 (1978).
[CrossRef]

Proc. IEEE (2)

D. A. DeWolf, “Waves in turbulent air: a phenomenological approach,” Proc. IEEE 62, 1523–1529 (1974).
[CrossRef]

A. M. Prokhorov, F. V. Bunkin, K. S. Gochelashvily, V. I. Shishov, “Laser irradiance propagation in turbulent media,” Proc. IEEE 63, 790–811 (1975).
[CrossRef]

Radio Sci. (3)

J. W. Strohbehn, T. Wang, J. P. Speck, “On the probability distribution of line-of-sight fluctuations of optical signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

D. L. Knepp, G. C. Valley, “Properties of joint Gaussian statistics,” Radio Sci. 13, 59–68 (1978).
[CrossRef]

K. Furutsu, “Review of the theory of the irradiance distribution function in a turbulent medium with a particular emphasis on analytical methods,” Radio Sci. 14, 287–299 (1979).
[CrossRef]

Other (3)

M. E. Gracheva, A. S. Gurvich, S. S. Kashkarov, V. I. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuation of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), pp. 107–127.
[CrossRef]

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971).

J. W. Strohbehn, “Modern theories in the propagation of optical waves in a turbulent medium,” in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, ed. (Springer-Verlag, New York, 1978), pp. 45–106.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Moment ratio <I2>3/<I3> as a function of coherence parameter.

Fig. 2
Fig. 2

Log-modulation variance σz2 as a function of Rytov log-irradiance variance σR2 for zero inner scale.

Fig. 3
Fig. 3

Coherence parameter r as a function of Rytov log-irradiance variance σR2.

Fig. 4
Fig. 4

Normalized variance of irradiance σI2 as a function of Rytov log-irradiance variance σR2 for zero inner scale.

Fig. 5
Fig. 5

Probability-distribution function of log-irradiance normalized by Rytov variance σR2 for σR2 = 0, 0.1, and 1.0. The vertical scale has been adjusted so that a log-normal distribution produces a straight line.

Fig. 6
Fig. 6

Measurement configuration.

Fig. 7
Fig. 7

Normalized variance of irradiance σI2 as a function of Rytov variance σR2. The solid line represents zero-inner-scale, theory, dashed lines include approximate inner-scale correction for 7- and 9-mm inner scales, and points represent measured values, including error bars.

Equations (45)

