Abstract

The measuring technique combining a phase-shifting algorithm and Gray-code light has been widely used in three-dimensional (3D) shape measurement for static scenes because of its high robustness and anti-noise ability. However, in the high-speed measurement, phase unwrapping errors occur easily on the boundaries of adjacent Gray-code words because of the defocus of the projector, the motion of the objects and the non-uniform reflectivity of the surface. To overcome this challenge, a high-speed 3D shape measurement method based on shifting Gray-code light has been proposed in this paper. Firstly, the average intensity of three captured phase-shifting fringe images are used as a pixel-wise threshold to binarize the Gray codes and to eliminate most phase unwrapping errors caused by the non-uniform reflectivity, ambient light variations, and the defocus of projector. Then, the shifting Gray-code (SGC) coding strategy is proposed to avoid the remaining errors of phase unwrapping on the edge of the code words. In this strategy, no additional patterns are projected, and two sets of decoding words with staggered boundaries are built in the temporal sequences for one wrapped phase. Finally, the simple, efficient, and robust phase unwrapping can be achieved in the high-speed dynamic measurement. This proposed method has been applied to reconstruct 3D shape of randomly collapsing objects in a large depth range, and the experimental results demonstrate that it can reliably obtain high-quality shape and texture information at 310 frames per second.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

Z. Wu, C. Zuo, W. Guo, T. Tao, and Q. Zhang, “High-speed three-dimensional shape measurement based on cyclic complementary Gray-code light,” Opt. Express 27(2), 1283–1297 (2019).
[Crossref] [PubMed]

2018 (2)

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. Lasers Eng. 102, 70–91 (2018).
[Crossref]

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

2017 (1)

2016 (4)

S. Van der Jeught and J. J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. 87, 18–31 (2016).
[Crossref]

C. Zuo, L. Huang, M. 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]

D. Zheng, F. Da, and H. Huang, “Phase unwrapping for fringe projection three-dimensional measurement with projector defocusing,” Opt. Eng. 55(3), 034107 (2016).
[Crossref]

Z. Zeng, Y. Fu, B. Li, and M. Chai, “Complex surface three-dimensional shape measurement method based on defocused gray code plus phase-shifting,” Opt. Rev. 23(4), 628–636 (2016).
[Crossref]

2013 (2)

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

Y. Wang, J. I. Laughner, I. R. Efimov, and S. Zhang, “3D absolute shape measurement of live rabbit hearts with a superfast two-frequency phase-shifting technique,” Opt. Express 21(5), 5822–5832 (2013).
[Crossref] [PubMed]

2012 (3)

2011 (2)

2010 (1)

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

2009 (1)

2007 (1)

K. R. Ford, G. D. Myer, and T. E. Hewett, “Reliability of landing 3D motion analysis: implications for longitudinal analyses,” Med. Sci. Sports Exerc. 39(11), 2021–2028 (2007).
[Crossref] [PubMed]

2005 (2)

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44(11), 113601 (2005).
[Crossref]

Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13(8), 3110–3116 (2005).
[Crossref] [PubMed]

2003 (1)

E. Malamas, E. Petrakis, M. Zervakis, L. Petit, and J. Legat, “A survey on industrial vision systems, applications and tools,” Image Vis. Comput. 21(2), 171–188 (2003).
[Crossref]

2002 (1)

Q. Zhang and X. Su, “An optical measurement of vortex shape at a free surface,” Opt. Laser Technol. 34(2), 107–113 (2002).
[Crossref]

2001 (2)

2000 (2)

Z. Zhang, “A Flexible New Technique for Camera Calibration,” IEEE T. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

1999 (2)

1997 (2)

1993 (1)

1991 (1)

V. Gushov and Y. Solodkin, “Automatic processing of fringe patterns in integer interferometers,” Opt. Lasers Eng. 14(4–5), 311–324 (1991).
[Crossref]

1988 (1)

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–393 (1988).
[Crossref]

1985 (1)

1984 (1)

1983 (1)

1982 (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Rev. Sci. Instrum. 72(12), 156–160 (1982).

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. Lasers 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. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

Cao, Y.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44(11), 113601 (2005).
[Crossref]

Carocci, M.

Chai, M.

