Abstract

The correlation properties of speckle fields are studied for general paraxial systems. The previous studies on lateral and longitudinal speckle size for the case of free-space propagation (Fresnel transform) are generalized to the case of the linear canonical transform. These results have implications for the control of speckle size, through appropriate design of optical systems, with particular relevance for speckle interferometry.

© 2007 Optical Society of America

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References

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2006

2005

J. M. Diazdelacruz, Appl. Opt. 44, 2250 (2005).
[CrossRef] [PubMed]

T. Alieva, M. J. Bastiaans, and M. L. Calvo, EURASIP J. Appl. Signal Process. 10, 1498 (2005).
[CrossRef]

2003

1999

1996

1995

1994

1992

1990

1972

H. Tiziani, Opt. Commun. 5, 271 (1972).
[CrossRef]

1970

Appl. Opt.

EURASIP J. Appl. Signal Process.

T. Alieva, M. J. Bastiaans, and M. L. Calvo, EURASIP J. Appl. Signal Process. 10, 1498 (2005).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

H. Tiziani, Opt. Commun. 5, 271 (1972).
[CrossRef]

Opt. Lett.

Other

J. C. Dainty, in Progress in Optics XIV, E.Wolf, ed. (North-Holland, 1976).

J. W. Goodman, in Statistical Optics (Wiley, 1985), pp. 286-360.

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

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Figures (2)

Fig. 1
Fig. 1

Contour plot of μ ( α , τ ) as a function of τ and α. SL, single lens; DP, decorrelation point.

Fig. 2
Fig. 2

(a) Variation of α and τ as a function of f Δ z l ( μ m ) for the SL.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

U i ( x ) = 1 j λ B i u ( x 0 ) p ( x 0 ) exp [ j π λ B i ( D i x 2 2 x 0 x + A i x 0 2 ) ] d x 0 ,
R ( x , x ̃ ) = I 1 ( x ) I 2 ( x ̃ ) + J A ( x , x ̃ ) 2 ,
J A ( x , x ̃ ) = U LCT 1 ( x ) U LCT 2 * ( x ̃ ) ,
J A ( x , x ̃ ) = C 1 1 exp [ j α x N ] exp ( j τ x N 2 ) d x N ,
τ = π L 2 A 1 4 λ B 1 ( 1 B 1 A 1 ψ ) , α = π L ( B 1 γ Δ B x ) λ B 1 ( B 1 + Δ B ) ,
μ I ( α , τ ) = J A ( x , x ̃ ) J A ( x , x ) J A ( x ̃ , x ̃ ) 2 .
γ LS = λ B 1 L .
A 1 = 1 z l f , B 1 = z l + ( z l S ) ( 1 z l f ) .

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