Abstract

Three-dimensional shape measurements by sinusoidal fringe projection using phase-shifting interferometry algorithms are distorted by the nonlinear response in intensity of commercial video projectors and digital cameras. To solve the problem, we present a method that consists in projecting and acquiring a temporal sequence of strictly binary patterns, whose (adequately weighted) average leads to a sinusoidal fringe pattern with the required number of bits. Since binary patterns consist of “ones” and “zeros”—and no half-tones are involved—the nonlinear response of the projector and the camera will not play a role, and a nearly unit contrast gray-level sinusoidal fringe pattern is obtained. Validation experiments are presented.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Creath, J. Schmit, and J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), Chap. 16.
  2. H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), Chap. 14.
    [CrossRef]
  3. S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
    [CrossRef]
  4. P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
    [CrossRef]
  5. S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46, 063601 (2007).
    [CrossRef]
  6. S. Zhang and S.-T. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. 46, 36–43 (2007).
    [CrossRef]
  7. H. Guo, H. He, and M. Chen, “Gamma correction for digital fringe projection profilometry,” Appl. Opt. 43, 2906–2914(2004).
    [CrossRef] [PubMed]
  8. B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. 34, 416–418 (2009).
    [CrossRef] [PubMed]
  9. T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett. 35, 1992–1994 (2010).
    [CrossRef] [PubMed]
  10. S. Lei and S. Zhang, “Flexible 3-D shape measurement using projector defocusing,” Opt. Lett. 34, 3080–3082 (2009).
    [CrossRef] [PubMed]
  11. G. Sansoni, S. Lazzari, S. Peli, and F. Docchio, “3-D imager for dimensional gauging of industrial workpieces: state-of-the-art of the development of a robust and versatile system,” in First International Conference on Recent Advances in 3-D Digital Imaging and Modeling (3DIM ’97) (IEEE, 1997), pp. 19–26.
  12. G. A. Ayubi, J. A. Ayubi, J. M. Di Martino, and J. A. Ferrari, “Pulse-width modulation in defocused three-dimensional fringe projection,” Opt. Lett. 35, 3682–3684 (2010).
    [CrossRef] [PubMed]
  13. G. Sansoni, M. Carocci, and R. Rodella, “Three-dimensional vision based on a combination of gray-code and phase-shift light projection: analysis and compensation of the systematic errors,” Appl. Opt. 38, 6565–6573 (1999).
    [CrossRef]
  14. J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Patt. Recog. 37, 827–849(2004).
    [CrossRef]
  15. G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, “Three-dimensional imaging based on gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications,” Appl. Opt. 36, 4463–4472 (1997).
    [CrossRef] [PubMed]
  16. N. Otsu, “A threshold selection method from gray level histograms,” IEEE Trans. Syst. Man Cybern. SMC-9, 62–66(1979).
    [CrossRef]

2010

2009

2007

S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46, 063601 (2007).
[CrossRef]

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

2004

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

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Patt. Recog. 37, 827–849(2004).
[CrossRef]

2003

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

1999

1997

1979

N. Otsu, “A threshold selection method from gray level histograms,” IEEE Trans. Syst. Man Cybern. SMC-9, 62–66(1979).
[CrossRef]

Asundi, A.

Ayubi, G. A.

Ayubi, J. A.

Batlle, J.

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Patt. Recog. 37, 827–849(2004).
[CrossRef]

Bruning, J. H.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), Chap. 14.
[CrossRef]

Carocci, M.

Chen, M.

Chiang, F.-P.

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

Corini, S.

Creath, K.

K. Creath, J. Schmit, and J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), Chap. 16.

Di Martino, J. M.

Docchio, F.

G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, “Three-dimensional imaging based on gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications,” Appl. Opt. 36, 4463–4472 (1997).
[CrossRef] [PubMed]

G. Sansoni, S. Lazzari, S. Peli, and F. Docchio, “3-D imager for dimensional gauging of industrial workpieces: state-of-the-art of the development of a robust and versatile system,” in First International Conference on Recent Advances in 3-D Digital Imaging and Modeling (3DIM ’97) (IEEE, 1997), pp. 19–26.

Ferrari, J. A.

Guo, H.

He, H.

Hoang, T.

Huang, L.

Huang, P. S.

S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46, 063601 (2007).
[CrossRef]

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

Kemao, Q.

Lazzari, S.

G. Sansoni, S. Corini, S. Lazzari, R. Rodella, and F. Docchio, “Three-dimensional imaging based on gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications,” Appl. Opt. 36, 4463–4472 (1997).
[CrossRef] [PubMed]

G. Sansoni, S. Lazzari, S. Peli, and F. Docchio, “3-D imager for dimensional gauging of industrial workpieces: state-of-the-art of the development of a robust and versatile system,” in First International Conference on Recent Advances in 3-D Digital Imaging and Modeling (3DIM ’97) (IEEE, 1997), pp. 19–26.

Lei, S.

Nguyen, D.

