Abstract

Fringe projection profilometry has been widely used in high-speed three-dimensional (3D) shape measurement. To improve the speed without loss of accuracy, we present a novel single-shot 3D shape measuring system that utilizes a coaxial fringe projection system and a 2CCD camera. The coaxial fringe projection system, comprising a visible light (red, green, and blue) projector and an infrared (IR) light projector, can simultaneously project red, green, blue, and IR fringe patterns. The 2CCD camera, as the name suggests, has two CCD chips that can acquire visible and IR fringe patterns at the same time. Combining the two-step phase-shifting algorithm, Fourier transform profilometry, and the optimum three-frequency selection method, 3D shape measurement of complex surfaces such as large slopes or discontinuous objects can be obtained from single-shot acquisition. A virtual fringe projection measurement system has been established to generate pre-deformed fringe patterns to correct positional deviations of the coaxial fringe projection system. This method has been applied to simulations and experiments on static and dynamic objects with promising results.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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  1. J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recogn. 43, 2666–2680 (2010).
    [Crossref]
  2. S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48, 133–140 (2010).
    [Crossref]
  3. F. Chen, G. M. Brown, and M. M. Song, “Overview of 3-D shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
    [Crossref]
  4. M. Takeda, Q. Gu, M. Kinoshita, H. Takai, and Y. Takahashi, “Frequency-multiplex Fourier-transform profilometry: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations,” Appl. Opt. 36, 5347–5354 (1997).
    [Crossref]
  5. L. C. Chen, H. W. Ho, and X. L. Nguyen, “Fourier transform profilometry (FTP) using an innovative band-pass filter for accurate 3-D surface reconstruction,” Opt. Lasers Eng. 48, 182–190 (2010).
    [Crossref]
  6. P. S. Huang, C. P. Zhang, and F. P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
    [Crossref]
  7. X. Y. Su, G. V. Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
    [Crossref]
  8. D. S. Mehta, S. K. Dubey, M. M. Hossain, and C. Shakher, “Simple multifrequency and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry for three-dimensional profilometry,” Appl. Opt. 44, 7515–7521 (2005).
    [Crossref]
  9. J. P. Zhu, P. Zhou, X. Y. Su, and Z. S. You, “Accurate and fast 3D surface measurement with temporal-spatial binary encoding structured illumination,” Opt. Express 24, 28549–28560 (2016).
    [Crossref]
  10. C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimized multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43, 788–800 (2005).
    [Crossref]
  11. K. Liu, Y. C. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18, 5229–5244 (2010).
    [Crossref]
  12. S. Zhang and S. T. Yau, “High-speed three-dimensional shape measurement system using a modified two-plus-one phase-shifting algorithm,” Opt. Eng. 46, 113603 (2007).
    [Crossref]
  13. S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 1269–1278 (2006).
    [Crossref]
  14. Z. H. Zhang, D. P. Towers, and C. E. Towers, “Snapshot color fringe projection for absolute three-dimensional metrology of video sequences,” Appl. Opt. 49, 5947–5953 (2010).
    [Crossref]
  15. W. H. Su, “Color-encoded fringe projection for 3D shape measurements,” Opt. Express 15, 13167–13181 (2007).
    [Crossref]
  16. W. Y. Liu, Z. Q. Wang, G. G. Mu, and Z. L. Fang, “Color-coded projection grating method for shape measurement with a single exposure,” Appl. Opt. 39, 3504–3508 (2000).
    [Crossref]
  17. S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
    [Crossref]
  18. S. Zhang, D. V. D. Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18, 9684–9689 (2010).
    [Crossref]
  19. J. S. Hyun, B. W. Li, and S. Zhang, “High-speed high-accuracy three-dimensional shape measurement using digital binary defocusing method versus sinusoidal method,” Opt. Eng. 56, 074102 (2017).
    [Crossref]
  20. P. Ou, B. W. Li, Y. J. Wang, and S. Zhang, “Flexible real-time natural 2D color and 3D shape measurement,” Opt. Express 21, 16736–16741 (2013).
    [Crossref]
  21. Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3D shape and colour texture of moving objects using IR and colour fringe projection techniques,” Opt. Lasers Eng. 61, 1–7 (2014).
    [Crossref]
  22. A. H. Phan, M. L. Piao, J. H. Park, and N. Kim, “Error analysis in parallel two-step phase-shifting method,” Appl. Opt. 52, 2385–2393 (2013).
    [Crossref]
  23. Z. H. Zhang, C. E. Towers, and D. P. Towers, “Time efficient color fringe projection system for 3D shape and color using optimum 3-frequency selection,” Opt. Express 14, 6444–6455 (2006).
    [Crossref]
  24. Z. H. Zhang, S. J. Huang, S. S. Meng, F. Gao, and X. Q. Jiang, “A simple, flexible and automatic 3D calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21, 12218–12227 (2013).
    [Crossref]
  25. X. X. Zhang, Y. M. Wang, S. J. Huang, N. Gao, and Z. H. Zhang, “A two-step phase-shifting algorithm for phase calculation,” Acta Photon. Sinica 46, 0311005 (2017).
    [Crossref]
  26. X. Y. Su and W. J. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).
    [Crossref]
  27. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
    [Crossref]
  28. B. Li, N. Karpinsky, and S. Zhang, “Novel calibration method for structured-light system with an out-of-focus projector,” Appl. Opt. 53, 3415–3426 (2014).
    [Crossref]
  29. S. J. Huang, L. L. Xie, Z. Y. Wang, Z. H. Zhang, F. Gao, and X. Q. Jiang, “Accurate projector calibration method by using an optical coaxial camera,” Appl. Opt. 54, 789–795 (2015).
    [Crossref]

