Abstract

A general form for the distribution of intensity in a medium with a random index of refraction is derived. From it, one can see why the K distribution is phenomenologically useful but also that it requires corrections.

© 1984 Optical Society of America

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References

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  1. R. Dashen, J. Math. Phys. 20, 894 (1979).
    [Crossref]
  2. K. Gochelagvili, V. Shishov, Sov. Phys. JETP 47, 1028 (1978).
  3. D. Bernstein, R. Dashen, S. Flatte (University of California, Santa Cruz, Santa Cruz, Calif. 95060), preprint.
  4. E. Jakeman, P. Pusey, Phys. Rev. Lett. 40, 546 (1978).
    [Crossref]
  5. See, for example, K. Huang, Statistical Mechanics (Wiley, New York, 1963).
  6. This extra term is hard to compute but is generally small; see Ref. 1.

1979 (1)

R. Dashen, J. Math. Phys. 20, 894 (1979).
[Crossref]

1978 (2)

K. Gochelagvili, V. Shishov, Sov. Phys. JETP 47, 1028 (1978).

E. Jakeman, P. Pusey, Phys. Rev. Lett. 40, 546 (1978).
[Crossref]

Bernstein, D.

D. Bernstein, R. Dashen, S. Flatte (University of California, Santa Cruz, Santa Cruz, Calif. 95060), preprint.

Dashen, R.

R. Dashen, J. Math. Phys. 20, 894 (1979).
[Crossref]

D. Bernstein, R. Dashen, S. Flatte (University of California, Santa Cruz, Santa Cruz, Calif. 95060), preprint.

Flatte, S.

D. Bernstein, R. Dashen, S. Flatte (University of California, Santa Cruz, Santa Cruz, Calif. 95060), preprint.

Gochelagvili, K.

K. Gochelagvili, V. Shishov, Sov. Phys. JETP 47, 1028 (1978).

Huang, K.

See, for example, K. Huang, Statistical Mechanics (Wiley, New York, 1963).

Jakeman, E.

E. Jakeman, P. Pusey, Phys. Rev. Lett. 40, 546 (1978).
[Crossref]

Pusey, P.

E. Jakeman, P. Pusey, Phys. Rev. Lett. 40, 546 (1978).
[Crossref]

Shishov, V.

K. Gochelagvili, V. Shishov, Sov. Phys. JETP 47, 1028 (1978).

J. Math. Phys. (1)

R. Dashen, J. Math. Phys. 20, 894 (1979).
[Crossref]

Phys. Rev. Lett. (1)

E. Jakeman, P. Pusey, Phys. Rev. Lett. 40, 546 (1978).
[Crossref]

Sov. Phys. JETP (1)

K. Gochelagvili, V. Shishov, Sov. Phys. JETP 47, 1028 (1978).

Other (3)

D. Bernstein, R. Dashen, S. Flatte (University of California, Santa Cruz, Santa Cruz, Calif. 95060), preprint.

See, for example, K. Huang, Statistical Mechanics (Wiley, New York, 1963).

This extra term is hard to compute but is generally small; see Ref. 1.

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Equations (12)

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I N = N ! [ 1 + ½ N ( N 1 ) γ + ] ,
I N = N ! γ N Γ ( N + γ 1 ) Γ ( γ 1 ) .
I N = N ! exp [ N ( N 1 ) 2 ! γ f 2 ( γ ) N ( N 1 ) ( N 2 ) 3 ! γ 2 f 3 ( γ ) + N ( N 1 ) ( N 2 ) ( N 3 ) 4 ! γ 3 f 4 ( γ ) + ] ,
I N = N ! exp [ ½ N ( N 1 ) γ + 0 ( N 3 γ 2 ) ] ,
i k z ψ = 1 2 2 x 2 ψ + k 2 μ ψ ,
ψ = i 2 k d ( paths ) exp [ i k S ( path ) ] ,
S = S 0 μ [ x ( z ) , z ] d z , S 0 = ½ [ d x ( z ) d z ] 2 d x .
I N = 1 ( 2 k ) 2 N d 2 N ( paths ) × exp ( i k ψ * S i k ψ * S ) ,
I N N ! ( 2 k ) 2 N one region d 2 N ( paths ) × exp ( i k ψ S 0 i k ψ * S 0 ) e M ,
e M = exp ( i k ψ μ d x + i k ψ * μ d x ) .
± k 2 2 d z d z μ [ x ( z ) , z ] μ [ x ( z ) , z ] ,
I N = N ! e M 1 ,

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