Abstract

The previously proposed binary defocusing technique and its variations have proven successful for high-quality three-dimensional (3D) shape measurement when fringe stripes are relatively narrow, but they suffer if fringe stripes are wide. This paper proposes to utilize the binary dithering technique to conquer this challenge. Both simulation and experimental results show the phase error is always less than 0.6% even when the fringe stripes are wide and the projector is nearly focused.

© 2012 Optical Society of America

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References

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  1. S. Lei and S. Zhang, “Flexible 3-D shape measurement using projector defocusing,” Opt. Lett. 34, 3080–3082 (2009).
    [CrossRef]
  2. Y. Wang and S. Zhang, “Optimum pulse width modulation for sinusoidal fringe generation with projector defocusing,” Opt. Lett. 35, 4121–4123 (2010).
    [CrossRef]
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    [CrossRef]
  4. Y. Wang and S. Zhang, “Comparison among square binary, sinusoidal pulse width modulation, and optimal pulse width modulation methods for three-dimensional shape measurement,” Appl. Opt. 51, 861–872 (2012).
    [CrossRef]
  5. T. Xian and X. Su, “Area modulation grating for sinusoidal structure illumination on phase-measuring profilometry,” Appl. Opt. 40, 1201–1206 (2001).
    [CrossRef]
  6. W. Lohry and S. Zhang, “3D shape measurement with 2D area modulated binary patterns,” Opt. Laser Eng. 50, 917–921 (2012).
    [CrossRef]
  7. T. L. Schuchman, “Dither signals and their effect on quantization noise,” IEEE Trans. Commun. Technol. 12, 162–165 (1964).
    [CrossRef]
  8. B. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” in Proceedings of IEEE International Conference on Communications (1973), Vol. 1, pp. 11–15.
  9. S. Lei and S. Zhang, “Digital sinusoidal fringe generation: defocusing binary patterns vs. focusing sinusoidal patterns,” Opt. Laser Eng. 48, 561–569 (2010).
    [CrossRef]
  10. Y. Gong and S. Zhang, “Ultrafast 3-D shape measurement with an off-the-shelf DLP projector,” Opt. Express 18, 19743–19754 (2010).
    [CrossRef]
  11. S. Zhang, D. van der Weide, and J. Olvier, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18, 9684–9689 (2010).
    [CrossRef]
  12. W. Purgathofer, R. Tobler, and M. Geiler, “Forced random dithering: improved threshold matrices for ordered dithering,” in Proceedings of IEEE International Conference on Image Processing (1994), Vol. 2, pp. 1032–1035.
  13. T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” IEEE Trans. Image Proc. 9, 909–922 (2000).
    [CrossRef]
  14. Y. Xu, L. Ekstrand, J. Dai, and S. Zhang, “Phase error compensation for three-dimensional shape measurement with projector defocusing,” Appl. Opt. 50, 2572–2581 (2011).
    [CrossRef]
  15. 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]

2012

2011

2010

2009

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]

2001

2000

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” IEEE Trans. Image Proc. 9, 909–922 (2000).
[CrossRef]

1973

B. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” in Proceedings of IEEE International Conference on Communications (1973), Vol. 1, pp. 11–15.

1964

T. L. Schuchman, “Dither signals and their effect on quantization noise,” IEEE Trans. Commun. Technol. 12, 162–165 (1964).
[CrossRef]

Ajubi, G. A.

Ayubi, J. A.

Bayer, B.

B. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” in Proceedings of IEEE International Conference on Communications (1973), Vol. 1, pp. 11–15.

Bovik, A. C.

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” IEEE Trans. Image Proc. 9, 909–922 (2000).
[CrossRef]

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]

Dai, J.

Ekstrand, L.

Evans, B. L.

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” IEEE Trans. Image Proc. 9, 909–922 (2000).
[CrossRef]

Ferrari, J. A.

Geiler, M.

W. Purgathofer, R. Tobler, and M. Geiler, “Forced random dithering: improved threshold matrices for ordered dithering,” in Proceedings of IEEE International Conference on Image Processing (1994), Vol. 2, pp. 1032–1035.

Gong, Y.

Huang, P. S.

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]

Kite, T. D.

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” IEEE Trans. Image Proc. 9, 909–922 (2000).
[CrossRef]

Lei, S.

S. Lei and S. Zhang, “Digital sinusoidal fringe generation: defocusing binary patterns vs. focusing sinusoidal patterns,” Opt. Laser Eng. 48, 561–569 (2010).
[CrossRef]

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

Lohry, W.

