Abstract

The fourth statistical moment of a scalar wave propagating in a random medium is investigated. Starting with a partial differential equation obtained by various authors in a multiple-scattering approximation, we discuss the general properties of the fourth moment of an initially plane wave and then present numerical results for a two-dimensional plane wave. Results are presented for the variance and covariance of irradiance scintillations. Both results are shown to agree well with experiment. In particular, the variance exhibits the experimentally observed saturation phenomenon, and the covariance results indicate that the correlation length for irradiance scintillations is not proportional to (λ<i>z</i>)½. in the saturation region and that the aperture-averaging effect is less than that predicted by results based on the Born or Rytov approximations.

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  1. V. I. Shishov, Izv. Vuz. Radiofiz. (Russian) 11, 866 (1968).
  2. T. L. Ho and M. J. Beran, J. Opt. Soc. Am. 59, 1134 (1969).
  3. V. I. Tatarski, Zh. Eksperim. i Teor. Fiz. 56, 2106 (1969) [Sov. Phys. JETP 29, 1133 (1969)].
  4. J. E. Molyneux, J. Opt. Soc. Am. 61, 248 (1971).
  5. W. P. Brown, Jr., J. Opt. Soc. Am. 62, 45 (1972).
  6. I. M. Dagkesamanskaya and V. I. Shishov, Izv. Vuz. Radiofiz. (Russian) 13, 16 (1970).
  7. V. I. Klyatskin, Zh. Eksperim. i Teor. Fiz. 60, 1300 (1971) [Sov. Phys. JETP 33, 703 (1971)].
  8. K. S. Gochelashvily and V. I. Shishov, Preprint FIAN (Lebedev Institute), N71 (1971).
  9. Y. L. Luke, Integrals of Bessel Functions (McGraw-Hill, New York, 1962), p. 330.
  10. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  11. W. P. Brown, Jr., J. Opt. Soc. Am. 57, 1539 (1967).
  12. W. P. Brown, Jr., IEEE Trans. AP-15, 81 (1967).
  13. M. E. Gracheva, A. S. Gurvich, and M. A. Kallistratova, Izv. Vuz. Radiofiz. (Russian) 13, 56 (1970).
  14. We should not expect exact quantitative agreement between the results in Fig. 1 and experiment because the numerical results pertain to two-dimensional propagation, whereas the experimental results pertain to three-dimensional propagation. Nevertheless, aside from the fact that the experimental peak variance exceeds that given in Fig. 1, the agreement is pretty good.
  15. D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).
  16. J. R. Kerr, J. Opt. Soc. Am. 61, 674A (1971).

Beran, M. J.

T. L. Ho and M. J. Beran, J. Opt. Soc. Am. 59, 1134 (1969).

Brown, Jr., W. P.

W. P. Brown, Jr., J. Opt. Soc. Am. 62, 45 (1972).

W. P. Brown, Jr., IEEE Trans. AP-15, 81 (1967).

W. P. Brown, Jr., J. Opt. Soc. Am. 57, 1539 (1967).

Dagkesamanskaya, I. M.

I. M. Dagkesamanskaya and V. I. Shishov, Izv. Vuz. Radiofiz. (Russian) 13, 16 (1970).

Fried, D. L.

D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).

Gochelashvily, K. S.

K. S. Gochelashvily and V. I. Shishov, Preprint FIAN (Lebedev Institute), N71 (1971).

Gracheva, M. E.

M. E. Gracheva, A. S. Gurvich, and M. A. Kallistratova, Izv. Vuz. Radiofiz. (Russian) 13, 56 (1970).

Gurvich, A. S.

M. E. Gracheva, A. S. Gurvich, and M. A. Kallistratova, Izv. Vuz. Radiofiz. (Russian) 13, 56 (1970).

Ho, T. L.

T. L. Ho and M. J. Beran, J. Opt. Soc. Am. 59, 1134 (1969).

Kallistratova, M. A.

M. E. Gracheva, A. S. Gurvich, and M. A. Kallistratova, Izv. Vuz. Radiofiz. (Russian) 13, 56 (1970).

Kerr, J. R.

J. R. Kerr, J. Opt. Soc. Am. 61, 674A (1971).

Klyatskin, V. I.

V. I. Klyatskin, Zh. Eksperim. i Teor. Fiz. 60, 1300 (1971) [Sov. Phys. JETP 33, 703 (1971)].

Luke, Y. L.

Y. L. Luke, Integrals of Bessel Functions (McGraw-Hill, New York, 1962), p. 330.

Molyneux, J. E.

J. E. Molyneux, J. Opt. Soc. Am. 61, 248 (1971).

Shishov, V. I.

I. M. Dagkesamanskaya and V. I. Shishov, Izv. Vuz. Radiofiz. (Russian) 13, 16 (1970).

K. S. Gochelashvily and V. I. Shishov, Preprint FIAN (Lebedev Institute), N71 (1971).

V. I. Shishov, Izv. Vuz. Radiofiz. (Russian) 11, 866 (1968).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

V. I. Tatarski, Zh. Eksperim. i Teor. Fiz. 56, 2106 (1969) [Sov. Phys. JETP 29, 1133 (1969)].

Other (16)

V. I. Shishov, Izv. Vuz. Radiofiz. (Russian) 11, 866 (1968).

T. L. Ho and M. J. Beran, J. Opt. Soc. Am. 59, 1134 (1969).

V. I. Tatarski, Zh. Eksperim. i Teor. Fiz. 56, 2106 (1969) [Sov. Phys. JETP 29, 1133 (1969)].

J. E. Molyneux, J. Opt. Soc. Am. 61, 248 (1971).

W. P. Brown, Jr., J. Opt. Soc. Am. 62, 45 (1972).

I. M. Dagkesamanskaya and V. I. Shishov, Izv. Vuz. Radiofiz. (Russian) 13, 16 (1970).

V. I. Klyatskin, Zh. Eksperim. i Teor. Fiz. 60, 1300 (1971) [Sov. Phys. JETP 33, 703 (1971)].

K. S. Gochelashvily and V. I. Shishov, Preprint FIAN (Lebedev Institute), N71 (1971).

Y. L. Luke, Integrals of Bessel Functions (McGraw-Hill, New York, 1962), p. 330.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

W. P. Brown, Jr., J. Opt. Soc. Am. 57, 1539 (1967).

W. P. Brown, Jr., IEEE Trans. AP-15, 81 (1967).

M. E. Gracheva, A. S. Gurvich, and M. A. Kallistratova, Izv. Vuz. Radiofiz. (Russian) 13, 56 (1970).

We should not expect exact quantitative agreement between the results in Fig. 1 and experiment because the numerical results pertain to two-dimensional propagation, whereas the experimental results pertain to three-dimensional propagation. Nevertheless, aside from the fact that the experimental peak variance exceeds that given in Fig. 1, the agreement is pretty good.

D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).

J. R. Kerr, J. Opt. Soc. Am. 61, 674A (1971).

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