Abstract

Fringe projection systems encode the scanned object shape as a phase distribution according to the system parameters. However, to obtain the object shape in physical units of length, the demodulated phase must be converted to the coordinates of the observed points on the object surface. The design of a phase-to-coordinate conversion algorithm is straightforward when the following key concepts are considered: cameras and projectors as direction sensors, gratings as coordinate-encoding devices, absolute phase, and triangulation. In this paper, the theoretical principles of these concepts are formalized. Then, an efficient and generalized phase-to-coordinate conversion method, which supports systems with multiple cameras and projectors arranged arbitrarily, is proposed. The usefulness of this approach is illustrated by a 3D surface imaging experiment.

© 2019 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2019 (2)

L. Wang, Y. Chen, X. Han, Y. Fu, K. Zhong, and G. Jiang, “A 3D shape measurement method based on novel segmented quantization phase coding,” Opt. Laser Eng. 113, 62–70 (2019).
[Crossref]

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Flexible camera-projector calibration using superposed color checkerboards,” Opt. Laser Eng. 120, 59–65 (2019).
[Crossref]

2018 (8)

M. E. Deetjen and D. Lentink, “Automated calibration of multi-camera-projector structured light systems for volumetric high-speed 3D surface reconstructions,” Opt. Express 26, 33278–33304 (2018).
[Crossref]

S. Zhang, “High-speed 3D shape measurement with structured light methods: a review,” Opt. Laser Eng. 106, 119–131 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier transform profilometry (μftp): 3D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

H. Yue, Y. Yu, W. Chen, and X. Wu, “Accurate three dimensional body scanning system based on structured light,” Opt. Express 26, 28544–28559 (2018).
[Crossref]

S. Zhang, “Absolute phase retrieval methods for digital fringe projection profilometry: a review,” Opt. Laser Eng. 107, 28–37 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: a review,” Opt. Laser Eng. 109, 23–59 (2018).
[Crossref]

R. Juarez-Salazar, C. Mendoza-Rodriguez, J. E. Hernandez-Beltran, and C. Robledo-Sanchez, “How do phase-shifting algorithms work?” Eur. J. Phys. 39, 065302 (2018).
[Crossref]

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Homography estimation for camera document scanning applications,” Proc. SPIE 10751, 107510H (2018).
[Crossref]

2017 (2)

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Operator-based homogeneous coordinates: application in camera document scanning,” Opt. Eng. 56, 070801 (2017).
[Crossref]

R. Juarez-Salazar, V. H. Diaz-Ramirez, C. Robledo-Sanchez, and G. Diaz-Gonzalez, “On the use of video projectors for three-dimensional scanning,” Proc. SPIE 10395, 103950C (2017).
[Crossref]

2016 (2)

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

J. Lu, R. Mo, H. Sun, and Z. Chang, “Flexible calibration of phase-to-height conversion in fringe projection profilometry,” Appl. Opt. 55, 6381–6388 (2016).
[Crossref]

2015 (2)

2014 (2)

R. Juarez-Salazar, C. Robledo-Sanchez, and F. Guerrero-Sanchez, “Phase-unwrapping algorithm by a rounding-least-squares approach,” Opt. Eng. 53, 024102 (2014).
[Crossref]

H. Luo, J. Xu, N. H. Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Laser Eng. 57, 6–12 (2014).
[Crossref]

2012 (5)

J. Huang, Z. Wang, Q. Xue, and J. Gao, “Calibration of a camera-projector measurement system and error impact analysis,” Meas. Sci. Technol. 23, 125402 (2012).
[Crossref]

Y. Xiao, Y. Cao, and Y. Wu, “Improved algorithm for phase-to-height mapping in phase measuring profilometry,” Appl. Opt. 51, 1149–1155 (2012).
[Crossref]

