Abstract

In phase-measuring profilometry, the lens distortion of commercial projectors may introduce additional bending carrier phase and thus lead to measurement errors. To address this problem, this paper presents an adaptive fringe projection technique in which the carrier phase in the projected fringe patterns is modified according to the projector distortion. After projecting these adaptive fringe patterns, the bending carrier phase induced by the projector distortion is eliminated. Experimental results demonstrate this method to be effective and efficient in suppressing the projector distortion for phase-measuring profilometry. More importantly, this method does not need to calibrate the projector and system parameters, such as the distortion coefficients of the projector and the angle between the optical axes of projector and camera lenses. Hence, it has low computational complexity and enables us to improve the measurement precision for an arbitrary phase-measuring profilometry system.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Sub-pixel projector calibration method for fringe projection profilometry

Wei Zhang, Weishi Li, Liandong Yu, Hui Luo, Huining Zhao, and Haojie Xia
Opt. Express 25(16) 19158-19169 (2017)

Self-correction of projector nonlinearity in phase-shifting fringe projection profilometry

Fuxing Lü, Shuo Xing, and Hongwei Guo
Appl. Opt. 56(25) 7204-7216 (2017)

References

  • View by:
  • |
  • |
  • |

  1. S. S. Gorthi and P. Pastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
    [Crossref]
  2. M. Takeda and K. Mutoh, “Fourier-transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
    [Crossref] [PubMed]
  3. K. Qian, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2692–2702 (2004).
  4. H. Schreiber and J. H. Bruning, “Phase Shifting Interferometry,” in Optical Shop Testing, D. Malacara, (John Wiley and Sons, 2007), pp. 547–612.
    [Crossref]
  5. J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32(17), 3047–3052 (1993).
    [Crossref] [PubMed]
  6. S. Cui and X. Zhu, “A generalized reference-plane-based calibration method in optical triangular profilometry,” Opt. Express 17(23), 20735–20746 (2009).
    [Crossref] [PubMed]
  7. Z. Zhang, “A flexible new technique for camera calibration,” IEEE T. Pattern Anal. 22(1), 1330–1334 (2000).
    [Crossref]
  8. J. Salvi, X. Armangué, and J. Batlle, “A comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recogn. 35(7), 1617–1635 (2002).
    [Crossref]
  9. L. Huang, Q. Zhang, and A. Asundi, “Flexible camera calibration using not-measured imperfect target,” Appl. Opt. 52(25), 6278–6286 (2013).
    [Crossref] [PubMed]
  10. W. Lohry, V. Chen, and S. Zhang, “Absolute three-dimensional shape measurement using coded fringe patterns without phase unwrapping or projector calibration,” Opt. Express 22(2), 1287–1301 (2014).
    [Crossref] [PubMed]
  11. S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
    [Crossref]
  12. Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
    [Crossref]
  13. Z. Huang, J. Xi, Y. Yu, and Q. Guo, “Accurate projector calibration based on a new point-to-point mapping relationship between the camera and projector images,” Appl. Opt. 54(3), 347–356 (2015).
    [Crossref]
  14. S. Huang, L. Xie, Z. Wang, Z. Zhang, F. Gao, and X. Jiang, “Accurate projector calibration method by using an optical coaxial camera,” Appl. Opt. 54(4), 789–795 (2015).
    [Crossref] [PubMed]
  15. Y. Yin, X. Peng, A. Li, X. Liu, and B. Z. Gao, “Calibration of fringe projection profilometry with bundle adjustment strategy,” Opt. Lett. 37(4), 542–544 (2012).
    [Crossref] [PubMed]
  16. X. Zhang and L. Zhu, “Projector calibration from the camera image point of view,” Opt. Eng. 48(11), 117208 (2009).
    [Crossref]
  17. Z. Zhang, C. E. Towers, and D. P. Towers, “Uneven fringe projection for efficient calibration in high-resolution 3d shape metrology,” Appl. Opt. 46(24), 6113–6119 (2007).
    [Crossref] [PubMed]
  18. Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3d calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 101–105 (2013).
    [Crossref]
  19. 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]
  20. E. U. Wagemann, M. Schönleber, and H.-J. Tiziani, “Grazing holographic projection of object-adapted fringes for shape measurements with enhanced sensitivity,” Opt. Lett. 23(20), 1621–1623 (1998).
    [Crossref]
  21. W. Li, T. Bothe, W. Osten, and M. Kalms, “Object adapted pattern projection - Part I: Generation of inverse patterns,” Opt. Lasers Eng. 41(1), 31–50 (2004).
    [Crossref]
  22. J. Peng, Y. Yu, W. Zhou, and M. Chen, “Using triangle-based cubic interpolation in generation of object-adaptive fringe pattern,” Opt. Lasers Eng. 52(1), 41–52 (2014).
    [Crossref]
  23. S. Matthias, C. Ohrt, A. Pösch, M. Kästner, and E. Reithmeier, “Single image geometry inspection using inverse endoscopic fringe projection,” ACTA IMEKO 4, 4–9 (2015).
    [Crossref]
  24. T. Peng and S. K. Gupta, “Model and algorithms for point cloud construction using digital projection patterns,” J. Comput. Inf. Sci. Eng. 7, 372–381 (2007).
    [Crossref]
  25. D. Li and J. Kofman, “Adaptive fringe-pattern projection for image saturation avoidance in 3d surface-shape measurement,” Opt. Express 22(8), 9887–9901 (2014).
    [Crossref] [PubMed]
  26. H. Lin, J. Gao, Q. Mei, Y. He, J. Liu, and X. Wang, “Adaptive digital fringe projection technique for high dynamic range three-dimensional shape measurement,” Opt. Express 24(7), 7703–7718 (2016)
    [Crossref] [PubMed]
  27. C. E. Towers, D. P. Towers, and J. D. C. Jones, “Optimum frequency selection in multifrequency interferometry.” Opt. Lett. 28(11), 887–889 (2004).
    [Crossref]
  28. C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43(7), 788–800 (2005).
    [Crossref]
  29. H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
    [Crossref]

