Abstract

A novel technique using color-encoded stripes embedded into a sinusoidal fringe pattern for finding the absolute shape of an object is proposed. Phases of the projected fringes on the surface are evaluated by Fourier transform method. Unwrapping is then performed with reference to the color-encoded stripes. When surfaces of interest contain large depth discontinuities, the color-encoded stripes can easily identify the fringe order. Compared with other phase unwrapping schemes, this method offers many major advantages, including: (1) very low computation cost for the 3D reconstruction, (2) reliable phase unwrapping to complex objects, especially for surfaces with large depth discontinuities, (3) only one-shot measurement is required, and (4) robust performance to analyze dynamic objects.

© 2007 Optical Society of America

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  1. M. D. Altschuler, B. R. Altschuler, and J. Taboada, "Laser electro-optic system for rapid three-dimensional topographic mapping of surfaces," Opt. Eng. 20, 953-961 (1981).
  2. M. Minou, T. Kanade, and T. Sakai, "A method of time-coded parallel planes of light for depth measurement," Trans. IECE Japan 64, 521-528 (1981).
  3. G. Sansoni, S. Corini, S. Lazzari and F. Docchio, "Three-dimensional imaging based on Gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications," Appl. Opt. 36, 4463-4472 (1997).
    [CrossRef] [PubMed]
  4. K. Sato, and S. Inokuchi, "Three-dimensional surface measurement by space encoding range image," J. Rob. Syst. 2, 27-39 (1985).
  5. 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]
  6. G. Indebetouw, "Profile measurement using projection of running fringes," Appl. Opt. 17, 2930-2933 (1978).
    [CrossRef] [PubMed]
  7. 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]
  8. 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]
  9. K. G. Larkin, and B. F. Oreb, "Design and assessment of symmetrical phase-shifting algorithms," J. Opt. Soc. Am. A 9, 1740-1748 (1992).
    [CrossRef]
  10. V. Y. Su, G. Bally, and D. Vukicevic, "Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation," Opt. Commun. 98, 141-150 (1993).
    [CrossRef]
  11. Y. Surrel, "Design of algorithms for phase measurements by the use of phase stepping," Appl. Opt. 35, 51-60 (1996).
    [CrossRef] [PubMed]
  12. L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42, 3307-3314 (2003).
    [CrossRef]
  13. 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]
  14. W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, "Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry," Opt. Eng. 42, 1730-1740 (2003).
    [CrossRef]
  15. J. M. Huntley, and H. O. Saldner, "Temporal phase-unwrapping algorithm for automated inteferogram analysis," Appl. Opt. 32, 3047-3052 (1993).
    [CrossRef] [PubMed]
  16. H. O. Saldner, and J. M. Huntley, "Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector," Opt. Eng. 36, 610-615 (1997).
    [CrossRef]
  17. 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]
  18. 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]
  19. 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]
  20. 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]
  21. J. L. Li, H. J. Su, and X. Y. Su, "Two-frequency grating used in phase-measuring profilometry," Appl. Opt. 36, 277-280 (1997).
    [CrossRef] [PubMed]
  22. 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]

2006

2005

2003

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

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, "Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry," Opt. Eng. 42, 1730-1740 (2003).
[CrossRef]

2000

1999

1997

1996

1994

1993

V. Y. Su, G. Bally, and D. Vukicevic, "Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation," Opt. Commun. 98, 141-150 (1993).
[CrossRef]

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

1992

1985

K. Sato, and S. Inokuchi, "Three-dimensional surface measurement by space encoding range image," J. Rob. Syst. 2, 27-39 (1985).

1984

1983

1981

M. D. Altschuler, B. R. Altschuler, and J. Taboada, "Laser electro-optic system for rapid three-dimensional topographic mapping of surfaces," Opt. Eng. 20, 953-961 (1981).

M. Minou, T. Kanade, and T. Sakai, "A method of time-coded parallel planes of light for depth measurement," Trans. IECE Japan 64, 521-528 (1981).

1978

Altschuler, B. R.

M. D. Altschuler, B. R. Altschuler, and J. Taboada, "Laser electro-optic system for rapid three-dimensional topographic mapping of surfaces," Opt. Eng. 20, 953-961 (1981).

Altschuler, M. D.

M. D. Altschuler, B. R. Altschuler, and J. Taboada, "Laser electro-optic system for rapid three-dimensional topographic mapping of surfaces," Opt. Eng. 20, 953-961 (1981).

Bally, G.