J. Villa, M. Araiza, D. Alaniz, R. Ivanov, and M. Ortiz, “Transformation of phase to (x, y, z)-coordinates for the calibration of a fringe projection profilometer,” Opt. Laser Eng. 50, 256–261 (2012).
[Crossref]

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

Y. Yin, X. Peng, A. Li, X. Liu, and B. Z. Gao, “Calibration of fringe projection profilometry with bundle adjustment strategy,” Opt. Lett. 37, 542–544 (2012).
[Crossref]

2011 (1)

2010 (6)

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

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

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Laser Eng. 48, 141–148 (2010).
[Crossref]

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

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

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

2009 (3)

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, 380–392 (2009).
[Crossref]

S. Zhang, “Digital multiple wavelength phase shifting algorithm,” Proc. SPIE 7432, 74320N (2009).
[Crossref]

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

2007 (1)

A. Patil and P. Rastogi, “Moving ahead with phase,” Opt. Laser Eng. 45, 253–257 (2007).
[Crossref]

2006 (2)

2002 (1)

J. Burke, T. Bothe, W. Osten, and C. F. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[Crossref]

2000 (4)

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224–231 (2000).
[Crossref]

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[Crossref]

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body 3-D-measurement systems using fringe projection technique,” Opt. Eng. 39, 159–169 (2000).
[Crossref]

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[Crossref]

1983 (1)

Alaniz, D.

J. Villa, M. Araiza, D. Alaniz, R. Ivanov, and M. Ortiz, “Transformation of phase to (x, y, z)-coordinates for the calibration of a fringe projection profilometer,” Opt. Laser Eng. 50, 256–261 (2012).
[Crossref]

Araiza, M.

J. Villa, M. Araiza, D. Alaniz, R. Ivanov, and M. Ortiz, “Transformation of phase to (x, y, z)-coordinates for the calibration of a fringe projection profilometer,” Opt. Laser Eng. 50, 256–261 (2012).
[Crossref]

Asundi, A.

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier transform profilometry (μftp): 3D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

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

Asundi, A. K.

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Laser Eng. 48, 141–148 (2010).
[Crossref]

Barnes, J. C.

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

Binh, N. H.

H. Luo, J. Xu, N. H. Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Laser Eng. 57, 6–12 (2014).
[Crossref]

Bothe, T.

J. Burke, T. Bothe, W. Osten, and C. F. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[Crossref]

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[Crossref]

Burke, J.

J. Burke, T. Bothe, W. Osten, and C. F. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[Crossref]

Cao, Y.

Chang, Z.

Chen, F.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[Crossref]

Chen, K.

H. Luo, J. Xu, N. H. Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Laser Eng. 57, 6–12 (2014).
[Crossref]

Chen, Q.

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier transform profilometry (μftp): 3D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: a review,” Opt. Laser Eng. 109, 23–59 (2018).
[Crossref]

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

Chen, W.

H. Yue, Y. Yu, W. Chen, and X. Wu, “Accurate three dimensional body scanning system based on structured light,” Opt. Express 26, 28544–28559 (2018).
[Crossref]

C. Quan, W. Chen, and C. Tay, “Phase-retrieval techniques in fringe-projection profilometry,” Opt. Laser Eng. 48, 235–243 (2010).
[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. Laser Eng. 47, 310–319 (2009).
[Crossref]

Chen, Y.

L. Wang, Y. Chen, X. Han, Y. Fu, K. Zhong, and G. Jiang, “A 3D shape measurement method based on novel segmented quantization phase coding,” Opt. Laser Eng. 113, 62–70 (2019).
[Crossref]

Cobelli, P.

Deetjen, M. E.

Diaz-Gonzalez, G.

R. Juarez-Salazar, V. H. Diaz-Ramirez, C. Robledo-Sanchez, and G. Diaz-Gonzalez, “On the use of video projectors for three-dimensional scanning,” Proc. SPIE 10395, 103950C (2017).
[Crossref]

Diaz-Ramirez, V. H.