2016 (1)

2015 (3)

2014 (3)

2013 (2)

Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3d calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 101–105 (2013).
[Crossref]

L. Huang, Q. Zhang, and A. Asundi, “Flexible camera calibration using not-measured imperfect target,” Appl. Opt. 52(25), 6278–6286 (2013).
[Crossref] [PubMed]

2012 (1)

2010 (1)

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

2009 (2)

2008 (1)

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

2007 (2)

T. Peng and S. K. Gupta, “Model and algorithms for point cloud construction using digital projection patterns,” J. Comput. Inf. Sci. Eng. 7, 372–381 (2007).
[Crossref]

Z. Zhang, C. E. Towers, and D. P. Towers, “Uneven fringe projection for efficient calibration in high-resolution 3d shape metrology,” Appl. Opt. 46(24), 6113–6119 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (2)

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43(7), 788–800 (2005).
[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]

2004 (3)

W. Li, T. Bothe, W. Osten, and M. Kalms, “Object adapted pattern projection - Part I: Generation of inverse patterns,” Opt. Lasers Eng. 41(1), 31–50 (2004).
[Crossref]

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Optimum frequency selection in multifrequency interferometry.” Opt. Lett. 28(11), 887–889 (2004).
[Crossref]

K. Qian, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2692–2702 (2004).

2002 (1)

J. Salvi, X. Armangué, and J. Batlle, “A comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recogn. 35(7), 1617–1635 (2002).
[Crossref]

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE T. Pattern Anal. 22(1), 1330–1334 (2000).
[Crossref]

1998 (1)

1993 (1)

1983 (1)

Armangué, X.

J. Salvi, X. Armangué, and J. Batlle, “A comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recogn. 35(7), 1617–1635 (2002).
[Crossref]

Asundi, A.

Batlle, J.

J. Salvi, X. Armangué, and J. Batlle, “A comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recogn. 35(7), 1617–1635 (2002).
[Crossref]

Bothe, T.

W. Li, T. Bothe, W. Osten, and M. Kalms, “Object adapted pattern projection - Part I: Generation of inverse patterns,” Opt. Lasers Eng. 41(1), 31–50 (2004).
[Crossref]

Bruning, J. H.

H. Schreiber and J. H. Bruning, “Phase Shifting Interferometry,” in Optical Shop Testing, D. Malacara, (John Wiley and Sons, 2007), pp. 547–612.
[Crossref]

Chen, M.

