Abstract

We present a discussion on how an area-encoded fringe pattern is applied to describe the 3D shape of objects that have spatially isolated surfaces. Phases of the fringes can be carried out without ambiguity to retrieve the 3D shape. Compared with conventional fringe projection techniques, the proposed scheme is relatively reliable and robust to identify the fringe order. Only one phase measurement is required. This makes it possible to analyze dynamic objects.

© 2008 Optical Society of America

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  1. M. Takeda, and K. Mutoh, "Fourier transform profilometry for the automatic measurement of 3-D object shaped," Appl. Opt. 22, 3977-3982 (1983).
    [CrossRef] [PubMed]
  2. V. Srinivasan, H. C. Liu, and M. Halioua, "Automated phase-measuring profilometry of 3-D diffuse objects," Appl. Opt. 23, 3105-3108 (1984).
    [CrossRef] [PubMed]
  3. F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000).
    [CrossRef]
  4. T. R. Judge, P. J. Bryanston-Cross, "Review of phase unwrapping techniques in fringe analysis," Opt. Lasers Eng. 21, 199-239 (1994).
    [CrossRef]
  5. X. Su and W. Chen, "Reliability-guided phase unwrapping algorithm: a review," Opt. Lasers Eng. 42, 245-261 (2004).
    [CrossRef]
  6. J. M. Huntley and H. O. Saldner, "Temporal phase-unwrapping algorithm for automated inteferogram analysis," Appl. Opt. 32, 3047-3052 (1993).
    [CrossRef] [PubMed]
  7. D. R. Burton and M. J. Lalor, "Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping," Appl. Opt. 33, 2939-2948 (1994).
    [CrossRef] [PubMed]
  8. H. Zhao, W. Chen, and Y. Tan, "Phase-unwrapping algorithm for the measurement of three-dimensional object shapes," Appl. Opt. 33, 4497-4500 (1994).
    [CrossRef] [PubMed]
  9. W. Nadeborn, P. Andrä, and W. Osten, "A robust procedure for absolute phase measurement," Opt. Lasers Eng. 24, 245-260 (1996).
    [CrossRef]
  10. H. O. Saldner and J. M. Huntley, "Temporal phase-unwrapping: application to surface profiling of discontinuous objects," Appl. Opt. 36, 2770-2775 (1997).
    [CrossRef] [PubMed]
  11. Y. Hao, Y. Zhao, and D. Li, "Multifrequency grating projection profilometry based on the nonlinear excess fraction method," Appl. Opt. 38, 4106-4110 (1999).
    [CrossRef]
  12. E. B. Li, X. Peng, J. Xi, J. F. Chicharo, J. Q. Yao, and D.W. Zhang, "Multi-frequency and multiple phase-shift sinusoidal fringe projection for 3D profilometry," Opt. Express 13, 1561-1569 (2005).
    [CrossRef] [PubMed]
  13. M. Takeda, Q. Gu, M. Kinoshita, H. Takai, and Y. Takahashi, "Frequency-multiplex Fourier-transform profilomery: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations," Appl. Opt. 36, 5347-5354 (1997).
    [CrossRef] [PubMed]
  14. W. H. Su, and H. Liu, "Calibration-based two frequency projected fringe profilometry: a robust, accurate, and single-shot meaurement for objects with large depth discontinuities," Opt. Express 14, 9178-9187 (2006).
    [CrossRef] [PubMed]
  15. P. Vuylsteke and A. Oosterkinck, "Range image acquisition with a single binary-encoded light pattern," IEEE Trans. Pattern Anal. Mach. Intell. 12, 148-164 (1990)
    [CrossRef]
  16. W. Liu, Z. Wang, G. Mu, and Z. Fang, "Color-coded projection grating method for shape measurement with a single exposure," Appl. Opt. 39, 3504-3508 (2000).
    [CrossRef]
  17. S. Y. Chen and Y. F. Li, "Self-recalibration of a colour-encoded light system for automated three-dimensional measurements" Meas. Sci. Technol. 14, 33-40 (2003).
    [CrossRef]
  18. W. H. Su, "Color-encoded fringe projection for 3D shape measurements," Opt. Express 15, 13167-13181 (2007).
    [CrossRef] [PubMed]
  19. W. S. Zhou and X. Y. Su, "A direct mapping algorithm for phase measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
    [CrossRef]
  20. Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, "Calibration of a three-dimensional shape measurement system," Opt. Eng. 42, 487-493 (2003).
    [CrossRef]
  21. H. Liu, W. H. Su, K. R., and S. Yin, "Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement," Opt. Commun. 216, 65-80 (2003).
    [CrossRef]
  22. B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, "A new model for meaureing object shape using non-collimated frnge-pattern projections," J. Opt. A: Pure Appl. Opt. 9, S66-S75 (2007).
    [CrossRef]

