Abstract

The out-of-plane shape determination in a generalized fringe projection profilometry is presented. The proposed technique corrects the problems in existing approaches, and it can cope well with the divergent illumination encountered in the generalized profilometry. In addition, the technique can automatically detect the geometric parameters of the experimental setup, which makes the generalized fringe projection profilometry simple and practical. The concept was verified by both computer simulations and actual experiments. The technique can be easily employed for out-of-plane shape measurements with high accuracies.

© 2006 Optical Society of America

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References

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  1. K. Creath and J. Wyant, "Moir´e and fringe projection techniques," in. Optical Shop Testing, 2nd Ed., Ed. by D. Malacara, New York: Wiley, 653-685 (1992).
  2. F. Chen, G. Brown, and M. Song, "Overview of 3-D shape measurement using optical methods," Opt. Eng. 39,10-22 (2000).
    [CrossRef]
  3. M. Takeda and K. Mutoh, "Fourier transform profilometry for the automatic measurement of 3-D object shapes," Appl. Opt. 22,3977-3982 (1983).
    [CrossRef] [PubMed]
  4. V. Srinivasan, H. Liu, and M. Halioua, "Automated phase-measuring profilometry of 3-D diffuse objects," Appl. Opt. 23,3105-3108 (1984).
    [CrossRef] [PubMed]
  5. V. Srinivasan, H. Liu, and M. Halioua, "Automated phase-measuring profilometry: a phase mapping approach," Appl. Opt. 24,185-188 (1985).
    [CrossRef] [PubMed]
  6. P. Huang, Q. Hu, F. Jin, and F. Chiang, "Color-encoded digital fringe projection technique for high-speed threedimensional surface contouring," Opt. Eng. 38,1065-1071 (1999).
    [CrossRef]
  7. W. Schreiber and G. Notni, "Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique," Opt. Eng. 39,159-169 (2000).
    [CrossRef]
  8. L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42,3307- 3314 (2003).
    [CrossRef]
  9. C. Quan, C. Tay, X. Kang, X. He, and H. Shang, "Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting," Appl. Opt. 42,2329-2335 (2003).
    [CrossRef] [PubMed]
  10. C. Tay, C. Quan, H. Shang, T. Wu, and S. Wang, "New method for measuring dynamic response of small components by fringe projection," Opt. Eng. 42,1715-1720 (2003).
    [CrossRef]
  11. C. Tay, C. Quan, T. Wu, and Y. Huang, "Integrated method for 3-D rigid-body displacement measurement using fringe projection," Opt. Eng. 43,1152-1159 (2004).
    [CrossRef]
  12. J. Pan, P. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44,, 023606 (2005).
    [CrossRef]
  13. H. Guo, H. He, Y. Yu, and M. Chen, "Least-squares calibration method for fringe projection profilometry," Opt. Eng. 44,033603, (2005).
    [CrossRef]
  14. L. Chen and C. Quan, "Fringe projection profilometry with nonparallel illumination : a least-squares approach," Opt. Lett. 30,2101-2103 (2005).
    [CrossRef] [PubMed]
  15. Z. Wang and H. Bi, "Comment on "Fringe projection profilometry with nonparallel illumination: a least-squares approach"," Opt. Lett. 31,1972-1973 (2006).
    [CrossRef] [PubMed]
  16. L. Chen and C. Quan, "Reply to Comment on "Fringe projection profilometry with nonparallel illumination: a least-squares approach"," Opt. Lett. 31,1974-1975 (2006).
    [CrossRef]
  17. Z. Wang and B. Han, "Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms," Opt. Lett. 29,1671-1673 (2004).
    [CrossRef] [PubMed]
  18. Z. Wang, "Development and application of computer-aided fringe analysis," Ph.D. Dissertation, University of Maryland at College Park, 2003. http://hdl.handle.net/1903/31

2006 (2)

2005 (3)