J. Peng, Y. Yu, W. Zhou, and M. Chen, “Using triangle-based cubic interpolation in generation of object-adaptive fringe pattern,” Opt. Lasers Eng. 52(1), 41–52 (2014).
[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]

Chen, V.

Cui, S.

Gao, B. Z.

Gao, F.

S. Huang, L. Xie, Z. Wang, Z. Zhang, F. Gao, and X. Jiang, “Accurate projector calibration method by using an optical coaxial camera,” Appl. Opt. 54(4), 789–795 (2015).
[Crossref] [PubMed]

Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3d calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 101–105 (2013).
[Crossref]

Gao, J.

Gorthi, S. S.

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

Guo, H.

Guo, Q.

Gupta, S. K.

T. Peng and S. K. Gupta, “Model and algorithms for point cloud construction using digital projection patterns,” J. Comput. Inf. Sci. Eng. 7, 372–381 (2007).
[Crossref]

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]

He, Y.

Huang, L.

Huang, P. S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

Huang, S.

S. Huang, L. Xie, Z. Wang, Z. Zhang, F. Gao, and X. Jiang, “Accurate projector calibration method by using an optical coaxial camera,” Appl. Opt. 54(4), 789–795 (2015).
[Crossref] [PubMed]

Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3d calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 101–105 (2013).
[Crossref]

Huang, Z.

Huntley, J. M.

Jiang, X.

S. Huang, L. Xie, Z. Wang, Z. Zhang, F. Gao, and X. Jiang, “Accurate projector calibration method by using an optical coaxial camera,” Appl. Opt. 54(4), 789–795 (2015).
[Crossref] [PubMed]

Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3d calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 101–105 (2013).
[Crossref]

Jones, J. D. C.

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43(7), 788–800 (2005).
[Crossref]

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Optimum frequency selection in multifrequency interferometry.” Opt. Lett. 28(11), 887–889 (2004).
[Crossref]

Kalms, M.

W. Li, T. Bothe, W. Osten, and M. Kalms, “Object adapted pattern projection - Part I: Generation of inverse patterns,” Opt. Lasers Eng. 41(1), 31–50 (2004).
[Crossref]

Kästner, M.

S. Matthias, C. Ohrt, A. Pösch, M. Kästner, and E. Reithmeier, “Single image geometry inspection using inverse endoscopic fringe projection,” ACTA IMEKO 4, 4–9 (2015).
[Crossref]

Kofman, J.

Li, A.

Li, D.

Li, W.

W. Li, T. Bothe, W. Osten, and M. Kalms, “Object adapted pattern projection - Part I: Generation of inverse patterns,” Opt. Lasers Eng. 41(1), 31–50 (2004).
[Crossref]

Li, Z.

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

Lin, H.

Liu, J.

Liu, X.

Lohry, W.

Matthias, S.

S. Matthias, C. Ohrt, A. Pösch, M. Kästner, and E. Reithmeier, “Single image geometry inspection using inverse endoscopic fringe projection,” ACTA IMEKO 4, 4–9 (2015).
[Crossref]

Mei, Q.

Meng, S.

Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3d calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 101–105 (2013).
[Crossref]

Mutoh, K.

Ohrt, C.

S. Matthias, C. Ohrt, A. Pösch, M. Kästner, and E. Reithmeier, “Single image geometry inspection using inverse endoscopic fringe projection,” ACTA IMEKO 4, 4–9 (2015).
[Crossref]

Osten, W.

W. Li, T. Bothe, W. Osten, and M. Kalms, “Object adapted pattern projection - Part I: Generation of inverse patterns,” Opt. Lasers Eng. 41(1), 31–50 (2004).
[Crossref]

Pastogi, P.

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

Peng, J.

J. Peng, Y. Yu, W. Zhou, and M. Chen, “Using triangle-based cubic interpolation in generation of object-adaptive fringe pattern,” Opt. Lasers Eng. 52(1), 41–52 (2014).
[Crossref]

Peng, T.

T. Peng and S. K. Gupta, “Model and algorithms for point cloud construction using digital projection patterns,” J. Comput. Inf. Sci. Eng. 7, 372–381 (2007).
[Crossref]

Peng, X.