Z. Zeng, Y. Fu, B. Li, and M. Chai, “Complex surface three-dimensional shape measurement method based on defocused gray code plus phase-shifting,” Opt. Rev. 23(4), 628–636 (2016).
[Crossref]

Chen, F.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

Chen, Q.

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[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. Lasers 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. Lasers Eng. 85, 84–103 (2016).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
[Crossref] [PubMed]

Chen, W.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44(11), 113601 (2005).
[Crossref]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

Cheng, Y. Y.

Corini, S.

Creath, K.

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–393 (1988).
[Crossref]

Da, F.

D. Zheng, F. Da, Q. Kemao, and H. S. Seah, “Phase-shifting profilometry combined with Gray-code patterns projection: unwrapping error removal by an adaptive median filter,” Opt. Express 25(5), 4700–4713 (2017).
[Crossref] [PubMed]

D. Zheng, F. Da, and H. Huang, “Phase unwrapping for fringe projection three-dimensional measurement with projector defocusing,” Opt. Eng. 55(3), 034107 (2016).
[Crossref]

Dirckx, J. J. J.

S. Van der Jeught and J. J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. 87, 18–31 (2016).
[Crossref]

Docchio, F.

Efimov, I. R.

Y. Wang, J. I. Laughner, I. R. Efimov, and S. Zhang, “3D absolute shape measurement of live rabbit hearts with a superfast two-frequency phase-shifting technique,” Opt. Express 21(5), 5822–5832 (2013).
[Crossref] [PubMed]

J. I. Laughner, S. Zhang, H. Li, C. C. Shao, and I. R. Efimov, “Mapping cardiac surface mechanics with structured light imaging,” Am. J. Physiol. Heart Circ. Physiol. 303(6), H712–H720 (2012).
[PubMed]

Feng, F.

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
[Crossref] [PubMed]

Feng, S.

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[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. Lasers Eng. 102, 70–91 (2018).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
[Crossref] [PubMed]

Ford, K. R.

K. R. Ford, G. D. Myer, and T. E. Hewett, “Reliability of landing 3D motion analysis: implications for longitudinal analyses,” Med. Sci. Sports Exerc. 39(11), 2021–2028 (2007).
[Crossref] [PubMed]

Fu, Y.

Z. Zeng, Y. Fu, B. Li, and M. Chai, “Complex surface three-dimensional shape measurement method based on defocused gray code plus phase-shifting,” Opt. Rev. 23(4), 628–636 (2016).
[Crossref]

Gu, G.

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
[Crossref] [PubMed]

Guo, W.

Gushov, V.

V. Gushov and Y. Solodkin, “Automatic processing of fringe patterns in integer interferometers,” Opt. Lasers Eng. 14(4–5), 311–324 (1991).
[Crossref]

Hewett, T. E.

K. R. Ford, G. D. Myer, and T. E. Hewett, “Reliability of landing 3D motion analysis: implications for longitudinal analyses,” Med. Sci. Sports Exerc. 39(11), 2021–2028 (2007).
[Crossref] [PubMed]

Hu, Y.

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

Huang, H.

D. Zheng, F. Da, and H. Huang, “Phase unwrapping for fringe projection three-dimensional measurement with projector defocusing,” Opt. Eng. 55(3), 034107 (2016).
[Crossref]

Huang, L.

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[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. Lasers 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. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Huntley, J. M.

Ina, H.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Rev. Sci. Instrum. 72(12), 156–160 (1982).

Kemao, Q.

Kobayashi, S.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Rev. Sci. Instrum. 72(12), 156–160 (1982).

Laughner, J. I.

Y. Wang, J. I. Laughner, I. R. Efimov, and S. Zhang, “3D absolute shape measurement of live rabbit hearts with a superfast two-frequency phase-shifting technique,” Opt. Express 21(5), 5822–5832 (2013).
[Crossref] [PubMed]

J. I. Laughner, S. Zhang, H. Li, C. C. Shao, and I. R. Efimov, “Mapping cardiac surface mechanics with structured light imaging,” Am. J. Physiol. Heart Circ. Physiol. 303(6), H712–H720 (2012).
[PubMed]

Lazzari, S.

Legat, J.

