Abstract

Object motion can introduce unknown phase shift and thus measurement error in multi-image phase-shifting methods of fringe projection profilometry. This paper presents a new method to estimate the unknown phase shifts and reduce the motion-induced error by using three phase maps computed over a multiple measurement sequence and calculating the difference between phase maps. The pixel-wise estimation of the motion-induced phase shifts permits phase-error compensation for non-homogeneous surface motion. Experiments demonstrated the ability of the method to reduce motion-induced error in real-time, for shape measurement of surfaces with high depth variation, and moving and deforming surfaces.

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

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References

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    [Crossref]

2019 (2)

X. Liu and J. Kofman, “Real-time 3D surface-shape measurement using background-modulated modified Fourier transform profilometry with geometry-constraint,” Opt. Lasers Eng. 115, 217–224 (2019).
[Crossref]

J. Qian, T. Tao, S. Feng, Q. Chen, and C. Zuo, “Motion-artifact-free dynamic 3D shape measurement with hybrid Fourier-transform phase-shifting profilometry,” Opt. Express 27(3), 2713–2731 (2019).
[Crossref] [PubMed]

2018 (10)

Z. Liu, P. C. Zibley, and S. Zhang, “Motion-induced error compensation for phase shifting profilometry,” Opt. Express 26(10), 12632–12637 (2018).
[Crossref] [PubMed]

H. Chen, Y. Yin, Z. Cai, W. Xu, X. Liu, X. Meng, and X. Peng, “Suppression of the nonlinear phase error in phase shifting profilometry: considering non-smooth reflectivity and fractional period,” Opt. Express 26(10), 13489–13505 (2018).
[Crossref] [PubMed]

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3D shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref] [PubMed]

L. Lu, Y. Yin, Z. Su, X. Ren, Y. Luan, and J. Xi, “General model for phase shifting profilometry with an object in motion,” Appl. Opt. 57(36), 10364–10369 (2018).
[Crossref] [PubMed]

Y. Wang, Z. Liu, C. Jiang, and S. Zhang, “Motion induced phase error reduction using a Hilbert transform,” Opt. Express 26(26), 34224–34235 (2018).
[Crossref] [PubMed]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (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. Lasers Eng. 109, 23–59 (2018).
[Crossref]

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

S. Zhang, “High-speed 3D shape measurement with structured light methods: A review,” Opt. Lasers 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. Lasers Eng. 102, 70–91 (2018).
[Crossref]

2017 (5)

C. Jiang, B. Li, and S. Zhang, “Pixel-by-pixel absolute phase retrieval using three phase-shifted fringe patterns without markers,” Opt. Lasers Eng. 91, 232–241 (2017).
[Crossref]

J.-S. Hyun, B. Li, and S. Zhang, “High-speed high-accuracy three-dimensional shape measurement using digital binary defocusing method versus sinusoidal method,” Opt. Eng. 56(7), 074102 (2017).
[Crossref]

R. Ramm, C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “High-resolution mobile optical 3D scanner with color mapping,” Proc. SPIE 10331, 103310D (2017).

X. Liu and J. Kofman, “High-frequency background modulation fringe patterns based on a fringe-wavelength geometry-constraint model for 3D surface-shape measurement,” Opt. Express 25(14), 16618–16628 (2017).
[Crossref] [PubMed]

L. Lu, Y. Ding, Y. Luan, Y. Yin, Q. Liu, and J. Xi, “Automated approach for the surface profile measurement of moving objects based on PSP,” Opt. Express 25(25), 32120–32131 (2017).
[Crossref] [PubMed]

2016 (4)

A. J. Das, T. A. Valdez, J. A. Vargas, P. Saksupapchon, P. Rachapudi, Z. Ge, J. C. Estrada, and R. Raskar, “Volume estimation of tonsil phantoms using an oral camera with 3D imaging,” Biomed. Opt. Express 7(4), 1445–1457 (2016).
[Crossref] [PubMed]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

W. H. Su and W. T. Co, “A real-time, full-field, and low-cost velocity sensing approach for linear motion using fringe projection techniques,” Opt. Lasers Eng. 81, 11–20 (2016).
[Crossref]

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).
[Crossref]

2015 (2)

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: A review,” Opt. Lasers Eng. 66, 67–73 (2015).
[Crossref]

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3D sensing with Fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9(3), 396–408 (2015).
[Crossref]

2014 (2)

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2014).