V. Y. Su, G. Bally, and D. Vukicevic, "Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation," Opt. Commun. 98, 141-150 (1993).
[CrossRef]

Burton, D. R.

Chicharo, J. F.

Corini, S.

Docchio, F.

Fang, Z.

Garcia, V.

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

Gu, Q.

Halioua, M.

Hao, Y.

Huntley, J. M.

H. O. Saldner, and J. M. Huntley, "Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector," Opt. Eng. 36, 610-615 (1997).
[CrossRef]

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

Indebetouw, G.

Inokuchi, S.

K. Sato, and S. Inokuchi, "Three-dimensional surface measurement by space encoding range image," J. Rob. Syst. 2, 27-39 (1985).

Kanade, T.

M. Minou, T. Kanade, and T. Sakai, "A method of time-coded parallel planes of light for depth measurement," Trans. IECE Japan 64, 521-528 (1981).

Kinoshita, M.

Lalor, M. J.

Larkin, K. G.

Lazzari, S.

Li, D.

Li, E. B.

Li, J. L.

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]

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, "Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry," Opt. Eng. 42, 1730-1740 (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]

Liu, H. C.

Liu, W.

Luna, E.

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

Minou, M.

M. Minou, T. Kanade, and T. Sakai, "A method of time-coded parallel planes of light for depth measurement," Trans. IECE Japan 64, 521-528 (1981).

Mu, G.

Mutoh, K.

Oreb, B. F.

Peng, X.

Reichard, K.

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, "Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry," Opt. Eng. 42, 1730-1740 (2003).
[CrossRef]

Sakai, T.

M. Minou, T. Kanade, and T. Sakai, "A method of time-coded parallel planes of light for depth measurement," Trans. IECE Japan 64, 521-528 (1981).

Salas, L.

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

Saldner, H. O.

H. O. Saldner, and J. M. Huntley, "Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector," Opt. Eng. 36, 610-615 (1997).
[CrossRef]

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

Salinas, J.

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

Sansoni, G.

Sato, K.

K. Sato, and S. Inokuchi, "Three-dimensional surface measurement by space encoding range image," J. Rob. Syst. 2, 27-39 (1985).

Servin, M.

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

Srinivasan, V.

Su, H. J.

Su, V. Y.

V. Y. Su, G. Bally, and D. Vukicevic, "Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation," Opt. Commun. 98, 141-150 (1993).
[CrossRef]

Su, W. 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]

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, "Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry," Opt. Eng. 42, 1730-1740 (2003).
[CrossRef]

Su, X. Y.

Surrel, Y.

Taboada, J.

M. D. Altschuler, B. R. Altschuler, and J. Taboada, "Laser electro-optic system for rapid three-dimensional topographic mapping of surfaces," Opt. Eng. 20, 953-961 (1981).

Takahashi, Y.

Takai, H.

Takeda, M.

Vukicevic, D.

V. Y. Su, G. Bally, and D. Vukicevic, "Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation," Opt. Commun. 98, 141-150 (1993).
[CrossRef]

Wang, Z.

Xi, J.

Yao, J. Q.

Yin, S.

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, "Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry," Opt. Eng. 42, 1730-1740 (2003).
[CrossRef]

Yu, F. T. S.

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, "Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry," Opt. Eng. 42, 1730-1740 (2003).
[CrossRef]

Zhang, D.W.

Zhao, Y.

Appl. Opt.

G. Sansoni, S. Corini, S. Lazzari and F. Docchio, "Three-dimensional imaging based on Gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications," Appl. Opt. 36, 4463-4472 (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]

G. Indebetouw, "Profile measurement using projection of running fringes," Appl. Opt. 17, 2930-2933 (1978).
[CrossRef] [PubMed]

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]

Y. Surrel, "Design of algorithms for phase measurements by the use of phase stepping," Appl. Opt. 35, 51-60 (1996).
[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]

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]

J. L. Li, H. J. Su, and X. Y. Su, "Two-frequency grating used in phase-measuring profilometry," Appl. Opt. 36, 277-280 (1997).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J. Rob. Syst.

K. Sato, and S. Inokuchi, "Three-dimensional surface measurement by space encoding range image," J. Rob. Syst. 2, 27-39 (1985).

Opt. Commun.

V. Y. Su, G. Bally, and D. Vukicevic, "Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation," Opt. Commun. 98, 141-150 (1993).
[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]

Opt. Eng.

