Abstract

General relationships are shown relating the log-amplitude and the phase fluctuations to the Rytov geometric optical solution for the phase fluctuation under the assumption of normal distribution for the log-amplitude and the phase fluctuations. In the weak fluctuation region, this general relationship reduces to the Rytov solution. In the strong fluctuation region, the phase correlation function is shown to approach the Rytov geometric optical solution.

© 1977 Optical Society of America

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References

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  1. V. I. Tatarski, “The effects of the turbulent atmosphere on wave propagation,” (U.S. Dept. of Commerce, TT-68-50464, Springfield, Va., 1971).
  2. J. W. Strohbehn, T-I Wang, J. P. Speck, Radio Sci. 10, 59 (1975).
    [CrossRef]
  3. J. W. Strohbehn, T-I Wang, J. Opt. Soc. Am. 62, 1061 (1972).
    [CrossRef]
  4. D. A. de Wolf, J. Opt. Soc. Am. 64, 360 (1974).
    [CrossRef]
  5. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1977).
  6. R. S. Lawrence, J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
    [CrossRef]
  7. R. Woo, F-C Yang, A. Ishimaru, Astrophys. J. 21, Part 1, 593 (1976).
    [CrossRef]
  8. R. Woo, F-C Yang, K. W. Yip, W. B. Kendall, Astrophys. J. 210, Part 1, 568 (1976).
    [CrossRef]
  9. D. L. Fried, J. Opt. Soc. Am. 67, 421 (1977).
    [CrossRef]
  10. Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, V. I. Tatarski, Sov. Phys. Usp. 13, 551 (1971).
    [CrossRef]

1977 (1)

D. L. Fried, J. Opt. Soc. Am. 67, 421 (1977).
[CrossRef]

1976 (2)

R. Woo, F-C Yang, A. Ishimaru, Astrophys. J. 21, Part 1, 593 (1976).
[CrossRef]

R. Woo, F-C Yang, K. W. Yip, W. B. Kendall, Astrophys. J. 210, Part 1, 568 (1976).
[CrossRef]

1975 (1)

J. W. Strohbehn, T-I Wang, J. P. Speck, Radio Sci. 10, 59 (1975).
[CrossRef]

1974 (1)

1972 (1)

1971 (1)

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, V. I. Tatarski, Sov. Phys. Usp. 13, 551 (1971).
[CrossRef]

1970 (1)

R. S. Lawrence, J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
[CrossRef]

Barabanenkov, Y. N.

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, V. I. Tatarski, Sov. Phys. Usp. 13, 551 (1971).
[CrossRef]

de Wolf, D. A.

Fried, D. L.

D. L. Fried, J. Opt. Soc. Am. 67, 421 (1977).
[CrossRef]

Ishimaru, A.

R. Woo, F-C Yang, A. Ishimaru, Astrophys. J. 21, Part 1, 593 (1976).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1977).

Kendall, W. B.

R. Woo, F-C Yang, K. W. Yip, W. B. Kendall, Astrophys. J. 210, Part 1, 568 (1976).
[CrossRef]

Kravtsov, Y. A.

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, V. I. Tatarski, Sov. Phys. Usp. 13, 551 (1971).
[CrossRef]

Lawrence, R. S.

R. S. Lawrence, J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
[CrossRef]

Rytov, S. M.

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, V. I. Tatarski, Sov. Phys. Usp. 13, 551 (1971).
[CrossRef]

Speck, J. P.

J. W. Strohbehn, T-I Wang, J. P. Speck, Radio Sci. 10, 59 (1975).
[CrossRef]

Strohbehn, J. W.

J. W. Strohbehn, T-I Wang, J. P. Speck, Radio Sci. 10, 59 (1975).
[CrossRef]

J. W. Strohbehn, T-I Wang, J. Opt. Soc. Am. 62, 1061 (1972).
[CrossRef]

R. S. Lawrence, J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
[CrossRef]

Tatarski, V. I.

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, V. I. Tatarski, Sov. Phys. Usp. 13, 551 (1971).
[CrossRef]

V. I. Tatarski, “The effects of the turbulent atmosphere on wave propagation,” (U.S. Dept. of Commerce, TT-68-50464, Springfield, Va., 1971).

Wang, T-I

J. W. Strohbehn, T-I Wang, J. P. Speck, Radio Sci. 10, 59 (1975).
[CrossRef]

J. W. Strohbehn, T-I Wang, J. Opt. Soc. Am. 62, 1061 (1972).
[CrossRef]

Woo, R.

R. Woo, F-C Yang, A. Ishimaru, Astrophys. J. 21, Part 1, 593 (1976).
[CrossRef]

R. Woo, F-C Yang, K. W. Yip, W. B. Kendall, Astrophys. J. 210, Part 1, 568 (1976).
[CrossRef]

Yang, F-C

R. Woo, F-C Yang, K. W. Yip, W. B. Kendall, Astrophys. J. 210, Part 1, 568 (1976).
[CrossRef]

R. Woo, F-C Yang, A. Ishimaru, Astrophys. J. 21, Part 1, 593 (1976).
[CrossRef]

Yip, K. W.

