Abstract

A novel fast convergent algorithm to extract arbitrary unknown phase shifts in generalized phase-shifting interferometry (PSI) is proposed and verified by a series of computer simulations. In this algorithm an error function is introduced and then the unknown phase shifts are found by an iterative tangent approach. In combination with the statistical method, this algorithm can give the most exact results in the fewest iteration steps. It can be used for generalized PSI of arbitrary frames for both smooth and diffusing objects and can usually reach the exact phase shifts with only four or five iterations for three- or four-frame PSI.

© 2006 Optical Society of America

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2004 (2)

2003 (1)

2002 (1)

2001 (1)

2000 (1)

1998 (1)

N. A. Ochoa and J. M. Huntley, Opt. Eng. 37, 2501 (1998).
[CrossRef]

1997 (1)

S. W. Kim, M. Kang, and G. S. Han, Opt. Eng. 36, 3101 (1997).
[CrossRef]

1994 (2)

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

G. S. Han and S. W. Kim, Appl. Opt. 33, 7321 (1994).
[CrossRef] [PubMed]

1991 (2)

K. Okada, A. Sato, and J. Tsujiuchi, Opt. Commun. 84, 118 (1991).
[CrossRef]

G. Lai and T. Yatagai, J. Opt. Soc. Am. A 8, 822 (1991).
[CrossRef]

1984 (1)

J. E. Greivenkamp, Opt. Eng. 23, 350 (1984).

1974 (1)

Brangaccio, D. J.

Bruning, J. H.

Cai, L. Z.

Chen, X.

Deason, V. A.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Gallagher, J. E.

Gramaglia, M.

Greivenkamp, J. E.

J. E. Greivenkamp, Opt. Eng. 23, 350 (1984).

Guo, C. S.

Han, B.

Han, G. S.

S. W. Kim, M. Kang, and G. S. Han, Opt. Eng. 36, 3101 (1997).
[CrossRef]

G. S. Han and S. W. Kim, Appl. Opt. 33, 7321 (1994).
[CrossRef] [PubMed]

Herriott, D. R.

Huntley, J. M.

N. A. Ochoa and J. M. Huntley, Opt. Eng. 37, 2501 (1998).
[CrossRef]

Kang, M.

S. W. Kim, M. Kang, and G. S. Han, Opt. Eng. 36, 3101 (1997).
[CrossRef]

Kato, J.

Kim, S. W.

S. W. Kim, M. Kang, and G. S. Han, Opt. Eng. 36, 3101 (1997).
[CrossRef]

G. S. Han and S. W. Kim, Appl. Opt. 33, 7321 (1994).
[CrossRef] [PubMed]

Lai, G.

Lassahn, G. D.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Lassahn, J. K.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Liao, J.

Liu, Q.

Mizuno, J.

Ochoa, N. A.

N. A. Ochoa and J. M. Huntley, Opt. Eng. 37, 2501 (1998).
[CrossRef]

Ohta, S.

Okada, K.

K. Okada, A. Sato, and J. Tsujiuchi, Opt. Commun. 84, 118 (1991).
[CrossRef]

Rastogi, P. K.

P. K. Rastogi, Holographic Interferometry (Springer-Verlag, 1994).

Rosenfeld, D. P.

Sato, A.

K. Okada, A. Sato, and J. Tsujiuchi, Opt. Commun. 84, 118 (1991).
[CrossRef]

Taylor, P. L.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Tsujiuchi, J.

K. Okada, A. Sato, and J. Tsujiuchi, Opt. Commun. 84, 118 (1991).
[CrossRef]

Wang, H. T.

Wang, Z.

White, A. D.

Yamaguchi, I.

Yang, X. L.

Yatagai, T.

Yeazell, J. A.

Zhang, L.

Zhu, Y. Y.

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Figures (1)

Fig. 1
Fig. 1

Variation of the error function with α 1 for a fixed α 2 and the tangent approach.

Tables (2)

Tables Icon

Table 1 Comparison of Phase-Shift Extraction Results of Our Method and the LSM a for a Three-Frame PSI

Tables Icon

Table 2 Comparison of Phase-Shift Extraction Results of Our Method and the Direct Search a for a Four-Frame PSI

Equations (18)

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

I j ( x , y ) = A o 2 ( x , y ) + A r 2 + 2 A o ( x , y ) A r cos [ φ o ( x , y ) δ j ] ,
j = 1 , 2 , , N .
A o A r exp ( i φ o ) = A 1 + i A 2 ,
A 1 = 1 4 sin ( α 2 2 ) { cos ( α 1 2 ) sin [ ( α 1 + α 2 ) 2 ] ( I 1 I 3 ) cos [ ( α 1 + α 2 ) 2 ] sin ( α 1 2 ) ( I 1 I 2 ) } ,
A 2 = 1 4 sin ( α 2 2 ) { sin ( α 1 2 ) sin [ ( α 1 + α 2 ) 2 ] ( I 1 I 3 ) sin [ ( α 1 + α 2 ) 2 ] sin ( α 1 2 ) ( I 1 I 2 ) } .
A o A r = ( A 1 2 + A 2 2 ) 1 2 ,
cos φ o = A 1 ( A 1 2 + A 2 2 ) 1 2 ,
sin φ o = A 2 ( A 1 2 + A 2 2 ) 1 2 .
( A o + A r ) 2 = I 1 2 A 1 + 2 ( A 1 2 + A 2 2 ) 1 2 ,
( A r A o ) 2 = I 1 2 A 1 2 ( A 1 2 + A 2 2 ) 1 2 .
A r + A o = [ I 1 2 A 1 + 2 ( A 1 2 + A 2 2 ) 1 2 ] 1 2 ,
A r A o = I 1 2 A 1 2 ( A 1 2 + A 2 2 ) 1 2 1 2 .
A o = ( 1 2 ) [ I 1 2 A 1 + 2 ( A 1 2 + A 2 2 ) 1 2 ] 1 2 I 1 2 A 1 2 ( A 1 2 + A 2 2 ) 1 2 1 2 ,
A r = [ 1 ( 2 M ) ] { [ I 1 2 A 1 + 2 ( A 1 2 + A 2 2 ) 1 2 ] 1 2 + I 1 2 A 1 2 ( A 1 2 + A 2 2 ) 1 2 1 2 } .
ϵ = j = 1 3 I j ( x , y ) { A o 2 ( x , y ) + A r 2 + 2 A o ( x , y ) A r cos [ φ o ( x , y ) δ j ] } ,
α 1 k = α 1 , k 1 ϵ A β ,
I 4 ( x , y ) = A o 2 ( x , y ) + A r 2 + 2 A o ( x , y ) A r cos [ φ o ( x , y ) α 1 α 2 α 3 ] .
ϵ = I 4 ( x , y ) { A o 2 ( x , y ) + A r 2 + 2 A o ( x , y ) A r cos [ φ o ( x , y ) α 1 α 2 α 3 ] } .

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