Abstract

<p>The propagation of spherical waves in a turbulent medium is considered. In particular, the case of nonstationary statistics is examined in general and then applied to the specific case of vertical propagation in the atmosphere. The analysis uses the Rytov approximation and the perturbation technique of J. B. Keller. The model of C<sub>n</sub><sup>2</sup>(<i>h</i>) variation is exponential and similar to that utilized by Tatarski.</p><p>The results are compared to other known results for plane and spherical waves in both homogeneous and locally homogeneous random media. In addition, the optimum aperture results of D. L. Fried are examined for this nonstationary case. The marked dependence on the height of the observer and parameters describing the turbulence distribution are noted.</p>

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  1. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Co., New York, 1961).
  2. R. A. Silverman, IEEE Trans. Inform. Theory IT-3, 182 (1957).
  3. R. A. Silverman, Proc. Cambridge Phil. Soc. 54, 530 (1958).
  4. R. A. Silverman, Communs. Pure and Appl. Math. 12, 373 (1959).
  5. See Ref. 7, for a review of the validity of the Rytov procedure, particularly for the optical case.
  6. J. B. Keller, Proc. Sym. in Appl. Math., Am. Math. Soc. 13, 227 (1962).
  7. J. W. Strohbehn, Proc. IEEE 56, 1301 (1968); D. L. Fried, Proc. IEEE 55, 57 (1967).
  8. F. P. Carlson, dissertation, University of Washington (1967).
  9. See Appendix A for a different approach to the terms in the Rytov approximation.
  10. A. D. Wheelon, J. Res. Natl. Bur. Std. (U. S.) Radio Prop. 63D, 1959.
  11. A. N. Kolmogorov, Compt. Rend. Doklady Akad. Nauk U.S.S.R. 30, 301 (1941), contained in S. K. Friedlander and L. Topper, Turbulence (Interscience Publishers, Inc., John Wiley & Sons, Inc., New York, 1961).
  12. A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962).
  13. [Equation].
  14. D. L. Fried, J. Opt. Soc. Am. 56, 1380 (1966).
  15. W. E. Gordon, Proc. IRE 43, 23 (1955).
  16. I. Goldstein, P. A. Miles, and A. Chabot, Proc. IEEE 53, 1172 (1965).
  17. R. A. Schmeltzer, Quart. Appl. Math. 24, 339 (1967).
  18. W. Magnus and F. Oberhettinger, Formulas to Theorems for the Functions of Mathematical Physics (Chelsea Publishing Co., New York, 1949).
  19. D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).

Carlson, F. P.

F. P. Carlson, dissertation, University of Washington (1967).

Chabot, A.

I. Goldstein, P. A. Miles, and A. Chabot, Proc. IEEE 53, 1172 (1965).

Fried, D. L.

D. L. Fried, J. Opt. Soc. Am. 56, 1380 (1966).

D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).

Goldstein, I.

I. Goldstein, P. A. Miles, and A. Chabot, Proc. IEEE 53, 1172 (1965).

Gordon, W. E.

W. E. Gordon, Proc. IRE 43, 23 (1955).

Keller, J. B.

J. B. Keller, Proc. Sym. in Appl. Math., Am. Math. Soc. 13, 227 (1962).

Kolmogorov, A. N.

A. N. Kolmogorov, Compt. Rend. Doklady Akad. Nauk U.S.S.R. 30, 301 (1941), contained in S. K. Friedlander and L. Topper, Turbulence (Interscience Publishers, Inc., John Wiley & Sons, Inc., New York, 1961).

Magnus, W.

W. Magnus and F. Oberhettinger, Formulas to Theorems for the Functions of Mathematical Physics (Chelsea Publishing Co., New York, 1949).

Miles, P. A.

I. Goldstein, P. A. Miles, and A. Chabot, Proc. IEEE 53, 1172 (1965).

Oberhettinger, F.

W. Magnus and F. Oberhettinger, Formulas to Theorems for the Functions of Mathematical Physics (Chelsea Publishing Co., New York, 1949).

Schmeltzer, R. A.

R. A. Schmeltzer, Quart. Appl. Math. 24, 339 (1967).

Silverman, R. A.

R. A. Silverman, IEEE Trans. Inform. Theory IT-3, 182 (1957).

R. A. Silverman, Proc. Cambridge Phil. Soc. 54, 530 (1958).

R. A. Silverman, Communs. Pure and Appl. Math. 12, 373 (1959).

Strohbehn, J. W.

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968); D. L. Fried, Proc. IEEE 55, 57 (1967).

Tatarski, V. I.

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

Wheelon, A. D.

A. D. Wheelon, J. Res. Natl. Bur. Std. (U. S.) Radio Prop. 63D, 1959.

Yaglom, A. M.

A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962).

Other (19)

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

R. A. Silverman, IEEE Trans. Inform. Theory IT-3, 182 (1957).

R. A. Silverman, Proc. Cambridge Phil. Soc. 54, 530 (1958).

R. A. Silverman, Communs. Pure and Appl. Math. 12, 373 (1959).

See Ref. 7, for a review of the validity of the Rytov procedure, particularly for the optical case.

J. B. Keller, Proc. Sym. in Appl. Math., Am. Math. Soc. 13, 227 (1962).

J. W. Strohbehn, Proc. IEEE 56, 1301 (1968); D. L. Fried, Proc. IEEE 55, 57 (1967).

F. P. Carlson, dissertation, University of Washington (1967).

See Appendix A for a different approach to the terms in the Rytov approximation.

A. D. Wheelon, J. Res. Natl. Bur. Std. (U. S.) Radio Prop. 63D, 1959.

A. N. Kolmogorov, Compt. Rend. Doklady Akad. Nauk U.S.S.R. 30, 301 (1941), contained in S. K. Friedlander and L. Topper, Turbulence (Interscience Publishers, Inc., John Wiley & Sons, Inc., New York, 1961).

A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962).

[Equation].

D. L. Fried, J. Opt. Soc. Am. 56, 1380 (1966).

W. E. Gordon, Proc. IRE 43, 23 (1955).

I. Goldstein, P. A. Miles, and A. Chabot, Proc. IEEE 53, 1172 (1965).

R. A. Schmeltzer, Quart. Appl. Math. 24, 339 (1967).

W. Magnus and F. Oberhettinger, Formulas to Theorems for the Functions of Mathematical Physics (Chelsea Publishing Co., New York, 1949).

D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).

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