2017 (2)

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

X. X. Zhang, Y. M. Wang, S. J. Huang, N. Gao, and Z. H. Zhang, “A two-step phase-shifting algorithm for phase calculation,” Acta Photon. Sinica 46, 0311005 (2017).
[Crossref]

2016 (1)

2015 (1)

2014 (2)

B. Li, N. Karpinsky, and S. Zhang, “Novel calibration method for structured-light system with an out-of-focus projector,” Appl. Opt. 53, 3415–3426 (2014).
[Crossref]

Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3D shape and colour texture of moving objects using IR and colour fringe projection techniques,” Opt. Lasers Eng. 61, 1–7 (2014).
[Crossref]

2013 (3)

2010 (7)

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

S. Zhang, D. V. D. Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18, 9684–9689 (2010).
[Crossref]

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

Z. H. Zhang, D. P. Towers, and C. E. Towers, “Snapshot color fringe projection for absolute three-dimensional metrology of video sequences,” Appl. Opt. 49, 5947–5953 (2010).
[Crossref]

L. C. Chen, H. W. Ho, and X. L. Nguyen, “Fourier transform profilometry (FTP) using an innovative band-pass filter for accurate 3-D surface reconstruction,” Opt. Lasers Eng. 48, 182–190 (2010).
[Crossref]

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recogn. 43, 2666–2680 (2010).
[Crossref]

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

2007 (2)

W. H. Su, “Color-encoded fringe projection for 3D shape measurements,” Opt. Express 15, 13167–13181 (2007).
[Crossref]

S. Zhang and S. T. Yau, “High-speed three-dimensional shape measurement system using a modified two-plus-one phase-shifting algorithm,” Opt. Eng. 46, 113603 (2007).
[Crossref]

2006 (2)

2005 (2)

D. S. Mehta, S. K. Dubey, M. M. Hossain, and C. Shakher, “Simple multifrequency and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry for three-dimensional profilometry,” Appl. Opt. 44, 7515–7521 (2005).
[Crossref]

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimized multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43, 788–800 (2005).
[Crossref]

2003 (1)

P. S. Huang, C. P. Zhang, and F. P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[Crossref]

2001 (1)

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

2000 (3)

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

F. Chen, G. M. Brown, and M. M. Song, “Overview of 3-D shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[Crossref]

W. Y. Liu, Z. Q. Wang, G. G. Mu, and Z. L. Fang, “Color-coded projection grating method for shape measurement with a single exposure,” Appl. Opt. 39, 3504–3508 (2000).
[Crossref]

1997 (1)

1993 (1)

X. Y. Su, G. V. Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[Crossref]

Bally, G. V.

X. Y. Su, G. V. Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[Crossref]

Brown, G. M.

F. Chen, G. M. Brown, and M. M. Song, “Overview of 3-D shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[Crossref]

Chen, C.

Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3D shape and colour texture of moving objects using IR and colour fringe projection techniques,” Opt. Lasers Eng. 61, 1–7 (2014).
[Crossref]

Chen, F.

F. Chen, G. M. Brown, and M. M. Song, “Overview of 3-D shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[Crossref]

Chen, L. C.