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Flexible camera-projector calibration using superposed color checkerboards,” Opt. Laser Eng. 120, 59–65 (2019).
[Crossref]

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Homography estimation for camera document scanning applications,” Proc. SPIE 10751, 107510H (2018).
[Crossref]

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Operator-based homogeneous coordinates: application in camera document scanning,” Opt. Eng. 56, 070801 (2017).
[Crossref]

R. Juarez-Salazar, V. H. Diaz-Ramirez, C. Robledo-Sanchez, and G. Diaz-Gonzalez, “On the use of video projectors for three-dimensional scanning,” Proc. SPIE 10395, 103950C (2017).
[Crossref]

Feng, S.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: a review,” Opt. Laser Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier transform profilometry (μftp): 3D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

Fu, Y.

L. Wang, Y. Chen, X. Han, Y. Fu, K. Zhong, and G. Jiang, “A 3D shape measurement method based on novel segmented quantization phase coding,” Opt. Laser Eng. 113, 62–70 (2019).
[Crossref]

Gao, B. Z.

Gao, J.

J. Huang, Z. Wang, Q. Xue, and J. Gao, “Calibration of a camera-projector measurement system and error impact analysis,” Meas. Sci. Technol. 23, 125402 (2012).
[Crossref]

Geng, J.

Gorthi, S. S.

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

Guerrero-Sanchez, F.

R. Juarez-Salazar, F. Guerrero-Sanchez, and C. Robledo-Sanchez, “Theory and algorithms of an efficient fringe analysis technology for automatic measurement applications,” Appl. Opt. 54, 5364–5374 (2015).
[Crossref]

R. Juarez-Salazar, C. Robledo-Sanchez, and F. Guerrero-Sanchez, “Phase-unwrapping algorithm by a rounding-least-squares approach,” Opt. Eng. 53, 024102 (2014).
[Crossref]

Han, X.

L. Wang, Y. Chen, X. Han, Y. Fu, K. Zhong, and G. Jiang, “A 3D shape measurement method based on novel segmented quantization phase coding,” Opt. Laser Eng. 113, 62–70 (2019).
[Crossref]

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2003).

Hernandez-Beltran, J. E.

R. Juarez-Salazar, C. Mendoza-Rodriguez, J. E. Hernandez-Beltran, and C. Robledo-Sanchez, “How do phase-shifting algorithms work?” Eur. J. Phys. 39, 065302 (2018).
[Crossref]

Hess, C. F.

J. Burke, T. Bothe, W. Osten, and C. F. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[Crossref]

Huang, J.

J. Huang, Z. Wang, Q. Xue, and J. Gao, “Calibration of a camera-projector measurement system and error impact analysis,” Meas. Sci. Technol. 23, 125402 (2012).
[Crossref]

Huang, L.

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier transform profilometry (μftp): 3D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: a review,” Opt. Laser Eng. 109, 23–59 (2018).
[Crossref]

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

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Laser Eng. 48, 141–148 (2010).
[Crossref]

Huang, P. S.

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

Ivanov, R.

J. Villa, M. Araiza, D. Alaniz, R. Ivanov, and M. Ortiz, “Transformation of phase to (x, y, z)-coordinates for the calibration of a fringe projection profilometer,” Opt. Laser Eng. 50, 256–261 (2012).
[Crossref]

Jiang, G.

L. Wang, Y. Chen, X. Han, Y. Fu, K. Zhong, and G. Jiang, “A 3D shape measurement method based on novel segmented quantization phase coding,” Opt. Laser Eng. 113, 62–70 (2019).
[Crossref]

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. Laser Eng. 47, 310–319 (2009).
[Crossref]

Juarez-Salazar, R.