L. Chen and C. Quan, "Fringe projection profilometry with nonparallel illumination : a least-squares approach," Opt. Lett. 30,2101-2103 (2005).
[CrossRef] [PubMed]

J. Pan, P. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44,, 023606 (2005).
[CrossRef]

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

2004 (2)

C. Tay, C. Quan, T. Wu, and Y. Huang, "Integrated method for 3-D rigid-body displacement measurement using fringe projection," Opt. Eng. 43,1152-1159 (2004).
[CrossRef]

Z. Wang and B. Han, "Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms," Opt. Lett. 29,1671-1673 (2004).
[CrossRef] [PubMed]

2003 (3)

C. Quan, C. Tay, X. Kang, X. He, and H. Shang, "Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting," Appl. Opt. 42,2329-2335 (2003).
[CrossRef] [PubMed]

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42,3307- 3314 (2003).
[CrossRef]

C. Tay, C. Quan, H. Shang, T. Wu, and S. Wang, "New method for measuring dynamic response of small components by fringe projection," Opt. Eng. 42,1715-1720 (2003).
[CrossRef]

2000 (2)

F. Chen, G. Brown, and M. Song, "Overview of 3-D shape measurement using optical methods," Opt. Eng. 39,10-22 (2000).
[CrossRef]

W. Schreiber and G. Notni, "Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique," Opt. Eng. 39,159-169 (2000).
[CrossRef]

1999 (1)

P. Huang, Q. Hu, F. Jin, and F. Chiang, "Color-encoded digital fringe projection technique for high-speed threedimensional surface contouring," Opt. Eng. 38,1065-1071 (1999).
[CrossRef]

1985 (1)

1984 (1)

1983 (1)

Bi, H.

Brown, G.

F. Chen, G. Brown, and M. Song, "Overview of 3-D shape measurement using optical methods," Opt. Eng. 39,10-22 (2000).
[CrossRef]

Chen, F.

F. Chen, G. Brown, and M. Song, "Overview of 3-D shape measurement using optical methods," Opt. Eng. 39,10-22 (2000).
[CrossRef]

Chen, L.

Chen, M.

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

Chiang, F.

J. Pan, P. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44,, 023606 (2005).
[CrossRef]

P. Huang, Q. Hu, F. Jin, and F. Chiang, "Color-encoded digital fringe projection technique for high-speed threedimensional surface contouring," Opt. Eng. 38,1065-1071 (1999).
[CrossRef]

Garcia, V.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42,3307- 3314 (2003).
[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).
[CrossRef]

Halioua, M.

Han, B.

He, H.

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

He, X.

Hu, Q.

P. Huang, Q. Hu, F. Jin, and F. Chiang, "Color-encoded digital fringe projection technique for high-speed threedimensional surface contouring," Opt. Eng. 38,1065-1071 (1999).
[CrossRef]

Huang, P.

J. Pan, P. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44,, 023606 (2005).
[CrossRef]

P. Huang, Q. Hu, F. Jin, and F. Chiang, "Color-encoded digital fringe projection technique for high-speed threedimensional surface contouring," Opt. Eng. 38,1065-1071 (1999).
[CrossRef]

Huang, Y.

C. Tay, C. Quan, T. Wu, and Y. Huang, "Integrated method for 3-D rigid-body displacement measurement using fringe projection," Opt. Eng. 43,1152-1159 (2004).
[CrossRef]

Jin, F.

P. Huang, Q. Hu, F. Jin, and F. Chiang, "Color-encoded digital fringe projection technique for high-speed threedimensional surface contouring," Opt. Eng. 38,1065-1071 (1999).
[CrossRef]

Kang, X.

Liu, H.

Luna, E.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42,3307- 3314 (2003).
[CrossRef]

Mutoh, K.

Notni, G.

W. Schreiber and G. Notni, "Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique," Opt. Eng. 39,159-169 (2000).
[CrossRef]

Pan, J.