L. C. Chen, H. W. Ho, and X. L. Nguyen, “Fourier transform profilometry (FTP) using an innovative band-pass filter for accurate 3-D surface reconstruction,” Opt. Lasers Eng. 48, 182–190 (2010).
[Crossref]

Chen, W. J.

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

Chiang, F. P.

P. S. Huang, C. P. Zhang, and F. P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[Crossref]

Dubey, S. K.

Fang, Z. L.

Fernandez, S.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recogn. 43, 2666–2680 (2010).
[Crossref]

Gao, F.

Gao, N.

X. X. Zhang, Y. M. Wang, S. J. Huang, N. Gao, and Z. H. Zhang, “A two-step phase-shifting algorithm for phase calculation,” Acta Photon. Sinica 46, 0311005 (2017).
[Crossref]

Gorthi, S. S.

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

Gu, Q.

Hao, Q.

Hassebrook, L. G.

Ho, H. W.

L. C. Chen, H. W. Ho, and X. L. Nguyen, “Fourier transform profilometry (FTP) using an innovative band-pass filter for accurate 3-D surface reconstruction,” Opt. Lasers Eng. 48, 182–190 (2010).
[Crossref]

Hossain, M. M.

Huang, P. S.

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 1269–1278 (2006).
[Crossref]

P. S. Huang, C. P. Zhang, and F. P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[Crossref]

Huang, S. J.

X. X. Zhang, Y. M. Wang, S. J. Huang, N. Gao, and Z. H. Zhang, “A two-step phase-shifting algorithm for phase calculation,” Acta Photon. Sinica 46, 0311005 (2017).
[Crossref]

S. J. Huang, L. L. Xie, Z. Y. Wang, Z. H. Zhang, F. Gao, and X. Q. Jiang, “Accurate projector calibration method by using an optical coaxial camera,” Appl. Opt. 54, 789–795 (2015).
[Crossref]

Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3D shape and colour texture of moving objects using IR and colour fringe projection techniques,” Opt. Lasers Eng. 61, 1–7 (2014).
[Crossref]

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

Hyun, J. S.

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

Jiang, X. Q.

Jones, J. D. C.

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimized multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43, 788–800 (2005).
[Crossref]

Karpinsky, N.

Kim, N.

Kinoshita, M.

Lau, D. L.

Li, B.

Li, B. W.

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

P. Ou, B. W. Li, Y. J. Wang, and S. Zhang, “Flexible real-time natural 2D color and 3D shape measurement,” Opt. Express 21, 16736–16741 (2013).
[Crossref]

Liu, K.

Liu, W. Y.

Llado, X.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recogn. 43, 2666–2680 (2010).
[Crossref]

Mehta, D. S.

Meng, S. S.

Mu, G. G.

Nguyen, X. L.

L. C. Chen, H. W. Ho, and X. L. Nguyen, “Fourier transform profilometry (FTP) using an innovative band-pass filter for accurate 3-D surface reconstruction,” Opt. Lasers Eng. 48, 182–190 (2010).
[Crossref]

Oliver, J.

Ou, P.

Park, J. H.

Phan, A. H.

Piao, M. L.

Pribanic, T.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recogn. 43, 2666–2680 (2010).
[Crossref]

Rastogi, P.

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

Salvi, J.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recogn. 43, 2666–2680 (2010).
[Crossref]

Shakher, C.

Song, M. M.

F. Chen, G. M. Brown, and M. M. Song, “Overview of 3-D shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[Crossref]

Su, W. H.

Su, X. Y.

J. P. Zhu, P. Zhou, X. Y. Su, and Z. S. You, “Accurate and fast 3D surface measurement with temporal-spatial binary encoding structured illumination,” Opt. Express 24, 28549–28560 (2016).
[Crossref]

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

X. Y. Su, G. V. Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[Crossref]

Takahashi, Y.

Takai, H.

Takeda, M.

Towers, C. E.

Towers, D. P.

Vukicevic, D.

X. Y. Su, G. V. Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[Crossref]

Wang, Y. C.

Wang, Y. J.

Wang, Y. M.

X. X. Zhang, Y. M. Wang, S. J. Huang, N. Gao, and Z. H. Zhang, “A two-step phase-shifting algorithm for phase calculation,” Acta Photon. Sinica 46, 0311005 (2017).
[Crossref]

Wang, Z. Q.

Wang, Z. Y.

Weide, D. V. D.

Xie, L. L.

