Abstract

We present a method for synthesizing triangular intensity fringes as a way to solve the problems caused by projector/camera gamma nonlinearity in triangular-pattern phase-shifting profilometry. The fringe generation technique consists of projecting and acquiring a temporal sequence of strictly binary color patterns (code gray), whose (adequately weighted) average leads to triangular fringe patterns with the required number of bits, which allows a reliable three-dimensional profile reconstruction using these methods. Validation experiments are presented.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photon. 3, 128–160 (2011).
    [CrossRef]
  2. S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
    [CrossRef]
  3. P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
    [CrossRef]
  4. S. Zhang and S. T. Yau, “High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method,” Opt. Express 14, 2644–2649 (2006).
    [CrossRef]
  5. B. Carrihill and R. Hummel, “Experiments with the intensity ratio depth sensor,” Comput. Vis. Graph. Image Process. 32, 337–358 (1985).
    [CrossRef]
  6. C. Waddington and J. Kofman, “Analysis of measurement sensitivity to illuminance and fringe-pattern gray levels for fringe-pattern projection adaptive to ambient lighting,” Opt. Lasers Eng. 48, 251–256 (2010).
    [CrossRef]
  7. P. Jia, J. Kofman, and C. English, “Error compensation in two-step triangular-pattern phase-shifting profilometry,” Opt. Lasers Eng. 46, 311–320 (2008).
    [CrossRef]
  8. P. Jia, J. Kofman, and C. English, “Intensity-ratio error compensation for triangular pattern phase-shifting profilometry,” J. Opt. Soc. Am. A 24, 3150–5158 (2007).
    [CrossRef]
  9. P. Jia, J. Kofman, and C. English, “Multiple-step triangular-pattern phase shifting and the influence of number of steps and pitch on measurement accuracy,” Appl. Opt. 46, 3253–3262 (2007).
    [CrossRef]
  10. P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
    [CrossRef]
  11. P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46, 043601 (2007).
    [CrossRef]
  12. P. Jia, J. Kofman, and C. English, “Real-time full-field 3-D surface-shape measurement using off-the-shelf components and a single processor,” in Proceedings of IEEE Sixth International Conference on 3-D Digital Imaging and Modeling (IEEE, 2007).
  13. S. Inokuchi, K. Sato, and F. Matsuda, “Range-imaging for 3-D object recognition,” in Proceedings of International Conference on Pattern Recognition (IEEE, 1984), pp. 806–808.
  14. K. Sato and S. Inokuchi, “Three-dimensional surface measurement by space encoding range imaging,” J. Robot. Syst. 2, 27–39 (1985).
  15. G. A. Ayubi, J. M. Di Martino, J. R. Alonso, A. Fernández, J. L. Flores, and J. A. Ferrari, “Color encoding of binary fringes for gamma correction in 3-D profiling,” Opt. Lett. 37, 1325–1327 (2012).
    [CrossRef]
  16. J. D. Gaskill, Linear Systems, Fourier Transform and Optics (Wiley, 1978).
  17. Thorlabs, High Resolution USB 2.0 CMOS and CCD Cameras, http://www.thorlabs.com/Thorcat/15900/DCU224C-Manual.pdf .
  18. N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man. Cybern. SMC 9, 62–66 (1979).
    [CrossRef]

2012

2011

2010

C. Waddington and J. Kofman, “Analysis of measurement sensitivity to illuminance and fringe-pattern gray levels for fringe-pattern projection adaptive to ambient lighting,” Opt. Lasers Eng. 48, 251–256 (2010).
[CrossRef]

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
[CrossRef]

2008

P. Jia, J. Kofman, and C. English, “Error compensation in two-step triangular-pattern phase-shifting profilometry,” Opt. Lasers Eng. 46, 311–320 (2008).
[CrossRef]

2007

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46, 043601 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Multiple-step triangular-pattern phase shifting and the influence of number of steps and pitch on measurement accuracy,” Appl. Opt. 46, 3253–3262 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Intensity-ratio error compensation for triangular pattern phase-shifting profilometry,” J. Opt. Soc. Am. A 24, 3150–5158 (2007).
[CrossRef]

2006

2003

P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

1985

K. Sato and S. Inokuchi, “Three-dimensional surface measurement by space encoding range imaging,” J. Robot. Syst. 2, 27–39 (1985).

B. Carrihill and R. Hummel, “Experiments with the intensity ratio depth sensor,” Comput. Vis. Graph. Image Process. 32, 337–358 (1985).
[CrossRef]

1979

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man. Cybern. SMC 9, 62–66 (1979).
[CrossRef]

Alonso, J. R.

Ayubi, G. A.

Carrihill, B.

B. Carrihill and R. Hummel, “Experiments with the intensity ratio depth sensor,” Comput. Vis. Graph. Image Process. 32, 337–358 (1985).
[CrossRef]

Chiang, F.-P.