Pösch, A.

S. Matthias, C. Ohrt, A. Pösch, M. Kästner, and E. Reithmeier, “Single image geometry inspection using inverse endoscopic fringe projection,” ACTA IMEKO 4, 4–9 (2015).
[Crossref]

Qian, K.

K. Qian, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2692–2702 (2004).

Reithmeier, E.

S. Matthias, C. Ohrt, A. Pösch, M. Kästner, and E. Reithmeier, “Single image geometry inspection using inverse endoscopic fringe projection,” ACTA IMEKO 4, 4–9 (2015).
[Crossref]

Saldner, H.

Salvi, J.

J. Salvi, X. Armangué, and J. Batlle, “A comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recogn. 35(7), 1617–1635 (2002).
[Crossref]

Schönleber, M.

Schreiber, H.

H. Schreiber and J. H. Bruning, “Phase Shifting Interferometry,” in Optical Shop Testing, D. Malacara, (John Wiley and Sons, 2007), pp. 547–612.
[Crossref]

Shi, Y.

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

Takeda, M.

Tiziani, H.-J.

Towers, C. E.

Towers, D. P.

Wagemann, E. U.

Wang, C.

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

Wang, X.

Wang, Y.

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

Wang, Z.

Xi, J.

Xie, L.

Yin, Y.

Yu, Y.

Z. Huang, J. Xi, Y. Yu, and Q. Guo, “Accurate projector calibration based on a new point-to-point mapping relationship between the camera and projector images,” Appl. Opt. 54(3), 347–356 (2015).
[Crossref]

J. Peng, Y. Yu, W. Zhou, and M. Chen, “Using triangle-based cubic interpolation in generation of object-adaptive fringe pattern,” Opt. Lasers Eng. 52(1), 41–52 (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]

Zhang, Q.

Zhang, S.

Zhang, X.

X. Zhang and L. Zhu, “Projector calibration from the camera image point of view,” Opt. Eng. 48(11), 117208 (2009).
[Crossref]

Zhang, Z.

S. Huang, L. Xie, Z. Wang, Z. Zhang, F. Gao, and X. Jiang, “Accurate projector calibration method by using an optical coaxial camera,” Appl. Opt. 54(4), 789–795 (2015).
[Crossref] [PubMed]

Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3d calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 101–105 (2013).
[Crossref]

Z. Zhang, C. E. Towers, and D. P. Towers, “Uneven fringe projection for efficient calibration in high-resolution 3d shape metrology,” Appl. Opt. 46(24), 6113–6119 (2007).
[Crossref] [PubMed]

Z. Zhang, “A flexible new technique for camera calibration,” IEEE T. Pattern Anal. 22(1), 1330–1334 (2000).
[Crossref]

Zheng, P.

Zhou, W.

J. Peng, Y. Yu, W. Zhou, and M. Chen, “Using triangle-based cubic interpolation in generation of object-adaptive fringe pattern,” Opt. Lasers Eng. 52(1), 41–52 (2014).
[Crossref]

Zhu, L.

X. Zhang and L. Zhu, “Projector calibration from the camera image point of view,” Opt. Eng. 48(11), 117208 (2009).
[Crossref]

Zhu, X.

ACTA IMEKO (1)

S. Matthias, C. Ohrt, A. Pösch, M. Kästner, and E. Reithmeier, “Single image geometry inspection using inverse endoscopic fringe projection,” ACTA IMEKO 4, 4–9 (2015).
[Crossref]

Appl. Opt. (7)

IEEE T. Pattern Anal. (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE T. Pattern Anal. 22(1), 1330–1334 (2000).
[Crossref]

J. Comput. Inf. Sci. Eng. (1)

T. Peng and S. K. Gupta, “Model and algorithms for point cloud construction using digital projection patterns,” J. Comput. Inf. Sci. Eng. 7, 372–381 (2007).
[Crossref]

Opt. Eng. (4)

X. Zhang and L. Zhu, “Projector calibration from the camera image point of view,” Opt. Eng. 48(11), 117208 (2009).
[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]

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

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

Opt. Express (5)

Opt. Lasers Eng. (4)

