Abstract

A structured light system using a digital video projector is widely used for 3D shape measurement. However, the nonlinear γ of the projector causes the projected fringe patterns to be nonsinusoidal, which results in phase error and therefore measurement error. It has been shown that, by using a small look-up table (LUT), this type of phase error can be reduced significantly for a three-step phase-shifting algorithm. We prove that this algorithm is generic for any phase-shifting algorithm. Moreover, we propose a new LUT generation method by analyzing the captured fringe image of a flat board directly. Experiments show that this error compensation algorithm can reduce the phase error to at least 13 times smaller.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Davis, R. Ramamoorthi, and S. Rusinkiewicz, "Spacetime stereo: a unifying framework for depth from triangulation," IEEE Trans. Pattern Anal. Mach. Intell. 27, 1-7 (2005).
    [CrossRef]
  2. J. Salvi, J. Pages, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004).
    [CrossRef]
  3. D. Malacara, ed., Optical Shop Testing (Wiley, 1992).
  4. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, "Phase shifting for nonsinusoidal waveforms with phase-shift errors," J. Opt. Soc. Am. A 12, 761-768 (1995).
    [CrossRef]
  5. P. S. Huang, Q. Hu, and F.-P. Chiang, "Double three-step phase-shifting algorithm," Appl. Opt. 41, 4503-4509 (2002).
    [CrossRef] [PubMed]
  6. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, "Digital wave-front measuring interferometry: some systematic error sources," Appl. Opt. 22, 3421-3432 (1983).
    [CrossRef] [PubMed]
  7. J. C. Wyant and K. N. Prettyjohns, "Optical profiler using improved phase-shifting interferometry," U.S. patent 4,639,139 (27 January 1987).
  8. 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]
  9. H. Guo, H. He, and M. Chen, "Gamma correction for digital fringe projection profilometry," Appl. Opt. 43, 2906-2914 (2004).
    [CrossRef] [PubMed]
  10. D. Skocaj and A. Leonardis, "Range image acquisition of objects with nonuniform albedo using structured light range sensor," in Proceedings of the International Conference on Pattern Recognition (IEEE, 2000), Vol. 1, pp. 778-781.
    [CrossRef]
  11. S. Zhang and P. S. Huang, "Phase error compensation for a 3-D shape measurement system based on the phase-shifting method," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. G. Harding, ed., Proc. SPIE 6000, 133-142 (2005).
    [CrossRef]
  12. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  13. R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, "Accurate procedure for the calibration of a structured light system," Opt. Eng. 43, 464-471 (2004).
    [CrossRef]
  14. S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601 (2006).
    [CrossRef]
  15. S. Zhang and P. Huang, "High-resolution, real-time 3-D shape acquisition," in IEEE Computer Vision and Pattern Recognition Workshop (CVPRW) on Real-Time 3D Sensors and Their Uses (IEEE, 2004), Vol. 3, pp. 28-37.
  16. S. Zhang and P. S. Huang, "High-resolution, real-time 3-D shape measurement," Opt. Eng. , to be published.
  17. S. Zhang and S.-T. Yau, "High-resolution, real-time absolute coordinate measurement based on the phase shifting method," Opt. Express 14, 2644-2649 (2006).
    [CrossRef] [PubMed]

2006 (2)

2005 (2)

J. Davis, R. Ramamoorthi, and S. Rusinkiewicz, "Spacetime stereo: a unifying framework for depth from triangulation," IEEE Trans. Pattern Anal. Mach. Intell. 27, 1-7 (2005).
[CrossRef]

S. Zhang and P. S. Huang, "Phase error compensation for a 3-D shape measurement system based on the phase-shifting method," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. G. Harding, ed., Proc. SPIE 6000, 133-142 (2005).
[CrossRef]

2004 (3)

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, "Accurate procedure for the calibration of a structured light system," Opt. Eng. 43, 464-471 (2004).
[CrossRef]

J. Salvi, J. Pages, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004).
[CrossRef]

H. Guo, H. He, and M. Chen, "Gamma correction for digital fringe projection profilometry," Appl. Opt. 43, 2906-2914 (2004).
[CrossRef] [PubMed]

2003 (1)

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]

2002 (1)

1995 (1)

1983 (1)

Batlle, J.