W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, "Fabrication of digital sinusoidal gratings and precisely conytolled diffusive flats and their application to highly accurate projected fringe profilometry," Opt. Eng. 42, 1730-1740 (2003).
[CrossRef]

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

H. O. Saldner, and J. M. Huntley, "Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector," Opt. Eng. 36, 610-615 (1997).
[CrossRef]

M. D. Altschuler, B. R. Altschuler, and J. Taboada, "Laser electro-optic system for rapid three-dimensional topographic mapping of surfaces," Opt. Eng. 20, 953-961 (1981).

Opt. Express

Trans. IECE Japan

M. Minou, T. Kanade, and T. Sakai, "A method of time-coded parallel planes of light for depth measurement," Trans. IECE Japan 64, 521-528 (1981).

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Figures (14)

Fig. 1.
Fig. 1.

Optical geometry of the projected fringe profilometry.

Fig. 2.
Fig. 2.

Appearance of a color-encoded fringe pattern.

Fig. 3.
Fig. 3.

Color arrangement of the encoded scheme.

Fig. 4.
Fig. 4.

Color-encoded algorithm. (a) Appearance of the color-encoded stripes. (b) A code table created by (a). (c) A color-encoded fringe pattern. (d) Appearance of the projected pattern on a plate recorded by the color CCD camera (e) Binary mask generated from the red channel. (f) Binary mask created from the green channel. (g) Binary mask created from the blue channel.

Fig. 5.
Fig. 5.

Flow diagram of stages for color-encoded fringes transformed in gray intensity levels.

Fig. 6.
Fig. 6.

Projected color-encoded fringes displayed in gray intensity levels

Fig. 7.
Fig. 7.

Fringe order identification: (a) shows an observed image in which the tested object is projected with a color-encoded fringe pattern; (b), (c), and (d) show the same image in red, green, and blue channel, respectively; (e), (f), and (g) show the binary mask created by the red channel, green channel, and blue channel, respectively; (h) shows the evaluated distribution of the fringe order, with a color bar to represent the order.

Fig. 8.
Fig. 8.

Phase-extraction and unwrapping: (a) Appearance of the recorded image displayed in gray intensity levels. (b) Computed phase distribution using Fourier transform method. (c) Unwrapped phase map using Eq. (10).

Fig. 9.
Fig. 9.

Appearance of a projected color-encoded fringe pattern. A 24-bit color CCD camera with 1024× 78 pixels was used to record the fringes.

Fig. 10.
Fig. 10.

Appearance of three channel images: (a), (b), and (c) show the observed image in red, green, and blue channel, respectively; (d), (e), and (f) show the binary mask created by the red channel, green channel, and blue channel, respectively

Fig. 11.
Fig. 11.

Distribution of the fringe order. A color bar is utilized to address the order number.

Fig. 12
Fig. 12

Phase-extraction and unwrapping. (a) Appearance of an image in gray intensity levels. (b) Computed phase distribution using Fourier transform method. (c) Unwrapped phase map.

Fig. 13.
Fig. 13.

(a). Appearance of a projected color-encoded fringe pattern on the reference plane. (b) Unwrapped phase map.

Fig. 14.
Fig. 14.

Reconstructed 3D profile.

Tables (2)

Tables Icon

Table 1. Assigned digital numbers with the corresponding colors

Tables Icon

Table 2. Assigned binary values in red-green-blue model with the corresponding digital numbers

Equations (11)

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

Z x y = AC ¯ tan θ + tan θ n .
Z x y = AC ¯ cot θ = φ A φ C 2 π d o cot θ ,
Z x y = AC ¯ cot θ = φ Z φ C 2 π d o cot θ .
t ( x ) = 0.6 + 0.4 cos ( 2 π d x ) ,
I x y = a x y + b x y cos [ 2 π d x + Δ φ x y ]
= a x y + 1 2 b x y e j [ 2 π d x + Δ φ x y ] + 1 2 b x y e j [ 2 π d x + Δ φ x y ] ,
I x y = a x y + 1 2 b ˜ x y e j 2 π d x + 1 2 b ˜ * x y e j 2 π d x ,
{ I x y } = A f x y + 1 2 B ˜ f x 1 d y + 1 2 B ˜ * f x + 1 d y ,
s x y = 1 { 1 2 B ˜ f x 1 d y } = 1 2 b ˜ x y e j 2 π d x = 1 2 b x y e j [ 2 π d x + Δ φ x y ] .
Φ x y = tan 1 { Im { s x y } Re { s x y } } ,
2 πx d + Δ φ x y = Φ x y + 2 π ( n 1 ) ,

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