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

W. Li, T. Bothe, W. Osten, and M. Kalms, “Object adapted pattern projection - Part I: Generation of inverse patterns,” Opt. Lasers Eng. 41(1), 31–50 (2004).
[Crossref]

J. Peng, Y. Yu, W. Zhou, and M. Chen, “Using triangle-based cubic interpolation in generation of object-adaptive fringe pattern,” Opt. Lasers Eng. 52(1), 41–52 (2014).
[Crossref]

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43(7), 788–800 (2005).
[Crossref]

Opt. Lett. (4)

Pattern Recogn. (1)

J. Salvi, X. Armangué, and J. Batlle, “A comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recogn. 35(7), 1617–1635 (2002).
[Crossref]

Other (1)

H. Schreiber and J. H. Bruning, “Phase Shifting Interferometry,” in Optical Shop Testing, D. Malacara, (John Wiley and Sons, 2007), pp. 547–612.
[Crossref]

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (1482 KB)      3D reconstruction result with the proposed method

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1 Schematic of the adaptive fringe projection technique.
Fig. 2
Fig. 2 Flowchart for generating the adaptive fringe patterns.
Fig. 3
Fig. 3 Schematic diagram of the mapping results (the projector pixels are drawn in filled circles). (a) Mapping the camera pixels onto the projection plane (the correspondence points of the camera pixels are drawn with unfilled circles), (b) mapping G onto the projection plane (the correspondence points of plane G are drawn with filled stars).
Fig. 4
Fig. 4 Schematic of experimental setup.
Fig. 5
Fig. 5 Residual phase error after removing the principal carrier phase. (a–b) The captured pattern images that were undistorted based on the camera calibration results; (c–d) the captured pattern images that were not undistorted.
Fig. 6
Fig. 6 Reconstruction of the ceramic plate. (a) Residual phase map when projecting the adaptive fringe patterns and removing the principle carrier phase; (b) 3D result of the ceramic plate with the proposed method (See Visualization 1) ; (c) discrepancy distribution obtained with the proposed method; (d) discrepancy distribution obtained by projecting the fixed-pitch fringe pattern.
Fig. 7
Fig. 7 Re-projection errors of camera (a) and projector (b). (Units: Pixels)
Fig. 8
Fig. 8 Depth discrepancy of the ceramic plate when calibrating the projector and reconstructing the shape with the stereo-vision-based model.
Fig. 9
Fig. 9 Measurement distance along the middle-row direction for four positions: (a) 9.84mm, (b) 19.68mm, (c) 29.52mm, and (d) 54.12mm. The horizontal axis represents the pixel position along the row direction, and the vertical axis represents the measurement distance with respect to the reference plane.
Fig. 10
Fig. 10 Measurement result for a standard sphere. (a) A frame of the captured pattern image, (b) 3D result of the ceramic sphere, (c) radial deviation obtained by projecting adaptive fringe patterns, and (d) radial deviation obtained by projecting fixed-pitch fringe patterns.

Tables (2)

Tables Icon

Table 1 Statistical result of the discrepancy when the ceramic plate was measured at 11 different positions (Unit: mm).

Tables Icon

Table 2 Statistical results of the LS radius when the ceramic sphere was measured at different positions (Unit: mm).

Equations (8)

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

Φ c ( i , j ) = r + s i + t j 1 + u i + v j ,
Δ Φ a ( i , j ) = Φ m ( i , j ) Φ c ( i , j ) .
I c k ( i , j ) = I ( i , j ) + I ( i , j ) cos ( Φ ( i , j ) + δ k ) ,
Φ w ( i , j ) = tan 1 ( k = 1 N I c k ( i , j ) sin δ k k = 1 N I c k ( i , j ) cos δ k ) .
s 1 = Φ h ( i , j ) 2 π p , t 1 = Φ v ( i , j ) 2 π p ,
s 2 = s + Δ Φ a , h p ( s , t ) 2 π p , t 2 = t + Δ Φ a , v p ( s , t ) 2 π p ,
I p A ( s , t ) = I max 2 ( 1 + cos ( Φ p A ( s , t ) ) ) ,
h ( i , j ) = Δ ϕ ( i , j ) a ( i , j ) + b ( i , j ) Δ ϕ ( i , j ) ,

Metrics