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U = ( U C + U G ) exp ( χ + i S ) ,
I = U C + U G 2 exp ( 2 χ ) ,
p ( I ) = 0 p [ I exp ( 2 χ ) ] p [ exp ( 2 χ ) ] d [ exp ( 2 χ ) ] ,
p ( I ) = 0 d z ( 1 + r ) z exp ( - r - 1 + r z I ) I 0 { 2 [ ( 1 + r ) r z ] 1 / 2 I } × 1 ( 2 π ) 1 / 2 σ z z exp [ - ( ln z + ½ σ z 2 ) 2 σ z 2 ] ,
f ( z ) = ( 1 + r ) I z - ln ( I 0 { 2 [ ( 1 + r ) r z ] 1 / 2 I } ) + 2 ln z + 1 2 σ z 2 ( ln z + ½ σ z 2 ) 2 ,
p ( I ) 1 + r σ z [ f ( z 0 ) ] - 1 / 2 exp [ - r - f ( z 0 ) ] ,
I n = 0 d I I n p ( I )
I n = ( n ! ) 2 ( 1 + r ) n exp [ ½ n ( n - 1 ) σ z 2 ] m = 0 n r m ( n - m ) ! ( m ! ) 2 .
( r 2 + 4 r + 2 ) 3 ( r + 1 ) 3 ( r 3 + 9 r 2 + 18 r + 6 ) = I 2 3 I 3
σ z 2 = ln [ ( r + 1 ) 2 r 2 + 4 r + 2 I 2 ] .
σ 2 χ 2 = 16 π 2 k 2 L 0 1 d u 0 d κ κ Φ n ( κ ) sin 2 [ κ 2 L u ( 1 - u ) 2 k ] × M ST [ κ L u ( 1 - u ) k ] ,
Φ n ( κ ) = 0.033 C n 2 κ - 11 / 3 exp ( - 0.0285 l 0 2 κ 2 ) ,
M ST ( ρ ) = exp { - 48 k 2 L 0 1 d u 1 u 2 0 d κ κ × Φ n ( k u ) h ( k ) [ 1 - J 0 ( κ ρ ) ] } ,
h ( κ ) = κ δ ( κ - κ ) + H ( κ - κ ) ,
κ 1 / [ L u ( 1 - u ) k ] 1 / 2 ,
σ z 2 = 2.95 σ R 2 0 1 d u u 5 / 6 ( 1 - u ) 5 / 6 0 1 / 2 d y y 1 / 6 × exp [ - 2.39 σ R 2 y 5 / 6 u 5 / 6 ( 1 - u ) 5 / 6 ] ,
σ R 2 = 0.496 k 7 / 6 L 11 / 6 C n 2 .
σ z 2 = 2.95 σ R 2 0 1 d u u 5 / 6 ( 1 - u ) 5 / 6 0 1 / 2 d y y 1 / 6 × exp [ - 1.32 α 1 / 3 σ R 1 / 3 y u ( 1 - u ) - 4 y u ( 1 - u ) α 2 ] ,
α = 8.37 ( L / k l 0 2 ) 1 / 2 ,
M ( x 1 x 2 ) = U ( x 1 ) U * ( x 2 ) U 2 ,
[ U C ( x 1 ) + U G ( x 1 ) ] [ U C ( x 2 ) + U G ( x 2 ) ] * exp [ χ ( x 1 ) + χ ( x 2 ) + i S ( x 1 ) - i S ( x 2 ) ] = U C + U G 2 exp ( 2 χ ) M ( x 1 , x 2 ) .
U C 2 = [ U C 2 + U G 2 ] M HF ( ) ,
r = U C 2 U G 2 ,
r = [ 1 M HF ( ) - 1 ] - 1 .
M HF ( ) = exp [ - 48 k 2 L 0 1 d u 1 u 2 0 d κ κ Φ n ( κ u ) × ( κ δ { κ - 1 [ L u ( 1 - u ) k ] 1 / 2 } + H { κ - 1 [ L u ( 1 - u ) k ] 1 / 2 } ) ] .
r = [ exp ( 0.398 σ R 2 ) - 1 ] - 1 ,
σ I 2 = r 2 + 4 r + 2 ( r + 1 ) 2 exp ( σ z 2 ) - 1 ,
σ z 2 = 0.248 σ R 2 ,
r = 1 / ( 0.398 σ R 2 ) .
σ I 2 = σ z 2 + 2 r = 1.04 σ R 2 ,
I n = 1 + 0.522 n ( n - 1 ) σ R 2 ,
I n = exp [ 0.500 n ( n - 1 ) σ R 2 ] .
σ z 2 = 1.9 σ R - 4 / 5 .
σ z 2 = 4.1 α - 7 / 18 σ R - 1 / 3 .
r = exp ( - 0.398 σ R 2 ) ,
p ( I ) = 1 ( 2 π ) 1 / 2 σ z 0 d z 1 z 2 exp [ - I z - ( ln z + ½ σ z 2 ) 2 2 σ z 2 ] ,
I n = n ! exp [ ½ n ( n - 1 ) σ z 2 ] .
σ I 2 = 1 + 3.8 σ R - 4 / 5
σ I 2 = 1 + 1.9 σ R - 4 / 5 .
σ I 2 = 1 + 1.0 σ P - 4 / 5 ,
σ I 2 = 1 + 0.86 σ P - 4 / 5 ,
σ I 2 = 2 exp ( a σ z 2 ) - 1 ,
a ( λ L / l 0 ) = σ χ 2 ( λ L / l 0 ) / σ χ 2 ( ) .
ln a = 1.2 - 0.22 λ L / l 0 .
Δ σ I 2 0.3 mm - 1 Δ l 0

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