Abstract

This paper proposes an absolute phase retrieval method for complex object measurement based on quantized phase-coding and connected region labeling. A specific code sequence is embedded into quantized phase of three coded fringes. Connected regions of different codes are labeled and assigned with 3-digit-codes combining the current period and its neighbors. Wrapped phase, more than 36 periods, can be restored with reference to the code sequence. Experimental results verify the capability of the proposed method to measure multiple isolated objects.

© 2016 Optical Society of America

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References

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2016 (3)

C. Zuo, L. Huang, M. L. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Y. An, J.-S. Hyun, and S. Zhang, “Pixel-wise absolute phase unwrapping using geometric constraints of structured light system,” Opt. Express 24(16), 18445–18459 (2016).
[Crossref] [PubMed]

Y. Xing, C. Quan, and C. Tay, “A modified phase-coding method for absolute phase retrieval,” Opt. Lasers Eng. 87, 97–102 (2016).
[Crossref]

2015 (1)

B. Li, Y. Fu, J. Zhang, H. Wu, and Z. Zeng, “Period correction method of phase coding fringe,” Opt. Rev. 22(5), 717–723 (2015).
[Crossref]

2012 (5)

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

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

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik (Stuttg.) 123(24), 2272–2275 (2012).
[Crossref]

D. Zheng and F. Da, “Phase coding method for absolute phase retrieval with a large number of codewords,” Opt. Express 20(22), 24139–24150 (2012).
[Crossref] [PubMed]

Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
[Crossref]

2011 (2)

2010 (3)

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

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

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 (2)

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

L. He, Y. Chao, K. Suzuki, and K. Wu, “Fast connected-component labeling,” Pattern Recognit. 42(9), 1977–1987 (2009).
[Crossref]

2007 (1)

2006 (1)

2004 (1)

1999 (1)

1987 (1)

1985 (1)

1984 (1)

1983 (1)

An, Y.

Asundi, A.

C. Zuo, L. Huang, M. L. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Carocci, M.

Chao, Y.

L. He, Y. Chao, K. Suzuki, and K. Wu, “Fast connected-component labeling,” Pattern Recognit. 42(9), 1977–1987 (2009).
[Crossref]

Chen, F.

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik (Stuttg.) 123(24), 2272–2275 (2012).
[Crossref]

Chen, Q.

C. Zuo, L. Huang, M. L. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Chen, W.

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

Cheng, Y. Y.

Creath, K.

Da, F.

Fu, Y.

B. Li, Y. Fu, J. Zhang, H. Wu, and Z. Zeng, “Period correction method of phase coding fringe,” Opt. Rev. 22(5), 717–723 (2015).
[Crossref]

Geng, J.

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
[Crossref]

Halioua, M.

He, L.

L. He, Y. Chao, K. Suzuki, and K. Wu, “Fast connected-component labeling,” Pattern Recognit. 42(9), 1977–1987 (2009).
[Crossref]

Hoang, T.

Huang, L.

C. Zuo, L. Huang, M. L. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Huang, P. S.

Hyun, J.-S.

Jing, Z.

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

Kuang, D.

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

Li, B.

B. Li, Y. Fu, J. Zhang, H. Wu, and Z. Zeng, “Period correction method of phase coding fringe,” Opt. Rev. 22(5), 717–723 (2015).
[Crossref]

Liu, H. C.

Liu, Y.

Mutoh, K.

Nguyen, D.

Pan, B.

Quan, C.

Y. Xing, C. Quan, and C. Tay, “A modified phase-coding method for absolute phase retrieval,” Opt. Lasers Eng. 87, 97–102 (2016).
[Crossref]

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

Rodella, R.

Sansoni, G.

Srinivasan, V.

Su, W. H.

Su, X.

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik (Stuttg.) 123(24), 2272–2275 (2012).
[Crossref]

Y. Liu, X. Su, and Q. Zhang, “A novel encoded-phase technique for phase measuring profilometry,” Opt. Express 19(15), 14137–14144 (2011).
[Crossref] [PubMed]

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

Suzuki, K.

L. He, Y. Chao, K. Suzuki, and K. Wu, “Fast connected-component labeling,” Pattern Recognit. 42(9), 1977–1987 (2009).
[Crossref]

Takeda, M.

Tay, C.

Y. Xing, C. Quan, and C. Tay, “A modified phase-coding method for absolute phase retrieval,” Opt. Lasers Eng. 87, 97–102 (2016).
[Crossref]

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

Wang, Y.

Wang, Z.

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

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]

Weng, J.

Wu, H.

B. Li, Y. Fu, J. Zhang, H. Wu, and Z. Zeng, “Period correction method of phase coding fringe,” Opt. Rev. 22(5), 717–723 (2015).
[Crossref]

Wu, K.

L. He, Y. Chao, K. Suzuki, and K. Wu, “Fast connected-component labeling,” Pattern Recognit. 42(9), 1977–1987 (2009).
[Crossref]

Wyant, J. C.

Xing, Y.

