Abstract

An improved algorithm for phase-to-height mapping in phase-measuring profilometry (PMP) is proposed, in which the phase-to-height mapping relationship is no longer restricted to the condition that the optical axes of the imaging system must be orthogonal to the reference plane in the basic PMP. Only seven coefficients independent of the coordinate system need to be calibrated, and the system calibration can be accomplished using only two different gauge blocks, instead of more than three different standard planes. With the proposed algorithm, both the phase measurement and system calibration can be completed simultaneously, which makes the three-dimensional (3-D) measurement faster and more flexible. Experiments have verified its feasibility and validity.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601–123608 (2006).
    [CrossRef]
  4. S. S. Gorthi and P. Rastogi, “Fringe projection technique: whither we are?,” Opt. Lasers Eng. 48, 133–140 (2010).
    [CrossRef]
  5. X. Mao, W. Chen, X. Su, G. Xu, and X. Bian, “Fourier transform profilometry based on a projecting-imaging model,” J. Opt. Soc. Am. A 24, 3735–3740 (2007).
    [CrossRef]
  6. B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A 9, S66–S75 (2007).
    [CrossRef]
  7. X. Mao, W. Chen, and X. Su, “Improved Fourier-transform profilometry,” Appl. Opt. 46, 664–668 (2007).
    [CrossRef]
  8. W. Zhou and X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89–94 (1994).
    [CrossRef]
  9. A. Asundi and W. Zhou, “Unified calibration technique and its applications in optical triangulation profilometry,” Appl. Opt. 38, 3556–3561 (1999).
    [CrossRef]
  10. W. Li, X. Su, and Z. Liu, “Large-scale three-dimensional object measurement: a practical coordinate mapping and image data-patching method,” Appl. Opt. 40, 3326–3333 (2001).
    [CrossRef]
  11. H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44, 033603 (2005).
  12. P. J. Tavares and M. A. Vaz, “Linear calibration procedure for the phase-to-height relationship in phase measurement profilometry,” Opt. Commun. 274, 307–314 (2007).
    [CrossRef]
  13. Y. Wen, S. Li, H. Cheng, X. Su, and Q. Zhang, “Universal calculation formula and calibration method in Fourier transform profilometry,” Appl. Opt. 49, 6563–6569 (2010).
    [CrossRef]
  14. X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
    [CrossRef]
  15. Z. Wang and H. Du, “Out-of-plane shape determination in generalized fringe projection profilometry,” Opt. Express 14, 12122–12133 (2006).
    [CrossRef]
  16. H. Du and Z. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett. 32, 2438–2440 (2007).
    [CrossRef]
  17. G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Contouring of artwork surface by fringe projection and FFT analysis,” Opt. Lasers Eng. 33, 141–156 (2000).
    [CrossRef]
  18. X. De, T. Min, and L. Yuan, Visual Measurement and Control for Robots (Academic, 2008), pp. 39–119. (in Chinese).
  19. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330–1334 (2000).
    [CrossRef]
  20. J.-Y. Bouguet, “Camera calibration toolbox for MATLAB,” http://www.vision.caltech.edu/bouguetj/calib_doc .
  21. Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
    [CrossRef]
  22. S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
    [CrossRef]

2010 (2)

2007 (5)

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A 9, S66–S75 (2007).
[CrossRef]

P. J. Tavares and M. A. Vaz, “Linear calibration procedure for the phase-to-height relationship in phase measurement profilometry,” Opt. Commun. 274, 307–314 (2007).
[CrossRef]

X. Mao, W. Chen, and X. Su, “Improved Fourier-transform profilometry,” Appl. Opt. 46, 664–668 (2007).
[CrossRef]

H. Du and Z. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett. 32, 2438–2440 (2007).
[CrossRef]

X. Mao, W. Chen, X. Su, G. Xu, and X. Bian, “Fourier transform profilometry based on a projecting-imaging model,” J. Opt. Soc. Am. A 24, 3735–3740 (2007).
[CrossRef]

2006 (3)

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

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601–123608 (2006).
[CrossRef]

Z. Wang and H. Du, “Out-of-plane shape determination in generalized fringe projection profilometry,” Opt. Express 14, 12122–12133 (2006).
[CrossRef]

2005 (1)

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

2004 (1)

X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
[CrossRef]

2003 (1)

Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

2001 (1)

2000 (2)

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Contouring of artwork surface by fringe projection and FFT analysis,” Opt. Lasers Eng. 33, 141–156 (2000).
[CrossRef]

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

1999 (1)

1994 (1)

W. Zhou and X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89–94 (1994).
[CrossRef]

1985 (1)

1984 (1)

Accardo, G.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Contouring of artwork surface by fringe projection and FFT analysis,” Opt. Lasers Eng. 33, 141–156 (2000).
[CrossRef]

Ambrosini, D.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Contouring of artwork surface by fringe projection and FFT analysis,” Opt. Lasers Eng. 33, 141–156 (2000).
[CrossRef]

Asundi, A.

