Abstract

To determine the shape of a complex object with vertical measurement mode and higher accuracy, a novel modulation measuring profilometry realizing auto-synchronous phase shifting and vertical scanning is proposed. Coaxial optical system for projection and observation instead of triangulation system is adopted to avoid shadow and occlusion. In the projecting system, sinusoidal grating is perpendicular to optical axis. For moving the grating along a direction at a certain angle to optical axis, 1D precision translation platform is applied to achieve purposes of both phase-shifting and vertical scanning. A series of fringe patterns with different modulation variations are captured by a CCD camera while scanning. The profile of the tested object can be reconstructed by the relationship between the height values and the modulation distributions. Unlike the previous method based on Fourier transform for 2D fringe pattern, the modulation maps are calculated from the intensity curve formed by the points with definite pixel coordinates in the captured fringe patterns. The paper gives the principle of the proposed method, the set-up of measurement system and the method for system calibration. Computer simulation and experiment results proved its feasibility.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
  2. V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry: a phase mapping approach,” Appl. Opt. 24(2), 185–188 (1985).
    [Crossref] [PubMed]
  3. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
    [Crossref] [PubMed]
  4. X. Y. Su, L. K. Su, and W. S. Li, “A New Fourier transform profilometry based on modulation measurement,” Proc. SPIE 3749, 438–439 (1999).
    [Crossref]
  5. L. K. Su, X. Y. Su, W. S. Li, and L. Q. Xiang, “Application of Modulation Measurement Profilometry to Objects with Surface Holes,” Appl. Opt. 38(7), 1153–1158 (1999).
    [Crossref] [PubMed]
  6. M. Takeda, T. Aoki, Y. Miyamoto, H. Tanaka, R. W. Gu, and Z. B. Zhang, “Absolute three-dimensional shape measurements using coaxial and coimage plane optical systems and Fourier fringe analysis for focus detection,” Opt. Eng. 39(1), 61–68 (2000).
    [Crossref]
  7. T. Yoshizawa, T. Shinoda, and Y. Otani, “Uniaxis rangefinder using contrast detection of a projected pattern,” Proc. SPIE 4190, 115–122 (2001).
    [Crossref]
  8. Y. Mizutani, R. Kuwano, Y. Otani, N. Umeda, and T. Yoshizawa, “Three-dimensional shape measurement using focus method by using liquid crystal grating and liquid varifocus lens,” Proc. SPIE 600, 60000J (2005).
    [Crossref]
  9. Y. Otani, F. Kobayashi, Y. Mizutani, S. Watanabe, M. Harada, and T. Yoshizawa, “Uni-axial measurement of three-dimensional surface profile by liquid crystal digital shifter,” Proc. SPIE 7790, 77900A (2010).
    [Crossref]
  10. Y. Xu, L. Ekstrand, and S. Zhang, “Uniaxial 3-D shape measurement with projector defocusing,” Proc. SPIE 81330, 81330M (2011).
    [Crossref]
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    [Crossref]
  13. (Conference Proceedings) Authors: Proc. SPIE 9276, Optical Metrology and Inspection for Industrial Applications III, 92760I (13 November 2014); doi: .
    [Crossref]
  14. K. Korner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
    [Crossref]
  15. S. Chen, A. W. Palmer, K. T. Grattan, and B. T. Meggitt, “Digital signal-processing techniques for electronically scanned optical-fiber white-light interferometry,” Appl. Opt. 31(28), 6003–6010 (1992).
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    [Crossref] [PubMed]
  17. P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44(3), 519–534 (1997).
    [Crossref]

2014 (1)

D. Chen, J. Schmit, and M. Novak, “Real-time scanner error correction in white light interferometry,” Proc. SPIE 9276, 92760I (2014).
[Crossref]

2011 (1)

Y. Xu, L. Ekstrand, and S. Zhang, “Uniaxial 3-D shape measurement with projector defocusing,” Proc. SPIE 81330, 81330M (2011).
[Crossref]

2010 (1)

Y. Otani, F. Kobayashi, Y. Mizutani, S. Watanabe, M. Harada, and T. Yoshizawa, “Uni-axial measurement of three-dimensional surface profile by liquid crystal digital shifter,” Proc. SPIE 7790, 77900A (2010).
[Crossref]

