Abstract

In fringe projection profilometry, the original purpose of projecting multi-frequency fringe patterns is to determine fringe orders automatically, thus unwrapping the measured phase maps. This paper presents that using the same patterns, simultaneously, allows us to correct the effects of projector nonlinearity on the measured results. As is well known, the projector nonlinearity decreases the measurement accuracies by inducing ripple-like artifacts on the measured phase maps; and, theoretical analysis reveals that these artifacts, depending on the number of phase shifts, have multiplied frequencies higher than the fringe frequencies. Based on this fact, we deduce an error function for modeling the phase artifacts and then suggest an algorithm estimating the function coefficients from a couple of phase maps of fringe patterns having different frequencies. As a result, subtracting out the estimated phase errors yields the accurate phase maps with the effects of the projector nonlinearity on them being suppressed significantly. Experiment results demonstrated that this proposed method offers some advantages over others, such as working without a photometric calibration, being applicable when the projector nonlinearity varies over time, and having satisfied efficiency in implementation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2017 (3)

2016 (3)

2015 (2)

C. Zhang, H. Zhao, L. Zhang, and X. Wang, “Full-field phase error detection and compensation method for digital phase-shifting fringe projection profilometry,” Meas. Sci. Technol. 26(3), 035201 (2015).
[Crossref]

X. Ye, H.-B. Cheng, H.-Y. Wu, D.-M. Zhou, and H.-Y. Tam, “Gamma correction for three-dimensional object measurement by phase measuring profilometry,” Optik (Stuttg.) 126(24), 5534–5538 (2015).
[Crossref]

2014 (3)

K. Liu, S. Wang, D. L. Lau, K. E. Barner, and F. Kiamilev, “Nonlinearity calibrating algorithm for structured light illumination,” Opt. Eng. 53(5), 050501 (2014).
[Crossref]

Y. Fu, Z. Wang, G. Jiang, and J. Yang, “A novel three-dimensional shape measurement method based on a look-up table,” Optik (Stuttg.) 125(6), 1804–1808 (2014).
[Crossref]

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

2013 (3)

Y. Xiao, Y. Cao, Y. Wu, and S. Shi, “Single orthogonal sinusoidal grating for gamma correction in digital projection phase measuring profilometry,” Opt. Eng. 52(5), 053605 (2013).
[Crossref]

Y. Fu, Y. Wang, W. Wang, and J. Wu, “Least-squares calibration method for fringe projection profilometry with some practical considerations,” Optik (Stuttg.) 124(19), 4041–4045 (2013).
[Crossref]

D. Zheng and F. Da, “Gamma correction for two step phase shifting fringe projection profilometry,” Optik (Stuttg.) 124(13), 1392–1397 (2013).
[Crossref]

2012 (4)

2011 (1)

S. Gai and F. Da, “A novel fringe adaptation method for digital projector,” Opt. Lasers Eng. 49(4), 547–552 (2011).
[Crossref]

2010 (4)

S. S. Gorthi and P. Rostogi, “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]

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

H. Guo, P. Feng, and T. Tao, “Specular surface measurement by using least squares light tracking technique,” Opt. Lasers Eng. 48(2), 166–171 (2010).
[Crossref]

2009 (2)

Z.-W. Li, Y.-S. Shi, C.-J. Wang, D.-H. Qin, and K. Huang, “Complex object 3D measurement based on phase-shifting and a neural network,” Opt. Commun. 282(14), 2699–2706 (2009).
[Crossref]

B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. 34(4), 416–418 (2009).
[Crossref] [PubMed]

2008 (1)

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

2007 (2)

H. Guo and Z. Zhao, “Nonlinearity correction in digital fringe projection profilometry by using histogram matching technique,” Proc. SPIE 6616, 66162I (2007).
[Crossref]

S. Zhang and S.-T. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. 46(1), 36–43 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (2)

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Proc. SPIE 6000, 133–142 (2005).
[Crossref]

2004 (1)

2003 (1)

H. Guo and M. Chen, “Fourier analysis of the sampling characteristics of the phase-shifting algorithm,” Proc. SPIE 5180, 437–444 (2003).
[Crossref]

1984 (1)

1974 (1)

Asundi, A.

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]

B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. 34(4), 416–418 (2009).
[Crossref] [PubMed]

Asundi, A. K.

Barner, K. E.