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Flexible camera-projector calibration using superposed color checkerboards,” Opt. Laser Eng. 120, 59–65 (2019).
[Crossref]

R. Juarez-Salazar, C. Mendoza-Rodriguez, J. E. Hernandez-Beltran, and C. Robledo-Sanchez, “How do phase-shifting algorithms work?” Eur. J. Phys. 39, 065302 (2018).
[Crossref]

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Homography estimation for camera document scanning applications,” Proc. SPIE 10751, 107510H (2018).
[Crossref]

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Operator-based homogeneous coordinates: application in camera document scanning,” Opt. Eng. 56, 070801 (2017).
[Crossref]

R. Juarez-Salazar, V. H. Diaz-Ramirez, C. Robledo-Sanchez, and G. Diaz-Gonzalez, “On the use of video projectors for three-dimensional scanning,” Proc. SPIE 10395, 103950C (2017).
[Crossref]

R. Juarez-Salazar, F. Guerrero-Sanchez, and C. Robledo-Sanchez, “Theory and algorithms of an efficient fringe analysis technology for automatic measurement applications,” Appl. Opt. 54, 5364–5374 (2015).
[Crossref]

R. Juarez-Salazar, C. Robledo-Sanchez, and F. Guerrero-Sanchez, “Phase-unwrapping algorithm by a rounding-least-squares approach,” Opt. Eng. 53, 024102 (2014).
[Crossref]

Kemao, Q.

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Laser Eng. 48, 141–148 (2010).
[Crossref]

Lentink, D.

Li, A.

Liu, S.

H. Luo, J. Xu, N. H. Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Laser Eng. 57, 6–12 (2014).
[Crossref]

Liu, X.

Lu, J.

Luo, H.

H. Luo, J. Xu, N. H. Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Laser Eng. 57, 6–12 (2014).
[Crossref]

Maurel, A.

Mendoza-Rodriguez, C.

R. Juarez-Salazar, C. Mendoza-Rodriguez, J. E. Hernandez-Beltran, and C. Robledo-Sanchez, “How do phase-shifting algorithms work?” Eur. J. Phys. 39, 065302 (2018).
[Crossref]

Mo, R.

Mutoh, K.

Nguyen, D. A.

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

Notni, G.

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body 3-D-measurement systems using fringe projection technique,” Opt. Eng. 39, 159–169 (2000).
[Crossref]

Ortiz, M.

J. Villa, M. Araiza, D. Alaniz, R. Ivanov, and M. Ortiz, “Transformation of phase to (x, y, z)-coordinates for the calibration of a fringe projection profilometer,” Opt. Laser Eng. 50, 256–261 (2012).
[Crossref]

Osten, W.

J. Burke, T. Bothe, W. Osten, and C. F. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[Crossref]

Pagneux, V.

Pan, B.

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Laser Eng. 48, 141–148 (2010).
[Crossref]

Patil, A.

A. Patil and P. Rastogi, “Moving ahead with phase,” Opt. Laser Eng. 45, 253–257 (2007).
[Crossref]

Peng, X.

Petitjeans, P.

Quan, C.

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

Rastogi, P.

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

A. Patil and P. Rastogi, “Moving ahead with phase,” Opt. Laser Eng. 45, 253–257 (2007).
[Crossref]

Reich, C.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224–231 (2000).
[Crossref]

Ritter, R.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224–231 (2000).
[Crossref]

Robledo-Sanchez, C.

R. Juarez-Salazar, C. Mendoza-Rodriguez, J. E. Hernandez-Beltran, and C. Robledo-Sanchez, “How do phase-shifting algorithms work?” Eur. J. Phys. 39, 065302 (2018).
[Crossref]

R. Juarez-Salazar, V. H. Diaz-Ramirez, C. Robledo-Sanchez, and G. Diaz-Gonzalez, “On the use of video projectors for three-dimensional scanning,” Proc. SPIE 10395, 103950C (2017).
[Crossref]

R. Juarez-Salazar, F. Guerrero-Sanchez, and C. Robledo-Sanchez, “Theory and algorithms of an efficient fringe analysis technology for automatic measurement applications,” Appl. Opt. 54, 5364–5374 (2015).
[Crossref]

R. Juarez-Salazar, C. Robledo-Sanchez, and F. Guerrero-Sanchez, “Phase-unwrapping algorithm by a rounding-least-squares approach,” Opt. Eng. 53, 024102 (2014).
[Crossref]

Schreiber, W.

