Abstract

We have extended the work of Goodman and of Fujii and Asakura to predict the phase distribution in noncircular Gaussian speckle patterns.

© 1978 Optical Society of America

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References

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  1. J. W. Goodman, in Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, Berlin, 1975), pp. 9–75.
    [CrossRef]
  2. H. Fujii and T. Asakura, Opt. Commun. 11, 35 (1974).
    [CrossRef]
  3. G. Da Costa, G. Guerri, and J. Tani, Appl. Opt. 16(June1977).
    [CrossRef]

1977 (1)

G. Da Costa, G. Guerri, and J. Tani, Appl. Opt. 16(June1977).
[CrossRef]

1974 (1)

H. Fujii and T. Asakura, Opt. Commun. 11, 35 (1974).
[CrossRef]

Asakura, T.

H. Fujii and T. Asakura, Opt. Commun. 11, 35 (1974).
[CrossRef]

Da Costa, G.

G. Da Costa, G. Guerri, and J. Tani, Appl. Opt. 16(June1977).
[CrossRef]

Fujii, H.

H. Fujii and T. Asakura, Opt. Commun. 11, 35 (1974).
[CrossRef]

Goodman, J. W.

J. W. Goodman, in Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, Berlin, 1975), pp. 9–75.
[CrossRef]

Guerri, G.

G. Da Costa, G. Guerri, and J. Tani, Appl. Opt. 16(June1977).
[CrossRef]

Tani, J.

G. Da Costa, G. Guerri, and J. Tani, Appl. Opt. 16(June1977).
[CrossRef]

Appl. Opt. (1)

G. Da Costa, G. Guerri, and J. Tani, Appl. Opt. 16(June1977).
[CrossRef]

Opt. Commun. (1)

H. Fujii and T. Asakura, Opt. Commun. 11, 35 (1974).
[CrossRef]

Other (1)

J. W. Goodman, in Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, Berlin, 1975), pp. 9–75.
[CrossRef]

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Figures (4)

FIG. 1
FIG. 1

Geometry of the considered experimental setup (from Refs. 1 and 2). The statistics of the phase of the speckle in the receiver plane (x, y) is studied as a function of the corresponding statistical properties of the diffuser in the object plane (ξ, η).

FIG. 2
FIG. 2

Computer calculated curves for σθ = π/15. a) N = 1;b) N = 0.5; c) N = 0.1; d) N = 0.05; e) N = 0.01

FIG. 3
FIG. 3

Idem for σθ = π/4 and the same values of N.

FIG. 4
FIG. 4

Idem for σθ = π/2 and the same values of N.

Equations (9)

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A ( r ) = λ z exp ( - σ θ 2 / 2 ) , A ( i ) = 0 , σ r 2 = ( I s / N ) [ Chi ( σ θ 2 ) - C - ln ( σ θ 2 ) ] , σ i 2 = ( I s / N ) Shi ( σ θ 2 ) .
I s = { A ( r ) } 2 , N = λ 2 z 2 / S p π r c 2 .
p ( A ( r ) , A ( i ) ) = 1 2 π σ r σ i exp ( - [ A ( r ) - A ( r ) ] 2 2 σ r 2 - [ A ( i ) ] 2 2 σ i 2 ) .
A ( r ) = I cos ϕ , A ( i ) = I sin ϕ .
p ( I , ϕ ) = 1 4 π σ r σ i exp [ - I 2 ( sin 2 ϕ σ i 2 - cos 2 ϕ σ r 2 ) + I A ( r ) cos ϕ σ r 2 - [ A ( r ) ] 2 2 σ r 2 ] .
p ( ϕ ) = 0 p ( I , ϕ ) d I .
p ( ϕ ) = n 2 π α { 1 + π c α cos ϕ [ 1 - erf ( - c α cos ϕ ) ] × exp ( c cos 2 ϕ / α ) } exp ( - c ) .
n = σ r σ i = ( Chi ( σ θ 2 ) - C - ln σ θ 2 Shi ( σ θ 2 ) ) 1 / 2 , c = { A ( r ) } 2 2 σ r 2 = 1 2 N Chi ( σ θ 2 ) - C - ln σ θ 2 ,
α = cos 2 ϕ + n 2 sin 2 ϕ .