L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the performance of fringe pattern profilometry using multiple triangular patterns for the measurement of objects in motion,” Opt. Eng. 53(11), 112211 (2014).
[Crossref]

2013 (2)

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the accuracy of 3-D shape measurement of moving object using phase shifting profilometry,” Opt. Express 21(25), 30610–30622 (2013).
[Crossref] [PubMed]

2012 (1)

L. R. Watkins, “Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50(8), 1015–1022 (2012).
[Crossref]

2010 (2)

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. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

Z. Zhang, D. P. Towers, and C. E. Towers, “Snapshot color fringe projection for absolute three-dimensional metrology of video sequences,” Appl. Opt. 49(31), 5947 (2010).
[Crossref]

2007 (1)

2003 (1)

1984 (1)

1983 (1)

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]

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. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

Bräuer-Burchardt, C.

R. Ramm, C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “High-resolution mobile optical 3D scanner with color mapping,” Proc. SPIE 10331, 103310D (2017).

Cai, Z.

Chen, H.

Chen, Q.

J. Qian, T. Tao, S. Feng, Q. Chen, and C. Zuo, “Motion-artifact-free dynamic 3D shape measurement with hybrid Fourier-transform phase-shifting profilometry,” Opt. Express 27(3), 2713–2731 (2019).
[Crossref] [PubMed]

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3D shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[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, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

Co, W. T.

W. H. Su and W. T. Co, “A real-time, full-field, and low-cost velocity sensing approach for linear motion using fringe projection techniques,” Opt. Lasers Eng. 81, 11–20 (2016).
[Crossref]

Cong, P.

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3D sensing with Fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9(3), 396–408 (2015).
[Crossref]

Da, J.

Das, A. J.

Dietrich, P.

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).
[Crossref]

Ding, Y.

Estrada, J. C.

Feng, S.

J. Qian, T. Tao, S. Feng, Q. Chen, and C. Zuo, “Motion-artifact-free dynamic 3D shape measurement with hybrid Fourier-transform phase-shifting profilometry,” Opt. Express 27(3), 2713–2731 (2019).
[Crossref] [PubMed]

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3D shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[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, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

Ge, Z.

Gu, G.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

Guan, C.

Guo, Q.

L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the performance of fringe pattern profilometry using multiple triangular patterns for the measurement of objects in motion,” Opt. Eng. 53(11), 112211 (2014).
[Crossref]

L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the accuracy of 3-D shape measurement of moving object using phase shifting profilometry,” Opt. Express 21(25), 30610–30622 (2013).
[Crossref] [PubMed]

Halioua, M.

Hassebrook, L.

Heist, S.

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).
[Crossref]

Hu, Y.

Huang, L.

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3D shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref] [PubMed]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers 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. Lasers Eng. 102, 70–91 (2018).
[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. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

Hyun, J.-S.

J.-S. Hyun, B. Li, and S. Zhang, “High-speed high-accuracy three-dimensional shape measurement using digital binary defocusing method versus sinusoidal method,” Opt. Eng. 56(7), 074102 (2017).
[Crossref]

Jiang, C.

Y. Wang, Z. Liu, C. Jiang, and S. Zhang, “Motion induced phase error reduction using a Hilbert transform,” Opt. Express 26(26), 34224–34235 (2018).
[Crossref] [PubMed]

C. Jiang, B. Li, and S. Zhang, “Pixel-by-pixel absolute phase retrieval using three phase-shifted fringe patterns without markers,” Opt. Lasers Eng. 91, 232–241 (2017).
[Crossref]

Kemao, Q.

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: A review,” Opt. Lasers Eng. 66, 67–73 (2015).
[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. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

Kofman, J.

