Abstract

A recently proposed phase coding method for absolute phase retrieval performs well because its codeword is embedded into phase domain rather than intensity. Then, the codeword can determine the fringe order for the phase unwrapping. However, for absolute phase retrieval with a large number of codewords, the traditional phase coding method becomes not so reliable. In this paper, we present a novel phase coding method to tackle this problem. Six additional fringe images can generate more than 64(26) unique codewords for correct absolute phase retrieval. The novel phase coding method can be used for absolute phase retrieval with high frequency. Experiment results demonstrate the proposed method is effective.

© 2012 OSA

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References

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2012 (4)

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng.50(4), 574–579 (2012).
[CrossRef]

D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng.50(8), 1130–1139 (2012).
[CrossRef]

Y. Wang and S. Zhang, “Novel phase-coding method for absolute phase retrieval,” Opt. Lett.37(11), 2067–2069 (2012).
[CrossRef] [PubMed]

Y. Ding, J. Xi, Y. Yu, W. Cheng, S. Wang, and J. F. Chicharo, “Frequency selection in absolute phase maps recovery with two frequency projection fringes,” Opt. Express20(12), 13238–13251 (2012).
[CrossRef] [PubMed]

2011 (4)

2010 (4)

C. Quan, W. Chen, and C. J. Tay, “phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng.48(2), 235–243 (2010).
[CrossRef]

Z. Wang, D. A. Nguyen, and J. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng.48(2), 218–225 (2010).
[CrossRef]

S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express18(9), 9684–9689 (2010).
[CrossRef] [PubMed]

T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett.35(12), 1992–1994 (2010).
[CrossRef] [PubMed]

2009 (4)

2008 (2)

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for threee-dimensional profilometry,” Opt. Lasers Eng.46(4), 336–342 (2008).
[CrossRef]

W. H. Su, “Projected fringe profilometry using the area-encoded algorithm for spatially isolated and dynamic objects,” Opt. Express16(4), 2590–2596 (2008).
[CrossRef] [PubMed]

2007 (1)

2005 (1)

2004 (1)

1999 (1)

J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-coded binary fringe projection technique for 3-D shape measurement,” Opt. Eng.44(2), 023606 (1999).
[CrossRef]

1993 (1)

Asundi, A.

Barnes, J.

Z. Wang, D. A. Nguyen, and J. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng.48(2), 218–225 (2010).
[CrossRef]

Carocci, M.

Chen, W.

C. Quan, W. Chen, and C. J. Tay, “phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng.48(2), 235–243 (2010).
[CrossRef]

S. Li, X. Su, and W. Chen, “Spatial carrier fringe pattern phase demodulation by use of a two-dimensional real wavelet,” Appl. Opt.48(36), 6893–6906 (2009).
[CrossRef] [PubMed]

Cheng, W.

Chiang, F. P.

J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-coded binary fringe projection technique for 3-D shape measurement,” Opt. Eng.44(2), 023606 (1999).
[CrossRef]

Chicharo, J.

Chicharo, J. F.

Da, F.

D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng.50(8), 1130–1139 (2012).
[CrossRef]

Ding, Y.

Hahn, J.

Hoang, T.

Huang, L.

Huang, P. S.

J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-coded binary fringe projection technique for 3-D shape measurement,” Opt. Eng.44(2), 023606 (1999).
[CrossRef]

Huntley, J. M.

Kemao, Q.

Kim, E. H.

Kim, H.

Lee, B.

Li, S.

Liu, Y.

Nguyen, D.

Nguyen, D. A.

Z. Wang, D. A. Nguyen, and J. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng.48(2), 218–225 (2010).
[CrossRef]

Oliver, J.

Oliver, J. H.

Pan, B.

Pan, J. H.

J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-coded binary fringe projection technique for 3-D shape measurement,” Opt. Eng.44(2), 023606 (1999).
[CrossRef]

Peng, X.

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for threee-dimensional profilometry,” Opt. Lasers Eng.46(4), 336–342 (2008).
[CrossRef]

Quan, C.

C. Quan, W. Chen, and C. J. Tay, “phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng.48(2), 235–243 (2010).
[CrossRef]

Rodella, R.

Saldner, H. O.

Sansoni, G.

Su, W. H.

Su, X.

Sun, X.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng.50(4), 574–579 (2012).
[CrossRef]

Tay, C. J.

C. Quan, W. Chen, and C. J. Tay, “phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng.48(2), 235–243 (2010).
[CrossRef]

Tian, J.

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for threee-dimensional profilometry,” Opt. Lasers Eng.46(4), 336–342 (2008).
[CrossRef]

Van Der Weide, D.

Wang, S.

Wang, Y.

Wang, Z.

T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett.35(12), 1992–1994 (2010).
[CrossRef] [PubMed]

Z. Wang, D. A. Nguyen, and J. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng.48(2), 218–225 (2010).
[CrossRef]

Weng, J.

