Abstract

An algorithm to extract the arbitrary unknown phase shift and then reconstruct the complex object wave in generalized phase-shifting interferometry (GPSI) without the iteration process and measurement of object wave intensity is proposed. This method can be used for GPSI of any frame number 2. Both computer simulations with smooth and diffusing object surfaces and optical experiments have verified the effectiveness of this method over a wide range of phase shifts with very satisfactory results.

© 2008 Optical Society of America

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References

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2007 (2)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, G. Y. Dong, and X. X. Shen, Opt. Commun. 273, 54 (2007).
[CrossRef]

2006 (3)

2005 (2)

L. Z. Cai, Q. Liu, M. Z. He, and X. F. Meng, Opt. Commun. 249, 95 (2005).
[CrossRef]

L. Z. Cai, Q. Liu, and X. L. Yang, J. Mod. Opt. 52, 45 (2005).
[CrossRef]

2004 (2)

2003 (1)

2002 (1)

2001 (1)

2000 (1)

1997 (2)

G. Stoilov and T. Dragostinov, Opt. Lasers Eng. 28, 61 (1997).
[CrossRef]

I. Yamaguchi and T. Zhang, Opt. Lett. 22, 1268 (1997).
[CrossRef] [PubMed]

1994 (1)

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

1991 (1)

1984 (1)

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

1974 (1)

Appl. Opt. (3)

Appl. Phys. Lett. (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Meng, G. Y. Dong, X. X. Shen, and H. Zhang, Appl. Phys. Lett. 90, 121124 (2007).
[CrossRef]

J. Mod. Opt. (1)

L. Z. Cai, Q. Liu, and X. L. Yang, J. Mod. Opt. 52, 45 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (3)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, G. Y. Dong, and X. X. Shen, Opt. Commun. 273, 54 (2007).
[CrossRef]

L. Z. Cai, Q. Liu, M. Z. He, and X. F. Meng, Opt. Commun. 249, 95 (2005).
[CrossRef]

S. Zhang, Opt. Commun. 268, 231 (2006).
[CrossRef]

Opt. Eng. (Bellingham) (2)

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

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

Opt. Lasers Eng. (1)

G. Stoilov and T. Dragostinov, Opt. Lasers Eng. 28, 61 (1997).
[CrossRef]

Opt. Lett. (7)

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Figures (3)

Fig. 1
Fig. 1

Simulation results of phase shift extraction and wavefront reconstruction. (a) Original smooth object surface, (b) phase map of (a), (c) reconstructed phase map of (a), (d) original diffusing object surface, (e) phase map of (d), and (f) reconstructed phase map of (d).

Fig. 2
Fig. 2

Results of phase-shift extraction for both the smooth and diffusing object surfaces.

Fig. 3
Fig. 3

Optical experimental results: (a) first interferogram I 1 , (b) second interferogram I 2 , (c) reconstructed image of a resolution target, and (d) enlarged central part of (c).

Equations (12)

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I 1 = A o 2 + A r 2 + 2 A o A r cos φ ,
I 2 = A o 2 + A r 2 + 2 A o A r cos ( φ α ) ,
I 2 I 1 = 4 A o A r sin ( φ α 2 ) sin ( α 2 ) ,
I 2 + I 1 = 2 A o 2 + 2 A r 2 + 4 A o A r cos ( φ α 2 ) cos ( α 2 ) .
( I 2 I 1 ) 2 = 16 A r 2 A o 2 sin 2 ( φ α 2 ) sin 2 ( α 2 ) ,
I 2 + I 1 = 2 A o 2 + 2 A r 2 + 4 A r A o cos ( φ α 2 ) cos ( α 2 ) .
( I 2 I 1 ) 2 = 4 A r 2 A o 2 ( 1 cos α ) ,
I 1 + I 2 = 2 ( A o 2 + A r 2 ) .
α = cos 1 [ 1 ( I 2 I 1 ) 2 4 I r ( I 2 2 + I 1 2 I r ) ] .
I o = [ b ( b 2 4 c ) 1 2 ] 2 ,
O ( x , y ) = I 1 I o I r 2 ( I r ) 1 2 + i I 2 I 1 cos α ( 1 cos α ) ( I o + I r ) 2 ( I r ) 1 2 sin α ,
W ( x , y ) = 20 λ sin { [ ( x + x 0 ) 2 + ( y + y 0 ) 2 ] 36 } + [ ( x x 1 ) 2 + ( y y 1 ) 2 ] ( 2 R ) ,

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