Abstract

The irradiance fluctuations of beams which propagate through a turbulent medium can be used to infer the spatial spectrum of the turbulent scatterers. The propagation of Goubau-type beam waves in a random medium is used to show that amplitude fluctuations depend upon the transmitter aperture size, observation distance, and wavelength. Most of the results are presented in terms of a parameter, α<i>L</i>, which is inversely proportional to the Fresnel number, π<i>W</i><sub>0</sub><sup>2</sup>/<i>L</i>λ. A Monte Carlo numerical procedure is used to obtain the normalized mean-square log-amplitude fluctuation as a function of the inverse Fresnel number for various magnitudes of the turbulence inner scale. The applicability of these procedures to measured turbulence spectra is also discussed.

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  1. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Co., New York, 1961).
  2. L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill Book Co., New York, 1960).
  3. D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).
  4. F. P. Carlson and A. Ishimaru, J. Opt. Soc. Am. 59, 319 (1969).
  5. R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
  6. F. P. Carlson, Ph.D. thesis, University of Washington (1967).
  7. Y. Kinoshita, M. Suzuki and T. Matsumoto, Radio Sci. 3, 287, (1968).
  8. Y. Kinoshita, T. Asakura, and M. Suzuki, J. Opt. Soc. Am. 58, 798 (1968).
  9. D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).
  10. D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., J. Opt. Soc. Am. 57, 787 (1967).
  11. D. L. Fried, J. Opt. Soc. Am. 57, 980 (1967).
  12. R. A. Schmeltzer, Quart. Appl. Math. 24, 339 (1967).
  13. G. Goubau and F. Schwering, Proc. IEEE Trans., AP-9, 248 (1961).
  14. G. Goubau, Electromagnetic Waves, R. E. Langer, Ed. (University of Wisconsin Press, Madison, 1962).
  15. G. Goubau, Electromagnetic Theory and Antennas (Macmillan Co., London, 1963).
  16. A. Ishimaru, Radio Sci. 4. No. 4, 295 (1969).
  17. See Ref. 1, p. 139.
  18. The merits of the Rytov procedure are discussed by J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).
  19. See Ref. 1, p. 140
  20. Large αL corresponds to the spherical-wave case and αL → 0 corresponds to the plane-wave case.
  21. αL=N-1, where N is the Fresnel number, πW02/Lλ.
  22. P. H. Deitz and N. J. Wright, J. Opt. Soc. Am. 69, 527 (1969).
  23. P. Beckmann, Radio Science J. Res. Natl. Bur. Std/USNCURSI 69D, 629 (1965).
  24. J. L. Lumley and H. A. Panofsky, Tue Structure of Atmospheric Turbulence (Wiley-Interscience, Inc., New York, 1964).
  25. L. S. Taylor, J. Opt. Soc. Am. 58, 1418 (1968)
  26. L. R. Tsvang, Izvestia ANSSSR, Geophys. Ser. 1960, 11, 1674 (1960).
  27. L. R. Tsvang, Izvestia ANSSSR, Geophys. Ser. 1960, 8, 1252 (1960).
  28. M. E. Gracheva and A. S. Gurvich, Radiofizika 8, 717 (1965).

Asakura, T.

Y. Kinoshita, T. Asakura, and M. Suzuki, J. Opt. Soc. Am. 58, 798 (1968).

Beckmann, P.

P. Beckmann, Radio Science J. Res. Natl. Bur. Std/USNCURSI 69D, 629 (1965).

Carlson, F. P.

F. P. Carlson, Ph.D. thesis, University of Washington (1967).

F. P. Carlson and A. Ishimaru, J. Opt. Soc. Am. 59, 319 (1969).

Chernov, L. A.

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

Deitz, P. H.

P. H. Deitz and N. J. Wright, J. Opt. Soc. Am. 69, 527 (1969).

Fried, D. L.

D. L. Fried, J. Opt. Soc. Am. 57, 980 (1967).

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

D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., J. Opt. Soc. Am. 57, 787 (1967).

Goubau, G.

G. Goubau, Electromagnetic Waves, R. E. Langer, Ed. (University of Wisconsin Press, Madison, 1962).

G. Goubau and F. Schwering, Proc. IEEE Trans., AP-9, 248 (1961).

G. Goubau, Electromagnetic Theory and Antennas (Macmillan Co., London, 1963).

Gracheva, M. E.

M. E. Gracheva and A. S. Gurvich, Radiofizika 8, 717 (1965).

Gurvich, A. S.