K. Liu, S. Wang, D. L. Lau, K. E. Barner, and F. Kiamilev, “Nonlinearity calibrating algorithm for structured light illumination,” Opt. Eng. 53(5), 050501 (2014).
[Crossref]

Barnes, J.

Z. Wang, D. Nguyen, and J. Barnes, “Recent advances in 3D shape measurement and imaging using fringe projection technique,” in Proceedings of the SEM Annual Congress and Exposition on Experimental and Applied Mechanics 2009 (Society for Experimental Mechanics, 2009), pp. 2644–2653.

Brangaccio, D. J.

Bruning, J. H.

Cao, Y.

Y. Xiao, Y. Cao, Y. Wu, and S. Shi, “Single orthogonal sinusoidal grating for gamma correction in digital projection phase measuring profilometry,” Opt. Eng. 52(5), 053605 (2013).
[Crossref]

Chen, L.

S. Ma, C. Quan, R. Zhu, L. Chen, B. Li, and C. J. Tay, “A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry,” Opt. Commun. 285(5), 533–538 (2012).
[Crossref]

Chen, M.

H. Guo, M. Chen, and P. Zheng, “Least-squares fitting of carrier phase distribution by using a rational function in fringe projection profilometry,” Opt. Lett. 31(24), 3588–3590 (2006).
[Crossref] [PubMed]

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

H. Guo, H. He, and M. Chen, “Gamma correction for digital fringe projection profilometry,” Appl. Opt. 43(14), 2906–2914 (2004).
[Crossref] [PubMed]

H. Guo and M. Chen, “Fourier analysis of the sampling characteristics of the phase-shifting algorithm,” Proc. SPIE 5180, 437–444 (2003).
[Crossref]

Chen, Q.

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]

Cheng, H.-B.

X. Ye, H.-B. Cheng, H.-Y. Wu, D.-M. Zhou, and H.-Y. Tam, “Gamma correction for three-dimensional object measurement by phase measuring profilometry,” Optik (Stuttg.) 126(24), 5534–5538 (2015).
[Crossref]

Da, F.

D. Zheng and F. Da, “Gamma correction for two step phase shifting fringe projection profilometry,” Optik (Stuttg.) 124(13), 1392–1397 (2013).
[Crossref]

S. Gai and F. Da, “A novel fringe adaptation method for digital projector,” Opt. Lasers Eng. 49(4), 547–552 (2011).
[Crossref]

Dai, J.

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

Dai, M.

Feng, P.

H. Guo, P. Feng, and T. Tao, “Specular surface measurement by using least squares light tracking technique,” Opt. Lasers Eng. 48(2), 166–171 (2010).
[Crossref]

Fu, Y.

Y. Fu, Z. Wang, G. Jiang, and J. Yang, “A novel three-dimensional shape measurement method based on a look-up table,” Optik (Stuttg.) 125(6), 1804–1808 (2014).
[Crossref]

Y. Fu, Y. Wang, W. Wang, and J. Wu, “Least-squares calibration method for fringe projection profilometry with some practical considerations,” Optik (Stuttg.) 124(19), 4041–4045 (2013).
[Crossref]

Gai, S.

S. Gai and F. Da, “A novel fringe adaptation method for digital projector,” Opt. Lasers Eng. 49(4), 547–552 (2011).
[Crossref]

Gallagher, J. E.

Gorthi, S. S.

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

Guo, H.

F. Lü, S. Xing, and H. Guo, “Self-correction of projector nonlinearity in phase-shifting fringe projection profilometry,” Appl. Opt. 56(25), 7204–7216 (2017).
[Crossref] [PubMed]

S. Xing and H. Guo, “Temporal phase unwrapping for fringe projection profilometry aided by recursion of Chebyshev polynomials,” Appl. Opt. 56(6), 1591–1602 (2017).
[Crossref] [PubMed]

R. Zhang and H. Guo, “Depth recovering method immune to projector errors in fringe projection profilometry by use of cross-ratio invariance,” Opt. Express 25(23), 29272–29286 (2017).
[Crossref]

Y. Lu, R. Zhang, and H. Guo, “Correction of illumination fluctuations in phase-shifting technique by use of fringe histograms,” Appl. Opt. 55(1), 184–197 (2016).
[Crossref] [PubMed]