J. Pan, P. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44,, 023606 (2005).
[CrossRef]

Quan, C.

Salas, L.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42,3307- 3314 (2003).
[CrossRef]

Salinas, J.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42,3307- 3314 (2003).
[CrossRef]

Schreiber, W.

W. Schreiber and G. Notni, "Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique," Opt. Eng. 39,159-169 (2000).
[CrossRef]

Servin, M.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42,3307- 3314 (2003).
[CrossRef]

Shang, H.

C. Tay, C. Quan, H. Shang, T. Wu, and S. Wang, "New method for measuring dynamic response of small components by fringe projection," Opt. Eng. 42,1715-1720 (2003).
[CrossRef]

C. Quan, C. Tay, X. Kang, X. He, and H. Shang, "Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting," Appl. Opt. 42,2329-2335 (2003).
[CrossRef] [PubMed]

Song, M.

F. Chen, G. Brown, and M. Song, "Overview of 3-D shape measurement using optical methods," Opt. Eng. 39,10-22 (2000).
[CrossRef]

Srinivasan, V.

Takeda, M.

Tay, C.

C. Tay, C. Quan, T. Wu, and Y. Huang, "Integrated method for 3-D rigid-body displacement measurement using fringe projection," Opt. Eng. 43,1152-1159 (2004).
[CrossRef]

C. Tay, C. Quan, H. Shang, T. Wu, and S. Wang, "New method for measuring dynamic response of small components by fringe projection," Opt. Eng. 42,1715-1720 (2003).
[CrossRef]

C. Quan, C. Tay, X. Kang, X. He, and H. Shang, "Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting," Appl. Opt. 42,2329-2335 (2003).
[CrossRef] [PubMed]

Wang, S.

C. Tay, C. Quan, H. Shang, T. Wu, and S. Wang, "New method for measuring dynamic response of small components by fringe projection," Opt. Eng. 42,1715-1720 (2003).
[CrossRef]

Wang, Z.

Wu, T.

C. Tay, C. Quan, T. Wu, and Y. Huang, "Integrated method for 3-D rigid-body displacement measurement using fringe projection," Opt. Eng. 43,1152-1159 (2004).
[CrossRef]

C. Tay, C. Quan, H. Shang, T. Wu, and S. Wang, "New method for measuring dynamic response of small components by fringe projection," Opt. Eng. 42,1715-1720 (2003).
[CrossRef]

Yu, Y.

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

Appl. Opt. (4)

Opt. Eng. (8)

F. Chen, G. Brown, and M. Song, "Overview of 3-D shape measurement using optical methods," Opt. Eng. 39,10-22 (2000).
[CrossRef]

P. Huang, Q. Hu, F. Jin, and F. Chiang, "Color-encoded digital fringe projection technique for high-speed threedimensional surface contouring," Opt. Eng. 38,1065-1071 (1999).
[CrossRef]

W. Schreiber and G. Notni, "Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique," Opt. Eng. 39,159-169 (2000).
[CrossRef]

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42,3307- 3314 (2003).
[CrossRef]

C. Tay, C. Quan, H. Shang, T. Wu, and S. Wang, "New method for measuring dynamic response of small components by fringe projection," Opt. Eng. 42,1715-1720 (2003).
[CrossRef]

C. Tay, C. Quan, T. Wu, and Y. Huang, "Integrated method for 3-D rigid-body displacement measurement using fringe projection," Opt. Eng. 43,1152-1159 (2004).
[CrossRef]

J. Pan, P. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44,, 023606 (2005).
[CrossRef]

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

Opt. Lett. (4)

Other (2)

Z. Wang, "Development and application of computer-aided fringe analysis," Ph.D. Dissertation, University of Maryland at College Park, 2003. http://hdl.handle.net/1903/31

K. Creath and J. Wyant, "Moir´e and fringe projection techniques," in. Optical Shop Testing, 2nd Ed., Ed. by D. Malacara, New York: Wiley, 653-685 (1992).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic experimental setup of a generalized fringe projection profilometry

Fig. 2.
Fig. 2.