P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

Di Martino, J. M.

English, C.

P. Jia, J. Kofman, and C. English, “Error compensation in two-step triangular-pattern phase-shifting profilometry,” Opt. Lasers Eng. 46, 311–320 (2008).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Multiple-step triangular-pattern phase shifting and the influence of number of steps and pitch on measurement accuracy,” Appl. Opt. 46, 3253–3262 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46, 043601 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Intensity-ratio error compensation for triangular pattern phase-shifting profilometry,” J. Opt. Soc. Am. A 24, 3150–5158 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Real-time full-field 3-D surface-shape measurement using off-the-shelf components and a single processor,” in Proceedings of IEEE Sixth International Conference on 3-D Digital Imaging and Modeling (IEEE, 2007).

Fernández, A.

Ferrari, J. A.

Flores, J. L.

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transform and Optics (Wiley, 1978).

Geng, J.

Huang, P. S.

P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

Hummel, R.

B. Carrihill and R. Hummel, “Experiments with the intensity ratio depth sensor,” Comput. Vis. Graph. Image Process. 32, 337–358 (1985).
[CrossRef]

Inokuchi, S.

K. Sato and S. Inokuchi, “Three-dimensional surface measurement by space encoding range imaging,” J. Robot. Syst. 2, 27–39 (1985).

S. Inokuchi, K. Sato, and F. Matsuda, “Range-imaging for 3-D object recognition,” in Proceedings of International Conference on Pattern Recognition (IEEE, 1984), pp. 806–808.

Jia, P.

P. Jia, J. Kofman, and C. English, “Error compensation in two-step triangular-pattern phase-shifting profilometry,” Opt. Lasers Eng. 46, 311–320 (2008).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46, 043601 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Multiple-step triangular-pattern phase shifting and the influence of number of steps and pitch on measurement accuracy,” Appl. Opt. 46, 3253–3262 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Intensity-ratio error compensation for triangular pattern phase-shifting profilometry,” J. Opt. Soc. Am. A 24, 3150–5158 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Real-time full-field 3-D surface-shape measurement using off-the-shelf components and a single processor,” in Proceedings of IEEE Sixth International Conference on 3-D Digital Imaging and Modeling (IEEE, 2007).

Kofman, J.

C. Waddington and J. Kofman, “Analysis of measurement sensitivity to illuminance and fringe-pattern gray levels for fringe-pattern projection adaptive to ambient lighting,” Opt. Lasers Eng. 48, 251–256 (2010).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Error compensation in two-step triangular-pattern phase-shifting profilometry,” Opt. Lasers Eng. 46, 311–320 (2008).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Multiple-step triangular-pattern phase shifting and the influence of number of steps and pitch on measurement accuracy,” Appl. Opt. 46, 3253–3262 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46, 043601 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Intensity-ratio error compensation for triangular pattern phase-shifting profilometry,” J. Opt. Soc. Am. A 24, 3150–5158 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Real-time full-field 3-D surface-shape measurement using off-the-shelf components and a single processor,” in Proceedings of IEEE Sixth International Conference on 3-D Digital Imaging and Modeling (IEEE, 2007).

Matsuda, F.

S. Inokuchi, K. Sato, and F. Matsuda, “Range-imaging for 3-D object recognition,” in Proceedings of International Conference on Pattern Recognition (IEEE, 1984), pp. 806–808.

Otsu, N.

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man. Cybern. SMC 9, 62–66 (1979).
[CrossRef]

Sato, K.

K. Sato and S. Inokuchi, “Three-dimensional surface measurement by space encoding range imaging,” J. Robot. Syst. 2, 27–39 (1985).

S. Inokuchi, K. Sato, and F. Matsuda, “Range-imaging for 3-D object recognition,” in Proceedings of International Conference on Pattern Recognition (IEEE, 1984), pp. 806–808.

Waddington, C.

C. Waddington and J. Kofman, “Analysis of measurement sensitivity to illuminance and fringe-pattern gray levels for fringe-pattern projection adaptive to ambient lighting,” Opt. Lasers Eng. 48, 251–256 (2010).
[CrossRef]

Yau, S. T.

Zhang, C.

P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

Zhang, S.

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
[CrossRef]

S. Zhang and S. T. Yau, “High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method,” Opt. Express 14, 2644–2649 (2006).
[CrossRef]

Adv. Opt. Photon.

Appl. Opt.

Comput. Vis. Graph. Image Process.

B. Carrihill and R. Hummel, “Experiments with the intensity ratio depth sensor,” Comput. Vis. Graph. Image Process. 32, 337–358 (1985).
[CrossRef]

IEEE Trans. Syst. Man. Cybern. SMC

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man. Cybern. SMC 9, 62–66 (1979).
[CrossRef]

J. Opt. Soc. Am. A

J. Robot. Syst.

K. Sato and S. Inokuchi, “Three-dimensional surface measurement by space encoding range imaging,” J. Robot. Syst. 2, 27–39 (1985).