X. Liu and J. Kofman, “Real-time 3D surface-shape measurement using background-modulated modified Fourier transform profilometry with geometry-constraint,” Opt. Lasers Eng. 115, 217–224 (2019).
[Crossref]

X. Liu and J. Kofman, “High-frequency background modulation fringe patterns based on a fringe-wavelength geometry-constraint model for 3D surface-shape measurement,” Opt. Express 25(14), 16618–16628 (2017).
[Crossref] [PubMed]

Kühmstedt, P.

R. Ramm, C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “High-resolution mobile optical 3D scanner with color mapping,” Proc. SPIE 10331, 103310D (2017).

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).
[Crossref]

Lau, D.

Lei, Y.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Li, B.

C. Jiang, B. Li, and S. Zhang, “Pixel-by-pixel absolute phase retrieval using three phase-shifted fringe patterns without markers,” Opt. Lasers Eng. 91, 232–241 (2017).
[Crossref]

J.-S. Hyun, B. Li, and S. Zhang, “High-speed high-accuracy three-dimensional shape measurement using digital binary defocusing method versus sinusoidal method,” Opt. Eng. 56(7), 074102 (2017).
[Crossref]

Li, X.

Li, Y.

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2014).

Li, Z.

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2014).

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Liu, H. C.

Liu, Q.

Liu, X.

Liu, Z.

Lu, L.

Luan, Y.

Lutzke, P.

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).
[Crossref]

Meng, X.

Mutoh, K.

Notni, G.

R. Ramm, C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “High-resolution mobile optical 3D scanner with color mapping,” Proc. SPIE 10331, 103310D (2017).

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).
[Crossref]

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. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

Peng, X.

Qian, J.

Rachapudi, P.

Ramm, R.

R. Ramm, C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “High-resolution mobile optical 3D scanner with color mapping,” Proc. SPIE 10331, 103310D (2017).

Raskar, R.

Ren, X.

Saksupapchon, P.

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S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).
[Crossref]

Shi, Y.

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2014).

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Srinivasan, V.

Su, W. H.

W. H. Su and W. T. Co, “A real-time, full-field, and low-cost velocity sensing approach for linear motion using fringe projection techniques,” Opt. Lasers Eng. 81, 11–20 (2016).
[Crossref]

Su, Z.

Takeda, M.

Tao, T.

J. Qian, T. Tao, S. Feng, Q. Chen, and C. Zuo, “Motion-artifact-free dynamic 3D shape measurement with hybrid Fourier-transform phase-shifting profilometry,” Opt. Express 27(3), 2713–2731 (2019).
[Crossref] [PubMed]

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3D shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref] [PubMed]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
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C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers 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. Lasers Eng. 102, 70–91 (2018).
[Crossref]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

Towers, C. E.

Towers, D. P.

Tünnermann, A.

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).
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Valdez, T. A.

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K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2014).

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
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Wang, Y.

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L. R. Watkins, “Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50(8), 1015–1022 (2012).
[Crossref]

Wu, F.

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3D sensing with Fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9(3), 396–408 (2015).
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L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the performance of fringe pattern profilometry using multiple triangular patterns for the measurement of objects in motion,” Opt. Eng. 53(11), 112211 (2014).
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L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the accuracy of 3-D shape measurement of moving object using phase shifting profilometry,” Opt. Express 21(25), 30610–30622 (2013).
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Zhang, M.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
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S. Zhang, “High-speed 3D shape measurement with structured light methods: A review,” Opt. Lasers Eng. 106, 119–131 (2018).
[Crossref]

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

Z. Liu, P. C. Zibley, and S. Zhang, “Motion-induced error compensation for phase shifting profilometry,” Opt. Express 26(10), 12632–12637 (2018).
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Y. Wang, Z. Liu, C. Jiang, and S. Zhang, “Motion induced phase error reduction using a Hilbert transform,” Opt. Express 26(26), 34224–34235 (2018).
[Crossref] [PubMed]

C. Jiang, B. Li, and S. Zhang, “Pixel-by-pixel absolute phase retrieval using three phase-shifted fringe patterns without markers,” Opt. Lasers Eng. 91, 232–241 (2017).
[Crossref]

J.-S. Hyun, B. Li, and S. Zhang, “High-speed high-accuracy three-dimensional shape measurement using digital binary defocusing method versus sinusoidal method,” Opt. Eng. 56(7), 074102 (2017).
[Crossref]

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P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3D sensing with Fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9(3), 396–408 (2015).
[Crossref]

Zhang, Z.