2007

W. H. Su, "Color-encoded fringe projection for 3D shape measurements," Opt. Express 15, 13167-13181 (2007).
[CrossRef] [PubMed]

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, "A new model for meaureing object shape using non-collimated frnge-pattern projections," J. Opt. A: Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

2006

2005

2004

X. Su and W. Chen, "Reliability-guided phase unwrapping algorithm: a review," Opt. Lasers Eng. 42, 245-261 (2004).
[CrossRef]

2003

S. Y. Chen and Y. F. Li, "Self-recalibration of a colour-encoded light system for automated three-dimensional measurements" Meas. Sci. Technol. 14, 33-40 (2003).
[CrossRef]

Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, "Calibration of a three-dimensional shape measurement system," Opt. Eng. 42, 487-493 (2003).
[CrossRef]

H. Liu, W. H. Su, K. R., and S. Yin, "Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement," Opt. Commun. 216, 65-80 (2003).
[CrossRef]

2000

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

W. Liu, Z. Wang, G. Mu, and Z. Fang, "Color-coded projection grating method for shape measurement with a single exposure," Appl. Opt. 39, 3504-3508 (2000).
[CrossRef]

1999

1997

1996

W. Nadeborn, P. Andrä, and W. Osten, "A robust procedure for absolute phase measurement," Opt. Lasers Eng. 24, 245-260 (1996).
[CrossRef]

1994

T. R. Judge, P. J. Bryanston-Cross, "Review of phase unwrapping techniques in fringe analysis," Opt. Lasers Eng. 21, 199-239 (1994).
[CrossRef]

D. R. Burton and M. J. Lalor, "Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping," Appl. Opt. 33, 2939-2948 (1994).
[CrossRef] [PubMed]

H. Zhao, W. Chen, and Y. Tan, "Phase-unwrapping algorithm for the measurement of three-dimensional object shapes," Appl. Opt. 33, 4497-4500 (1994).
[CrossRef] [PubMed]

W. S. Zhou and X. Y. Su, "A direct mapping algorithm for phase measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
[CrossRef]

1993

1990

P. Vuylsteke and A. Oosterkinck, "Range image acquisition with a single binary-encoded light pattern," IEEE Trans. Pattern Anal. Mach. Intell. 12, 148-164 (1990)
[CrossRef]

1984

1983

Andrä, P.

W. Nadeborn, P. Andrä, and W. Osten, "A robust procedure for absolute phase measurement," Opt. Lasers Eng. 24, 245-260 (1996).
[CrossRef]

Brown, G. M.

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

Bryanston-Cross, P. J.

T. R. Judge, P. J. Bryanston-Cross, "Review of phase unwrapping techniques in fringe analysis," Opt. Lasers Eng. 21, 199-239 (1994).
[CrossRef]

Burton, D. R.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, "A new model for meaureing object shape using non-collimated frnge-pattern projections," J. Opt. A: Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

D. R. Burton and M. J. Lalor, "Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping," Appl. Opt. 33, 2939-2948 (1994).
[CrossRef] [PubMed]

Chen, F.

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

Chen, S. Y.

S. Y. Chen and Y. F. Li, "Self-recalibration of a colour-encoded light system for automated three-dimensional measurements" Meas. Sci. Technol. 14, 33-40 (2003).
[CrossRef]

Chen, W.

Chiang, F. P.

Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, "Calibration of a three-dimensional shape measurement system," Opt. Eng. 42, 487-493 (2003).
[CrossRef]

Chicharo, J. F.

Fang, Z.

Fu, Q.

Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, "Calibration of a three-dimensional shape measurement system," Opt. Eng. 42, 487-493 (2003).
[CrossRef]

Gu, Q.

Halioua, M.