R. Woo, F-C Yang, K. W. Yip, W. B. Kendall, Astrophys. J. 210, Part 1, 568 (1976).
[CrossRef]

Astrophys. J. (2)

R. Woo, F-C Yang, A. Ishimaru, Astrophys. J. 21, Part 1, 593 (1976).
[CrossRef]

R. Woo, F-C Yang, K. W. Yip, W. B. Kendall, Astrophys. J. 210, Part 1, 568 (1976).
[CrossRef]

J. Opt. Soc. Am. (3)

Proc. IEEE (1)

R. S. Lawrence, J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
[CrossRef]

Radio Sci. (1)

J. W. Strohbehn, T-I Wang, J. P. Speck, Radio Sci. 10, 59 (1975).
[CrossRef]

Sov. Phys. Usp. (1)

Y. N. Barabanenkov, Y. A. Kravtsov, S. M. Rytov, V. I. Tatarski, Sov. Phys. Usp. 13, 551 (1971).
[CrossRef]

Other (2)

V. I. Tatarski, “The effects of the turbulent atmosphere on wave propagation,” (U.S. Dept. of Commerce, TT-68-50464, Springfield, Va., 1971).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1977).

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Figures (2)

Fig. 1
Fig. 1

The phase and log-amplitude variances when the saturation occurs at LL02/λ.

Fig. 2
Fig. 2

The phase and log-amplitude variances when the saturation occurs in the diffraction region (l02/λ < L < L02/λ).

Equations (20)

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Γ = U ( ρ ¯ 1 ) U * ( ρ ¯ 2 ) = exp { - 4 π 2 k 2 L 0 [ 1 - J 0 ( κ ρ ) ] Φ n ( κ ) κ d κ } ,
D s r g ( ρ ) = 8 π 2 k 2 L 0 [ 1 - J 0 ( κ ρ ) ] Φ n ( κ ) κ d κ ,
Γ = exp [ - 1 2 D s r g ( ρ ) ] .
U ( ρ ¯ 1 ) = exp ( χ 1 + i S 1 ) U ( ρ ¯ 2 ) = exp ( χ 2 + i S 2 ) .
U ( ρ ¯ 1 ) U * ( ρ ¯ 2 ) = exp [ χ 1 + χ 2 + i ( S 1 - S 2 ) ] = exp ( R + i I ) ,
R = χ 1 + χ 2 + 1 2 χ 1 2 + 1 2 χ 2 2 - 1 2 S 1 2 - 1 2 S 1 2 + χ 1 χ 2 + S 1 S 2 , I = S 1 - S 2 + χ 1 S 1 + χ 2 S 1 - χ 1 S 2 - χ 2 S 2 ,
I = exp ( 2 χ ) = exp ( 2 χ + 2 χ 2 ) = 1
χ 2 - χ 1 χ 2 + S 2 - S 1 S 2 = 4 π 2 k 2 L 0 [ 1 - J 0 ( κ ρ ) ] Φ n ( κ ) κ d κ .
D χ ( ρ ) + D s ( ρ ) = D s r g ( ρ ) ,
σ χ 2 + σ s 2 = ( σ s r g ) 2 = 4 π 2 k 2 L 0 Φ n ( κ ) κ d κ ,
B χ ( ρ ) + B s ( ρ ) = B s r g ( ρ ) = 4 π 2 k 2 L 0 J 0 ( κ ρ ) Φ n ( κ ) κ d κ .
B χ r ( ρ ) = 4 π 2 k 2 0 L d x 0 J 0 ( κ ρ ) sin 2 [ ( L - x ) 2 k κ 2 ] Φ n ( κ ) κ d κ , B s r ( ρ ) = 4 π 2 k 2 0 L d x 0 J 0 ( κ ρ ) cos 2 [ ( L - x ) 2 k κ 2 ] Φ n ( κ ) κ d κ ,
B χ r ( ρ ) + B s r ( ρ ) = B s r g ( ρ ) .
D χ r ( ρ ) + D s r ( ρ ) = D s r g ( ρ ) , ( σ χ r ) 2 + ( σ s r ) 2 = ( σ s r g ) 2 .
σ I 2 = I 2 I 2 - 1 = exp ( 4 χ ) - 1 = exp ( 4 ( χ ) + 8 χ 2 ) - 1 = exp ( 4 χ 2 ) - 1.
σ χ 2 = 1 4 ln ( σ I 2 + 1 ) .
σ s 2 = ( σ s r g ) 2 - 1 4 ln ( σ I 2 + 1 ) .
σ s 2 ( σ s r g ) 2 as L large .
B s ( ρ ) = B s r g ( ρ ) - 1 4 ln ( σ I 2 + 1 ) b s ( ρ ) ,
D s ( ρ ) = D s r g ( ρ ) - 1 2 ln ( σ I 2 + 1 ) [ 1 - b χ ( ρ ) ] ,

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