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body 3-D-measurement systems using fringe projection technique,” Opt. Eng. 39, 159–169 (2000).
[Crossref]

Song, M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[Crossref]

Su, X.

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

Sun, H.

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. Laser Eng. 47, 310–319 (2009).
[Crossref]

Takeda, M.

Tao, T.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: a review,” Opt. Laser Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier transform profilometry (μftp): 3D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

Tay, C.

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

Thesing, J.

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224–231 (2000).
[Crossref]

Villa, J.

J. Villa, M. Araiza, D. Alaniz, R. Ivanov, and M. Ortiz, “Transformation of phase to (x, y, z)-coordinates for the calibration of a fringe projection profilometer,” Opt. Laser Eng. 50, 256–261 (2012).
[Crossref]

Wang, L.

L. Wang, Y. Chen, X. Han, Y. Fu, K. Zhong, and G. Jiang, “A 3D shape measurement method based on novel segmented quantization phase coding,” Opt. Laser Eng. 113, 62–70 (2019).
[Crossref]

Wang, Z.

J. Huang, Z. Wang, Q. Xue, and J. Gao, “Calibration of a camera-projector measurement system and error impact analysis,” Meas. Sci. Technol. 23, 125402 (2012).
[Crossref]

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

Wu, X.

Wu, Y.

Xi, J.

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

Xiao, Y.

Xu, J.

H. Luo, J. Xu, N. H. Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Laser Eng. 57, 6–12 (2014).
[Crossref]

Xue, Q.

J. Huang, Z. Wang, Q. Xue, and J. Gao, “Calibration of a camera-projector measurement system and error impact analysis,” Meas. Sci. Technol. 23, 125402 (2012).
[Crossref]

Yau, S.-T.

Yin, W.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: a review,” Opt. Laser Eng. 109, 23–59 (2018).
[Crossref]

Yin, Y.

Yu, Y.

Yue, H.

Zhang, C.

H. Luo, J. Xu, N. H. Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Laser Eng. 57, 6–12 (2014).
[Crossref]

Zhang, M.

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

Zhang, Q.

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

Zhang, S.

S. Zhang, “High-speed 3D shape measurement with structured light methods: a review,” Opt. Laser Eng. 106, 119–131 (2018).
[Crossref]

S. Zhang, “Absolute phase retrieval methods for digital fringe projection profilometry: a review,” Opt. Laser Eng. 107, 28–37 (2018).
[Crossref]

S. Zhang, “Comparative study on passive and active projector nonlinear gamma calibration,” Appl. Opt. 54, 3834–3841 (2015).
[Crossref]

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

S. Zhang, “Digital multiple wavelength phase shifting algorithm,” Proc. SPIE 7432, 74320N (2009).
[Crossref]

S. Zhang and S.-T. Yau, “High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method,” Opt. Express 14, 2644–2649 (2006).
[Crossref]

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

Zhang, Z.

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

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[Crossref]

Zhong, K.

L. Wang, Y. Chen, X. Han, Y. Fu, K. Zhong, and G. Jiang, “A 3D shape measurement method based on novel segmented quantization phase coding,” Opt. Laser Eng. 113, 62–70 (2019).
[Crossref]

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2003).