Hao, Y.

Hu, Q.

Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, "Calibration of a three-dimensional shape measurement system," Opt. Eng. 42, 487-493 (2003).
[CrossRef]

Huang, P. S.

Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, "Calibration of a three-dimensional shape measurement system," Opt. Eng. 42, 487-493 (2003).
[CrossRef]

Huntley, J. M.

Judge, T. R.

T. R. Judge, P. J. Bryanston-Cross, "Review of phase unwrapping techniques in fringe analysis," Opt. Lasers Eng. 21, 199-239 (1994).
[CrossRef]

Karout, S. A.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, "A new model for meaureing object shape using non-collimated frnge-pattern projections," J. Opt. A: Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

Kinoshita, M.

Lalor, M. J.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, "A new model for meaureing object shape using non-collimated frnge-pattern projections," J. Opt. A: Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

D. R. Burton and M. J. Lalor, "Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping," Appl. Opt. 33, 2939-2948 (1994).
[CrossRef] [PubMed]

Li, D.

Li, E. B.

Li, Y. F.

S. Y. Chen and Y. F. Li, "Self-recalibration of a colour-encoded light system for automated three-dimensional measurements" Meas. Sci. Technol. 14, 33-40 (2003).
[CrossRef]

Liu, H.

W. H. Su, and H. Liu, "Calibration-based two frequency projected fringe profilometry: a robust, accurate, and single-shot meaurement for objects with large depth discontinuities," Opt. Express 14, 9178-9187 (2006).
[CrossRef] [PubMed]

H. Liu, W. H. Su, K. R., and S. Yin, "Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement," Opt. Commun. 216, 65-80 (2003).
[CrossRef]

Liu, H. C.

Liu, W.

Mu, G.

Mutoh, K.

Nadeborn, W.

W. Nadeborn, P. Andrä, and W. Osten, "A robust procedure for absolute phase measurement," Opt. Lasers Eng. 24, 245-260 (1996).
[CrossRef]

Oosterkinck, A.

P. Vuylsteke and A. Oosterkinck, "Range image acquisition with a single binary-encoded light pattern," IEEE Trans. Pattern Anal. Mach. Intell. 12, 148-164 (1990)
[CrossRef]

Osten, W.

W. Nadeborn, P. Andrä, and W. Osten, "A robust procedure for absolute phase measurement," Opt. Lasers Eng. 24, 245-260 (1996).
[CrossRef]

Peng, X.

Rajoub, B. A.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, "A new model for meaureing object shape using non-collimated frnge-pattern projections," J. Opt. A: Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

Saldner, H. O.

Song, M.

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

Srinivasan, V.

Su, W. H.

Su, X.

X. Su and W. Chen, "Reliability-guided phase unwrapping algorithm: a review," Opt. Lasers Eng. 42, 245-261 (2004).
[CrossRef]

Su, X. Y.

W. S. Zhou and X. Y. Su, "A direct mapping algorithm for phase measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
[CrossRef]

Takahashi, Y.

Takai, H.

Takeda, M.

Tan, Y.

Vuylsteke, P.

P. Vuylsteke and A. Oosterkinck, "Range image acquisition with a single binary-encoded light pattern," IEEE Trans. Pattern Anal. Mach. Intell. 12, 148-164 (1990)
[CrossRef]

Wang, Z.

Xi, J.

Yao, J. Q.

Zhang, D.W.

Zhao, H.

Zhao, Y.

Zhou, W. S.

W. S. Zhou and X. Y. Su, "A direct mapping algorithm for phase measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
[CrossRef]

Appl. Opt.

M. Takeda, and K. Mutoh, "Fourier transform profilometry for the automatic measurement of 3-D object shaped," Appl. Opt. 22, 3977-3982 (1983).
[CrossRef] [PubMed]

V. Srinivasan, H. C. Liu, and M. Halioua, "Automated phase-measuring profilometry of 3-D diffuse objects," Appl. Opt. 23, 3105-3108 (1984).
[CrossRef] [PubMed]

J. M. Huntley and H. O. Saldner, "Temporal phase-unwrapping algorithm for automated inteferogram analysis," Appl. Opt. 32, 3047-3052 (1993).
[CrossRef] [PubMed]