R. Zhang, H. Guo, and A. K. Asundi, “Geometric analysis of influence of fringe directions on phase sensitivities in fringe projection profilometry,” Appl. Opt. 55(27), 7675–7687 (2016).
[Crossref] [PubMed]

H. Guo and B. Lü, “Phase-shifting algorithm by use of Hough transform,” Opt. Express 20(23), 26037–26049 (2012).
[Crossref] [PubMed]

H. Guo, P. Feng, and T. Tao, “Specular surface measurement by using least squares light tracking technique,” Opt. Lasers Eng. 48(2), 166–171 (2010).
[Crossref]

H. Guo and Z. Zhao, “Nonlinearity correction in digital fringe projection profilometry by using histogram matching technique,” Proc. SPIE 6616, 66162I (2007).
[Crossref]

H. Guo, M. Chen, and P. Zheng, “Least-squares fitting of carrier phase distribution by using a rational function in fringe projection profilometry,” Opt. Lett. 31(24), 3588–3590 (2006).
[Crossref] [PubMed]

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

H. Guo, H. He, and M. Chen, “Gamma correction for digital fringe projection profilometry,” Appl. Opt. 43(14), 2906–2914 (2004).
[Crossref] [PubMed]

H. Guo and M. Chen, “Fourier analysis of the sampling characteristics of the phase-shifting algorithm,” Proc. SPIE 5180, 437–444 (2003).
[Crossref]

Halioua, M.

He, H.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

H. Guo, H. He, and M. Chen, “Gamma correction for digital fringe projection profilometry,” Appl. Opt. 43(14), 2906–2914 (2004).
[Crossref] [PubMed]

He, X.

Herriott, D. R.

Hoang, T.

Huang, K.

Z.-W. Li, Y.-S. Shi, C.-J. Wang, D.-H. Qin, and K. Huang, “Complex object 3D measurement based on phase-shifting and a neural network,” Opt. Commun. 282(14), 2699–2706 (2009).
[Crossref]

Huang, L.

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]

B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. 34(4), 416–418 (2009).
[Crossref] [PubMed]

Huang, P. S.

S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Proc. SPIE 6000, 133–142 (2005).
[Crossref]

Jiang, G.

Y. Fu, Z. Wang, G. Jiang, and J. Yang, “A novel three-dimensional shape measurement method based on a look-up table,” Optik (Stuttg.) 125(6), 1804–1808 (2014).
[Crossref]

Kemao, Q.

Kiamilev, F.

K. Liu, S. Wang, D. L. Lau, K. E. Barner, and F. Kiamilev, “Nonlinearity calibrating algorithm for structured light illumination,” Opt. Eng. 53(5), 050501 (2014).
[Crossref]

Lau, D. L.

K. Liu, S. Wang, D. L. Lau, K. E. Barner, and F. Kiamilev, “Nonlinearity calibrating algorithm for structured light illumination,” Opt. Eng. 53(5), 050501 (2014).
[Crossref]

Li, B.

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

S. Ma, C. Quan, R. Zhu, L. Chen, B. Li, and C. J. Tay, “A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry,” Opt. Commun. 285(5), 533–538 (2012).
[Crossref]

Li, Y.

Li, Z.

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

Li, Z.-W.

Z.-W. Li, Y.-S. Shi, C.-J. Wang, D.-H. Qin, and K. Huang, “Complex object 3D measurement based on phase-shifting and a neural network,” Opt. Commun. 282(14), 2699–2706 (2009).
[Crossref]

Liu, H. C.

Liu, K.

K. Liu, S. Wang, D. L. Lau, K. E. Barner, and F. Kiamilev, “Nonlinearity calibrating algorithm for structured light illumination,” Opt. Eng. 53(5), 050501 (2014).
[Crossref]

Lohry, W.

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

Lu, Y.

Lü, B.

Lü, F.

Ma, S.

S. Ma, C. Quan, R. Zhu, L. Chen, B. Li, and C. J. Tay, “A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry,” Opt. Commun. 285(5), 533–538 (2012).
[Crossref]

Nguyen, D.

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

Z. Wang, D. Nguyen, and J. Barnes, “Recent advances in 3D shape measurement and imaging using fringe projection technique,” in Proceedings of the SEM Annual Congress and Exposition on Experimental and Applied Mechanics 2009 (Society for Experimental Mechanics, 2009), pp. 2644–2653.

Pan, B.

Qin, D.-H.