Schematic geometry of the fringe projection system

Fig. 3.
Fig. 3.

Height detections of the points on object surface

Fig. 4.
Fig. 4.

Computer-generated projection fringe patterns

Fig. 5.
Fig. 5.

Out-of-plane shape detected by different techniques

Fig. 6.
Fig. 6.

Comparisons of the absolute heights obtained from different techniques

Fig. 7.
Fig. 7.

Fringe patterns captured in the first experiment

Fig. 8.
Fig. 8.

Height determination in the first experiment

Fig. 9.
Fig. 9.

Fringe patterns captured in the second experiment

Fig. 10.
Fig. 10.

Height determination in the second experiment

Tables (1)

Tables Icon

Table 1. Comparison of the techniques

Equations (18)

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ϕ r ( x ) = ϕ R = ϕ T = ϕ 0 + 2 π l OT p OQ
l OT = l OR cos β cos ( α β ) = x cos α + sin α tan β = x cos α + sin α d 0 + x d 1 = H x A + x
ϕ r ( x ) = ϕ 0 + 2 π p OQ ( H x A + x ) = B + C x A + x
p r ( x ) = 2 π d ϕ r ( x ) dx = 2 π ( A + x ) 2 AC B
A = [ ϕ e r ( x 1 ) x 1 ϕ e r ( x 2 ) x 2 ] ( x 2 x 3 ) [ ϕ e r ( x 2 ) x 2 ϕ e r ( x 3 ) x 3 ] ( x 1 x 2 ) [ ϕ e r ( x 2 ) ϕ e r ( x 1 ) ] ( x 2 x 3 ) [ ϕ e r ( x 3 ) ϕ e r ( x 2 ) ] ( x 1 x 2 )
C = [ ϕ e r ( x 1 ) x 1 ϕ e r ( x 2 ) x 2 ] [ ϕ e r ( x 3 ) ϕ e r ( x 2 ) ] [ ϕ e r ( x 2 ) x 2 ϕ e r ( x 3 ) x 3 ] [ ϕ e r ( x 2 ) ϕ e r ( x 1 ) ] [ ϕ e r ( x 3 ) ϕ e r ( x 2 ) ] ( x 1 x 2 ) [ ϕ e r ( x 2 ) ϕ e r ( x 1 ) ] ( x 2 x 3 )
B = ϕ e r ( x 1 ) ( A + x 1 ) C x 1
S = i = 1 i = N [ B + C x i ϕ e r ( x i ) A ϕ e r ( x i ) x i ] 2
S A = 0 , S B = 0 , S C = 0
ϕ s ( x ) = ϕ I s = ϕ J r = ϕ r ( x + Δ x ) = B + C x + C Δ x A + x + Δ x
Δ x h ( x ) = Δ x 1 h ( x ) + Δ x 2 h ( x ) = d 0 x d 2 + d 0 + x + Δ x d 1 = D 0 + D 1 x + D 2 Δ x
h ( x ) = Δ x D 0 + D 1 x + D 2 Δ x
Δ x = B + C x ( A + x ) ϕ e s ( x ) ϕ e s ( x ) C
h ( x ) = B + C x ( A + x ) ϕ e s ( x ) ( D 0 + D 1 x ) ( ϕ e s ( x ) C ) + D 2 [ B + C x ( A + x ) ϕ e s ( x ) ]
S = i = 1 i = M { B + C x i ( A + x i ) ϕ e s ( x i ) ( D 0 + D 1 x i ) ( ϕ e s ( x i ) C ) h g ( x i )
D 2 [ B + C x i ( A + x i ) ϕ e s ( x i ) ] h g ( x i ) } 2
S D 0 = 0 , S D 1 = 0 , S D 2 = 0
ϕ r ( x ) = B + C x + E y A + x + D y

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