Abstract

In a previous paper, we considered a perturbation solution for propagation of the fourth-order coherence function in a random medium. In this paper, it is shown how under certain conditions this solution may be extended to treat the propagation problem when the field fluctuations need not be small. A differential equation governing the fourth-order coherence function is derived. A solution is obtained in the geometricoptics limit when the four points of the coherence function are distinct.

© 1969 Optical Society of America

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  1. T. L. Ho and M. J. Beran, J. Opt. Soc. Am. 58, 1335 (1968).
  2. M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964). See p. 23 for the derivation of a similar relation for the Fourier transform of the mutual coherence function.
  3. In Ref. 1 we used the notation Ľ0\z instead of {Ľ0}z.
  4. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Co., New York 1961). See Eqs. (13.13), (7.54), and (7.56).
  5. M. J. Beran, J. Opt. Soc. Am. 56, 1475 (1966).
  6. Equation (20) can also be derived by a diagram technique, i.e., a partial summation of the infinite series representing {L⌃1}. See, V. I. Shishov, IVUZ-Radiophysics (Russian) 11, 866 (1968). Shishov used a gaussian form for the correlation function of refractive-index fluctuations.

Beran, M. J.

T. L. Ho and M. J. Beran, J. Opt. Soc. Am. 58, 1335 (1968).

M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964). See p. 23 for the derivation of a similar relation for the Fourier transform of the mutual coherence function.

M. J. Beran, J. Opt. Soc. Am. 56, 1475 (1966).

Ho, T. L.

T. L. Ho and M. J. Beran, J. Opt. Soc. Am. 58, 1335 (1968).

Parrent, Jr., G. B.

M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964). See p. 23 for the derivation of a similar relation for the Fourier transform of the mutual coherence function.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Co., New York 1961). See Eqs. (13.13), (7.54), and (7.56).

Other (6)

T. L. Ho and M. J. Beran, J. Opt. Soc. Am. 58, 1335 (1968).

M. J. Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964). See p. 23 for the derivation of a similar relation for the Fourier transform of the mutual coherence function.

In Ref. 1 we used the notation Ľ0\z instead of {Ľ0}z.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Co., New York 1961). See Eqs. (13.13), (7.54), and (7.56).

M. J. Beran, J. Opt. Soc. Am. 56, 1475 (1966).

Equation (20) can also be derived by a diagram technique, i.e., a partial summation of the infinite series representing {L⌃1}. See, V. I. Shishov, IVUZ-Radiophysics (Russian) 11, 866 (1968). Shishov used a gaussian form for the correlation function of refractive-index fluctuations.

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