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References

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  1. D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).
    [CrossRef]
  2. H. T. Yura, J. Opt. Soc. Am. 59, 111 (1969).
    [CrossRef]
  3. M. E. Gracheva, Radiofizika 10, 775 (1967).
  4. D. L. Fried and J. D. Cloud, J. Opt. Soc. Am. 56, 1667 (1966).
    [CrossRef]
  5. D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).
    [CrossRef]

1969 (1)

1967 (3)

1966 (1)

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Figures (3)

Fig. 1
Fig. 1

Irradiance variance as a function of log-amplitude variance as computed from the Rytov approximation. The dotted curve (i.e., Fried’s result) is calculated from Eq. (3), while the solid curve is calculated from Eq. (4).

Fig. 2
Fig. 2

Dependence of the aperture-averaging factor Θ upon normalized range 4z/kD2 for D = 5 cm, λ = 0.6328 μ, and Cn2 = 3 × 10−15 cm−2/3. Curves A and B were obtained from Eq. (4) and from Fried’s expression, respectively. The solid and dotted curves refer to spherical and plane waves, respectively.

Fig. 3
Fig. 3

Dependence of the aperture-averaging factor Θ upon normalized aperture diam D/(4z/k)1/2 for z = 1 km, μ = 0.6328 μ, and Cn2 = 3 × 10−15 cm−2/2. Curves A and B were obtained from Eq. (4) and from Fried’s expression, respectively. The solid and dotted curves refer to spherical and plane waves, respectively.

Equations (5)

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Θ = { [ ( S - ( S ) ] 2 } / ( S ) 2 = σ S 2 ( S ) 2 ,
Θ = 32 π D 4 0 D C I ( ρ , z ) C I ( 0 , z ) K ( ρ , D ) ρ d ρ ,
K ( ρ , D ) = D 2 2 { cos - 1 ( ρ / D ) - ( ρ / D ) [ 1 - ( ρ / D ) 2 ] 1 2 } , ρ D . 0 ρ > D
C I ( ρ , z ) = I 0 2 { exp [ 4 C l ( ρ , z ) ] - 1 }
C I ( ρ , z ) = I 0 2 [ 1 - exp { - 2 [ C l R ( ρ , z ) ] 1 2 } ] 2 .