Z.-W. Li, Y.-S. Shi, C.-J. Wang, D.-H. Qin, and K. Huang, “Complex object 3D measurement based on phase-shifting and a neural network,” Opt. Commun. 282(14), 2699–2706 (2009).
[Crossref]

Quan, C.

S. Ma, C. Quan, R. Zhu, L. Chen, B. Li, and C. J. Tay, “A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry,” Opt. Commun. 285(5), 533–538 (2012).
[Crossref]

Rosenfeld, D. P.

Rostogi, P.

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

Shi, S.

Y. Xiao, Y. Cao, Y. Wu, and S. Shi, “Single orthogonal sinusoidal grating for gamma correction in digital projection phase measuring profilometry,” Opt. Eng. 52(5), 053605 (2013).
[Crossref]

Shi, Y.

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

Shi, Y.-S.

Z.-W. Li, Y.-S. Shi, C.-J. Wang, D.-H. Qin, and K. Huang, “Complex object 3D measurement based on phase-shifting and a neural network,” Opt. Commun. 282(14), 2699–2706 (2009).
[Crossref]

Srinivasan, V.

Tam, H.-Y.

X. Ye, H.-B. Cheng, H.-Y. Wu, D.-M. Zhou, and H.-Y. Tam, “Gamma correction for three-dimensional object measurement by phase measuring profilometry,” Optik (Stuttg.) 126(24), 5534–5538 (2015).
[Crossref]

Tao, T.

H. Guo, P. Feng, and T. Tao, “Specular surface measurement by using least squares light tracking technique,” Opt. Lasers Eng. 48(2), 166–171 (2010).
[Crossref]

Tay, C. J.

S. Ma, C. Quan, R. Zhu, L. Chen, B. Li, and C. J. Tay, “A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry,” Opt. Commun. 285(5), 533–538 (2012).
[Crossref]

Tu, D.

Wang, C.

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Wang, C.-J.

Z.-W. Li, Y.-S. Shi, C.-J. Wang, D.-H. Qin, and K. Huang, “Complex object 3D measurement based on phase-shifting and a neural network,” Opt. Commun. 282(14), 2699–2706 (2009).
[Crossref]

Wang, S.

K. Liu, S. Wang, D. L. Lau, K. E. Barner, and F. Kiamilev, “Nonlinearity calibrating algorithm for structured light illumination,” Opt. Eng. 53(5), 050501 (2014).
[Crossref]

Wang, W.

Y. Fu, Y. Wang, W. Wang, and J. Wu, “Least-squares calibration method for fringe projection profilometry with some practical considerations,” Optik (Stuttg.) 124(19), 4041–4045 (2013).
[Crossref]

Wang, X.

C. Zhang, H. Zhao, L. Zhang, and X. Wang, “Full-field phase error detection and compensation method for digital phase-shifting fringe projection profilometry,” Meas. Sci. Technol. 26(3), 035201 (2015).
[Crossref]

Wang, Y.

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

Y. Fu, Y. Wang, W. Wang, and J. Wu, “Least-squares calibration method for fringe projection profilometry with some practical considerations,” Optik (Stuttg.) 124(19), 4041–4045 (2013).
[Crossref]

Wang, Z.

Y. Fu, Z. Wang, G. Jiang, and J. Yang, “A novel three-dimensional shape measurement method based on a look-up table,” Optik (Stuttg.) 125(6), 1804–1808 (2014).
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T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett. 35(12), 1992–1994 (2010).
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Z. Wang, D. Nguyen, and J. Barnes, “Recent advances in 3D shape measurement and imaging using fringe projection technique,” in Proceedings of the SEM Annual Congress and Exposition on Experimental and Applied Mechanics 2009 (Society for Experimental Mechanics, 2009), pp. 2644–2653.

White, A. D.

Wu, H.-Y.

X. Ye, H.-B. Cheng, H.-Y. Wu, D.-M. Zhou, and H.-Y. Tam, “Gamma correction for three-dimensional object measurement by phase measuring profilometry,” Optik (Stuttg.) 126(24), 5534–5538 (2015).
[Crossref]

Wu, J.

Y. Fu, Y. Wang, W. Wang, and J. Wu, “Least-squares calibration method for fringe projection profilometry with some practical considerations,” Optik (Stuttg.) 124(19), 4041–4045 (2013).
[Crossref]

Wu, Y.

