Abstract

In this paper an approximate solution is given for the development of the ensemble-averaged mutual-coherence function {Г(x<sub>1</sub>,x<sub>2</sub>,τ)} as it propagates through statistically homogeneous and isotropic random media. Only small-angle scattering about the principal propagation direction <i>z</i> is considered and it is assumed that {Г(x<sub>1</sub>,x<sub>2</sub>,τ)} is a function of [(<i>x</i><sub>1</sub>-<i>x</i><sub>2</sub>)<sup>2</sup>+(<i>y</i><sub>1</sub>-<i>y</i><sub>2</sub>)<sup>2</sup>]<sup>½</sup>, <i>z</i><sub>1</sub>-<i>Z</i><sub>2</sub>, and <i>z</i><sub>1</sub>. Under these conditions, it is possible to solve the governing equations using an iteration procedure. The solution is valid for long path lengths. The results are compared to the results given in Chernov, and Tatarski under those conditions where it is appropriate to do so.

PDF Article

References

  • View by:
  • |
  • |

  1. L. Chernov, Wave Propagation in a Random Medium (McGraw-Hill Book Co., Inc., New York, 1960).
  2. V. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Co., Inc., New York, 1961).
  3. V. Tatarski, in International Symposium on the Fine-Scale Structure of the Atmosphere, Moscow, 1965.
  4. Mark Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964), Ch. 6.
  5. Since we assume σ¯(x12,Y12) = σ¯(r12) and {Г0(x12,Y12,0,0,v)} = {Г0(r12,0,0,v)} then {ГjΔz(xl2,y12,0,0,v)} = {ГjΔz(r12,0,0,v)}. We will for the most part continue to display x12 and y12 separately, to exhibit the full three-dimensional nature of the problem.
  6. since we are using analytic signals this is actually twice the intensity for real fields.
  7. This expression was obtained previously by Hufnagel and Stanley8. without adequate proof. See Eqs. (3.5), (4.6), (5.3), and (5.10) of their paper. See Chase [D. M. Chase, J. Opt. Soc. Am. 55, 1559 (1965)] for comments on the Hufnagel and Stanley derivation.. Note added in proof: See G. Keller [Astron. J. 58, 113 (1953)] for the derivation of a similar expression using geometrical optics and independence arguments.
  8. R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Beran, Mark

Mark Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964), Ch. 6.

Chernov, L.

L. Chernov, Wave Propagation in a Random Medium (McGraw-Hill Book Co., Inc., New York, 1960).

Hufnagel, R. E.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Parrent, Jr., G. B.

Mark Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964), Ch. 6.

Stanley, N. R.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Tatarski, V.

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

V. Tatarski, in International Symposium on the Fine-Scale Structure of the Atmosphere, Moscow, 1965.

Other

L. Chernov, Wave Propagation in a Random Medium (McGraw-Hill Book Co., Inc., New York, 1960).

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

V. Tatarski, in International Symposium on the Fine-Scale Structure of the Atmosphere, Moscow, 1965.

Mark Beran and G. B. Parrent, Jr., Theory of Partial Coherence (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1964), Ch. 6.

Since we assume σ¯(x12,Y12) = σ¯(r12) and {Г0(x12,Y12,0,0,v)} = {Г0(r12,0,0,v)} then {ГjΔz(xl2,y12,0,0,v)} = {ГjΔz(r12,0,0,v)}. We will for the most part continue to display x12 and y12 separately, to exhibit the full three-dimensional nature of the problem.

since we are using analytic signals this is actually twice the intensity for real fields.

This expression was obtained previously by Hufnagel and Stanley8. without adequate proof. See Eqs. (3.5), (4.6), (5.3), and (5.10) of their paper. See Chase [D. M. Chase, J. Opt. Soc. Am. 55, 1559 (1965)] for comments on the Hufnagel and Stanley derivation.. Note added in proof: See G. Keller [Astron. J. 58, 113 (1953)] for the derivation of a similar expression using geometrical optics and independence arguments.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.