Y. Xing, C. Quan, and C. Tay, “A modified phase-coding method for absolute phase retrieval,” Opt. Lasers Eng. 87, 97–102 (2016).
[Crossref]

Zeng, Z.

B. Li, Y. Fu, J. Zhang, H. Wu, and Z. Zeng, “Period correction method of phase coding fringe,” Opt. Rev. 22(5), 717–723 (2015).
[Crossref]

Zhang, J.

B. Li, Y. Fu, J. Zhang, H. Wu, and Z. Zeng, “Period correction method of phase coding fringe,” Opt. Rev. 22(5), 717–723 (2015).
[Crossref]

Zhang, M. L.

C. Zuo, L. Huang, M. L. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Zhang, Q.

Y. Liu, X. Su, and Q. Zhang, “A novel encoded-phase technique for phase measuring profilometry,” Opt. Express 19(15), 14137–14144 (2011).
[Crossref] [PubMed]

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

Zhang, S.

Zhang, Z.

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

Zhang, Z. H.

Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
[Crossref]

Zheng, D.

Zhong, J.

Zuo, C.

C. Zuo, L. Huang, M. L. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Adv. Opt. Photonics (1)

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3(2), 128–160 (2011).
[Crossref]

Appl. Opt. (7)

Opt. Eng. (1)

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

Opt. Express (4)

Opt. Lasers Eng. (6)

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

Z. Zhang, Z. Jing, Z. Wang, and D. Kuang, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry,” Opt. Lasers Eng. 50(8), 1152–1160 (2012).
[Crossref]

Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
[Crossref]

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

C. Zuo, L. Huang, M. L. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Y. Xing, C. Quan, and C. Tay, “A modified phase-coding method for absolute phase retrieval,” Opt. Lasers Eng. 87, 97–102 (2016).
[Crossref]

Opt. Lett. (2)

Opt. Rev. (1)

B. Li, Y. Fu, J. Zhang, H. Wu, and Z. Zeng, “Period correction method of phase coding fringe,” Opt. Rev. 22(5), 717–723 (2015).
[Crossref]

Optik (Stuttg.) (1)

F. Chen and X. Su, “Phase-unwrapping algorithm for the measurement of 3D object,” Optik (Stuttg.) 123(24), 2272–2275 (2012).
[Crossref]

Pattern Recognit. (1)

L. He, Y. Chao, K. Suzuki, and K. Wu, “Fast connected-component labeling,” Pattern Recognit. 42(9), 1977–1987 (2009).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 Fringe projection profilometry(FPP) system.
Fig. 2
Fig. 2 Principle of conventional phase-coding method.
Fig. 3
Fig. 3 Principle of quantized phase-coding method. (a) The wrapped phase and quantized phase, (b) the corresponding codes.
Fig. 4
Fig. 4 Procedure to calculate the fringe orders.
Fig. 5
Fig. 5 Six binary masks created from the code map.
Fig. 6
Fig. 6 Simulations of the proposed method and conventional phase-coding method when the SNR = 20. (a) Quantized phase-coding fringe patterns, (b) conventional phase-coding fringe patterns, (c) coded phases of the two methods, (d) code of our method, (e) fringe order of our method, (f) fringe order of conventional phase-coding method.
Fig. 7
Fig. 7 One cross section of the reference plane. (a) The wrapped phase and quantized phase, (b) the corresponding codes, (c) the corrected codes.
Fig. 8
Fig. 8 (a)–(c) Three sinusoidal fringe images, (d) wrapped phase map, (e)–(g) three coded fringe patterns, (h) quantized phase map.
Fig. 9
Fig. 9 Region labeling method, where the green points denote the centroids of connected regions, the blue lines denote the rows of regions where their centroids located, the yellow points denote the left-most points, and the cyan points denote the right-most points.
Fig. 10
Fig. 10 Phase retrieval of two isolated objects. (a) The fringe order, (b) the absolute phase map.
Fig. 11
Fig. 11 3D reconstruction of two isolated sculptures.
Fig. 12
Fig. 12 Experiment to measure objects with different colors. (a) Tested objects with different colors, (b) Phase code map with 3-digit-codes, (c) 3D reconstruction of two isolated sculptures

Equations (8)

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

CS="135246351462513624153642531426315264"
ϕ Q (x,y)=CS[ floor( x/T ) ]2π/T
I n =b(x,y)+m(x,y)cos[ ϕ Q (x,y)+2πn/3 ]
ϕ Q (x,y)= tan 1 [ 3 ( I 2 I 1 )/( 2 I 3 I 1 I 2 ) ]
C(x,y)=round[ M ϕ Q (x,y)/2π ]
B i (x,y)={ 1,ifC(x,y)=i 0,otherwise wherei=1,2,3,4,5,6
( x ij , y ij )=( x,y x R ij (x,y) x,y R ij (x,y) , x,y y R ij (x,y) x,y R ij (x,y) )
Φ(x,y)=ϕ(x,y)+2πk(x,y)

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