Zhao, S.

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3D sensing with Fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9(3), 396–408 (2015).
[Crossref]

Zhong, K.

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2014).

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Zhou, X.

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2014).

Zibley, P. C.

Zuo, C.

J. Qian, T. Tao, S. Feng, Q. Chen, and C. Zuo, “Motion-artifact-free dynamic 3D shape measurement with hybrid Fourier-transform phase-shifting profilometry,” Opt. Express 27(3), 2713–2731 (2019).
[Crossref] [PubMed]

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3D shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref] [PubMed]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (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. Lasers 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. Lasers Eng. 109, 23–59 (2018).
[Crossref]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

Appl. Opt. (5)

Biomed. Opt. Express (1)

IEEE J. Sel. Top. Signal Process. (1)

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3D sensing with Fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9(3), 396–408 (2015).
[Crossref]

Int. J. Adv. Manuf. Technol. (1)

K. Zhong, Z. Li, X. Zhou, Y. Li, Y. Shi, and C. Wang, “Enhanced phase measurement profilometry for industrial 3D inspection automation,” Int. J. Adv. Manuf. Technol. 76(9–12), 1563–1574 (2014).

Opt. Eng. (2)

J.-S. Hyun, B. Li, and S. Zhang, “High-speed high-accuracy three-dimensional shape measurement using digital binary defocusing method versus sinusoidal method,” Opt. Eng. 56(7), 074102 (2017).
[Crossref]

L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the performance of fringe pattern profilometry using multiple triangular patterns for the measurement of objects in motion,” Opt. Eng. 53(11), 112211 (2014).
[Crossref]

Opt. Express (10)

L. Lu, Y. Ding, Y. Luan, Y. Yin, Q. Liu, and J. Xi, “Automated approach for the surface profile measurement of moving objects based on PSP,” Opt. Express 25(25), 32120–32131 (2017).
[Crossref] [PubMed]

L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the accuracy of 3-D shape measurement of moving object using phase shifting profilometry,” Opt. Express 21(25), 30610–30622 (2013).
[Crossref] [PubMed]

J. Qian, T. Tao, S. Feng, Q. Chen, and C. Zuo, “Motion-artifact-free dynamic 3D shape measurement with hybrid Fourier-transform phase-shifting profilometry,” Opt. Express 27(3), 2713–2731 (2019).
[Crossref] [PubMed]

Y. Wang, Z. Liu, C. Jiang, and S. Zhang, “Motion induced phase error reduction using a Hilbert transform,” Opt. Express 26(26), 34224–34235 (2018).
[Crossref] [PubMed]

H. Chen, Y. Yin, Z. Cai, W. Xu, X. Liu, X. Meng, and X. Peng, “Suppression of the nonlinear phase error in phase shifting profilometry: considering non-smooth reflectivity and fractional period,” Opt. Express 26(10), 13489–13505 (2018).
[Crossref] [PubMed]

Z. Liu, P. C. Zibley, and S. Zhang, “Motion-induced error compensation for phase shifting profilometry,” Opt. Express 26(10), 12632–12637 (2018).
[Crossref] [PubMed]

C. Guan, L. Hassebrook, and D. Lau, “Composite structured light pattern for three-dimensional video,” Opt. Express 11(5), 406–417 (2003).
[Crossref] [PubMed]

T. Tao, Q. Chen, S. Feng, J. Qian, Y. Hu, L. Huang, and C. Zuo, “High-speed real-time 3D shape measurement based on adaptive depth constraint,” Opt. Express 26(17), 22440–22456 (2018).
[Crossref] [PubMed]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

X. Liu and J. Kofman, “High-frequency background modulation fringe patterns based on a fringe-wavelength geometry-constraint model for 3D surface-shape measurement,” Opt. Express 25(14), 16618–16628 (2017).
[Crossref] [PubMed]