J. Salvi, J. Pages, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004).
[CrossRef]

Bothe, T.

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, "Accurate procedure for the calibration of a structured light system," Opt. Eng. 43, 464-471 (2004).
[CrossRef]

Burow, R.

Chen, M.

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]

P. S. Huang, Q. Hu, and F.-P. Chiang, "Double three-step phase-shifting algorithm," Appl. Opt. 41, 4503-4509 (2002).
[CrossRef] [PubMed]

Davis, J.

J. Davis, R. Ramamoorthi, and S. Rusinkiewicz, "Spacetime stereo: a unifying framework for depth from triangulation," IEEE Trans. Pattern Anal. Mach. Intell. 27, 1-7 (2005).
[CrossRef]

Elssner, K.-E.

Farrant, D. I.

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Grzanna, J.

Guo, H.

He, H.

Hibino, K.

Hu, Q.

Huang, P.

S. Zhang and P. Huang, "High-resolution, real-time 3-D shape acquisition," in IEEE Computer Vision and Pattern Recognition Workshop (CVPRW) on Real-Time 3D Sensors and Their Uses (IEEE, 2004), Vol. 3, pp. 28-37.

Huang, P. S.

S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601 (2006).
[CrossRef]

S. Zhang and P. S. Huang, "Phase error compensation for a 3-D shape measurement system based on the phase-shifting method," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. G. Harding, ed., Proc. SPIE 6000, 133-142 (2005).
[CrossRef]

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. S. Huang, Q. Hu, and F.-P. Chiang, "Double three-step phase-shifting algorithm," Appl. Opt. 41, 4503-4509 (2002).
[CrossRef] [PubMed]

S. Zhang and P. S. Huang, "High-resolution, real-time 3-D shape measurement," Opt. Eng. , to be published.

Jüptner, W. P.

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, "Accurate procedure for the calibration of a structured light system," Opt. Eng. 43, 464-471 (2004).
[CrossRef]

Larkin, K. G.

Legarda-Sáenz, R.

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, "Accurate procedure for the calibration of a structured light system," Opt. Eng. 43, 464-471 (2004).
[CrossRef]

Leonardis, A.

D. Skocaj and A. Leonardis, "Range image acquisition of objects with nonuniform albedo using structured light range sensor," in Proceedings of the International Conference on Pattern Recognition (IEEE, 2000), Vol. 1, pp. 778-781.
[CrossRef]

Malacara, D.

D. Malacara, ed., Optical Shop Testing (Wiley, 1992).

Merkel, K.

Oreb, B. F.

Pages, J.

J. Salvi, J. Pages, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004).
[CrossRef]

Prettyjohns, K. N.

J. C. Wyant and K. N. Prettyjohns, "Optical profiler using improved phase-shifting interferometry," U.S. patent 4,639,139 (27 January 1987).

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Ramamoorthi, R.

J. Davis, R. Ramamoorthi, and S. Rusinkiewicz, "Spacetime stereo: a unifying framework for depth from triangulation," IEEE Trans. Pattern Anal. Mach. Intell. 27, 1-7 (2005).
[CrossRef]

Rusinkiewicz, S.

J. Davis, R. Ramamoorthi, and S. Rusinkiewicz, "Spacetime stereo: a unifying framework for depth from triangulation," IEEE Trans. Pattern Anal. Mach. Intell. 27, 1-7 (2005).
[CrossRef]

Salvi, J.

J. Salvi, J. Pages, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004).
[CrossRef]

Schwider, J.

Skocaj, D.

D. Skocaj and A. Leonardis, "Range image acquisition of objects with nonuniform albedo using structured light range sensor," in Proceedings of the International Conference on Pattern Recognition (IEEE, 2000), Vol. 1, pp. 778-781.
[CrossRef]

Spolaczyk, R.