Xu, Y. J.

Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3D shape and colour texture of moving objects using IR and colour fringe projection techniques,” Opt. Lasers Eng. 61, 1–7 (2014).
[Crossref]

Yau, S. T.

S. Zhang and S. T. Yau, “High-speed three-dimensional shape measurement system using a modified two-plus-one phase-shifting algorithm,” Opt. Eng. 46, 113603 (2007).
[Crossref]

You, Z. S.

Zhang, C. P.

P. S. Huang, C. P. Zhang, and F. P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[Crossref]

Zhang, S.

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

B. Li, N. Karpinsky, and S. Zhang, “Novel calibration method for structured-light system with an out-of-focus projector,” Appl. Opt. 53, 3415–3426 (2014).
[Crossref]

P. Ou, B. W. Li, Y. J. Wang, and S. Zhang, “Flexible real-time natural 2D color and 3D shape measurement,” Opt. Express 21, 16736–16741 (2013).
[Crossref]

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

S. Zhang, D. V. D. Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18, 9684–9689 (2010).
[Crossref]

S. Zhang and S. T. Yau, “High-speed three-dimensional shape measurement system using a modified two-plus-one phase-shifting algorithm,” Opt. Eng. 46, 113603 (2007).
[Crossref]

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 1269–1278 (2006).
[Crossref]

Zhang, X. X.

X. X. Zhang, Y. M. Wang, S. J. Huang, N. Gao, and Z. H. Zhang, “A two-step phase-shifting algorithm for phase calculation,” Acta Photon. Sinica 46, 0311005 (2017).
[Crossref]

Zhang, Z. H.

Zhang, Z. Y.

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

Zhou, P.

Zhu, J. P.

Acta Photon. Sinica (1)

X. X. Zhang, Y. M. Wang, S. J. Huang, N. Gao, and Z. H. Zhang, “A two-step phase-shifting algorithm for phase calculation,” Acta Photon. Sinica 46, 0311005 (2017).
[Crossref]

Appl. Opt. (7)

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

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

Opt. Commun. (1)

X. Y. Su, G. V. Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Opt. Commun. 98, 141–150 (1993).
[Crossref]

Opt. Eng. (5)

S. Zhang and S. T. Yau, “High-speed three-dimensional shape measurement system using a modified two-plus-one phase-shifting algorithm,” Opt. Eng. 46, 113603 (2007).
[Crossref]

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 1269–1278 (2006).
[Crossref]

F. Chen, G. M. Brown, and M. M. Song, “Overview of 3-D shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[Crossref]

P. S. Huang, C. P. Zhang, and F. P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[Crossref]

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

Opt. Express (7)

Opt. Lasers Eng. (6)

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

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimized multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43, 788–800 (2005).
[Crossref]

L. C. Chen, H. W. Ho, and X. L. Nguyen, “Fourier transform profilometry (FTP) using an innovative band-pass filter for accurate 3-D surface reconstruction,” Opt. Lasers Eng. 48, 182–190 (2010).
[Crossref]

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

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

Y. J. Xu, C. Chen, S. J. Huang, and Z. H. Zhang, “Simultaneously measuring 3D shape and colour texture of moving objects using IR and colour fringe projection techniques,” Opt. Lasers Eng. 61, 1–7 (2014).
[Crossref]

Pattern Recogn. (1)

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recogn. 43, 2666–2680 (2010).
[Crossref]

Supplementary Material (1)

NameDescription
» Visualization 1       3D shape data of a human hand

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Figures (22)

