Abstract

A fringe projection technique to trace the shape of a fast-moving object is proposed. A binary-encoded fringe pattern is illuminated by a strobe lamp and then projected onto the moving object at a sequence of time. Phases of the projected fringes obtained from the sequent measurements are extracted by the Fourier transform method. Unwrapping is then performed with reference to the binary-encoded fringe pattern. Even though the inspected object is colorful, fringe orders can be identified. A stream of profiles is therefore retrieved from the sequent unwrapped phases. This makes it possible to analyze physical properties of the dynamic objects. Advantages of the binary-encoded fringe pattern for phase unwrapping also include (1) reliable performance for colorful objects, spatially isolated objects, and surfaces with large depth discontinuities; (2) unwrapped errors only confined in a local area; and (3) low computation cost.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [CrossRef]
  2. W. H. Su and C. K. Lee, “3D shape reconstruction from images blurred by motion,” Opt. Eng. 48, 073604 (2009).
    [CrossRef]
  3. Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601 (2005).
    [CrossRef]
  4. E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46, 106–116 (2008).
    [CrossRef]
  5. J. M. Huntley and H. O. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
    [CrossRef]
  6. H. O. Saldner and J. M. Huntley, “Temporal phase-unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
    [CrossRef]
  7. 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]
  8. 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]
  9. M. Takeda, Q. Gu, M. Kinoshita, H. Takai, and Y. Takahashi, “Frequency-multiplex Fourier-transform profilometry: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations,” Appl. Opt. 36, 5347–5354 (1997).
    [CrossRef]
  10. W. H. Su and H. Liu, “Calibration-based two frequency projected fringe profilometry: a robust, accurate, and single-shot measurement for objects with large depth discontinuities,” Opt. Express 14, 9178–9187 (2006).
    [CrossRef]
  11. W. H. Su, “Color-encoded fringe projection for 3D shape measurements,” Opt. Express 15, 13167–13181 (2007).
    [CrossRef]
  12. Y. Wang, S. Yang, and X. Gou, “Modified Fourier transform method for 3D profile measurement without phase unwrapping,” Opt. Lett. 35, 790–792 (2010).
    [CrossRef]
  13. W. H. Su, H. Liu, K. Reichard, S. Yin, and F. T. S. Yu, “Fabrication of digital sinusoidal gratings and precisely controlled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
    [CrossRef]
  14. H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216, 65–80 (2003).
    [CrossRef]
  15. F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39, 35–50 (2003).
    [CrossRef]

2010

2009

W. H. Su and C. K. Lee, “3D shape reconstruction from images blurred by motion,” Opt. Eng. 48, 073604 (2009).
[CrossRef]

2008

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46, 106–116 (2008).
[CrossRef]

2007

2006

2005

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]

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601 (2005).
[CrossRef]

2003

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

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

F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39, 35–50 (2003).
[CrossRef]

1999

1997

1993

1983

Berryman, F.

F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39, 35–50 (2003).
[CrossRef]

Busca, G.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46, 106–116 (2008).
[CrossRef]

Cao, Y.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601 (2005).
[CrossRef]

Chen, W.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601 (2005).
[CrossRef]

Chicharo, J. F.

Cubillo, J.

F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39, 35–50 (2003).
[CrossRef]

Gou, X.

Gu, Q.

Hao, Y.

Huntley, J. M.

Kinoshita, M.

Lee, C. K.

W. H. Su and C. K. Lee, “3D shape reconstruction from images blurred by motion,” Opt. Eng. 48, 073604 (2009).
[CrossRef]

Li, D.

Li, E. B.

Li, Y.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601 (2005).
[CrossRef]

Liu, H.

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

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

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

Mutoh, K.

Peng, X.

Pynsent, P.

F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39, 35–50 (2003).
[CrossRef]

Reichard, K.

H. Liu, W. H. Su, K. Reichard, 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 controlled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
[CrossRef]

Saldner, H. O.

Su, W. H.

W. H. Su and C. K. Lee, “3D shape reconstruction from images blurred by motion,” Opt. Eng. 48, 073604 (2009).
[CrossRef]

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

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

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

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

Su, X.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601 (2005).
[CrossRef]

Takahashi, Y.

Takai, H.

Takeda, M.

Wang, Y.

Xi, J.

Xiang, L.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601 (2005).
[CrossRef]

Yang, S.

