Abstract

In a previous paper [ J. Opt. Soc. Am. A 2, 2133 ( 1985)] we presented three-dimensional numerical solutions for the scintillation index versus the range for a plane wave propagating in the atmosphere, based on the two-scale approximate solution to the fourth-moment equation. In that paper the refraction-index fluctuations were represented by a modified Kolmogorov spectrum, which included an inner scale. In the present paper we present the equivalent results for a point source. The spectrum here is modeled by a function that is somewhat different from that used in the previous paper, and we discuss the relation between the two. The results of the present paper are of interest because they can be compared with recent experimental data.

© 1988 Optical Society of America

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References

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  1. A. M. Whitman, M. J. Beran, “Two-scale solution for atmospheric scintillation,” J. Opt. Soc. Am. A2, 2133–2143 (1985).
    [Crossref]
  2. R. L. Fante, “Inner-scale size effect on the scintillation of light in the turbulent atmosphere,” J. Opt. Soc. Am. 73, 277–281 (1983).
    [Crossref]
  3. W. A. Coles, R. G. Frehlich, “Simultaneous measurements of angular scattering and intensity scintillation in the atmosphere,” J. Opt. Soc. Am. 72, 1042–1048 (1982).
    [Crossref]
  4. G. Parry, P. M. Pusey, “K distributions in atmospheric propagation of laser light,” J. Opt. Soc. Am. 69, 796–798 (1979).
    [Crossref]
  5. R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978).
    [Crossref]
  6. R. J. Hill, S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,” J. Opt. Soc. Am. 68, 892–899 (1978).
    [Crossref]
  7. G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2438–2432 (1985).
    [Crossref]

1985 (2)

A. M. Whitman, M. J. Beran, “Two-scale solution for atmospheric scintillation,” J. Opt. Soc. Am. A2, 2133–2143 (1985).
[Crossref]

G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2438–2432 (1985).
[Crossref]

1983 (1)

1982 (1)

1979 (1)

1978 (2)

Beran, M. J.

A. M. Whitman, M. J. Beran, “Two-scale solution for atmospheric scintillation,” J. Opt. Soc. Am. A2, 2133–2143 (1985).
[Crossref]

Clifford, S. F.

Coles, W. A.

Fante, R. L.

Frehlich, R. G.

Hill, R. J.

G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2438–2432 (1985).
[Crossref]

R. J. Hill, S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,” J. Opt. Soc. Am. 68, 892–899 (1978).
[Crossref]

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978).
[Crossref]

Ochs, G. R.

G. R. Ochs, R. J. Hill, “Optical-scintillation method of measuring turbulence inner scale,” Appl. Opt. 24, 2438–2432 (1985).
[Crossref]

Parry, G.

Pusey, P. M.

Whitman, A. M.

A. M. Whitman, M. J. Beran, “Two-scale solution for atmospheric scintillation,” J. Opt. Soc. Am. A2, 2133–2143 (1985).
[Crossref]

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Figures (2)

Fig. 1
Fig. 1

Scintillation indices as a function of dimensionless range for plane-wave and point-source initial conditions propagating through a pure Kolmogorov medium. The curve with the higher maximum corresponds to the point source.

Fig. 2
Fig. 2

Scintillation index versus range for a point source in a Kolmogorov medium with a dissipation region. The numbers on the curves correspond to values of ζ−1/2. Thus each curve represents a constant value of the inner scale.

Equations (17)

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D ( r ) = C n 2 [ ( l m 2 + r 2 ) 5 / 6 l m 5 / 3 ] ,
σ 1 2 = [ I 2 I 2 / I 2 ] = 0 0 f ( x , y ) d x d y 1 ,
f ( x , y ) = x y π 0 π exp [ ixy cos θ ζ ¯ K 11 / 6 Q ] d θ .
Q = 0 1 h ( x t , y , cos θ ) d t
h = 2 | x t | 5 / 3 + 2 | y | 5 / 3 | x 2 t 2 + y 2 + 2 xty cos θ | 5 / 6 | x 2 t 2 + y 2 2 xty cos θ | 5 / 6 .
ζ K = 1.23 k 7 / 11 ( C n 2 ) 6 / 11 z = 1.096 β 0 12 / 11 ,
σ I 2 = 1 + 0.475 / β 0 4 / 5 = 1 + 0.508 / ζ K 11 / 15 ,
σ I 2 = 1 + 0.861 / β 0 4 / 5 = 1 + 0.921 / ζ K 11 / 5 ,
σ I 2 = 1 + 0.760 / β 0 4 / 5 = 1 + 0.813 / ζ K 11 / 5 ,
Q = 0 1 h [ x t , y ( 1 t ) , cos θ ] d t ,
h = 2 D ( x t ) + 2 D ( y ) D ( | x 2 t 2 + y 2 + 2 xty cos θ | 1 / 2 ) D ( | x 2 t 2 + y 2 2 xty cos θ | 1 / 2 ) ,
D ( u ) = [ ζ 1 + u 2 ] 5 / 6 ζ 5 / 6
Φ ( κ ) = 0.033 C n 2 exp ( κ 2 l n 2 / 4 ) κ 11 / 3 ,
D ( r ) = Γ ( 11 / 6 ) C n 2 l m 5 / 3 [ M ( 5 / 6 , 1 , r 2 / l m 2 ) 1 ] .
D C n 2 r 5 / 3 .
D F 5 6 C n 2 l m 1 / 3 r 2 , D M 5 6 Γ ( 11 / 6 ) C n 2 l m 1 / 3 r 2
l m F = r * 1.73 , l m M = r * 2.08 ,

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