2005 (1)

Y. Mizutani, R. Kuwano, Y. Otani, N. Umeda, and T. Yoshizawa, “Three-dimensional shape measurement using focus method by using liquid crystal grating and liquid varifocus lens,” Proc. SPIE 600, 60000J (2005).
[Crossref]

2001 (2)

T. Yoshizawa, T. Shinoda, and Y. Otani, “Uniaxis rangefinder using contrast detection of a projected pattern,” Proc. SPIE 4190, 115–122 (2001).
[Crossref]

K. Korner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[Crossref]

2000 (1)

M. Takeda, T. Aoki, Y. Miyamoto, H. Tanaka, R. W. Gu, and Z. B. Zhang, “Absolute three-dimensional shape measurements using coaxial and coimage plane optical systems and Fourier fringe analysis for focus detection,” Opt. Eng. 39(1), 61–68 (2000).
[Crossref]

1999 (2)

X. Y. Su, L. K. Su, and W. S. Li, “A New Fourier transform profilometry based on modulation measurement,” Proc. SPIE 3749, 438–439 (1999).
[Crossref]

L. K. Su, X. Y. Su, W. S. Li, and L. Q. Xiang, “Application of Modulation Measurement Profilometry to Objects with Surface Holes,” Appl. Opt. 38(7), 1153–1158 (1999).
[Crossref] [PubMed]

1997 (1)

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44(3), 519–534 (1997).
[Crossref]

1992 (2)

1988 (1)

M. Subbarao and N. Gurumoorthy, “Depth recovery from blurred edges,” Proc. IEEE 1988, 498–503 (1988).

1985 (1)

1984 (1)

1983 (1)

Aoki, T.

M. Takeda, T. Aoki, Y. Miyamoto, H. Tanaka, R. W. Gu, and Z. B. Zhang, “Absolute three-dimensional shape measurements using coaxial and coimage plane optical systems and Fourier fringe analysis for focus detection,” Opt. Eng. 39(1), 61–68 (2000).
[Crossref]

Chen, D.

D. Chen, J. Schmit, and M. Novak, “Real-time scanner error correction in white light interferometry,” Proc. SPIE 9276, 92760I (2014).
[Crossref]

Chen, S.

Chim, S. S.

Devillers, R.

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44(3), 519–534 (1997).
[Crossref]

Ekstrand, L.

Y. Xu, L. Ekstrand, and S. Zhang, “Uniaxial 3-D shape measurement with projector defocusing,” Proc. SPIE 81330, 81330M (2011).
[Crossref]

Fleischer, M.

K. Korner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[Crossref]

Grattan, K. T.

Gu, R. W.

M. Takeda, T. Aoki, Y. Miyamoto, H. Tanaka, R. W. Gu, and Z. B. Zhang, “Absolute three-dimensional shape measurements using coaxial and coimage plane optical systems and Fourier fringe analysis for focus detection,” Opt. Eng. 39(1), 61–68 (2000).
[Crossref]

Gurumoorthy, N.

M. Subbarao and N. Gurumoorthy, “Depth recovery from blurred edges,” Proc. IEEE 1988, 498–503 (1988).

Halioua, M.

Harada, M.

Y. Otani, F. Kobayashi, Y. Mizutani, S. Watanabe, M. Harada, and T. Yoshizawa, “Uni-axial measurement of three-dimensional surface profile by liquid crystal digital shifter,” Proc. SPIE 7790, 77900A (2010).
[Crossref]

Kino, G. S.

Kobayashi, F.

Y. Otani, F. Kobayashi, Y. Mizutani, S. Watanabe, M. Harada, and T. Yoshizawa, “Uni-axial measurement of three-dimensional surface profile by liquid crystal digital shifter,” Proc. SPIE 7790, 77900A (2010).
[Crossref]

Korner, K.

K. Korner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[Crossref]

Kuwano, R.

Y. Mizutani, R. Kuwano, Y. Otani, N. Umeda, and T. Yoshizawa, “Three-dimensional shape measurement using focus method by using liquid crystal grating and liquid varifocus lens,” Proc. SPIE 600, 60000J (2005).
[Crossref]

Li, W. S.