Xi, J.

Xiang, L.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng.50(4), 574–579 (2012).
[CrossRef]

Yau, S. T.

Yu, Y.

Zhang, Q.

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng.50(4), 574–579 (2012).
[CrossRef]

Y. Liu, X. Su, and Q. Zhang, “A novel encoded-phase technique for phase measuring profilometry,” Opt. Express19(15), 14137–14144 (2011).
[CrossRef] [PubMed]

Zhang, S.

Zhao, X.

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for threee-dimensional profilometry,” Opt. Lasers Eng.46(4), 336–342 (2008).
[CrossRef]

Zheng, D.

D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng.50(8), 1130–1139 (2012).
[CrossRef]

Zhong, J.

Appl. Opt. (6)

Opt. Eng. (2)

S. Zhang, “Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm,” Opt. Eng.48(10), 105601 (2009).
[CrossRef]

J. H. Pan, P. S. Huang, and F. P. Chiang, “Color-coded binary fringe projection technique for 3-D shape measurement,” Opt. Eng.44(2), 023606 (1999).
[CrossRef]

Opt. Express (6)

Opt. Lasers Eng. (5)

Q. Zhang, X. Su, L. Xiang, and X. Sun, “3-D shape measurement based on complementary Gray-code light,” Opt. Lasers Eng.50(4), 574–579 (2012).
[CrossRef]

D. Zheng and F. Da, “Self-correction phase unwrapping method based on Gray-code light,” Opt. Lasers Eng.50(8), 1130–1139 (2012).
[CrossRef]

C. Quan, W. Chen, and C. J. Tay, “phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng.48(2), 235–243 (2010).
[CrossRef]

Z. Wang, D. A. Nguyen, and J. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng.48(2), 218–225 (2010).
[CrossRef]

J. Tian, X. Peng, and X. Zhao, “A generalized temporal phase unwrapping algorithm for threee-dimensional profilometry,” Opt. Lasers Eng.46(4), 336–342 (2008).
[CrossRef]

Opt. Lett. (4)

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Figures (9)

Fig. 1
Fig. 1

(a) One cross section of the coding phase and wrapped phase, (b) The unwrapped absolute phase.

Fig. 2
Fig. 2

(a) One cross section of the coding phase and wrapped phase, (b) The result Codeword 1 and Codeword 2.

Fig. 3
Fig. 3

(a)-(c) Phase shifting fringe images for wrapped phase, (d)-(f) Phase shifting fringe images for the first coding phase, (g)-(i) Phase shifting fringe images for the second coding phase.

Fig. 4
Fig. 4

The result unique codeword.

Fig. 5
Fig. 5

(a) One cross section of the coding phase and wrapped phase, (b) The result codeword, (c) The unwrapped absolute phase.

Fig. 6
Fig. 6

The phase error for phase coding method with different lengths of fringe period.

Fig. 7
Fig. 7

(a) One view of the absolute reference phase before correction, (b) Another view of The absolute reference phase before correction, (c) One view of the absolute reference phase after correction, (d) Another view of the absolute reference phase after correction.

Fig. 8
Fig. 8

(a) The tested object, (b) One of the sinusoidal distribution fringe images, (c) One of the fringe images for the first coding phase, (d) One of the fringe images for the second coding phase, (e) The wrapped phase of the tested object, (f) The absolute phase of the object.

Fig. 9
Fig. 9

(a) One view of 3-D reconstruction phase for Gray-code method, (b) Another view of 3-D reconstruction for Gray-code method, (c) One view of 3-D reconstruction phase for the proposed method, (d) Another view of 3-D reconstruction phase for the proposed method.

Equations (11)

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I i C ( x,y )=f( I i ),
ϕ S' ( x,y )= ϕ S ( x,y )+Δ ϕ S ( x,y ).
C=[ N( ϕ S +π ) / 2π ]
C ' =[ N ( ϕ S' +π ) / 2π ]=[ N( ϕ S +π ) / 2π +NΔ ϕ S / 2π ],
C( i,j )={ ( n+1C_2( i,j ) )×m+1C_1( i,j ),C_2( i,j )even ( nC_2( i,j ) )×m+C_1( i,j ), C_2( i,j )odd
ϕ 1 S ( x,y )={ π[ x/P ]× 2π m , [ x/ ( m×P ) ]even π+( [ x/P ]+1 )× 2π m , [ x/ ( m×P ) ]odd ,
ϕ 2 S ( x,y )=π[ x/ ( m×P ) ]× 2π n .
I k ( x,y )= I ' ( x,y )+ I " ( x,y )cos( ϕ S + δ k ),
C_1=[ m ( ϕ 1 S +π ) / 2π ],
C_2=[ n ( ϕ 2 S +π ) / 2π ].
Φ( x,y )=ϕ( x,y )C×2π.

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