Y. Xiao, Y. Cao, Y. Wu, and S. Shi, “Single orthogonal sinusoidal grating for gamma correction in digital projection phase measuring profilometry,” Opt. Eng. 52(5), 053605 (2013).
[Crossref]

Xiao, Y.

Y. Xiao, Y. Cao, Y. Wu, and S. Shi, “Single orthogonal sinusoidal grating for gamma correction in digital projection phase measuring profilometry,” Opt. Eng. 52(5), 053605 (2013).
[Crossref]

Xing, S.

Yang, F.

Yang, J.

Y. Fu, Z. Wang, G. Jiang, and J. Yang, “A novel three-dimensional shape measurement method based on a look-up table,” Optik (Stuttg.) 125(6), 1804–1808 (2014).
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Yau, S.-T.

Ye, X.

X. Ye, H.-B. Cheng, H.-Y. Wu, D.-M. Zhou, and H.-Y. Tam, “Gamma correction for three-dimensional object measurement by phase measuring profilometry,” Optik (Stuttg.) 126(24), 5534–5538 (2015).
[Crossref]

Yu, Y.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

Zhang, C.

C. Zhang, H. Zhao, L. Zhang, and X. Wang, “Full-field phase error detection and compensation method for digital phase-shifting fringe projection profilometry,” Meas. Sci. Technol. 26(3), 035201 (2015).
[Crossref]

Zhang, L.

C. Zhang, H. Zhao, L. Zhang, and X. Wang, “Full-field phase error detection and compensation method for digital phase-shifting fringe projection profilometry,” Meas. Sci. Technol. 26(3), 035201 (2015).
[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. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Zhang, R.

Zhang, S.

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[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 and S.-T. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. 46(1), 36–43 (2007).
[Crossref] [PubMed]

S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Proc. SPIE 6000, 133–142 (2005).
[Crossref]

Zhang, X.

Zhao, H.

C. Zhang, H. Zhao, L. Zhang, and X. Wang, “Full-field phase error detection and compensation method for digital phase-shifting fringe projection profilometry,” Meas. Sci. Technol. 26(3), 035201 (2015).
[Crossref]

Zhao, Z.

H. Guo and Z. Zhao, “Nonlinearity correction in digital fringe projection profilometry by using histogram matching technique,” Proc. SPIE 6616, 66162I (2007).
[Crossref]

Zheng, D.

D. Zheng and F. Da, “Gamma correction for two step phase shifting fringe projection profilometry,” Optik (Stuttg.) 124(13), 1392–1397 (2013).
[Crossref]

Zheng, P.

Zhou, D.-M.

X. Ye, H.-B. Cheng, H.-Y. Wu, D.-M. Zhou, and H.-Y. Tam, “Gamma correction for three-dimensional object measurement by phase measuring profilometry,” Optik (Stuttg.) 126(24), 5534–5538 (2015).
[Crossref]

Zhu, L.

Zhu, R.

S. Ma, C. Quan, R. Zhu, L. Chen, B. Li, and C. J. Tay, “A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry,” Opt. Commun. 285(5), 533–538 (2012).
[Crossref]

Zuo, C.

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).
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H. Guo, H. He, and M. Chen, “Gamma correction for digital fringe projection profilometry,” Appl. Opt. 43(14), 2906–2914 (2004).
[Crossref] [PubMed]

S. Zhang and S.-T. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. 46(1), 36–43 (2007).
[Crossref] [PubMed]

Y. Lu, R. Zhang, and H. Guo, “Correction of illumination fluctuations in phase-shifting technique by use of fringe histograms,” Appl. Opt. 55(1), 184–197 (2016).
[Crossref] [PubMed]

R. Zhang, H. Guo, and A. K. Asundi, “Geometric analysis of influence of fringe directions on phase sensitivities in fringe projection profilometry,” Appl. Opt. 55(27), 7675–7687 (2016).
[Crossref] [PubMed]

S. Xing and H. Guo, “Temporal phase unwrapping for fringe projection profilometry aided by recursion of Chebyshev polynomials,” Appl. Opt. 56(6), 1591–1602 (2017).
[Crossref] [PubMed]

F. Lü, S. Xing, and H. Guo, “Self-correction of projector nonlinearity in phase-shifting fringe projection profilometry,” Appl. Opt. 56(25), 7204–7216 (2017).
[Crossref] [PubMed]