Wyant, J. C.

J. C. Wyant and K. N. Prettyjohns, "Optical profiler using improved phase-shifting interferometry," U.S. patent 4,639,139 (27 January 1987).

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 and S.-T. Yau, "High-resolution, real-time absolute coordinate measurement based on the phase shifting method," Opt. Express 14, 2644-2649 (2006).
[CrossRef] [PubMed]

S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601 (2006).
[CrossRef]

S. Zhang and P. S. Huang, "Phase error compensation for a 3-D shape measurement system based on the phase-shifting method," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. G. Harding, ed., Proc. SPIE 6000, 133-142 (2005).
[CrossRef]

S. Zhang and P. Huang, "High-resolution, real-time 3-D shape acquisition," in IEEE Computer Vision and Pattern Recognition Workshop (CVPRW) on Real-Time 3D Sensors and Their Uses (IEEE, 2004), Vol. 3, pp. 28-37.

S. Zhang and P. S. Huang, "High-resolution, real-time 3-D shape measurement," Opt. Eng. , to be published.

Appl. Opt. (3)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

J. Davis, R. Ramamoorthi, and S. Rusinkiewicz, "Spacetime stereo: a unifying framework for depth from triangulation," IEEE Trans. Pattern Anal. Mach. Intell. 27, 1-7 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (4)

S. Zhang and P. S. Huang, "High-resolution, real-time 3-D shape measurement," Opt. Eng. , to be published.

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]

R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, "Accurate procedure for the calibration of a structured light system," Opt. Eng. 43, 464-471 (2004).
[CrossRef]

S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601 (2006).
[CrossRef]

Opt. Express (1)

Pattern Recogn. (1)

J. Salvi, J. Pages, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004).
[CrossRef]

Proc. SPIE (1)

S. Zhang and P. S. Huang, "Phase error compensation for a 3-D shape measurement system based on the phase-shifting method," in Two- and Three-Dimensional Methods for Inspection and Metrology III, K. G. Harding, ed., Proc. SPIE 6000, 133-142 (2005).
[CrossRef]

Other (5)

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

S. Zhang and P. Huang, "High-resolution, real-time 3-D shape acquisition," in IEEE Computer Vision and Pattern Recognition Workshop (CVPRW) on Real-Time 3D Sensors and Their Uses (IEEE, 2004), Vol. 3, pp. 28-37.

D. Malacara, ed., Optical Shop Testing (Wiley, 1992).

J. C. Wyant and K. N. Prettyjohns, "Optical profiler using improved phase-shifting interferometry," U.S. patent 4,639,139 (27 January 1987).

D. Skocaj and A. Leonardis, "Range image acquisition of objects with nonuniform albedo using structured light range sensor," in Proceedings of the International Conference on Pattern Recognition (IEEE, 2000), Vol. 1, pp. 778-781.
[CrossRef]

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 (10)

Fig. 1
Fig. 1

Camera image generation procedure.

Fig. 2
Fig. 2

(Color online) Phase error LUT generation. (a) Real wrapped phase and the ideal wrapped phase. (b) Phase error relative to the real wrapped phase.

Fig. 3
Fig. 3

(Color online) Phase error with a fringe pitch of 120.

Fig. 4
Fig. 4

(Color online) Phase error for fringe pitches 60 and 120.

Fig. 5
Fig. 5

(Color online) Phase error for multiple fringe pitches ( Pitch = 60 + 30 × k , k = 1 , 2 , , 6 ) .

Fig. 6
Fig. 6

(Color online) Phase error LUT creation.

Fig. 7
Fig. 7

Phase-shifted fringe images for the flat board: (a) I 1 ( δ 1 = 0 ° ) , (b) I 2 ( δ 2 = 270 ° ) , (c) I 3 ( δ 3 = 130 ° ) , (d) I 4 ( δ 4 = 220 ° ) .