E. Malamas, E. Petrakis, M. Zervakis, L. Petit, and J. Legat, “A survey on industrial vision systems, applications and tools,” Image Vis. Comput. 21(2), 171–188 (2003).
[Crossref]

Lei, S.

Li, B.

Z. Zeng, Y. Fu, B. Li, and M. Chai, “Complex surface three-dimensional shape measurement method based on defocused gray code plus phase-shifting,” Opt. Rev. 23(4), 628–636 (2016).
[Crossref]

Li, H.

J. I. Laughner, S. Zhang, H. Li, C. C. Shao, and I. R. Efimov, “Mapping cardiac surface mechanics with structured light imaging,” Am. J. Physiol. Heart Circ. Physiol. 303(6), H712–H720 (2012).
[PubMed]

Li, R.

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

Li, W.

Li, Y.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44(11), 113601 (2005).
[Crossref]

Liu, Z.

Ma, J.

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

Malamas, E.

E. Malamas, E. Petrakis, M. Zervakis, L. Petit, and J. Legat, “A survey on industrial vision systems, applications and tools,” Image Vis. Comput. 21(2), 171–188 (2003).
[Crossref]

Mutoh, K.

Myer, G. D.

K. R. Ford, G. D. Myer, and T. E. Hewett, “Reliability of landing 3D motion analysis: implications for longitudinal analyses,” Med. Sci. Sports Exerc. 39(11), 2021–2028 (2007).
[Crossref] [PubMed]

Oliver, J. H.

Petit, L.

E. Malamas, E. Petrakis, M. Zervakis, L. Petit, and J. Legat, “A survey on industrial vision systems, applications and tools,” Image Vis. Comput. 21(2), 171–188 (2003).
[Crossref]

Petrakis, E.

E. Malamas, E. Petrakis, M. Zervakis, L. Petit, and J. Legat, “A survey on industrial vision systems, applications and tools,” Image Vis. Comput. 21(2), 171–188 (2003).
[Crossref]

Rodella, R.

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C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

Solodkin, Y.

V. Gushov and Y. Solodkin, “Automatic processing of fringe patterns in integer interferometers,” Opt. Lasers Eng. 14(4–5), 311–324 (1991).
[Crossref]

Song, M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

Su, X.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44(11), 113601 (2005).
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Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13(8), 3110–3116 (2005).
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Q. Zhang and X. Su, “An optical measurement of vortex shape at a free surface,” Opt. Laser Technol. 34(2), 107–113 (2002).
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X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

W. Li, X. Su, and Z. Liu, “Large-scale three-dimensional object measurement: a practical coordinate mapping and image data-patching method,” Appl. Opt. 40(20), 3326–3333 (2001).
[Crossref] [PubMed]

Takeda, M.

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
[Crossref] [PubMed]

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Rev. Sci. Instrum. 72(12), 156–160 (1982).

Tao, T.

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
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Z. Wu, C. Zuo, W. Guo, T. Tao, and Q. Zhang, “High-speed three-dimensional shape measurement based on cyclic complementary Gray-code light,” Opt. Express 27(2), 1283–1297 (2019).
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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. Lasers Eng. 102, 70–91 (2018).
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Wyant, J. C.

Xiang, L.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44(11), 113601 (2005).
[Crossref]

Yin, W.

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

Zeng, Z.

Z. Zeng, Y. Fu, B. Li, and M. Chai, “Complex surface three-dimensional shape measurement method based on defocused gray code plus phase-shifting,” Opt. Rev. 23(4), 628–636 (2016).
[Crossref]

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E. Malamas, E. Petrakis, M. Zervakis, L. Petit, and J. Legat, “A survey on industrial vision systems, applications and tools,” Image Vis. Comput. 21(2), 171–188 (2003).
[Crossref]

Zhang, M.

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[Crossref]

Zhang, Q.

