Abstract

We present a 3-D shape-measurement technique using a defocused projector. The ideal sinusoidal fringe patterns are generated by defocusing binary structured patterns, and the phase shift is realized by shifting the binary patterns spatially. Because this technique does not require calibration of the gamma of the projector, it is easy to implement and thus is promising for developing flexible 3-D shape measurement systems using digital video projectors.

© 2009 Optical Society of America

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References

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  1. Y. Huang, C. Quan, C. J. Tay, and L. J. Chen, Opt. Eng. 44, 1552 (2005).
  2. M. E. Pawlowski, M. Kujawinska, and M. G. Wgiel, Opt. Eng. 41, 450 (2002).
    [CrossRef]
  3. C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, Opt. Commun. 119, 479 (1995).
    [CrossRef]
  4. M. Takeda and K. Mutoh, Appl. Opt. 22, 3977 (1983).
    [CrossRef] [PubMed]
  5. S. Zhang and P. S. Huang, Opt. Eng. 45, 123601 (2006).
    [CrossRef]
  6. P. S. Huang, C. Zhang, and F.-P. Chiang, Opt. Eng. 42, 163 (2002).
    [CrossRef]
  7. S. Kakunai, T. Sakamoto, and K. Iwata, Appl. Opt. 38, 2824 (1999).
    [CrossRef]
  8. S. Zhang and P. S. Huang, Opt. Eng. 46, 063601 (2007).
    [CrossRef]
  9. S. Zhang and S.-T. Yau, Appl. Opt. 46, 36 (2007).
    [CrossRef]
  10. H. Guo, H. He, and M. Chen, Appl. Opt. 43, 2906 (2004).
    [CrossRef] [PubMed]
  11. B. Pan, Q. Kemao, L. Huang, and A. Asundi, Opt. Lett. 34, 2906 (2009).
    [CrossRef]
  12. D.Malacara, ed., Optical Shop Testing3rd ed. (John Wiley and Sons, 2007).
    [CrossRef]
  13. S. Zhang, X. Li, and S.-T. Yau, Appl. Opt. 46, 50 (2007).
    [CrossRef]
  14. S. Zhang and P. S. Huang, Opt. Eng. 45, 083601 (2006).
    [CrossRef]
  15. Wikipedia, http://en.wikipedia.org/wiki/Point_spread_function (retrieved September 22, 2009).
  16. Wikipedia, http://en.wikipedia.org/wiki/Airy_disc (retrieved September 22, 2009).

2009 (1)

2007 (3)

2006 (2)

S. Zhang and P. S. Huang, Opt. Eng. 45, 083601 (2006).
[CrossRef]

S. Zhang and P. S. Huang, Opt. Eng. 45, 123601 (2006).
[CrossRef]

2005 (1)

Y. Huang, C. Quan, C. J. Tay, and L. J. Chen, Opt. Eng. 44, 1552 (2005).

2004 (1)

2002 (2)

M. E. Pawlowski, M. Kujawinska, and M. G. Wgiel, Opt. Eng. 41, 450 (2002).
[CrossRef]

P. S. Huang, C. Zhang, and F.-P. Chiang, Opt. Eng. 42, 163 (2002).
[CrossRef]

1999 (1)

1995 (1)

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, Opt. Commun. 119, 479 (1995).
[CrossRef]

1983 (1)

Asundi, A.

Bryanston-Cross, P. J.

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, Opt. Commun. 119, 479 (1995).
[CrossRef]

Chen, L. J.

Y. Huang, C. Quan, C. J. Tay, and L. J. Chen, Opt. Eng. 44, 1552 (2005).

Chen, M.

Chiang, F.-P.

P. S. Huang, C. Zhang, and F.-P. Chiang, Opt. Eng. 42, 163 (2002).
[CrossRef]

Guo, H.

He, H.

Huang, L.

Huang, P. S.

S. Zhang and P. S. Huang, Opt. Eng. 46, 063601 (2007).
[CrossRef]

S. Zhang and P. S. Huang, Opt. Eng. 45, 123601 (2006).
[CrossRef]

S. Zhang and P. S. Huang, Opt. Eng. 45, 083601 (2006).
[CrossRef]

P. S. Huang, C. Zhang, and F.-P. Chiang, Opt. Eng. 42, 163 (2002).
[CrossRef]

Huang, Y.

