Abstract

The mean-square fluctuations of log amplitude and phase are analytically obtained for gaussian light-beam propagating through a randomly inhomogeneous medium with gaussian covariance of the refractive-index fluctuations. The beam used is radiated from an extended source with a circularly symmetric gaussian amplitude distribution and a curved wavefront (phase variation) which characterize the beam shape. The dependence of the fluctuation distribution upon the beam shape and the scale of the medium turbulence is discussed.

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  1. V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (McGraw-Hill Book Co., New York, 1961).
  2. L. A. Chernov, Wave Propagation in a Random Medium, translated by R. A. Silverman (McGraw-Hill Book Co., New York, 1960).
  3. R. A. Schmeltzer, Quart. Appl. Math. 24, 339 (1966). 4. D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).
  4. Y. Kinoshita, thesis, Hokkaido University, 1966. Y. Kinoshita, M. Suzuki, and T. Matsumoto, Radio Science 3, 287 (1968).
  5. H. Kogelnik and T. Li, Proc. IEEE 54, 1312 (1966).
  6. This restriction comes from both the perturbation used in Eq. (6b) and the approximation ln(φ/ φ0)≃δφ/φ0. Instead of it, another form of restriction equivalent to that of the usual Rytov approximation can be used and given in such a way that, after introducing the Rytov transform in Eq. (4), we obtain the equation of Riccati type and solve it by means of the method of smooth perturbations.1 To avoid a long procedure for that method, the present deduction was used, which leads to this restriction.
  7. For instance, see Ref.2, p.83.9. See Ref. 1, p.186.
  8. W. P. Brown, J. Opt. Soc. Am. 56, 1045 (1966).
  9. L. S. Taylor, Radio Science 2, 437 (1967).
  10. D. L. Fried, J. Opt. Soc. Am. 57, 268 (1967).
  11. D. A. deWolf, J. Opt. Soc. Am. 57, 1057 (1967).

Brown, W. P.

W. P. Brown, J. Opt. Soc. Am. 56, 1045 (1966).

Chernov, L. A.

L. A. Chernov, Wave Propagation in a Random Medium, translated by R. A. Silverman (McGraw-Hill Book Co., New York, 1960).

deWolf, D. A.

D. A. deWolf, J. Opt. Soc. Am. 57, 1057 (1967).

Fried, D. L.

D. L. Fried, J. Opt. Soc. Am. 57, 268 (1967).

Kinoshita, Y.

Y. Kinoshita, thesis, Hokkaido University, 1966. Y. Kinoshita, M. Suzuki, and T. Matsumoto, Radio Science 3, 287 (1968).

Kogelnik, H.

H. Kogelnik and T. Li, Proc. IEEE 54, 1312 (1966).

Li, T.

H. Kogelnik and T. Li, Proc. IEEE 54, 1312 (1966).

Schmeltzer, R. A.

R. A. Schmeltzer, Quart. Appl. Math. 24, 339 (1966). 4. D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (McGraw-Hill Book Co., New York, 1961).

Taylor, L. S.

L. S. Taylor, Radio Science 2, 437 (1967).

Other

V. I. Tatarski, Wave Propagation in a Turbulent Medium, translated by R. A. Silverman (McGraw-Hill Book Co., New York, 1961).

L. A. Chernov, Wave Propagation in a Random Medium, translated by R. A. Silverman (McGraw-Hill Book Co., New York, 1960).

R. A. Schmeltzer, Quart. Appl. Math. 24, 339 (1966). 4. D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).

Y. Kinoshita, thesis, Hokkaido University, 1966. Y. Kinoshita, M. Suzuki, and T. Matsumoto, Radio Science 3, 287 (1968).

H. Kogelnik and T. Li, Proc. IEEE 54, 1312 (1966).

This restriction comes from both the perturbation used in Eq. (6b) and the approximation ln(φ/ φ0)≃δφ/φ0. Instead of it, another form of restriction equivalent to that of the usual Rytov approximation can be used and given in such a way that, after introducing the Rytov transform in Eq. (4), we obtain the equation of Riccati type and solve it by means of the method of smooth perturbations.1 To avoid a long procedure for that method, the present deduction was used, which leads to this restriction.

For instance, see Ref.2, p.83.9. See Ref. 1, p.186.

W. P. Brown, J. Opt. Soc. Am. 56, 1045 (1966).

L. S. Taylor, Radio Science 2, 437 (1967).

D. L. Fried, J. Opt. Soc. Am. 57, 268 (1967).

D. A. deWolf, J. Opt. Soc. Am. 57, 1057 (1967).

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