Fig. 1.
Fig. 1. Geometry of FPP.
Fig. 2.
Fig. 2. Schematic diagram of coaxial projection measurement system.
Fig. 3.
Fig. 3. Four ideal independent patterns for four channels.
Fig. 4.
Fig. 4. Model of virtual fringe projection system.
Fig. 5.
Fig. 5. Simulation experiments.
Fig. 6.
Fig. 6. Deformed fringe patterns captured by virtual camera.
Fig. 7.
Fig. 7. Unwrapped phase map: (a) by single projector P1; (b) partly by projector P1and projector P2.
Fig. 8.
Fig. 8. Photograph of coaxial projection measurement system.
Fig. 9.
Fig. 9. “Captured images” created for projector calibration.
Fig. 10.
Fig. 10. Reprojection error of two projectors. (a) VLP; (b) ILP.
Fig. 11.
Fig. 11. Profile along row 130 for three unwrapped phase maps.
Fig. 12.
Fig. 12. Profile along row 130 for phase errors. (a) Coaxial projectors without deviation correction; (b) coaxial projectors after deviation correction.
Fig. 13.
Fig. 13. Simulated measured object. (a) Height distribution of simulated object; (b) deformed fringe pattern of the simulated object.
Fig. 14.
Fig. 14. Unwrapped phase maps. (a) Traditional FTP; (b) improved FTP; (c) proposed method; (d) four-step phase-shifting algorithm.
Fig. 15.
Fig. 15. Profile along row 760 for phase errors.
Fig. 16.
Fig. 16. Fringe patterns of the mask. (a) Projected composite color fringe pattern; (b) projected IR fringe pattern; (c) captured deformed composite color fringe pattern; (d) captured deformed IR fringe pattern.
Fig. 17.
Fig. 17. Phase maps of the mask. (a) Wrapped phase in red and blue components; (b) wrapped phase in green component; (c) wrapped phase in IR component; (d) unwrapped phase.
Fig. 18.
Fig. 18. 3D shape data of the mask.
Fig. 19.
Fig. 19. Captured patterns of a set of steps. (a) Deformed composite color fringe pattern; (b) deformed IR fringe pattern.
Fig. 20.
Fig. 20. Phase maps of a set of steps. (a) Wrapped phase in red and blue components; (b) wrapped phase in green component; (c) wrapped phase in IR component; (d) unwrapped phase.
Fig. 21.
Fig. 21. 3D shape data of a set of steps.
Fig. 22.
Fig. 22. 3D shape data of a human hand (see Visualization 1).

Tables (3)

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Table 1. Allowable Deviations of Coaxial Projectors

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Table 2. Calibrated Intrinsic Parameters and Coefficients of Lens Distortion of Projectors

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Table 3. Deviations of Coaxial Projectors After Correction

Equations (29)

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h(x,y)=L02πL02dcosθP0Δφ(x,y)(L0+xcosθsinθ)2dcosθsinθL0+xcosθsinθ+1.
h(x,y)=n=0Nan(x,y)Δφ(x,y)n,n=0,1,,N,
IR(x,y)=IR(x,y)+IR(x,y)cos[2πf0x+φ(x,y)],
IB(x,y)=IB(x,y)+IB(x,y)cos[2πf0x+φ(x,y)+π2],
IG(x,y)=IG(x,y)+IG(x,y)cos[2πf0x+φ(x,y)],
IIR(x,y)=IIR(x,y)+IIR(x,y)cos[2πf0x+φ(x,y)],
IB(x,y)IR(x,y)=IB(x,y)cos[2πf0x+φ(x,y)+π2]IR(x,y)cos[2πf0x+φ(x,y)]=tan[φ(x,y)].
2πf0x+φ(x,y)=arctan[IB(x,y)IR(x,y)].
I(x,y)=I(x,y)+c(x,y)exp(2πjfoxx+2πjfoyy)+c*(x,y)exp(2πjfoxx2πjfoyy),
c(x,y)=12I(x,y)exp[jφ(x,y)].
I(u,v)=C(uf0x,vf0y)+C*(u+f0x,v+f0y).
φ(x,y)=arctanIm[c(X,Y)]Re[c(X,Y)],
|h(x,y)x|<L03d.
|h(x,y)x|<L0d.
spc=Ac[RcTc]Pw=HcPw,
Ac=[fuc0u0c00fvcv0c00010],
xdc=(1+k1r2+k2r4)xnc,+(2k3xncync+k4(r2+2(xnc)2)),ydc=(1+k1r2+k2r4)ync+(k3(r2+2(ync)2)+2k4xncync)r2=(xnc)2+(ync)2,
pc=Acpdc.
spp=Ap[RpTp]Pw=HpPw,
F(xc,yc,zc)=0.
spc=AcPc.
(Hc)1pc=Pw.
spp=HpPw=Hp(Hc)1pc=Hpcpc,
spp=Hpcpc=HpcAcPc.
sPp1=Rp1Pw+Tp1,
sPp2=Rp2Pw+Tp2.
sPp2=Rp2(Rp1)1(Pp1Tp1)+Tp2=Rp12Pp1+Tp12,
Rp12=Rp2(Rp1)1,Tp12=Rp2(Rp1)1Tp1+Tp2.
z=3(1x)2exp[x2(y+1)2]10(15xx3y5)exp(x2y2)13exp[(x+1)2y2].