Z. Wu, C. Zuo, W. Guo, T. Tao, and Q. Zhang, “High-speed three-dimensional shape measurement based on cyclic complementary Gray-code light,” Opt. Express 27(2), 1283–1297 (2019).
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Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13(8), 3110–3116 (2005).
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Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44(11), 113601 (2005).
[Crossref]

Q. Zhang and X. Su, “An optical measurement of vortex shape at a free surface,” Opt. Laser Technol. 34(2), 107–113 (2002).
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J. Zhong and M. Wang, “Phase unwrapping by a lookup table method: application to phase maps with singular points,” Opt. Eng. 38(12), 2075–2080 (1999).
[Crossref]

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W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

Z. Wu, C. Zuo, W. Guo, T. Tao, and Q. Zhang, “High-speed three-dimensional shape measurement based on cyclic complementary Gray-code light,” Opt. Express 27(2), 1283–1297 (2019).
[Crossref] [PubMed]

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. Lasers 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. Lasers Eng. 85, 84–103 (2016).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
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C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
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Am. J. Physiol. Heart Circ. Physiol. (1)

J. I. Laughner, S. Zhang, H. Li, C. C. Shao, and I. R. Efimov, “Mapping cardiac surface mechanics with structured light imaging,” Am. J. Physiol. Heart Circ. Physiol. 303(6), H712–H720 (2012).
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M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
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J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32(17), 3047–3052 (1993).
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H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36(13), 2770–2775 (1997).
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G. Sansoni, M. Carocci, and R. Rodella, “Three-dimensional vision based on a combination of gray-code and phase-shift light projection: analysis and compensation of the systematic errors,” Appl. Opt. 38(31), 6565–6573 (1999).
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IEEE T. Pattern Anal. Mach. Intell. (1)

Z. Zhang, “A Flexible New Technique for Camera Calibration,” IEEE T. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Image Vis. Comput. (1)

E. Malamas, E. Petrakis, M. Zervakis, L. Petit, and J. Legat, “A survey on industrial vision systems, applications and tools,” Image Vis. Comput. 21(2), 171–188 (2003).
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K. R. Ford, G. D. Myer, and T. E. Hewett, “Reliability of landing 3D motion analysis: implications for longitudinal analyses,” Med. Sci. Sports Exerc. 39(11), 2021–2028 (2007).
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Opt. Eng. (4)

J. Zhong and M. Wang, “Phase unwrapping by a lookup table method: application to phase maps with singular points,” Opt. Eng. 38(12), 2075–2080 (1999).
[Crossref]

D. Zheng, F. Da, and H. Huang, “Phase unwrapping for fringe projection three-dimensional measurement with projector defocusing,” Opt. Eng. 55(3), 034107 (2016).
[Crossref]

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000).
[Crossref]

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44(11), 113601 (2005).
[Crossref]

Opt. Express (7)

Opt. Laser Technol. (1)

Q. Zhang and X. Su, “An optical measurement of vortex shape at a free surface,” Opt. Laser Technol. 34(2), 107–113 (2002).
[Crossref]

Opt. Lasers Eng. (9)

C. Zuo, L. Huang, M. 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]

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

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, “High-speed 3D shape measurement with structured light methods: A review,” Opt. Lasers Eng. 106, 119–131 (2018).
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S. Van der Jeught and J. J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. 87, 18–31 (2016).
[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. Lasers Eng. 102, 70–91 (2018).
[Crossref]

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[Crossref]

Opt. Lett. (1)

Opt. Rev. (1)

Z. Zeng, Y. Fu, B. Li, and M. Chai, “Complex surface three-dimensional shape measurement method based on defocused gray code plus phase-shifting,” Opt. Rev. 23(4), 628–636 (2016).
[Crossref]

Prog. Opt. (1)

K. Creath, “Phase-Measurement Interferometry Techniques,” Prog. Opt. 26, 349–393 (1988).
[Crossref]

Rev. Sci. Instrum. (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” Rev. Sci. Instrum. 72(12), 156–160 (1982).

Supplementary Material (3)

NameDescription
» Visualization 1       Projecting sequences of cyclic complementary Gray-code method and shifting Gray-code method.
» Visualization 2       Comparative experiments on a large measuring depth range.
» Visualization 3       Measuring results on the dynamic process of collapsing building blocks.