L. K. Su, X. Y. Su, W. S. Li, and L. Q. Xiang, “Application of Modulation Measurement Profilometry to Objects with Surface Holes,” Appl. Opt. 38(7), 1153–1158 (1999).
[Crossref] [PubMed]

X. Y. Su, L. K. Su, and W. S. Li, “A New Fourier transform profilometry based on modulation measurement,” Proc. SPIE 3749, 438–439 (1999).
[Crossref]

Liu, H. C.

Meggitt, B. T.

Miyamoto, Y.

M. Takeda, T. Aoki, Y. Miyamoto, H. Tanaka, R. W. Gu, and Z. B. Zhang, “Absolute three-dimensional shape measurements using coaxial and coimage plane optical systems and Fourier fringe analysis for focus detection,” Opt. Eng. 39(1), 61–68 (2000).
[Crossref]

Mizutani, Y.

Y. Otani, F. Kobayashi, Y. Mizutani, S. Watanabe, M. Harada, and T. Yoshizawa, “Uni-axial measurement of three-dimensional surface profile by liquid crystal digital shifter,” Proc. SPIE 7790, 77900A (2010).
[Crossref]

Y. Mizutani, R. Kuwano, Y. Otani, N. Umeda, and T. Yoshizawa, “Three-dimensional shape measurement using focus method by using liquid crystal grating and liquid varifocus lens,” Proc. SPIE 600, 60000J (2005).
[Crossref]

Mutoh, K.

Novak, M.

D. Chen, J. Schmit, and M. Novak, “Real-time scanner error correction in white light interferometry,” Proc. SPIE 9276, 92760I (2014).
[Crossref]

Otani, Y.

Y. Otani, F. Kobayashi, Y. Mizutani, S. Watanabe, M. Harada, and T. Yoshizawa, “Uni-axial measurement of three-dimensional surface profile by liquid crystal digital shifter,” Proc. SPIE 7790, 77900A (2010).
[Crossref]

Y. Mizutani, R. Kuwano, Y. Otani, N. Umeda, and T. Yoshizawa, “Three-dimensional shape measurement using focus method by using liquid crystal grating and liquid varifocus lens,” Proc. SPIE 600, 60000J (2005).
[Crossref]

T. Yoshizawa, T. Shinoda, and Y. Otani, “Uniaxis rangefinder using contrast detection of a projected pattern,” Proc. SPIE 4190, 115–122 (2001).
[Crossref]

Palmer, A. W.

Plata, A.

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44(3), 519–534 (1997).
[Crossref]

Sandoz, P.

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44(3), 519–534 (1997).
[Crossref]

Schmit, J.

D. Chen, J. Schmit, and M. Novak, “Real-time scanner error correction in white light interferometry,” Proc. SPIE 9276, 92760I (2014).
[Crossref]

Shinoda, T.

T. Yoshizawa, T. Shinoda, and Y. Otani, “Uniaxis rangefinder using contrast detection of a projected pattern,” Proc. SPIE 4190, 115–122 (2001).
[Crossref]

Srinivasan, V.

Su, L. K.

L. K. Su, X. Y. Su, W. S. Li, and L. Q. Xiang, “Application of Modulation Measurement Profilometry to Objects with Surface Holes,” Appl. Opt. 38(7), 1153–1158 (1999).
[Crossref] [PubMed]

X. Y. Su, L. K. Su, and W. S. Li, “A New Fourier transform profilometry based on modulation measurement,” Proc. SPIE 3749, 438–439 (1999).
[Crossref]

Su, X. Y.

X. Y. Su, L. K. Su, and W. S. Li, “A New Fourier transform profilometry based on modulation measurement,” Proc. SPIE 3749, 438–439 (1999).
[Crossref]

L. K. Su, X. Y. Su, W. S. Li, and L. Q. Xiang, “Application of Modulation Measurement Profilometry to Objects with Surface Holes,” Appl. Opt. 38(7), 1153–1158 (1999).
[Crossref] [PubMed]

Subbarao, M.

M. Subbarao and N. Gurumoorthy, “Depth recovery from blurred edges,” Proc. IEEE 1988, 498–503 (1988).

Takeda, M.

M. Takeda, T. Aoki, Y. Miyamoto, H. Tanaka, R. W. Gu, and Z. B. Zhang, “Absolute three-dimensional shape measurements using coaxial and coimage plane optical systems and Fourier fringe analysis for focus detection,” Opt. Eng. 39(1), 61–68 (2000).
[Crossref]

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
[Crossref] [PubMed]

Tanaka, H.

