Abstract

In speckle-based metrology systems, a finite range of possible motion or deformation can be measured. When coherent imaging systems with a single limiting aperture are used in speckle metrology, the observed de correlation effects that ultimately define this range are described by the well-known Yamaguchi correlation factor. We extend this result to all coherent quadratic phase paraxial optical systems with a single aperture and provide experimental results to support our theoretical conclusions.

© 2006 Optical Society of America

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References

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    [CrossRef]
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2006 (2)

2005 (3)

2003 (2)

1994 (1)

1972 (1)

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

1970 (1)

Abe, S.

Alieva, T.

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

Bastiaans, M. J.

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

Calvo, M. L.

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

Collins, S. A.

Dainty, J. C.

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

Diazdelacruz, J. M.

Ding, J. J.

Fricke-Begemann, T.

T. Fricke-Begemann, Appl. Opt. 42, 6783 (2003).
[CrossRef] [PubMed]

T. Fricke-Begemann, "Optical measurement of deformation fields and surface processes with digital speckle correlation," Ph.D. dissertation (Carl von Ossietzky Universitat Oldenburg, 2002).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Co., 2005).

J. W. Goodman, Statistical Optics (Wiley, 1985).

Gopinathan, U.

Hennelly, B. M.

Kelly, D. P.

Liu, Y.

O'Neill, F. T.

Patten, R. F.

Pei, S. C.

Rastogi, P. K.

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

Rhodes, W. T.

W. T. Rhodes, Lecture Series: Fourier Optics and Holography, Imaging Technology Center, Florida Atlantic University (personal communication, 2006).

Sheppard, C.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Sheridan, J. T.

Tiziani, H.

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

Ward, J. E.

Wilson, T.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Appl. Opt. (3)

EURASIP J. Appl. Signal Process. (1)

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

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

Opt. Lett. (2)

Other (7)

T. Fricke-Begemann, "Optical measurement of deformation fields and surface processes with digital speckle correlation," Ph.D. dissertation (Carl von Ossietzky Universitat Oldenburg, 2002).

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

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

J. W. Goodman, Statistical Optics (Wiley, 1985).

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

W. T. Rhodes, Lecture Series: Fourier Optics and Holography, Imaging Technology Center, Florida Atlantic University (personal communication, 2006).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Co., 2005).

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Figures (3)

Fig. 1
Fig. 1

Optical setup for (a) System I, (b) System II.

Fig. 2
Fig. 2

Theoretical and experimental maximum correlation values as a function of input plane translation for System I. The motion of the input surface, ξ and the corresponding shift of the distribution in aperture plane, ξ a , are identical.

Fig. 3
Fig. 3

Maximum correlation values for System II. The shift of the input plane is denoted as { ξ } , and the corresponding shift in the aperture plane is denoted as ξ a .

Equations (8)

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u a ( x a ) = ( 1 j λ B ) u ( x o ) exp [ j π λ B ( D x a 2 + A x o 2 2 x a x o ) ] d x o ,
( x a k a ) = [ A B C D ] ( x o k o ) ,
v c ( x c ) = v a ( x a ) exp [ j π λ B 2 ( D 2 x c 2 + A 2 x a 2 2 x a x c ) ] d x a .
c I I ̃ ( s ) = v c * ( r ) v ̃ c ( r + s ) 2 σ I σ I ̃ ,
c I I ̃ = p * ( x a ) p ( x a + A 1 ξ + B 1 κ ) d x a p ( x a ) 2 d x a 2 ,
[ 0 f 1 f 0 ] = { [ 1 z 2 0 1 ] [ 1 0 1 f 1 ] } M 2 I [ 1 z 1 0 1 ] M 1 I ,
= [ 1 z 3 0 1 ] M 2 II { [ 1 z 2 0 1 ] [ 1 0 1 f 1 ] [ 1 z 1 0 1 ] } M 1 II .
c I I ̃ ( r a ) = [ 2 π cos 1 ( r a l ) ( r a l ) 1 ( r a l ) 2 ] 2 .

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