Abstract

This Letter investigates the effects of different phase-shifting algorithms on the quality of high-resolution three-dimensional (3-D) profilometry produced with nearly focused binary patterns. From theoretical analyses, simulations, and experiments, we found that the nine-step phase-shifting algorithm produces accurate 3-D measurements at high speed without the limited depth range and calibration difficulties that typically plague binary defocusing methods. We also found that the use of more fringe patterns does not necessarily enhance measurement quality.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Geng, Adv. Opt. Photon. 3, 128 (2011).
    [CrossRef]
  2. S. Lei and S. Zhang, Opt. Lett. 34, 3080 (2009).
    [CrossRef] [PubMed]
  3. X. Y. Su, W. S. Zhou, G. von Bally, and D. Vukicevic, Opt. Commun. 94, 561 (1992).
    [CrossRef]
  4. Y. Xu, L. Ekstrand, J. Dai, and S. Zhang, Appl. Opt. 50, 2572 (2011).
    [CrossRef] [PubMed]
  5. G. A. Ayubi, J. A. Ayubi, J. M. D. Martino, and J. A. Ferrari, Opt. Lett. 35, 3682 (2010).
    [CrossRef] [PubMed]
  6. Y. Wang and S. Zhang, Opt. Lett. 35, 4121 (2010).
    [CrossRef] [PubMed]
  7. G. A. Ayubi, J. M. D. Martino, J. R. Alonso, A. Fernandez, C. D. Perciante, and J. A. Ferrari, Appl. Opt. 50, 147(2011).
    [CrossRef] [PubMed]
  8. S. Zhang, Appl. Opt. 50, 1753 (2011).
    [CrossRef] [PubMed]
  9. S. Zhang, X. Li, and S.-T. Yau, Appl. Opt. 46, 50 (2007).
    [CrossRef]

2011 (4)

2010 (2)

2009 (1)

2007 (1)

1992 (1)

X. Y. Su, W. S. Zhou, G. von Bally, and D. Vukicevic, Opt. Commun. 94, 561 (1992).
[CrossRef]

Alonso, J. R.

Ayubi, G. A.

Ayubi, J. A.

Dai, J.

Ekstrand, L.

Fernandez, A.

Ferrari, J. A.

Geng, G.

Lei, S.

Li, X.

Martino, J. M. D.

Perciante, C. D.

Su, X. Y.

X. Y. Su, W. S. Zhou, G. von Bally, and D. Vukicevic, Opt. Commun. 94, 561 (1992).
[CrossRef]

von Bally, G.

X. Y. Su, W. S. Zhou, G. von Bally, and D. Vukicevic, Opt. Commun. 94, 561 (1992).
[CrossRef]

Vukicevic, D.

X. Y. Su, W. S. Zhou, G. von Bally, and D. Vukicevic, Opt. Commun. 94, 561 (1992).
[CrossRef]

Wang, Y.

Xu, Y.

Yau, S.-T.

Zhang, S.

Zhou, W. S.

X. Y. Su, W. S. Zhou, G. von Bally, and D. Vukicevic, Opt. Commun. 94, 561 (1992).
[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 (3)

Fig. 1
Fig. 1

Measurement results for a flat board using different phase-shifting algorithms. (a) One of the fringe patterns. (b) Cross section of the fringe pattern. (c) The rms errors are 0.19, 0.35, 0.08, 0.19, 0.05, 0.12, and 0.05   rad for three-, four-, five-, six-, seven-, eight-, and nine-step algorithms, respectively.

Fig. 2
Fig. 2

Experimental results of different binary phase-shifting algorithms with a nearly focused projector. (a) Photograph of the captured statue. (b), (c), (d), (e), (f), (g), (h) 3-D results of the three-, four-, five-, six-, seven-, eight-, and nine-step algorithms, respectively.

Fig. 3
Fig. 3

Experimental results without phase-shift error under the same defocusing degree as Fig. 2. (a)–(b) Close-up view of one of the binary patterns and its 210th column cross section (indicated by red squares). (c) 3-D result by the seven-step algorithm ( P = 42 ). (d) 3-D result by the nine-step algorithm ( P = 36 ).

Tables (4)

Tables Icon

Table 1 Phase Errors Caused by Different Harmonics for Different Phase-Shifting Algorithms a

Tables Icon

Table 2 Phase Errors Caused by Random Noise

Tables Icon

Table 3 Phase Errors with Different Fringe Widths a

Tables Icon

Table 4 Phase Errors with Different Defocusing Degrees a

Equations (6)

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

I n ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ + 2 π n / N ) ,
ϕ ( x , y ) = tan 1 n = 1 N I n ( x , y ) sin ( 2 π n / N ) n = 1 N I n ( x , y ) cos ( 2 π n / N ) .
y ( x ) = { 0 x [ ( 2 n 1 ) π , 2 n π ) 1 x [ 2 n π , ( 2 n + 1 ) π ) .
y ( x ) = 0.5 + k = 0 2 ( 2 k + 1 ) π sin [ ( 2 k + 1 ) x ] .
I n k = I + I [ cos γ + cos ( M γ ) / M ] .
Δ ϕ k ( x , y ) = ϕ k ( x , y ) ϕ b ( x , y ) .

Metrics