Otsu, N.

N. Otsu, “A threshold selection method from gray level histograms,” IEEE Trans. Syst. Man Cybern. SMC-9, 62–66(1979).
[CrossRef]

Pagès, J.

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Patt. Recog. 37, 827–849(2004).
[CrossRef]

Pan, B.

Peli, S.

G. Sansoni, S. Lazzari, S. Peli, and F. Docchio, “3-D imager for dimensional gauging of industrial workpieces: state-of-the-art of the development of a robust and versatile system,” in First International Conference on Recent Advances in 3-D Digital Imaging and Modeling (3DIM ’97) (IEEE, 1997), pp. 19–26.

Rodella, R.

Salvi, J.

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Patt. Recog. 37, 827–849(2004).
[CrossRef]

Sansoni, G.

Schmit, J.

K. Creath, J. Schmit, and J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), Chap. 16.

Schreiber, H.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), Chap. 14.
[CrossRef]

Wang, Z.

Wyant, J. C.

K. Creath, J. Schmit, and J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), Chap. 16.

Yau, S.-T.

Zhang, C.

P. S. Huang, C. 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.

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

S. Lei and S. Zhang, “Flexible 3-D shape measurement using projector defocusing,” Opt. Lett. 34, 3080–3082 (2009).
[CrossRef] [PubMed]

S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46, 063601 (2007).
[CrossRef]

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

Appl. Opt.

IEEE Trans. Syst. Man Cybern.

N. Otsu, “A threshold selection method from gray level histograms,” IEEE Trans. Syst. Man Cybern. SMC-9, 62–66(1979).
[CrossRef]

Opt. Eng.

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

S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46, 063601 (2007).
[CrossRef]

Opt. Lasers Eng.

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

Opt. Lett.

Patt. Recog.

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Patt. Recog. 37, 827–849(2004).
[CrossRef]

Other

G. Sansoni, S. Lazzari, S. Peli, and F. Docchio, “3-D imager for dimensional gauging of industrial workpieces: state-of-the-art of the development of a robust and versatile system,” in First International Conference on Recent Advances in 3-D Digital Imaging and Modeling (3DIM ’97) (IEEE, 1997), pp. 19–26.

K. Creath, J. Schmit, and J. C. Wyant, “Moiré and fringe projection techniques,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), Chap. 16.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), Chap. 14.
[CrossRef]

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 (7)

Fig. 1
Fig. 1

Binary sequence M 1 i ( x , y ) (with i = 1 , 2 , 8 ) representing the sinusoidal pattern shown at the bottom (right corner) of the figure.

Fig. 2
Fig. 2

Experimental setup. T is the test surface and CCD is a digital camera.

Fig. 3
Fig. 3

(a) Image of a digital sinusoidal pattern projected over a plane orthogonal to the projection direction and acquired by the camera (without a binarization procedure); (b) representative intensity cut along the pattern horizontal direction; (c) FFT of the intensity cut.

Fig. 4
Fig. 4

(a) Gray-level pattern reconstructed from Eq. (5) using the proposed method; (b) representative intensity cut along the pattern horizontal direction; (c) FFT of the intensity cut.

Fig. 5
Fig. 5

Deformed binary sequence M 1 i ( i = 1 , 2 , 8 ) after binarization of the acquired images. The pattern reconstructed using Eq. (5) is shown at the bottom (right corner) of the figure.

Fig. 6
Fig. 6

Deformed binary sequence M 1 i ( i = 1 , 2 , 8 ) after binarization of the acquired images. The pattern reconstructed using Eq. (5) is shown at the bottom (right corner) of the figure.

Fig. 7
Fig. 7

Different views of the reconstructed 3-D surface (after unwrapping and filtering). (a), (b) Smooth surface profile reconstructed using the proposed method; (c), (d) reconstructed profile using standard four-frame PSI algorithm by gray-level fringe projection and acquisition.

Equations (7)

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

I ( x , y ) = i = 1 8 2 ( 8 i ) M i ( x , y ) .
I k ( x , y ) = ( 255 / 2 ) [ 1 + cos ( 2 π f 0 x + α k ) ] ,
I k ( x , y ) = i = 1 8 2 ( 8 i ) M k i ( x , y ) ,
x = cos ( θ ) x + sin ( θ ) z ( x , y ) ,
I k ( x , y ) = ( 255 / 2 ) { 1 + cos [ 2 π f 0 ( cos ( θ ) x + sin ( θ ) z ) + α k ] } = i = 1 8 2 ( 8 i ) M k i ( cos ( θ ) x + sin ( θ ) z ( x , y ) , y ) .
I k ( x , y ) = R ( x , y ) i = 1 8 2 ( 8 i ) M k i ( cos ( θ ) x + sin ( θ ) z , y ) ,
z ( x , y ) = ( 1 2 π f 0 sin ( θ ) ) arctan [ 255 2 I 2 ( x , y ) 2 I 1 ( x , y ) 255 ] x tan ( θ ) .

Metrics