M. Dai, F. Yang, and X. He, “Single-shot color fringe projection for three-dimensional shape measurement of objects with discontinuities,” Appl. Opt. 51(12), 2062–2069 (2012).
[Crossref] [PubMed]

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

Meas. Sci. Technol. (1)

C. Zhang, H. Zhao, L. Zhang, and X. Wang, “Full-field phase error detection and compensation method for digital phase-shifting fringe projection profilometry,” Meas. Sci. Technol. 26(3), 035201 (2015).
[Crossref]

Opt. Commun. (2)

S. Ma, C. Quan, R. Zhu, L. Chen, B. Li, and C. J. Tay, “A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry,” Opt. Commun. 285(5), 533–538 (2012).
[Crossref]

Z.-W. Li, Y.-S. Shi, C.-J. Wang, D.-H. Qin, and K. Huang, “Complex object 3D measurement based on phase-shifting and a neural network,” Opt. Commun. 282(14), 2699–2706 (2009).
[Crossref]

Opt. Eng. (4)

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

Y. Xiao, Y. Cao, Y. Wu, and S. Shi, “Single orthogonal sinusoidal grating for gamma correction in digital projection phase measuring profilometry,” Opt. Eng. 52(5), 053605 (2013).
[Crossref]

K. Liu, S. Wang, D. L. Lau, K. E. Barner, and F. Kiamilev, “Nonlinearity calibrating algorithm for structured light illumination,” Opt. Eng. 53(5), 050501 (2014).
[Crossref]

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (6)

H. Guo, P. Feng, and T. Tao, “Specular surface measurement by using least squares light tracking technique,” Opt. Lasers Eng. 48(2), 166–171 (2010).
[Crossref]

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[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]

S. Gai and F. Da, “A novel fringe adaptation method for digital projector,” Opt. Lasers Eng. 49(4), 547–552 (2011).
[Crossref]

S. S. Gorthi and P. Rostogi, “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]

Opt. Lett. (3)

Optik (Stuttg.) (4)

Y. Fu, Y. Wang, W. Wang, and J. Wu, “Least-squares calibration method for fringe projection profilometry with some practical considerations,” Optik (Stuttg.) 124(19), 4041–4045 (2013).
[Crossref]

D. Zheng and F. Da, “Gamma correction for two step phase shifting fringe projection profilometry,” Optik (Stuttg.) 124(13), 1392–1397 (2013).
[Crossref]

X. Ye, H.-B. Cheng, H.-Y. Wu, D.-M. Zhou, and H.-Y. Tam, “Gamma correction for three-dimensional object measurement by phase measuring profilometry,” Optik (Stuttg.) 126(24), 5534–5538 (2015).
[Crossref]

Y. Fu, Z. Wang, G. Jiang, and J. Yang, “A novel three-dimensional shape measurement method based on a look-up table,” Optik (Stuttg.) 125(6), 1804–1808 (2014).
[Crossref]

Proc. SPIE (3)

H. Guo and M. Chen, “Fourier analysis of the sampling characteristics of the phase-shifting algorithm,” Proc. SPIE 5180, 437–444 (2003).
[Crossref]

H. Guo and Z. Zhao, “Nonlinearity correction in digital fringe projection profilometry by using histogram matching technique,” Proc. SPIE 6616, 66162I (2007).
[Crossref]

S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Proc. SPIE 6000, 133–142 (2005).
[Crossref]

Other (2)

Z. Wang, D. Nguyen, and J. Barnes, “Recent advances in 3D shape measurement and imaging using fringe projection technique,” in Proceedings of the SEM Annual Congress and Exposition on Experimental and Applied Mechanics 2009 (Society for Experimental Mechanics, 2009), pp. 2644–2653.

X. Colonna De Lega and P. de Groot, “Lateral resolution and instrument transfer function as criteria for selecting surface metrology instruments,” in Imaging and Applied Optics Technical Papers, OSA Technical Digest (online) (Optical Society of America, 2012), paper OTu1D.4.