Zuo, C.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: a review,” Opt. Laser Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier transform profilometry (μftp): 3D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

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

Adv. Opt. Photon. (1)

Appl. Opt. (6)

Eur. J. Phys. (1)

R. Juarez-Salazar, C. Mendoza-Rodriguez, J. E. Hernandez-Beltran, and C. Robledo-Sanchez, “How do phase-shifting algorithms work?” Eur. J. Phys. 39, 065302 (2018).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[Crossref]

Meas. Sci. Technol. (1)

J. Huang, Z. Wang, Q. Xue, and J. Gao, “Calibration of a camera-projector measurement system and error impact analysis,” Meas. Sci. Technol. 23, 125402 (2012).
[Crossref]

Opt. Eng. (6)

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Operator-based homogeneous coordinates: application in camera document scanning,” Opt. Eng. 56, 070801 (2017).
[Crossref]

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

W. Schreiber and G. Notni, “Theory and arrangements of self-calibrating whole-body 3-D-measurement systems using fringe projection technique,” Opt. Eng. 39, 159–169 (2000).
[Crossref]

C. Reich, R. Ritter, and J. Thesing, “3-D shape measurement of complex objects by combining photogrammetry and fringe projection,” Opt. Eng. 39, 224–231 (2000).
[Crossref]

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[Crossref]

R. Juarez-Salazar, C. Robledo-Sanchez, and F. Guerrero-Sanchez, “Phase-unwrapping algorithm by a rounding-least-squares approach,” Opt. Eng. 53, 024102 (2014).
[Crossref]

Opt. Express (3)

Opt. Laser Eng. (18)

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

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Flexible camera-projector calibration using superposed color checkerboards,” Opt. Laser Eng. 120, 59–65 (2019).
[Crossref]

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

H. Luo, J. Xu, N. H. Binh, S. Liu, C. Zhang, and K. Chen, “A simple calibration procedure for structured light system,” Opt. Laser Eng. 57, 6–12 (2014).
[Crossref]

J. Villa, M. Araiza, D. Alaniz, R. Ivanov, and M. Ortiz, “Transformation of phase to (x, y, z)-coordinates for the calibration of a fringe projection profilometer,” Opt. Laser Eng. 50, 256–261 (2012).
[Crossref]

A. Patil and P. Rastogi, “Moving ahead with phase,” Opt. Laser Eng. 45, 253–257 (2007).
[Crossref]

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

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: a review,” Opt. Laser Eng. 109, 23–59 (2018).
[Crossref]

L. Wang, Y. Chen, X. Han, Y. Fu, K. Zhong, and G. Jiang, “A 3D shape measurement method based on novel segmented quantization phase coding,” Opt. Laser Eng. 113, 62–70 (2019).
[Crossref]

S. Zhang, “Absolute phase retrieval methods for digital fringe projection profilometry: a review,” Opt. Laser Eng. 107, 28–37 (2018).
[Crossref]

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

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Laser Eng. 48, 141–148 (2010).
[Crossref]

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

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

S. Zhang, “High-speed 3D shape measurement with structured light methods: a review,” Opt. Laser Eng. 106, 119–131 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier transform profilometry (μftp): 3D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

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

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

Opt. Lett. (1)

Proc. SPIE (4)

J. Burke, T. Bothe, W. Osten, and C. F. Hess, “Reverse engineering by fringe projection,” Proc. SPIE 4778, 312–324 (2002).
[Crossref]

R. Juarez-Salazar, V. H. Diaz-Ramirez, C. Robledo-Sanchez, and G. Diaz-Gonzalez, “On the use of video projectors for three-dimensional scanning,” Proc. SPIE 10395, 103950C (2017).
[Crossref]

S. Zhang, “Digital multiple wavelength phase shifting algorithm,” Proc. SPIE 7432, 74320N (2009).
[Crossref]

R. Juarez-Salazar and V. H. Diaz-Ramirez, “Homography estimation for camera document scanning applications,” Proc. SPIE 10751, 107510H (2018).
[Crossref]

Other (1)

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2003).