M. E. Gracheva and A. S. Gurvich, Radiofizika 8, 717 (1965).

Hufnagel, R. E.

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

Ishimaru, A.

F. P. Carlson and A. Ishimaru, J. Opt. Soc. Am. 59, 319 (1969).

A. Ishimaru, Radio Sci. 4. No. 4, 295 (1969).

Keister, Jr., M. P.

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., J. Opt. Soc. Am. 57, 787 (1967).

Kinoshita, Y.

Y. Kinoshita, T. Asakura, and M. Suzuki, J. Opt. Soc. Am. 58, 798 (1968).

Y. Kinoshita, M. Suzuki and T. Matsumoto, Radio Sci. 3, 287, (1968).

Lumley, J. L.

J. L. Lumley and H. A. Panofsky, Tue Structure of Atmospheric Turbulence (Wiley-Interscience, Inc., New York, 1964).

Matsumoto, T.

Y. Kinoshita, M. Suzuki and T. Matsumoto, Radio Sci. 3, 287, (1968).

Mevers, G. E.

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., J. Opt. Soc. Am. 57, 787 (1967).

Panofsky, H. A.

J. L. Lumley and H. A. Panofsky, Tue Structure of Atmospheric Turbulence (Wiley-Interscience, Inc., New York, 1964).

Schmeltzer, R. A.

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

Schwering, F.

G. Goubau and F. Schwering, Proc. IEEE Trans., AP-9, 248 (1961).

Seidman, J. B.

D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).

Stanley, N. R.

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

Strohbehn, J. W.

The merits of the Rytov procedure are discussed by J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).

Suzuki, M.

Y. Kinoshita, M. Suzuki and T. Matsumoto, Radio Sci. 3, 287, (1968).

Y. Kinoshita, T. Asakura, and M. Suzuki, J. Opt. Soc. Am. 58, 798 (1968).

Tatarski, V. I.

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

Taylor, L. S.

L. S. Taylor, J. Opt. Soc. Am. 58, 1418 (1968)

Tsvang, L. R.

L. R. Tsvang, Izvestia ANSSSR, Geophys. Ser. 1960, 8, 1252 (1960).

L. R. Tsvang, Izvestia ANSSSR, Geophys. Ser. 1960, 11, 1674 (1960).

Wright, N. J.

P. H. Deitz and N. J. Wright, J. Opt. Soc. Am. 69, 527 (1969).

Other

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

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

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

F. P. Carlson and A. Ishimaru, J. Opt. Soc. Am. 59, 319 (1969).

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

F. P. Carlson, Ph.D. thesis, University of Washington (1967).

Y. Kinoshita, M. Suzuki and T. Matsumoto, Radio Sci. 3, 287, (1968).

Y. Kinoshita, T. Asakura, and M. Suzuki, J. Opt. Soc. Am. 58, 798 (1968).

D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., J. Opt. Soc. Am. 57, 787 (1967).

D. L. Fried, J. Opt. Soc. Am. 57, 980 (1967).

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

G. Goubau and F. Schwering, Proc. IEEE Trans., AP-9, 248 (1961).

G. Goubau, Electromagnetic Waves, R. E. Langer, Ed. (University of Wisconsin Press, Madison, 1962).

G. Goubau, Electromagnetic Theory and Antennas (Macmillan Co., London, 1963).

A. Ishimaru, Radio Sci. 4. No. 4, 295 (1969).

See Ref. 1, p. 139.

The merits of the Rytov procedure are discussed by J. W. Strohbehn, Proc. IEEE 56, 1301 (1968).

See Ref. 1, p. 140

Large αL corresponds to the spherical-wave case and αL → 0 corresponds to the plane-wave case.

αL=N-1, where N is the Fresnel number, πW02/Lλ.

P. H. Deitz and N. J. Wright, J. Opt. Soc. Am. 69, 527 (1969).

P. Beckmann, Radio Science J. Res. Natl. Bur. Std/USNCURSI 69D, 629 (1965).

J. L. Lumley and H. A. Panofsky, Tue Structure of Atmospheric Turbulence (Wiley-Interscience, Inc., New York, 1964).

L. S. Taylor, J. Opt. Soc. Am. 58, 1418 (1968)

L. R. Tsvang, Izvestia ANSSSR, Geophys. Ser. 1960, 11, 1674 (1960).

L. R. Tsvang, Izvestia ANSSSR, Geophys. Ser. 1960, 8, 1252 (1960).

M. E. Gracheva and A. S. Gurvich, Radiofizika 8, 717 (1965).

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