Opt. Lasers Eng. (13)

X. Liu and J. Kofman, “Real-time 3D surface-shape measurement using background-modulated modified Fourier transform profilometry with geometry-constraint,” Opt. Lasers Eng. 115, 217–224 (2019).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Lasers Eng. 103, 127–138 (2018).
[Crossref]

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: A review,” Opt. Lasers Eng. 66, 67–73 (2015).
[Crossref]

L. R. Watkins, “Review of fringe pattern phase recovery using the 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50(8), 1015–1022 (2012).
[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. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

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

W. H. Su and W. T. Co, “A real-time, full-field, and low-cost velocity sensing approach for linear motion using fringe projection techniques,” Opt. Lasers Eng. 81, 11–20 (2016).
[Crossref]

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

C. Jiang, B. Li, and S. Zhang, “Pixel-by-pixel absolute phase retrieval using three phase-shifted fringe patterns without markers,” Opt. Lasers Eng. 91, 232–241 (2017).
[Crossref]

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

S. Zhang, “High-speed 3D shape measurement with structured light methods: A review,” Opt. Lasers 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. Lasers Eng. 102, 70–91 (2018).
[Crossref]

S. Heist, P. Lutzke, I. Schmidt, P. Dietrich, P. Kühmstedt, A. Tünnermann, and G. Notni, “High-speed three-dimensional shape measurement using GOBO projection,” Opt. Lasers Eng. 87, 90–96 (2016).
[Crossref]

Proc. SPIE (1)

R. Ramm, C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “High-resolution mobile optical 3D scanner with color mapping,” Proc. SPIE 10331, 103310D (2017).

Other (2)

N. Pears, Y. Liu, and P. Bunting, 3D Imaging, Analysis and Applications (Springer, 2012).

P. Viola and M. J. Jones, “Robust Real-time Object Detection,” in Proceedings of IEEE Workshop on Statistical and Computational Theories of Vision (IEEE, 2001), pp. 137–154.

Supplementary Material (5)

NameDescription
» Visualization 1       3D measurement of moving multi-step object
» Visualization 2       Depth of a row of points
» Visualization 3       3D measurement of moving double hemisphere object
» Visualization 4       Real-time measurement result of a manikin head after motion-induced-error compensation
» Visualization 5       Real-time measurement result of a deflating balloon after motion-induced-error compensation

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Figures (11)

Fig. 1
Fig. 1 Object surface motion-induced phase-shift error.
Fig. 2
Fig. 2 Phase measurement simulation with constant speed motion: (a) unwrapped phase computed by standard 4-step PSP (black) and phase at four positions p1, p2, p3, p4, (b) motion-induced phase error computed using ϕ′−ϕ (blue) and simulated using Eq. (13) (red).
Fig. 3
Fig. 3 Phase measurement simulation with varying speed object motion: (a) unwrapped phase computed by standard 4-step PSP (black) and phase at four positions p1, p2, p3, p4, (b) motion-induced phase error computed using ϕ′−ϕ (blue) and simulated using Eq. (13) (red).
Fig. 4
Fig. 4 Object motion at eight successive frames and motion-induced phase-shift errors.
Fig. 5
Fig. 5 Simulation of the π offset phase difference of two phase maps with different phase-shift errors.
Fig. 6
Fig. 6 3D measurement of moving multi-step object (associated with Visualization 1): (a) image of stepped object (b) one captured fringe image; (c) measurement result using standard 4-step PSP method; (d) measurement result using new motion-induced-error compensation method.
Fig. 7
Fig. 7 Depth of a row of points located on the red line segment in Fig. 6(b) (associated with Visualization 2): (a) measurement result using standard 4-step PSP method; (b) measurement result using new motion-induced-error compensation method.
Fig. 8
Fig. 8 3D measurement of moving double hemisphere object (associated with Visualization 3): (a) measurement result using standard 4-step PSP method; (b) measurement result using new motion-induced-error compensation method.
Fig. 9
Fig. 9 Errors in 3D measurement of a moving double-hemisphere object using: (a) standard 4-step PSP method, (c) new motion-induced-error compensation method, (e) single-image FTP method; and measurement error distribution (number of points versus error (mm) for the three methods: (b) standard 4-step PSP, (d) error compensation, and (f) single-image FTP.
Fig. 10
Fig. 10 Real-time measurement result of a manikin head after motion-induced-error compensation (associated with Visualization 4).
Fig. 11
Fig. 11 Real-time measurement result of a deflating balloon after motion-induced-error compensation (associated with Visualization 5).