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 controlled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
[CrossRef]

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216, 65–80 (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 controlled diffusive flats and their application to highly accurate projected fringe profilometry,” Opt. Eng. 42, 1730–1740 (2003).
[CrossRef]

Zappa, E.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46, 106–116 (2008).
[CrossRef]

Zhang, D. W.

Zhang, Q.

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601 (2005).
[CrossRef]

Zhao, Y.

Appl. Opt.

Opt. Commun.

H. Liu, W. H. Su, K. Reichard, 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 and C. K. Lee, “3D shape reconstruction from images blurred by motion,” Opt. Eng. 48, 073604 (2009).
[CrossRef]

Q. Zhang, X. Su, Y. Cao, Y. Li, L. Xiang, and W. Chen, “Optical 3-D shape and deformation measurement of rotating blades using stroboscopic structured illumination,” Opt. Eng. 44, 113601 (2005).
[CrossRef]

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

Opt. Express

Opt. Lasers Eng.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46, 106–116 (2008).
[CrossRef]

F. Berryman, P. Pynsent, and J. Cubillo, “A theoretical comparison of three fringe analysis methods for determining the three-dimensional shape of an object in the presence of noise,” Opt. Lasers Eng. 39, 35–50 (2003).
[CrossRef]

Opt. Lett.

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 (15)

Fig. 1.
Fig. 1.

Binary-encoded fringe pattern when six sequent digital numbers are used to form a code word. (a) Appearance of the binary-encoded fringe pattern. (b) Appearance of the sinusoidal fringe pattern. (c) Appearance of the binary-encoded stripes. (d) Corresponding binary codes. (e) Corresponding fringe orders.

Fig. 2.
Fig. 2.

Binary encoded fringe pattern when five sequent digital numbers are used to form a code word. (a) Appearance of the pattern. (b) Corresponding binary codes.

Fig. 3.
Fig. 3.

Appearance of the binary encoded fringe pattern. (a) Three digital numbers are used to form a code word. (b) Four digital numbers are used to form a code word.

Fig. 4.
Fig. 4.

Binary encoded fringe pattern when seven sequent digital numbers are used to form a code word.

Fig. 5.
Fig. 5.

Schematic setup of projected fringe profilometry.

Fig. 6.
Fig. 6.

(a) Flow diagram of the decoding procedure. (b) Example given to address the decoding procedure.

Fig. 7.
Fig. 7.

(a) Appearance of fringes projected on the discontinuous surface. A set of code words is built based on the decoding algorithm. (b) Fringe order determined with reference to the lookup table.

Fig. 8.
Fig. 8.

Configuration of a pendulum. (a) A massive ball hung by a string from a fixed support vibrates both along y axis and z axis. (b) The ball approximately traced an ellipse on the yz plane.

Fig. 9.
Fig. 9.

Schematic setup of projected fringe profilometry for the pendulum.

Fig. 10.
Fig. 10.

(a) Appearance of the projected fringes on the inspected pendulum. Six pulsed illuminations were recorded in one image. (b) Phase map extracted by the Fourier transform method. (c) Phases unwrapped with reference to the binary-encoded scheme. (d) Retrieved 3D profile measured at a sequence of time.

Fig. 11.
Fig. 11.

(a) Appearance of a projected binary-encoded fringe pattern on the flat surface. (b) Reconstructed 3D profile. (c) Profile described in the scale of submillimeters.

Fig. 12.
Fig. 12.

(a) Appearance of projected binary-encoded fringes on the colorful object. (b) Projected binary-encoded fringes displayed in gray intensity levels. (c) Phases extracted by the Fourier transform method. (d) Phases unwrapped with reference to the binary-encoded pattern.

Fig. 13.
Fig. 13.

Reconstructed 3D profile.

Fig. 14.
Fig. 14.

(a) Appearance of the inspected objects. (b) Projected fringes recorded by a color CCD camera. (c) Projected fringes recorded by a monochrome CCD camera. (d) Unwrapped phase map in which six fringes were unwrapped with wrong phases.

Fig. 15.
Fig. 15.

Reconstructed 3D profiles with inappropriate discontinuities.

Tables (1)

Tables Icon

Table 1. Center Points of the Profiles Retrieved by the Sequent Pulsed Measurements

Equations (3)

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

T=2n,
φ(x,y)=Φ(x,y)+2π(n1),
{z=n=0Ncnφnx=a1z+a0y=b1z+b0,

Metrics