Fig. 8
Fig. 8

(Color online) Three-dimensional measurement result of flat board before and after error compensation. (a) Three-dimensional geometry without correction. (b) Three-dimensional geometry after correcting the phase. (c) Cross section of the 250th row of the above image (rms: 0.16   rad ). (d) Cross section of the 250th row of the above image (rms: 0.02   rad ).

Fig. 9
Fig. 9

(Color online) Comparison of the proposed method and the method developed in Ref. 11. (a) Phase error before compensation (rms: 0.16   rad ). (b) Phase error after error compensation with the algorithm proposed in this paper (rms: 0.012   rad ). (c) Phase error after error compensation using the previously proposed algorithm (rms: 0.006   rad ).

Fig. 10
Fig. 10

(Color online) Three-dimensional measurement results of a sculpture (a) before and (b) after error compensation.

Equations (23)

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

I i ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ ( x , y ) + δ i ) ,
ϕ ( x , y ) = tan 1 ( a 2 ( x , y ) a 1 ( x , y ) ) ,
γ ( x , y ) = I ( x , y ) I ( x , y ) = [ a 1 ( x , y ) 2 + a 2 ( x , y ) 2 ] 1 / 2 a 0 ( x , y ) ,
[ a 0 ( x , y ) a 1 ( x , y ) a 2 ( x , y ) ] = A 1 ( δ i ) B ( x , y , δ i ) .
A ( δ i ) = [ N cos ( δ i ) sin ( δ i ) cos ( δ i ) cos 2 ( δ i ) cos ( δ i ) sin ( δ i ) sin ( δ i ) cos ( δ i ) sin ( δ i ) sin 2 ( δ i ) ] ,
B ( x , y , δ i ) = [ I i I i cos ( δ i ) I i sin ( δ i ) ] ,
I i s ( x , y ) = b 1 { 1 + cos [ ϕ ( x , y ) + δ i ] } + b 0 ,
I i p ( x , y ) = f i ( I i s ) ,
I i o ( x , y ) = r ( x , y ) [ I i p ( x , y ) + a 1 ( x , y ) ] ,
I i c ( x , y ) = α [ I i o + a 2 ( x , y ) ] ,
= α r ( x , y ) I i p + α r ( x , y ) a 1 ( x , y ) + α a 2 ( x , y ) ,
= c 1 I i p + c 2 ,
C = A 1 = [ C 00 C 01 C 02 C 10 C 11 C 12 C 20 C 21 C 22 ] ,
a 2 ( x , y ) = C 20 I i c + C 21 I i c cos ( δ i ) + C 22 I i c sin ( δ i ) ,
= C 20 ( c 1 I i p + c 2 ) + C 21 ( c 1 I i p + c 2 ) × cos ( δ i ) + C 22 ( c 1 I i p + c 2 ) sin ( δ i ) ,
= c 1 [ C 20 I i p + C 21 I i p cos ( δ i ) + C 22 I i p sin ( δ i ) ] + C 2 [ C 20 N + C 21 cos ( δ i ) + C 22 sin ( δ i ) ] .
C 20 N + C 21 cos ( δ i ) + C 22 sin ( δ i ) = 0 .
a 2 ( x , y ) = c 1 [ C 20 I i p + C 21 I i p cos ( δ i ) + C 22 I i p sin ( δ i ) ] .
a 1 ( x , y ) = c 1 [ C 10 I i p + C 11 I i p cos ( δ i ) + C 12 I i p sin ( δ i ) ] .
ϕ ( x , y ) = tan 1 { a 2 ( x , y ) a 1 ( x , y ) } ,
= tan 1 { c 1 [ C 20 I i p + C 21 I i p cos ( δ i ) + C 22 I i p sin ( δ i ) ] c 1 [ C 10 I i p + C 11 I i p cos ( δ i ) + C 12 I i p sin ( δ i ) ] } ,
= tan 1 { C 20 I i p + C 21 I i p cos ( δ i ) + C 22 I i p sin ( δ i ) C 10 I i p + C 11 I i p cos ( δ i ) + C 12 I i p sin ( δ i ) } .
Δ ( ϕ ( x , y ) ) = ϕ ( x , y ) k x .

Metrics