Tables (1)

Tables Icon

Table 1 Measurement results for the standard PSP method, new motion-induced-error compensation method, and single-image FTP method.

Equations (21)

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

I n (x,y)=A(x,y)+B(x,y)cos[ϕ(x,y) θ n ],
I n (x,y)=A(x,y)+ B 1 (x,y)cos( θ n )+ B 2 (x,y)sin( θ n ),
Χ(x,y)= ( M T M ) 1 M T Ι(x,y),
M=[ 1 cos( θ 1 ) sin( θ 1 ) 1 cos( θ 2 ) sin( θ 2 ) 1 cos( θ N ) sin( θ N ) ].
ϕ(x,y)= tan 1 [ B 2 (x,y) B 1 (x,y) ].
ϕ(x,y)= tan 1 [ I 2 (x,y) I 4 (x,y) I 1 (x,y) I 3 (x,y) ].
I 1 (x,y)=A(x,y)+B(x,y)cos[ ϕ(x,y) ε 2 (x,y)/2 ε 1 (x,y) ], I 2 (x,y)=A(x,y)+B(x,y)cos[ ϕ(x,y)π/2 ε 2 (x,y)/2 ], I 3 (x,y)=A(x,y)+B(x,y)cos[ ϕ(x,y)π+ ε 2 (x,y)/2 ], I 4 (x,y)=A(x,y)+B(x,y)cos[ ϕ(x,y) 3π/2 + ε 2 (x,y)/2 + ε 3 (x,y) ].
ϕ (x,y)= tan 1 [ I 2 (x,y) I 4 (x,y) I 1 (x,y) I 3 (x,y) ],
Δϕ(x,y)= ϕ (x,y)ϕ(x,y).
ϕ (x,y)= tan 1 [ sin( ϕ ε 2 /2 )+sin( ϕ+ ε 2 /2 + ε 3 ) cos( ϕ ε 2 /2 ε 1 )+cos( ϕ+ ε 2 /2 ) ].
ϕ (x,y) tan 1 [ 2sinϕ+ ε 3 cosϕ 2cosϕ+ ε 1 sinϕ ].
Δϕ(x,y)= tan 1 [ ε 3 cos 2 ϕ ε 1 sin 2 ϕ 2+( ε 1 + ε 3 )sinϕcosϕ ].
Δϕ(x,y) ε 3 ε 1 4 + ε 3 + ε 1 4 cos2ϕ.
Δ ϕ 2 (x,y) ε 3 ε 1 4 + ε 3 + ε 1 4 cos2 ϕ 2 .
Δ ϕ 4 (x,y) ε 5 ε 3 4 + ε 5 + ε 3 4 cos2 ϕ 4 .
ϕ 4 (x,y) ϕ 2 (x,y)=π+ ε 3 + ( ε 2 + ε 4 )/2 .
ε i+2 (x,y) ε i+1 (x,y) ε i+1 (x,y) ε i (x,y).
ϕ 4 (x,y) ϕ 2 (x,y)+π=( ϕ 4 +Δ ϕ 4 )( ϕ 2 +Δ ϕ 2 )+π 2 ε 3 + ε 4 ε 2 2 cos( 2 ϕ 2 )2 ε 3 ε 4 sin( 2 ϕ 2 ).
ε 3 (x,y)= ϕ 4 ϕ 2 +π 2 V .
ε 1 (x,y)= ϕ 2 ϕ 0 +π 2 V .
θ 1 (x,y)= ε 2 /2 + ε 1 , θ 2 (x,y)=π/2 + ε 2 /2 , θ 3 (x,y)=π ε 2 /2 , θ 4 (x,y)= 3π/2 ε 2 /2 ε 3 .

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