Bian, X.

Burton, D. R.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A 9, S66–S75 (2007).
[CrossRef]

Cao, Y.

X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
[CrossRef]

Chen, M.

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

Chen, W.

Cheng, H.

Chiang, F.

Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

De, X.

X. De, T. Min, and L. Yuan, Visual Measurement and Control for Robots (Academic, 2008), pp. 39–119. (in Chinese).

Du, H.

Fu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

Gorthi, S. S.

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

Guattari, G.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Contouring of artwork surface by fringe projection and FFT analysis,” Opt. Lasers Eng. 33, 141–156 (2000).
[CrossRef]

Guo, H.

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

Halioua, M.

He, H.

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

Hu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

Huang, P. S.

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601–123608 (2006).
[CrossRef]

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

Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

Karout, S. A.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A 9, S66–S75 (2007).
[CrossRef]

Lalor, M. J.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A 9, S66–S75 (2007).
[CrossRef]

Li, S.

Li, W.

Liu, H. C.

Liu, Z.

Mao, X.

Min, T.

X. De, T. Min, and L. Yuan, Visual Measurement and Control for Robots (Academic, 2008), pp. 39–119. (in Chinese).

Paoletti, D.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Contouring of artwork surface by fringe projection and FFT analysis,” Opt. Lasers Eng. 33, 141–156 (2000).
[CrossRef]

Rajoub, B. A.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A 9, S66–S75 (2007).
[CrossRef]

Rastogi, P.

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

Sapia, C.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Contouring of artwork surface by fringe projection and FFT analysis,” Opt. Lasers Eng. 33, 141–156 (2000).
[CrossRef]

Song, W.

X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
[CrossRef]

Spagnolo, G. S.

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Contouring of artwork surface by fringe projection and FFT analysis,” Opt. Lasers Eng. 33, 141–156 (2000).
[CrossRef]

Srinivasan, V.

Su, X.

Tavares, P. J.

P. J. Tavares and M. A. Vaz, “Linear calibration procedure for the phase-to-height relationship in phase measurement profilometry,” Opt. Commun. 274, 307–314 (2007).
[CrossRef]

Vaz, M. A.

P. J. Tavares and M. A. Vaz, “Linear calibration procedure for the phase-to-height relationship in phase measurement profilometry,” Opt. Commun. 274, 307–314 (2007).
[CrossRef]

Wang, Z.

Wen, Y.

Xiang, L.

X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
[CrossRef]

Xu, G.

Yu, Y.

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

Yuan, L.

X. De, T. Min, and L. Yuan, Visual Measurement and Control for Robots (Academic, 2008), pp. 39–119. (in Chinese).

Zhang, Q.

Zhang, S.

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

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601–123608 (2006).
[CrossRef]

Zhang, Z.

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

Zhou, W.

A. Asundi and W. Zhou, “Unified calibration technique and its applications in optical triangulation profilometry,” Appl. Opt. 38, 3556–3561 (1999).
[CrossRef]

W. Zhou and X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89–94 (1994).
[CrossRef]

Appl. Opt. (6)

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

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

J. Mod. Opt. (1)

W. Zhou and X. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41, 89–94 (1994).
[CrossRef]

J. Opt. A (1)

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A 9, S66–S75 (2007).
[CrossRef]

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

Opt. Commun. (1)

P. J. Tavares and M. A. Vaz, “Linear calibration procedure for the phase-to-height relationship in phase measurement profilometry,” Opt. Commun. 274, 307–314 (2007).
[CrossRef]

Opt. Eng. (5)

X. Su, W. Song, Y. Cao, and L. Xiang, “Phase-height mapping and coordinate calibration simultaneously in phase-measuring profilometry,” Opt. Eng. 43, 708–712 (2004).
[CrossRef]

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

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601–123608 (2006).
[CrossRef]

Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42, 487–493 (2003).
[CrossRef]

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

Opt. Express (1)

Opt. Lasers Eng. (2)

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

G. S. Spagnolo, G. Guattari, C. Sapia, D. Ambrosini, D. Paoletti, and G. Accardo, “Contouring of artwork surface by fringe projection and FFT analysis,” Opt. Lasers Eng. 33, 141–156 (2000).
[CrossRef]

Opt. Lett. (1)

Other (2)

X. De, T. Min, and L. Yuan, Visual Measurement and Control for Robots (Academic, 2008), pp. 39–119. (in Chinese).

J.-Y. Bouguet, “Camera calibration toolbox for MATLAB,” http://www.vision.caltech.edu/bouguetj/calib_doc .

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