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Figures (9)

Fig. 1
Fig. 1 Measurement system.
Fig. 2
Fig. 2 (a) simulates a continuous one-dimensional phase curve, and (b) shows the nonlinearity relationship between the brightness and the gray level of the projector.
Fig. 3
Fig. 3 Effect of projector nonlinearity on the phase measuring results. (a) The first frame of three phase-shifting patterns of high frequency. (b) The calculated phase curve with the carrier having been removed. (c) The phase errors in (b). The second row is parallel with the first one, but the fringe pattern has a half frequency of the one in (a).
Fig. 4
Fig. 4 Simulation results. (a) shows the corrected phases, and (b) plots the residual errors in (a).
Fig. 5
Fig. 5 (a) RMS phase errors decrease with the number of iterations. (b) RMS phase errors decrease with the number of terms kept in the truncated error function.
Fig. 6
Fig. 6 Phase measuring by use of phase-shifting algorithm. The first row shows, from left to right, the first one of three phase-shifting fringe patterns, its wrapped phase map, its unwrapped phase map, and the phase map without carrier. The second row is similar to the first one, but the fringe pattern in (e) has a half frequency of (a). The colorbars have the unit of radian.
Fig. 7
Fig. 7 Phase error correction using the proposed technique. (a) shows the phase map with the errors induced by the projector nonlinearity having been corrected. (b) is the same phase map but the carrier has been subtracted out. The colorbars have the unit of radian.
Fig. 8
Fig. 8 (a) RMS values of phase deviations decrease with the number of iterations in practical measurement. (b) RMS values of phase deviations decrease with the number of terms kept in the truncated error function.
Fig. 9
Fig. 9 Top row compares the depth maps in millimeters, in which the errors induced by the projector nonlinearity are processed using different methods. Below the depth maps are their cross sections along the 12th pixel column indicated by the red lines, with their vertical axes having a downward direction representing the pixel positions and their horizontal axes representing the depths in millimeters. (a) shows the results calculated from fringe patterns without any correction to the projector nonlinearity. (b) shows the results with the phase errors smoothed using a Gaussian low-pass filter. (c) gives the results of using the proposed technique. (d) is obtained by using the active photometric calibration method.

Tables (1)

Tables Icon

Table 1 Phase Errors under Different Noise Conditions (rad)

Equations (19)

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g k (u,v)=α+βcos(2πfu+2πk/K ),
I k (x,y)=R(x,y) n=0 N c n {α+βcos[ϕ(x,y)+ 2πk/K ]} n +B(x,y),
I k (x,y)=A(x,y)+M(x,y) n=0 N d n cos n [ϕ(x,y)+2πk/K ] .
ψ(x,y)=arctan[ k=0 K1 I k (x,y)sin(2πk/K ) k=0 K1 I k (x,y)cos(2πk/K ) ].
ψ R (x,y)=W{ ψ H (x,y) ψ L (x,y)},
f R = f H f L .
ψ R (x,y)= ψ L (x,y),
f R = f L .
l H (x,y)=round[ ( f H / f L ) ψ R (x,y) ψ H (x,y) 2π ],
Ψ H (x,y)=2π l H (x,y)+ ψ H (x,y).
ε(x,y)=Ψ(x,y)Φ(x,y) m=1 int[ (N+1)/K ] ( n=2 N ρ m,n ) sin[mKΦ(x,y)],
ρ m,n ={ d n mK C n+1 (n+1mK)/2 (n+1) 2 n-1 {[1m(n+1)/K] AND (both K and mn are odd)]} OR {[1m(n+1)/K] AND (K is even and m is odd)]} 0 otherwise
Ψ(x,y)Φ(x,y) m=1 int[ (N+1)/K ] ξ m sin[mKΦ(x,y)].
{ Ψ H Φ H = m=1 int[ (N+1)/K ] ξ m sin(mK Φ H ) Ψ L Φ L = m=1 int[ (N+1)/K ] ξ m sin(mK Φ L )
Φ H Φ L = f H f L ,
{ Ψ H Φ H = m=1 int[ (N+1)/K ] ξ m sin(mK Φ H ) Ψ L f L f H Φ H = m=1 int[ (N+1)/K ] ξ m sin( f L f H mK Φ H )
Φ H (0) = Ψ H ,
{ m=1 M ξ m (i) sin(mK Φ H (i) )= Ψ H Φ H (i) m=1 M ξ m (i) sin( f L f H mK Φ H (i) )= Ψ L f L f H Φ H (i)
Φ H (i+1) = { [ Ψ H m=1 M ξ m (i) sin(mK Φ H (i) ) ]+[ Ψ L m=1 M ξ m (i) sin( f L f H mK Φ H (i) ) ] }/ ( 1+ f L f H ) .