Abstract

Two major methods for 3D reconstruction in fringe projection profilometry, phase-height mapping and stereovision, have their respective problems: the former has low-flexibility in practical application due to system restrictions and the latter requires time-consuming homogenous points searching. Given these limitations, we propose a phase-3D mapping method developed from back-projection stereovision model to achieve flexible and high-efficient 3D reconstruction for fringe projection profilometry. We showed that all dimensional coordinates (X, Y, and Z), but not just the height coordinate (Z), of a measured point can be mapped from phase through corresponding rational functions directly and independently. To determine the phase-3D mapping coefficients, we designed a flexible two-step calibration strategy. The first step, ray reprojection calibration, is to determine the stereovision system parameters; the second step, sampling-mapping calibration, is to fit the mapping coefficients using the calibrated stereovision system parameters. Experimental results demonstrated that the proposed method was suitable for flexible and high-efficient 3D reconstruction that eliminates practical restrictions and dispenses with the time-consuming homogenous point searching.

© 2017 Optical Society of America

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References

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2016 (1)

2014 (3)

Z. Huang, J. Xi, Y. Yu, Q. Guo, and L. Song, “Improved geometrical model of fringe projection profilometry,” Opt. Express 22(26), 32220–32232 (2014).
[Crossref] [PubMed]

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53(2), 024105 (2014).
[Crossref]

J. Huang and Q. Wu, “A new reconstruction method based on fringe projection of three-dimensional measuring system,” Opt. Lasers Eng. 52, 115–122 (2014).
[Crossref]

2013 (2)

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik (Stuttg.) 124(21), 5052–5056 (2013).
[Crossref]

Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3D calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 12218–12227 (2013).
[Crossref] [PubMed]

2012 (4)

2011 (2)

2010 (4)

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[Crossref] [PubMed]

L. Huang, P. S. Chua, and A. Asundi, “Least-squares calibration method for fringe projection profilometry considering camera lens distortion,” Appl. Opt. 49(9), 1539–1548 (2010).
[Crossref] [PubMed]

2009 (2)

A. Maurel, P. Cobelli, V. Pagneux, and P. Petitjeans, “Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry,” Appl. Opt. 48(2), 380–392 (2009).
[Crossref] [PubMed]

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47(3–4), 310–319 (2009).
[Crossref]

2008 (1)

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

2007 (4)

P. Kuhmstedt, C. Munckelt, M. Heinze, C. Brauer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[Crossref]

H. Du and Z. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett. 32(16), 2438–2440 (2007).
[Crossref] [PubMed]

J. Vargas, J. A. Quiroga, and M. J. Terron-Lopez, “Flexible calibration procedure for fringe projection profilometry,” Opt. Eng. 46(2), 023601 (2007).
[Crossref]

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46(4), 043601 (2007).
[Crossref]

2006 (2)

S. Zhang, D. Royer, and S.-T. Yau, “GPU-assisted high-resolution, real-time 3-D shape measurement,” Opt. Express 14(20), 9120–9129 (2006).
[Crossref] [PubMed]

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

2005 (1)

B. A. Rajoub, D. R. Burton, and M. J. Lalor, “A new phase-to-height model for measuring object shape using collimated projections of structured light,” J. Opt. A, Pure Appl. Opt. 7(6), S368–S375 (2005).
[Crossref]

2004 (2)

Z. Zhang, D. Zhang, and X. Peng, “Performance analysis of a 3D full-field sensor based on fringe projection,” Opt. Lasers Eng. 42(3), 341–353 (2004).
[Crossref]

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

2003 (3)

J. Li, L. G. Hassebrook, and C. Guan, “Optimized two-frequency phase-measuring-profilometry light-sensor temporal-noise sensitivity,” J. Opt. Soc. Am. A 20(1), 106–115 (2003).
[Crossref] [PubMed]

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

X. Peng, Z. Yang, and H. Niu, “Multi-resolution reconstruction of 3-D image with modified temporal unwrapping algorithm,” Opt. Commun. 224(1–3), 35–44 (2003).
[Crossref]

2002 (2)