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Figures (11)

Fig. 1
Fig. 1 Sketch map of the coding strategy of SGC patterns. (a)-(c) Phase-shifting dithered patterns in pattern sequence n. (d)-(g) Gray-code patterns in pattern sequence n. (h) Wrapped phase in pattern sequence n. (i)-(p) Corresponding patterns in pattern sequence n + 1.
Fig. 2
Fig. 2 Simulation on the reliable pixel-wise threshold.
Fig. 3
Fig. 3 Captured images for the reliable pixel-wise threshold. (a)-(c) Phase-shifting dithered patterns. (d) One of the defocused Gray-code patterns. (e) The reversed Gray-code pattern of (d). (f) The average intensity of sinusoidal patterns. (g) The average intensity of two Gray-code patterns. (h) The cross sections of (f) and (g) along the marked line.
Fig. 4
Fig. 4 Decoding process of Gray codes in the even pattern sequence.
Fig. 5
Fig. 5 Correction of the decoding numbers (the used parts of the phase orders are labeled in yellow).
Fig. 6
Fig. 6 Overview of the SGC method. (a) Processing flow. (b) Projected sequences in the SGC method.
Fig. 7
Fig. 7 Accuracy analysis of the SGC method. (a) Test scene consisting of a standard ceramic ball and a standard flat. (b) Reconstructed result. (c) Error distribution of the standard flat in the dashed box. (d) Fitting sphere of the standard ball. (e) Error distribution of the standard ball.
Fig. 8
Fig. 8 Measurement of the complex static scenes. (a) One captured sinusoidal image of the scene I including a portrait sculpture with a cooling fan. (b) One captured sinusoidal image of the scene II including a portrait sculpture with a petaloid model. (c) Reconstructed result of the scene I. (d) Reconstructed result of the scene II.
Fig. 9
Fig. 9 Comparative experiments on a large measuring depth range. (a) Reconstructed results by the CCGC method. (b) Reconstructed results by the proposed SGC method (Visualization 2).
Fig. 10
Fig. 10 Measurement on the complex dynamic scene. (a)-(h) Representative collapsing scenes and corresponding 3D reconstructions at different moments (Visualization 3).
Fig. 11
Fig. 11 Measuring results and error rates of three methods. (a) The traditional Gray-code-based method using a unique threshold. (b) The traditional Gray-code-based method using a pixel-wise threshold. (c) The SGC method.

Equations (11)

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I 1 (x,y,n)=A(x,y,n)+B(x,y,n)cos[ϕ(x,y,n)2π/3]
I 2 (x,y,n)=A(x,y,n)+B(x,y,n)cos[ϕ(x,y,n)]
I 3 (x,y,n)=A(x,y,n)+B(x,y,n)cos[ϕ(x,y,n)+2π/3]
ϕ(x,y,n)= tan 1 3 ( I 1 (x,y,n) I 3 (x,y,n)) 2 I 2 (x,y,n) I 1 (x,y,n) I 3 (x,y,n)
T(x,y,n)=A(x,y,n)= 1 3 i=1 3 I i (x,y,n)
V(x,y,n)= i=1 4 G C i (x,y,n)* 2 (4i)
k(x,y,n)=i(V(x,y,n))
k( x c , y c , n c )={ 16 ,if{mod( n c ,2)=1 && k( x c , y c , n c )=0 && ϕ( x c , y c , n c )>0}=1 k( x c , y c , n c ),if{mod( n c ,2)=1 && k( x c , y c , n c )=0 && ϕ( x c , y c , n c )>0}=0
Φ(n)={ ϕ(n)+2πk(n1), if{mod(n,2)=0 && ϕ(n)-π/2}=1 ϕ(n)+2πk(n), if{mod(n,2)=0 && -π/2<ϕ(n)<π/2}=1 ϕ(n)+2πk(n1)-2π, if{mod(n,2)=0 && ϕ(n)π/2}=1
Φ(n)={ ϕ(n)+2πk(n), if{mod(n,2)=1 && ϕ(n)-π/2}=1 ϕ(n)+2πk(n1), if{mod(n,2)=1 && -π/2<ϕ(n)<π/2}=1 ϕ(n)+2πk(n)-2π, if{mod(n,2)=1 && ϕ(n)π/2}=1
1 h(x,y,n) =u(x,y)+ v(x,y) ΔΦ(x,y,n) + w(x,y) Δ Φ 2 (x,y,n) ,