Opt. Eng.

P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng. 46, 043601 (2007).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

C. Waddington and J. Kofman, “Analysis of measurement sensitivity to illuminance and fringe-pattern gray levels for fringe-pattern projection adaptive to ambient lighting,” Opt. Lasers Eng. 48, 251–256 (2010).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Error compensation in two-step triangular-pattern phase-shifting profilometry,” Opt. Lasers Eng. 46, 311–320 (2008).
[CrossRef]

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
[CrossRef]

Opt. Lett.

Other

J. D. Gaskill, Linear Systems, Fourier Transform and Optics (Wiley, 1978).

Thorlabs, High Resolution USB 2.0 CMOS and CCD Cameras, http://www.thorlabs.com/Thorcat/15900/DCU224C-Manual.pdf .

P. Jia, J. Kofman, and C. English, “Real-time full-field 3-D surface-shape measurement using off-the-shelf components and a single processor,” in Proceedings of IEEE Sixth International Conference on 3-D Digital Imaging and Modeling (IEEE, 2007).

S. Inokuchi, K. Sato, and F. Matsuda, “Range-imaging for 3-D object recognition,” in Proceedings of International Conference on Pattern Recognition (IEEE, 1984), pp. 806–808.

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 (11)

Fig. 1.
Fig. 1.

Experimental setup.

Fig. 2.
Fig. 2.

Two-step triangular-pattern phase shifting method. (a) Triangular fringe patterns [intensity cut of two triangular fringe pattern shifted by half of the pitch, i.e., I1(x,y) and I2(x,y), respectively]. (b) (Black line) intensity ratio with triangular shape and (red line) region number. Finally, (c) intensity-ratio ramp after removal of the triangular shape.

Fig. 3.
Fig. 3.

(a) Gray-level “triangular” pattern. (b) Horizontal intensity cut. The straight line was intentionally drawn between a maximum and a minimum. The encircled region shows the low sensitivity of the camera/projector system.

Fig. 4.
Fig. 4.

(a)–(d) 8 bit color encoded binary (gray code) images representing a triangular pattern; their RB components correspond to the bit planes i=1,2,3,,8.

Fig. 5.
Fig. 5.

(a) Reconstructed triangular pattern. (b) Intensity cut along the x axis.

Fig. 6.
Fig. 6.

(a)–(e) Deformed patterns acquired by the camera when the patterns shown in Figs. 4(a)4(d) are projected on a plaster figurine of Moon–Sun as test object.

Fig. 7.
Fig. 7.

3-D shape measurement of a mask with the two-step triangular-pattern phase-shifting method. (a) Intensity triangular fringe synthesized from 8 bit color encoded binary patterns. (b) Wrapped intensity-ratio map [r0(x,y)]. (c) Region number map [R(x,y)]. (d) 3-D shape profile reconstructed using Eqs. (4) and (A4).

Fig. 8.
Fig. 8.

Comparison of 3-D shape profiles obtained with different methods. Reconstructed 3-D shape profile with the two-step phase-shifting method. (a) Binary patterns, method proposed in the present paper. (b) Gray-level triangular fringe pattern. (c) Phase-shifted, gray-level sinusoidal fringe patterns.

Fig. 9.
Fig. 9.

Unwrapped intensity ratio obtained in measurement of a flat plate: red line correspond to two-step triangular-pattern phase-shifting method and blue line correspond to binary patterns.

Fig. 10.
Fig. 10.

Schematic diagram of intensity ratio to eight conversion.

Fig. 11.
Fig. 11.

Intensity ratio as a ramp function: red line across to the projector plane: blue line across to reference plane.

Equations (13)

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

Ii(x,y)={2Im(x,y)T(x+δi)+Im(x,y)2x+δi[0,T4)2Im(x,y)T(x+δi)+3Im(x,y)2x+δi[T4,3T4)2Im(x,y)T(x+δi)3Im(x,y)2x+δi[3T4,T),
δi=(i1)TN,i=1,2,,N,N2.
r0(x,y)=I1(x,y)I2(x,y)Im(x,y),
r(x,y)=2(R(x,y)1)+(1)R(x,y)+1r0(x,y),
I1(x,y)=gray2bin(i=182(8i)Mi(x,y)).
I2(x,y)=|I1(x,y)Im|sgn(x,y),
sgn=(M1(x,y)0.5),
ZLZ=d1d2orZ=LZd2d1,
r(xmb)={o,xmb0xmb,xmb>0,
rArB=AB¯Tp
d1p=rArBT.
Z=L1+Td2/pΔrAB.
ZpLTd2Δr.

Metrics