R. Sitnik, M. Kujavinska, and J. Woznicki, “Digital fringe projection system for large-volume 360-deg shape measurement,” Opt. Eng. 41(2), 443–449 (2002).
[Crossref]

T. Bothe, W. Osten, A. Gesierich, and W. P. O. Jueptner, “Compact 3D camera,” Proc. SPIE 4778, 48–59 (2002).
[Crossref]

1999 (1)

1998 (1)

C. Brenner, J. Boehm, and J. Guehring, “Photogrammetric calibration and accuracy evaluation of a cross-pattern stripe projector,” Proc. SPIE 3641, 164–172 (1998).
[Crossref]

1997 (1)

V. Kirschner, W. Schreiber, R. M. Kowarschik, and G. Notni, “Self-calibration shape-measuring system based on fringe projection,” Proc. SPIE 3102, 5–13 (1997).
[Crossref]

1994 (2)

G. Sansoni, L. Biancardi, U. Minoni, and F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43(4), 558–566 (1994).
[Crossref]

W. S. Zhou and X. Y. Su, “A direct mapping algorithem for phase-measuring profilometry,” J. Mod. Opt. 41(1), 89–94 (1994).
[Crossref]

1984 (1)

1983 (1)

Asundi, A.

Biancardi, L.

G. Sansoni, L. Biancardi, U. Minoni, and F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43(4), 558–566 (1994).
[Crossref]

Boehm, J.

C. Brenner, J. Boehm, and J. Guehring, “Photogrammetric calibration and accuracy evaluation of a cross-pattern stripe projector,” Proc. SPIE 3641, 164–172 (1998).
[Crossref]

Bothe, T.

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

T. Bothe, W. Osten, A. Gesierich, and W. P. O. Jueptner, “Compact 3D camera,” Proc. SPIE 4778, 48–59 (2002).
[Crossref]

Brauer-Burchardt, C.

P. Kuhmstedt, C. Munckelt, M. Heinze, C. Brauer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[Crossref]

Brenner, C.

C. Brenner, J. Boehm, and J. Guehring, “Photogrammetric calibration and accuracy evaluation of a cross-pattern stripe projector,” Proc. SPIE 3641, 164–172 (1998).
[Crossref]

Brèque, C.

I. Léandry, C. Brèque, and V. Vallea, “Calibration of a structured-light projection system: Development to large dimension objects,” Opt. Lasers Eng. 50(3), 373–379 (2012).
[Crossref]

Burton, D. R.

B. A. Rajoub, D. R. Burton, and M. J. Lalor, “A new phase-to-height model for measuring object shape using collimated projections of structured light,” J. Opt. A, Pure Appl. Opt. 7(6), S368–S375 (2005).
[Crossref]

Cao, Y.

Chen, H.

Chen, K.

Chen, R.

Chen, V.

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53(2), 024105 (2014).
[Crossref]

Chen, X.

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47(3–4), 310–319 (2009).
[Crossref]

Chua, P. S.

Cobelli, P.

Docchio, F.

G. Sansoni, L. Biancardi, U. Minoni, and F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43(4), 558–566 (1994).
[Crossref]

Du, H.

English, C.

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46(4), 043601 (2007).
[Crossref]

Gao, B. Z.

Gao, F.

Gesierich, A.

T. Bothe, W. Osten, A. Gesierich, and W. P. O. Jueptner, “Compact 3D camera,” Proc. SPIE 4778, 48–59 (2002).
[Crossref]

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Guan, C.

Guehring, J.

C. Brenner, J. Boehm, and J. Guehring, “Photogrammetric calibration and accuracy evaluation of a cross-pattern stripe projector,” Proc. SPIE 3641, 164–172 (1998).
[Crossref]

Guo, Q.

Guo, T.

Halioua, M.

Hao, Q.

Hassebrook, L. G.

He, D.

Heinze, M.

P. Kuhmstedt, C. Munckelt, M. Heinze, C. Brauer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[Crossref]

Hoke, M.

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53(2), 024105 (2014).
[Crossref]

Huang, J.

J. Huang and Q. Wu, “A new reconstruction method based on fringe projection of three-dimensional measuring system,” Opt. Lasers Eng. 52, 115–122 (2014).
[Crossref]

Huang, L.