M. Takeda, T. Aoki, Y. Miyamoto, H. Tanaka, R. W. Gu, and Z. B. Zhang, “Absolute three-dimensional shape measurements using coaxial and coimage plane optical systems and Fourier fringe analysis for focus detection,” Opt. Eng. 39(1), 61–68 (2000).
[Crossref]

Tiziani, H. J.

K. Korner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[Crossref]

Umeda, N.

Y. Mizutani, R. Kuwano, Y. Otani, N. Umeda, and T. Yoshizawa, “Three-dimensional shape measurement using focus method by using liquid crystal grating and liquid varifocus lens,” Proc. SPIE 600, 60000J (2005).
[Crossref]

Watanabe, S.

Y. Otani, F. Kobayashi, Y. Mizutani, S. Watanabe, M. Harada, and T. Yoshizawa, “Uni-axial measurement of three-dimensional surface profile by liquid crystal digital shifter,” Proc. SPIE 7790, 77900A (2010).
[Crossref]

Windecker, R.

K. Korner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[Crossref]

Xiang, L. Q.

Xu, Y.

Y. Xu, L. Ekstrand, and S. Zhang, “Uniaxial 3-D shape measurement with projector defocusing,” Proc. SPIE 81330, 81330M (2011).
[Crossref]

Yoshizawa, T.

Y. Otani, F. Kobayashi, Y. Mizutani, S. Watanabe, M. Harada, and T. Yoshizawa, “Uni-axial measurement of three-dimensional surface profile by liquid crystal digital shifter,” Proc. SPIE 7790, 77900A (2010).
[Crossref]

Y. Mizutani, R. Kuwano, Y. Otani, N. Umeda, and T. Yoshizawa, “Three-dimensional shape measurement using focus method by using liquid crystal grating and liquid varifocus lens,” Proc. SPIE 600, 60000J (2005).
[Crossref]

T. Yoshizawa, T. Shinoda, and Y. Otani, “Uniaxis rangefinder using contrast detection of a projected pattern,” Proc. SPIE 4190, 115–122 (2001).
[Crossref]

Zhang, S.

Y. Xu, L. Ekstrand, and S. Zhang, “Uniaxial 3-D shape measurement with projector defocusing,” Proc. SPIE 81330, 81330M (2011).
[Crossref]

Zhang, Z. B.

M. Takeda, T. Aoki, Y. Miyamoto, H. Tanaka, R. W. Gu, and Z. B. Zhang, “Absolute three-dimensional shape measurements using coaxial and coimage plane optical systems and Fourier fringe analysis for focus detection,” Opt. Eng. 39(1), 61–68 (2000).
[Crossref]

Appl. Opt. (6)

J. Mod. Opt. (1)

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44(3), 519–534 (1997).
[Crossref]

Opt. Eng. (2)

K. Korner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[Crossref]

M. Takeda, T. Aoki, Y. Miyamoto, H. Tanaka, R. W. Gu, and Z. B. Zhang, “Absolute three-dimensional shape measurements using coaxial and coimage plane optical systems and Fourier fringe analysis for focus detection,” Opt. Eng. 39(1), 61–68 (2000).
[Crossref]

Proc. IEEE (1)

M. Subbarao and N. Gurumoorthy, “Depth recovery from blurred edges,” Proc. IEEE 1988, 498–503 (1988).

Proc. SPIE (6)

D. Chen, J. Schmit, and M. Novak, “Real-time scanner error correction in white light interferometry,” Proc. SPIE 9276, 92760I (2014).
[Crossref]

T. Yoshizawa, T. Shinoda, and Y. Otani, “Uniaxis rangefinder using contrast detection of a projected pattern,” Proc. SPIE 4190, 115–122 (2001).
[Crossref]

Y. Mizutani, R. Kuwano, Y. Otani, N. Umeda, and T. Yoshizawa, “Three-dimensional shape measurement using focus method by using liquid crystal grating and liquid varifocus lens,” Proc. SPIE 600, 60000J (2005).
[Crossref]