D. R. Burton and M. J. Lalor, "Multichannel Fourier fringe analysis as an aid to automatic phase unwrapping," Appl. Opt. 33, 2939-2948 (1994).
[CrossRef] [PubMed]

H. Zhao, W. Chen, and Y. Tan, "Phase-unwrapping algorithm for the measurement of three-dimensional object shapes," Appl. Opt. 33, 4497-4500 (1994).
[CrossRef] [PubMed]

H. O. Saldner and J. M. Huntley, "Temporal phase-unwrapping: application to surface profiling of discontinuous objects," Appl. Opt. 36, 2770-2775 (1997).
[CrossRef] [PubMed]

Y. Hao, Y. Zhao, and D. Li, "Multifrequency grating projection profilometry based on the nonlinear excess fraction method," Appl. Opt. 38, 4106-4110 (1999).
[CrossRef]

M. Takeda, Q. Gu, M. Kinoshita, H. Takai, and Y. Takahashi, "Frequency-multiplex Fourier-transform profilomery: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations," Appl. Opt. 36, 5347-5354 (1997).
[CrossRef] [PubMed]

W. Liu, Z. Wang, G. Mu, and Z. Fang, "Color-coded projection grating method for shape measurement with a single exposure," Appl. Opt. 39, 3504-3508 (2000).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

P. Vuylsteke and A. Oosterkinck, "Range image acquisition with a single binary-encoded light pattern," IEEE Trans. Pattern Anal. Mach. Intell. 12, 148-164 (1990)
[CrossRef]

J. Mod. Opt.

W. S. Zhou and X. Y. Su, "A direct mapping algorithm for phase measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, "A new model for meaureing object shape using non-collimated frnge-pattern projections," J. Opt. A: Pure Appl. Opt. 9, S66-S75 (2007).
[CrossRef]

Meas. Sci. Technol.

S. Y. Chen and Y. F. Li, "Self-recalibration of a colour-encoded light system for automated three-dimensional measurements" Meas. Sci. Technol. 14, 33-40 (2003).
[CrossRef]

Opt. Commun.

H. Liu, W. H. Su, K. R., and S. Yin, "Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement," Opt. Commun. 216, 65-80 (2003).
[CrossRef]

Opt. Eng.

Q. Hu, P. S. Huang, Q. Fu, F. P. Chiang, "Calibration of a three-dimensional shape measurement system," Opt. Eng. 42, 487-493 (2003).
[CrossRef]

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

Opt. Express

Opt. Lasers Eng.

T. R. Judge, P. J. Bryanston-Cross, "Review of phase unwrapping techniques in fringe analysis," Opt. Lasers Eng. 21, 199-239 (1994).
[CrossRef]

X. Su and W. Chen, "Reliability-guided phase unwrapping algorithm: a review," Opt. Lasers Eng. 42, 245-261 (2004).
[CrossRef]

W. Nadeborn, P. Andrä, and W. Osten, "A robust procedure for absolute phase measurement," Opt. Lasers Eng. 24, 245-260 (1996).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Appearance of a transmittance-encoded fringe pattern.

Fig. 2.
Fig. 2.

Color arrangement of the encoding scheme.

Fig. 3.
Fig. 3.

Sinusoidal fringes encoded with binary stripes.

Fig. 4.
Fig. 4.

Optical configuration for 3D shape measurements.

Fig. 5.
Fig. 5.

Appearance of area encoded sinusoidal fringes.

Fig. 6.
Fig. 6.

3D sensing to spatially isolated objects: (a) appearance of projected fringes on the tested samples; (b) phase-extraction by Fourier transform method; (c) unwrapped phase identified by the proposed scheme; and (d) the reconstructed 3D shape.

Fig. 7.
Fig. 7.

3D shape sensing for a standard flat plate. (a) Retrieved shape. (b) One-line surface plot of the retrieved shape.

Fig. 8.
Fig. 8.

Profile measurements for surfaces with large depth discontinuities: (a) appearance of projected fringes on the tested sample, and (b) reconstructed 3D shape by the proposed measurement scheme.

Equations (2)

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t ( x ) = C ( x ) · B ( x ) · [ 0.4 + 0.4 cos ( 2 π d x ) ] + 0.2 ,
{ z = n = 0 N c n φ n x = a 1 z + a 0 y = b 1 z + b 0 ,

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