Huang, P. S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

Huang, S.

Huang, Z.

Jia, P.

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46(4), 043601 (2007).
[Crossref]

Jiang, X.

Jin, Y.

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47(3–4), 310–319 (2009).
[Crossref]

Jueptner, W. P. O.

T. Bothe, W. Osten, A. Gesierich, and W. P. O. Jueptner, “Compact 3D camera,” Proc. SPIE 4778, 48–59 (2002).
[Crossref]

Jüptner, W. P.

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

Karpinsky, N.

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53(2), 024105 (2014).
[Crossref]

Kirschner, V.

V. Kirschner, W. Schreiber, R. M. Kowarschik, and G. Notni, “Self-calibration shape-measuring system based on fringe projection,” Proc. SPIE 3102, 5–13 (1997).
[Crossref]

Kofman, J.

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46(4), 043601 (2007).
[Crossref]

Körner, K.

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik (Stuttg.) 124(21), 5052–5056 (2013).
[Crossref]

Kowarschik, R. M.

V. Kirschner, W. Schreiber, R. M. Kowarschik, and G. Notni, “Self-calibration shape-measuring system based on fringe projection,” Proc. SPIE 3102, 5–13 (1997).
[Crossref]

Kuhmstedt, P.

P. Kuhmstedt, C. Munckelt, M. Heinze, C. Brauer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[Crossref]

Kujavinska, M.

R. Sitnik, M. Kujavinska, and J. Woznicki, “Digital fringe projection system for large-volume 360-deg shape measurement,” Opt. Eng. 41(2), 443–449 (2002).
[Crossref]

Lalor, M. J.

B. A. Rajoub, D. R. Burton, and M. J. Lalor, “A new phase-to-height model for measuring object shape using collimated projections of structured light,” J. Opt. A, Pure Appl. Opt. 7(6), S368–S375 (2005).
[Crossref]

Lau, D. L.

Léandry, I.

I. Léandry, C. Brèque, and V. Vallea, “Calibration of a structured-light projection system: Development to large dimension objects,” Opt. Lasers Eng. 50(3), 373–379 (2012).
[Crossref]

Legarda-Sáenz, R.

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

Li, A.

Li, J.

Li, Z.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Liu, H.

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

Liu, H. C.

Liu, K.

Liu, X.

Ma, H.

Maurel, A.

Meng, S.

Minoni, U.

G. Sansoni, L. Biancardi, U. Minoni, and F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43(4), 558–566 (1994).
[Crossref]

Munckelt, C.

P. Kuhmstedt, C. Munckelt, M. Heinze, C. Brauer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[Crossref]

Mutoh, K.

Niu, H.

X. Peng, Z. Yang, and H. Niu, “Multi-resolution reconstruction of 3-D image with modified temporal unwrapping algorithm,” Opt. Commun. 224(1–3), 35–44 (2003).
[Crossref]

Notni, G.

P. Kuhmstedt, C. Munckelt, M. Heinze, C. Brauer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[Crossref]

V. Kirschner, W. Schreiber, R. M. Kowarschik, and G. Notni, “Self-calibration shape-measuring system based on fringe projection,” Proc. SPIE 3102, 5–13 (1997).
[Crossref]

Osten, W.

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik (Stuttg.) 124(21), 5052–5056 (2013).
[Crossref]

T. Bothe, W. Osten, A. Gesierich, and W. P. O. Jueptner, “Compact 3D camera,” Proc. SPIE 4778, 48–59 (2002).
[Crossref]

Pagneux, V.

Peng, X.

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik (Stuttg.) 124(21), 5052–5056 (2013).
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X. Peng, Z. Yang, and H. Niu, “Multi-resolution reconstruction of 3-D image with modified temporal unwrapping algorithm,” Opt. Commun. 224(1–3), 35–44 (2003).
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Petitjeans, P.

Quiroga, J. A.

J. Vargas, J. A. Quiroga, and M. J. Terron-Lopez, “Flexible calibration procedure for fringe projection profilometry,” Opt. Eng. 46(2), 023601 (2007).
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Rajoub, B. A.