W. Lohry and S. Zhang, “3D shape measurement with 2D area modulated binary patterns,” Opt. Laser Eng. 50, 917–921 (2012).
[CrossRef]

Martino, J. M. D.

Olvier, J.

Purgathofer, W.

W. Purgathofer, R. Tobler, and M. Geiler, “Forced random dithering: improved threshold matrices for ordered dithering,” in Proceedings of IEEE International Conference on Image Processing (1994), Vol. 2, pp. 1032–1035.

Schuchman, T. L.

T. L. Schuchman, “Dither signals and their effect on quantization noise,” IEEE Trans. Commun. Technol. 12, 162–165 (1964).
[CrossRef]

Su, X.

Tobler, R.

W. Purgathofer, R. Tobler, and M. Geiler, “Forced random dithering: improved threshold matrices for ordered dithering,” in Proceedings of IEEE International Conference on Image Processing (1994), Vol. 2, pp. 1032–1035.

van der Weide, D.

Wang, Y.

Xian, T.

Xu, Y.

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.

Appl. Opt.

IEEE Trans. Commun. Technol.

T. L. Schuchman, “Dither signals and their effect on quantization noise,” IEEE Trans. Commun. Technol. 12, 162–165 (1964).
[CrossRef]

IEEE Trans. Image Proc.

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” IEEE Trans. Image Proc. 9, 909–922 (2000).
[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]

Opt. Express

Opt. Laser Eng.

W. Lohry and S. Zhang, “3D shape measurement with 2D area modulated binary patterns,” Opt. Laser Eng. 50, 917–921 (2012).
[CrossRef]

S. Lei and S. Zhang, “Digital sinusoidal fringe generation: defocusing binary patterns vs. focusing sinusoidal patterns,” Opt. Laser Eng. 48, 561–569 (2010).
[CrossRef]

Opt. Lett.

Proceedings of IEEE International Conference on Communications

B. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” in Proceedings of IEEE International Conference on Communications (1973), Vol. 1, pp. 11–15.

Other

W. Purgathofer, R. Tobler, and M. Geiler, “Forced random dithering: improved threshold matrices for ordered dithering,” in Proceedings of IEEE International Conference on Image Processing (1994), Vol. 2, pp. 1032–1035.

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Figures (6)

Fig. 1.
Fig. 1.

Binary dithering technique for 8 bit grayscale images. (a) Original 8 bit image of David head. (b) Binary dithered image of (a). (c) Original 8 bit sinusoidal structured pattern. (d) Binary dithered pattern of (c).

Fig. 2.
Fig. 2.

Binary dithering techniques for a 8 bit grayscale image. (a) Original 8 bit image of the David head. (b) Binary dithered image of (a) by applying the thresholding technique. (c) Binary dithered image of (a) by applying random dithering technique. (d) Binary dithered image of (a) by applying the Bayer ordered dithering technique. (e) Binary dithered image of (a) by applying the error-diffusion dithering technique.

Fig. 3.
Fig. 3.

Simulation results of the proposed technique. (a) Binary dithered pattern and its smoothed pattern (T=600); top image shows the dithered pattern and the bottom image shows the smoothed pattern. (b) Cross section of the blurred pattern. (c) Fourier spectrum of the cross section shown in (b). (d)–(f) Corresponding results to above image when T=150.

Fig. 4.
Fig. 4.

Phase errors with varying amount of defocusing by simulations. (a) Fringe patterns (T=600). (b) Fringe patterns (T=150). (c) Phase error percentage. (a) and (b) from top to bottom show defocusing levels of 1, 4, and 8, respectively.

Fig. 5.
Fig. 5.

Phase errors with varying amount of defocusing by experiments. (a) Fringe patterns (T=600). (b) Fringe patterns (T=150). (c) Phase error percentage. (a) and (b) from top to bottom show defocusing levels of 1, 4, and 8, respectively.

Fig. 6.
Fig. 6.

Experimental results of measuring a complex 3D object. (a)–(c) Representative captured dithered patterns. (d)–(f) 3D results using the dithered patterns. (g)–(i) 3D results using ideal sinusoidal patterns.

Equations (4)

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

In(x,y)=I(x,y)+I(x,y)cos(ϕ+2πn/5),
ϕ(x,y)=tan1[n=15In(x,y)sin(2πn/5)n=15In(x,y)cos(2πn/5)].
M1=[0231],
Mn+1=[4Mn4Mn+2Un4Mn+3Un4Mn+Un],

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