Abstract

A wavefront reconstruction and three-dimensional (3-D) shape measurement method by a two-step phase-shifting algorithm with arbitrary phase shift in (0,π) is proposed. In this method, only two phase-shifted intensities, with the removal of the dc term by an averaging technique in spatial domain or low-pass filter operation in the frequency domain, are needed, and the other additional measurements are no longer required. The simulation for an irregular wavefront has shown the feasibility, and the optical experiment for a 3-D face mask in the case of a sinusoidal fringe projection system has illustrated the validity of the proposed method.

© 2009 Optical Society of America

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C. S. Guo, Q. Y. Yue, G. X. Wei, L. L. Lu, and S. J. Yue, Opt. Lett. 33, 1945 (2008).
[Crossref] [PubMed]

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, Opt. Commun. 281, 5701 (2008).
[Crossref]

2007 (4)

2006 (1)

2003 (2)

2002 (1)

U. Schnars and W. Jüptner, Meas. Sci. Technol. 13, R85 (2002).
[Crossref]

2001 (1)

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, Opt. Commun. 189, 21 (2001).
[Crossref]

1997 (1)

1990 (2)

Cai, L. Z.

Chang, C. C.

Chen, G. L.

Cheng, X. C.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, Opt. Commun. 281, 5701 (2008).
[Crossref]

Dong, G. Y.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, Opt. Commun. 281, 5701 (2008).
[Crossref]

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, Opt. Lett. 31, 1414 (2006).
[Crossref] [PubMed]

Garcia-Sucerquia, J.

J. A. H. Ramírez and J. Garcia-Sucerquia, Opt. Commun. 277, 259 (2007).
[Crossref]

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002).

Guo, C. S.

He, X. Y.

Jüptner, W.

U. Schnars and W. Jüptner, Meas. Sci. Technol. 13, R85 (2002).
[Crossref]

Kang, X.

Kerr, D.

Kuo, M. K.

Lin, C. Y.

Liu, Q.

Lu, L. L.

Meng, X. F.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, Opt. Commun. 281, 5701 (2008).
[Crossref]

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, Opt. Lett. 31, 1414 (2006).
[Crossref] [PubMed]

Quan, C.

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, Opt. Commun. 189, 21 (2001).
[Crossref]

Quan, C. G.

Ramírez, J. A. H.

J. A. H. Ramírez and J. Garcia-Sucerquia, Opt. Commun. 277, 259 (2007).
[Crossref]

Santoyo, F. M.

Schnars, U.

U. Schnars and W. Jüptner, Meas. Sci. Technol. 13, R85 (2002).
[Crossref]

Shang, H. M.

C. G. Quan, C. J. Tay, X. Kang, X. Y. He, and H. M. Shang, Appl. Opt. 42, 2329 (2003).
[Crossref] [PubMed]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, Opt. Commun. 189, 21 (2001).
[Crossref]

Shen, X. X.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, Opt. Commun. 281, 5701 (2008).
[Crossref]

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, Opt. Lett. 31, 1414 (2006).
[Crossref] [PubMed]

Tay, C. J.

C. G. Quan, C. J. Tay, X. Kang, X. Y. He, and H. M. Shang, Appl. Opt. 42, 2329 (2003).
[Crossref] [PubMed]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, Opt. Commun. 189, 21 (2001).
[Crossref]

Tyrer, J. R.

Wang, C. F.

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, Opt. Commun. 189, 21 (2001).
[Crossref]

Wang, Y. R.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, Opt. Commun. 281, 5701 (2008).
[Crossref]

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, Opt. Lett. 31, 1414 (2006).
[Crossref] [PubMed]

Wei, G. X.

Wizinowich, P. L.

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002).

Xu, X. F.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, Opt. Commun. 281, 5701 (2008).
[Crossref]

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, Opt. Lett. 31, 1414 (2006).
[Crossref] [PubMed]

Yamaguchi, I.

Yang, F. J.

Yang, X. L.

Yau, H. F.

Yau, S. T.

S. Zhang and S. T. Yau, Opt. Eng. 46, 113603 (2007).
[Crossref]

Yue, Q. Y.

Yue, S. J.

Zhang, S.

S. Zhang and S. T. Yau, Opt. Eng. 46, 113603 (2007).
[Crossref]

Zhang, T.

Appl. Opt. (3)

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

Meas. Sci. Technol. (1)

U. Schnars and W. Jüptner, Meas. Sci. Technol. 13, R85 (2002).
[Crossref]

Opt. Commun. (3)

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, Opt. Commun. 281, 5701 (2008).
[Crossref]

J. A. H. Ramírez and J. Garcia-Sucerquia, Opt. Commun. 277, 259 (2007).
[Crossref]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, Opt. Commun. 189, 21 (2001).
[Crossref]

Opt. Eng. (1)

S. Zhang and S. T. Yau, Opt. Eng. 46, 113603 (2007).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Other (1)

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002).

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Figures (4)

Fig. 1
Fig. 1

Simulation results for an irregular wavefront: (a) phase map of the original object wave, (b) one of the interferograms I 1 , (c) Fourier spectrum of (b) after log transformation, (d) an enlarged central part of (c), (e) extracted dc-term from (d), (f) retrieved wrapped phase map.

Fig. 2
Fig. 2

Unwrapped phase map of Fig. 1f.

Fig. 3
Fig. 3

3-D shape measurement of a human-face mask: (a) and (b) captured two fringe patterns I 1 and I 2 ; (c) and (d) Fourier spectra of (a) and (b), respectively; (e) and (f) filtered dc-term in the frequency domain by the Hanning filter technique; (g) and (h) two dc-term-suppressed phase-shifted patterns I 1 s and I 2 s .

Fig. 4
Fig. 4

Experimental results using the proposed method: some typical 3-D geometries of the human face mask in wireframe mode.

Equations (11)

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I 1 ( x , y ) = A o 2 ( x , y ) + A r 2 ( x , y ) + 2 A o ( x , y ) A r ( x , y ) cos φ ( x , y ) ,
I 2 ( x , y ) = A o 2 ( x , y ) + A r 2 ( x , y ) + 2 A o ( x , y ) A r ( x , y ) cos [ φ ( x , y ) δ ] ,
U ( x , y ) = I 1 a 2 A r + i ( I 2 a ) cos δ ( I 1 a ) 2 A r sin δ ,
a = I i a = 1 M N n = 0 N 1 m = 0 M 1 I i ( m Δ x , n Δ y ) , i = 1 , 2 ,
m = 0 , 1 M 1 , n = 0 , 1 N 1 ,
H ( u , v ) = { 1 , if D ( u , v ) D 0 0 , if D ( u , v ) > D 0 } ,
H ( u , v ) = 0.25 [ 1 cos ( 2 π u K ) ] [ 1 cos ( 2 π v L ) ] ,
0 u K 1 , 0 v L 1 ,
U ( x , y ) = I 1 s 2 A r + i I 2 s I 1 s cos δ 2 A r sin δ ,
φ ( x , y ) = tan 1 ( I 2 s I 1 s sin δ cot δ ) ;
W ( x , y ) = 3 ( x + 10 Δ x ) [ ( x 10 Δ x ) 2 + y 2 ] 4.375 × 10 4 ( x 10 Δ x ) 1.438 × 10 4 ( y + 50 Δ y ) ,

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