B. A. Rajoub, D. R. Burton, and M. J. Lalor, “A new phase-to-height model for measuring object shape using collimated projections of structured light,” J. Opt. A, Pure Appl. Opt. 7(6), S368–S375 (2005).
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S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
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Reichard, K.

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
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Royer, D.

Sansoni, G.

G. Sansoni, L. Biancardi, U. Minoni, and F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43(4), 558–566 (1994).
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V. Kirschner, W. Schreiber, R. M. Kowarschik, and G. Notni, “Self-calibration shape-measuring system based on fringe projection,” Proc. SPIE 3102, 5–13 (1997).
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Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
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R. Sitnik, M. Kujavinska, and J. Woznicki, “Digital fringe projection system for large-volume 360-deg shape measurement,” Opt. Eng. 41(2), 443–449 (2002).
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Song, L.

Srinivasan, V.

Su, J.

Su, W.-H.

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
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Su, X. Y.

W. S. Zhou and X. Y. Su, “A direct mapping algorithem for phase-measuring profilometry,” J. Mod. Opt. 41(1), 89–94 (1994).
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Sun, J.

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47(3–4), 310–319 (2009).
[Crossref]

Takeda, M.

Terron-Lopez, M. J.

J. Vargas, J. A. Quiroga, and M. J. Terron-Lopez, “Flexible calibration procedure for fringe projection profilometry,” Opt. Eng. 46(2), 023601 (2007).
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Towers, D. P.

Vallea, V.

I. Léandry, C. Brèque, and V. Vallea, “Calibration of a structured-light projection system: Development to large dimension objects,” Opt. Lasers Eng. 50(3), 373–379 (2012).
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Vargas, J.

J. Vargas, J. A. Quiroga, and M. J. Terron-Lopez, “Flexible calibration procedure for fringe projection profilometry,” Opt. Eng. 46(2), 023601 (2007).
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Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
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Woznicki, J.

R. Sitnik, M. Kujavinska, and J. Woznicki, “Digital fringe projection system for large-volume 360-deg shape measurement,” Opt. Eng. 41(2), 443–449 (2002).
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Wu, Q.

J. Huang and Q. Wu, “A new reconstruction method based on fringe projection of three-dimensional measuring system,” Opt. Lasers Eng. 52, 115–122 (2014).
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X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47(3–4), 310–319 (2009).
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Xiao, Y.

Xu, J.

Yang, Z.

X. Peng, Z. Yang, and H. Niu, “Multi-resolution reconstruction of 3-D image with modified temporal unwrapping algorithm,” Opt. Commun. 224(1–3), 35–44 (2003).
[Crossref]

Yau, S.-T.

Yin, S.

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

Yin, Y.

Yu, Y.

Zhang, D.

Z. Zhang, D. Zhang, and X. Peng, “Performance analysis of a 3D full-field sensor based on fringe projection,” Opt. Lasers Eng. 42(3), 341–353 (2004).
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Zhang, S.

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53(2), 024105 (2014).
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Z. Zhang, H. Ma, S. Zhang, T. Guo, C. E. Towers, and D. P. Towers, “Simple calibration of a phase-based 3D imaging system based on uneven fringe projection,” Opt. Lett. 36(5), 627–629 (2011).
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S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
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S. Zhang, D. Royer, and S.-T. Yau, “GPU-assisted high-resolution, real-time 3-D shape measurement,” Opt. Express 14(20), 9120–9129 (2006).
[Crossref] [PubMed]

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

Zhang, Z.

Zhao, Q.

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik (Stuttg.) 124(21), 5052–5056 (2013).
[Crossref]

Zhou, W. S.