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Figures (6)

Fig. 1.
Fig. 1. Calibrated cameras and projectors can be considered direction sensors.
Fig. 2.
Fig. 2. Orthogonal projection ξ of a point ξ in a line with point t and direction d .
Fig. 3.
Fig. 3. Depiction of the fringe projection system used for evaluation of the proposed phase-to-coordinate conversion method.
Fig. 4.
Fig. 4. (a) Gratings used in the experiment. (b) Captured phase-shifted fringe patterns. (c) Extracted wrapped phase.
Fig. 5.
Fig. 5. Absolute phases ϕ x and ϕ y obtained by processing the wrapped phase maps shown in Fig. 4(c).
Fig. 6.
Fig. 6. Result of the 3D scanning experiment.

Equations (37)

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

μ = H 1 [ K c L c H [ p ] ] ,
L c = [ R c T , R c T t c ] ,
λ c K c 1 H [ μ ] = L c H [ p ] = R c T ( p t c ) ,
p = t c + λ c d c ,
d c = R c K c 1 H [ μ ] .
p = t s + λ s d s ,
d s = R s K s 1 H [ ν ] .
G x ( ν ) = 1 2 + 1 2 cos ( 2 π f x ν x + δ x ) ,
G y ( ν ) = 1 2 + 1 2 cos ( 2 π f y ν y + δ y ) ,
G ˜ x = G x 1 / γ , and G ˜ y = G x 1 / γ ,
0 < f 1 1 ,
ψ 1 ( μ ) = ϕ 1 ( μ ) ,
ψ 2 ( μ ) = ϕ 2 ( μ ) 2 π h 2 ( μ ) ,
f 2 = α 1 f 1 , α > 1 ,
ϕ 2 ( μ ) = α 1 ϕ 1 ( μ ) .
h 2 ( μ ) = round ( α 1 ϕ 1 ( μ ) ψ 2 ( μ ) 2 π ) ,
ϕ 2 ( μ ) = ψ 2 ( μ ) + 2 π h 2 ( μ ) .
f k = α k 1 f k 1
h k ( μ ) = round ( α k 1 ϕ k 1 ( μ ) ψ k ( μ ) 2 π ) , ϕ k ( μ ) = ψ k ( μ ) + 2 π h k ( μ ) .
ν x ( μ ) = ϕ n , x ( μ ) 2 π f x k = 1 n 1 α k , x .
ν ( μ ) = 1 2 π [ ϕ n , x ( μ ) / f x k = 1 n 1 α k , x ϕ n , y ( μ ) / f y k = 1 n 1 α k , y ] .
f 1 = 1 , and f n = S / w ,
α 1 = α 2 = = α n 1 = α .
f k = α k 1 .
α = f n 1 / ( n 1 ) .
= t + λ d .
ξ = t + ( d T ( ξ t ) d ) d d = t + d d T d T d ( ξ t ) ,
r = ξ ξ = D ( ξ t ) ,
D = I 3 d d T d T d ,
r 2 = ξ T D ξ + t T D t 2 ξ T D t .
J ( ξ ) = k = 1 n ( ξ T D k ξ + t k T D k t k 2 ξ T D k t k ) ,
p J ( p ) = k = 1 n ( 2 D k p 2 D k t k ) = 0 3 ,
p = ( k = 1 n D k ) 1 ( k = 1 n D k t k ) .
p = ( D c + D s ) 1 ( D c t c + D s t s ) .
K c = [ 8.0504 0 0.0976 0 8.0256 0.0472 0 0 1 ] , R c = [ 0.8858 0.1302 0.4454 0.1573 0.9872 0.0242 0.4366 0.0915 0.8950 ] , t c = [ 317.4 48.5 648.7 ] ,
K s = [ 6.4090 0 0.0018 0 6.5156 1.4356 0 0 1 ] , R s = [ 0.9998 0.0026 0.0183 0.0022 0.9998 0.0214 0.0184 0.0213 0.9996 ] , t s = [ 7.2 126.2 407.1 ] .
α 1 , x = = α 4 , x = 3.1811 , α 1 , y = = α 4 , y = 2.9603 .

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