Y. Huang, C. Quan, C. J. Tay, and L. J. Chen, Opt. Eng. 44, 1552 (2005).

Iwata, K.

Kakunai, S.

Kemao, Q.

Kujawinska, M.

M. E. Pawlowski, M. Kujawinska, and M. G. Wgiel, Opt. Eng. 41, 450 (2002).
[CrossRef]

Li, X.

Mutoh, K.

Pan, B.

Pawlowski, M. E.

M. E. Pawlowski, M. Kujawinska, and M. G. Wgiel, Opt. Eng. 41, 450 (2002).
[CrossRef]

Quan, C.

Y. Huang, C. Quan, C. J. Tay, and L. J. Chen, Opt. Eng. 44, 1552 (2005).

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, Opt. Commun. 119, 479 (1995).
[CrossRef]

Sakamoto, T.

Shang, H. M.

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, Opt. Commun. 119, 479 (1995).
[CrossRef]

Takeda, M.

Tay, C. J.

Y. Huang, C. Quan, C. J. Tay, and L. J. Chen, Opt. Eng. 44, 1552 (2005).

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, Opt. Commun. 119, 479 (1995).
[CrossRef]

Wgiel, M. G.

M. E. Pawlowski, M. Kujawinska, and M. G. Wgiel, Opt. Eng. 41, 450 (2002).
[CrossRef]

Yau, S.-T.

Zhang, C.

P. S. Huang, C. Zhang, and F.-P. Chiang, Opt. Eng. 42, 163 (2002).
[CrossRef]

Zhang, S.

S. Zhang and P. S. Huang, Opt. Eng. 46, 063601 (2007).
[CrossRef]

S. Zhang, X. Li, and S.-T. Yau, Appl. Opt. 46, 50 (2007).
[CrossRef]

S. Zhang and S.-T. Yau, Appl. Opt. 46, 36 (2007).
[CrossRef]

S. Zhang and P. S. Huang, Opt. Eng. 45, 083601 (2006).
[CrossRef]

S. Zhang and P. S. Huang, Opt. Eng. 45, 123601 (2006).
[CrossRef]

Appl. Opt. (5)

Opt. Commun. (1)

C. Quan, C. J. Tay, H. M. Shang, and P. J. Bryanston-Cross, Opt. Commun. 119, 479 (1995).
[CrossRef]

Opt. Eng. (6)

S. Zhang and P. S. Huang, Opt. Eng. 45, 123601 (2006).
[CrossRef]

P. S. Huang, C. Zhang, and F.-P. Chiang, Opt. Eng. 42, 163 (2002).
[CrossRef]

S. Zhang and P. S. Huang, Opt. Eng. 46, 063601 (2007).
[CrossRef]

Y. Huang, C. Quan, C. J. Tay, and L. J. Chen, Opt. Eng. 44, 1552 (2005).

M. E. Pawlowski, M. Kujawinska, and M. G. Wgiel, Opt. Eng. 41, 450 (2002).
[CrossRef]

S. Zhang and P. S. Huang, Opt. Eng. 45, 083601 (2006).
[CrossRef]

Opt. Lett. (1)

Other (3)

Wikipedia, http://en.wikipedia.org/wiki/Point_spread_function (retrieved September 22, 2009).

Wikipedia, http://en.wikipedia.org/wiki/Airy_disc (retrieved September 22, 2009).

D.Malacara, ed., Optical Shop Testing3rd ed. (John Wiley and Sons, 2007).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Binary structured patterns projected with a projector at different defocusing levels, where level 1 is in focus and level 4 is severely defocused.

Fig. 2
Fig. 2

(a) 200th row of the fringe images; (b) 200th row of the phase error.

Fig. 3
Fig. 3

Comparison between the traditional and proposed methods: (a) phase error (rms) under different level of defocusing; (b) phase error without projector’s gamma calibration.

Fig. 4
Fig. 4

Measurement result of a complex sculpture with the proposed approach: (a) I 1 , (b) I 2 , (c) I 3 , (d) 3-D shape rendered in shaded mode.

Equations (4)

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

I 1 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ 2 π 3 ) ,
I 2 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ ) ,
I 3 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ + 2 π 3 ) .
ϕ ( x , y ) = tan 1 [ 3 ( I 1 I 3 ) 2 I 2 I 1 I 3 ] .

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