W. S. Zhou and X. Y. Su, “A direct mapping algorithem for phase-measuring profilometry,” J. Mod. Opt. 41(1), 89–94 (1994).
[Crossref]

Appl. Opt. (7)

IEEE Trans. Instrum. Meas. (1)

G. Sansoni, L. Biancardi, U. Minoni, and F. Docchio, “A novel, adaptive system for 3-D optical profilometry using a liquid crystal light projector,” IEEE Trans. Instrum. Meas. 43(4), 558–566 (1994).
[Crossref]

J. Mod. Opt. (1)

W. S. Zhou and X. Y. Su, “A direct mapping algorithem for phase-measuring profilometry,” J. Mod. Opt. 41(1), 89–94 (1994).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

B. A. Rajoub, D. R. Burton, and M. J. Lalor, “A new phase-to-height model for measuring object shape using collimated projections of structured light,” J. Opt. A, Pure Appl. Opt. 7(6), S368–S375 (2005).
[Crossref]

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

Opt. Commun. (2)

H. Liu, W.-H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1–3), 65–80 (2003).
[Crossref]

X. Peng, Z. Yang, and H. Niu, “Multi-resolution reconstruction of 3-D image with modified temporal unwrapping algorithm,” Opt. Commun. 224(1–3), 35–44 (2003).
[Crossref]

Opt. Eng. (7)

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46(4), 043601 (2007).
[Crossref]

N. Karpinsky, M. Hoke, V. Chen, and S. Zhang, “High-resolution, real-time three-dimensional shape measurement on graphics processing unit,” Opt. Eng. 53(2), 024105 (2014).
[Crossref]

J. Vargas, J. A. Quiroga, and M. J. Terron-Lopez, “Flexible calibration procedure for fringe projection profilometry,” Opt. Eng. 46(2), 023601 (2007).
[Crossref]

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

R. Sitnik, M. Kujavinska, and J. Woznicki, “Digital fringe projection system for large-volume 360-deg shape measurement,” Opt. Eng. 41(2), 443–449 (2002).
[Crossref]

Opt. Express (4)

Opt. Lasers Eng. (6)

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47(3–4), 310–319 (2009).
[Crossref]

J. Huang and Q. Wu, “A new reconstruction method based on fringe projection of three-dimensional measuring system,” Opt. Lasers Eng. 52, 115–122 (2014).
[Crossref]

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

Z. Zhang, D. Zhang, and X. Peng, “Performance analysis of a 3D full-field sensor based on fringe projection,” Opt. Lasers Eng. 42(3), 341–353 (2004).
[Crossref]

I. Léandry, C. Brèque, and V. Vallea, “Calibration of a structured-light projection system: Development to large dimension objects,” Opt. Lasers Eng. 50(3), 373–379 (2012).
[Crossref]

Opt. Lett. (5)

Optik (Stuttg.) (1)

A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. Körner, and W. Osten, “Fringe projection based quantitative 3D microscopy,” Optik (Stuttg.) 124(21), 5052–5056 (2013).
[Crossref]

Proc. SPIE (4)

V. Kirschner, W. Schreiber, R. M. Kowarschik, and G. Notni, “Self-calibration shape-measuring system based on fringe projection,” Proc. SPIE 3102, 5–13 (1997).
[Crossref]

C. Brenner, J. Boehm, and J. Guehring, “Photogrammetric calibration and accuracy evaluation of a cross-pattern stripe projector,” Proc. SPIE 3641, 164–172 (1998).
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T. Bothe, W. Osten, A. Gesierich, and W. P. O. Jueptner, “Compact 3D camera,” Proc. SPIE 4778, 48–59 (2002).
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P. Kuhmstedt, C. Munckelt, M. Heinze, C. Brauer-Burchardt, and G. Notni, “3D shape measurement with phase correlation based fringe projection,” Proc. SPIE 6616, 66160B (2007).
[Crossref]

Supplementary Material (1)

NameDescription
» Visualization 1: MOV (264 KB)      A video of 3D imaging of a moving object

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of FPP system

Fig. 2
Fig. 2

Schematic diagram of the mapping in SV-based FPP system.

Fig. 3
Fig. 3

The overall flow chart of the P3DM method

Fig. 4
Fig. 4

Ray reprojection calibration: (a-b) the cross phase maps; (c) the homologous benchmarks on the camera and DMD image planes.

Fig. 5
Fig. 5

Ray reprojection at one of the calibrated positions: (a) visual diagram; (b) error distributions of the reconstructed 3D coordinates related to image coordinates.

Fig. 6
Fig. 6

Fit error curves related to an image point (240, 112) in sampling mapping calibration.