Y. Otani, F. Kobayashi, Y. Mizutani, S. Watanabe, M. Harada, and T. Yoshizawa, “Uni-axial measurement of three-dimensional surface profile by liquid crystal digital shifter,” Proc. SPIE 7790, 77900A (2010).
[Crossref]

Y. Xu, L. Ekstrand, and S. Zhang, “Uniaxial 3-D shape measurement with projector defocusing,” Proc. SPIE 81330, 81330M (2011).
[Crossref]

X. Y. Su, L. K. Su, and W. S. Li, “A New Fourier transform profilometry based on modulation measurement,” Proc. SPIE 3749, 438–439 (1999).
[Crossref]

Other (1)

(Conference Proceedings) Authors: Proc. SPIE 9276, Optical Metrology and Inspection for Industrial Applications III, 92760I (13 November 2014); doi: .
[Crossref]

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Figures (14)

Fig. 1
Fig. 1 The setup of the proposed 3-D surface measurement.
Fig. 2
Fig. 2 The decomposition for the movement of grating.
Fig. 3
Fig. 3 Modulation distribution of eponymous pixels in the captured images.
Fig. 4
Fig. 4 (a) A series of fringe patterns captured by CCD camera; (b) The intensity distribution of a definite point (x,y) in the captured fringes.
Fig. 5
Fig. 5 Simulated object
Fig. 6
Fig. 6 (a) The 70th frame of fringe patterns; (b) Four curves respectively produced by the definite point of the captured fringe patterns; (c) Modulation distributions of the four curves respectively by the two methods; (d) Comparison of the modulation distribution by the two methods.
Fig. 7
Fig. 7 (a) Reconstruction by the proposed method; (b) Error distribution by the proposed method; (c) Reconstruction by the previous method; (d) Error distribution by the previous method.
Fig. 8
Fig. 8 (a) The 132nd row of the tested object, the reconstructed result of the same row by proposed method and that by the previous method; (b) The 175th column to the 205th column in the 132nd rows of the tested object, the reconstructed result of the same part of the object by proposed method and that by the previous method.
Fig. 9
Fig. 9 Diagram of calibration.
Fig. 10
Fig. 10 Relationship between the position of the grating and the height values.
Fig. 11
Fig. 11 (a) Reconstruction of the plane with height 44mm; (b) Reconstruction of the plane with height 36mm; (c) The error distribution for the 132nd row of the reconstructed plane with height 44mm; (d) The error distribution for the 132nd row of the reconstructed plane with height 36mm.
Fig. 12
Fig. 12 The measured object.
Fig. 13
Fig. 13 (a) The 100th frame of the images; (b) Three curves produced by three points (marked in (a)) of the captured fringes; (c) The modulation distributions obtained by the two methods; (d) Comparison of the modulation distribution by the two methods.
Fig. 14
Fig. 14 (a) Reconstruction by the proposed method; (b) Reconstruction by the previous method; (c) The 300th rows of the reconstructions by the two methods; (d) the 120th column to the 180th column in the 300th rows of the reconstructions by the two methods.

Equations (9)

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I(x,y,t)= R(x,y) A 2 { I 0 (t)+ C 0 (x,y,t)cos[ 2π f 0 x+ Φ 0 (x,y)+2πt/N ] } (t=0,1...T1)
I d (x,y,t;δ)=H(x,y)*I(x,y,t)
H(x,y)= 1 2π σ H 2 e x 2 + y 2 2 σ H 2
I d (x,y,t;δ)= R(x,y) A 2 { I 0 (t)+ C 0 (x,y,t) e 1 2 f 0 2 σ H 2 cos[ 2π f 0 x+ Φ 0 (x,y)+2πt/N ] }
M(x,y,t;δ)=R(x,y) M 0 (x,y,t) e f 0 2 2 ( Cδ R L l ) 2
I(t)= R A 2 { I 0 (t)+ C 0 (t) e 1 2 f 0 2 σ H 2 cos[ Φ+2πt/N ] } (t=0,1...T1)
G ( ζ ) (x,y) = G 0 ( ζ ) (x,y) + G 1 ( ζ ) (x,y) + G 1 ( ζ ) (x,y)
B(t)= 1 2 C 1 ( t ) e i( Φ )
D(n)=a(x,y)+b(x,y)t (n) (max) +c(x,y) t 2 (n) (max) (n=0,1...,N1)

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