Fig. 7
Fig. 7

The result of 3D reconstruction of a standard sphere: (a) the image; (b-c) the 3D models: related to the P3DM method and the SV method, respectively.

Fig. 8
Fig. 8

The results of 3D reconstruction of three scenes: the second row is related to the P3DM method; the third row is related to the SV method.

Fig. 9
Fig. 9

The high-speed FPP system.

Fig. 10
Fig. 10

3D imaging of a moving object.

Tables (5)

Tables Icon

Table 1 System parameters of ray reprojection calibration.

Tables Icon

Table 2 Mapping coefficients related to an image point (240, 112).

Tables Icon

Table 3 MAX and RMS of fit errors related to different camera image points (mm)

Tables Icon

Table 4 MAX and RMS of point distance between the two 3D reconstructions.

Tables Icon

Table 5 Data related to the efficiency of 3D reconstruction.

Equations (17)

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

{ X c = R c X w + t c λ c x ˜ c =[ I|0 ] X ˜ c m ˜ c = K c x ˜ c , K c =( f u|c s c f u|c u 0|c 0 f v|c v 0|c 0 0 1 )
x c = x c Δ( x c ), Δ( x c )=( x c ( k 1 r 2 + k 2 r 4 + k 3 r 6 + )+[ 2 p 1 x c y c + p 2 ( r 2 +2 x c 2 ) ]( 1+ p 3 r 2 + ) y c ( k 1 r 2 + k 2 r 4 + k 3 r 6 + )+[ 2 p 2 x c y c + p 1 ( r 2 +2 y c 2 ) ]( 1+ p 3 r 2 + ) )
{ X c = R c X w + t c λ c x ˜ c =[ I|0 ] X ˜ c x c = x c Δ( x c ; k c ) m ˜ c = K c x ˜ c
{ R s = R p R c 1 t s = t p R p R c 1 t c
{ X c = R c X w + t c λ c x ˜ c =[ I|0 ] X ˜ c x c = x c Δ( x c ; k c ) m ˜ c = K c x ˜ c λ p x ˜ p =[ R s | t s ] X ˜ c x p = x p Δ( x p ; k p ) m ˜ p = K p x ˜ p
f u p L : ϕ c u p
f v p P : u p v p
x ˜ p = K p 1 m ˜ p
{ f x p L :( u p , v p ) x p f y p L :( u p , v p ) y p
{ f x p P :( x p , y p ) x p f y p P :( x p , y p ) y p
{ λ c x ˜ c =[ I|0 ] X ˜ c λ p x ˜ p =[ R s | t s ] X ˜ c
{ X c = t 1 x c t 3 x c x p ( r 31 x c + r 32 y c + r 33 ) x p ( r 11 x c + r 12 y c + r 13 ) Y c = t 1 y c t 3 y c x p ( r 31 x c + r 32 y c + r 33 ) x p ( r 11 x c + r 12 y c + r 13 ) Z c = t 1 t 3 x p ( r 31 x c + r 32 y c + r 33 ) x p ( r 11 x c + r 12 y c + r 13 )
X c = 1 f X L ( x p ) + c X , Y c = 1 f Y L ( x p ) + c Y , Z c = 1 f Z L ( x p ) + c Z
X c = 1 n=0 N a n ϕ c n + c X , Y c = 1 n=0 N b n ϕ c n + c Y , Z c = 1 n=0 N c n ϕ c n + c Z
arg τ min i=1 N j=1 M [ d ray ( X w j ; m ^ c ij , Θ c , Φ c i )+ d ray ( X w j ; m ^ p ij , Θ p , Φ s , Φ c i ) ]
arg τ min i=1 N j=1 M [ d ray ( X w j ; m ^ c ij , Θ c , Φ c i )+ d ray ( X w j ; m ^ p ij , Θ p , Φ s , Φ c i )+ d epi ( m ^ c ij , m ^ p ij , Θ c , Θ p , Φ s ) ]
1 X c = n=0 N a n ϕ c n , 1 Y c = n=0 N b n ϕ c n , 1 Z c = n=0 N c n ϕ c n

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