Abstract

An important step of phase calculation-based fringe projection systems is 3D calibration, which builds up the relationship between an absolute phase map and 3D shape data. The existing 3D calibration methods are complicated and hard to implement in practical environments due to the requirement of a precise translating stage or gauge block. This paper presents a 3D calibration method which uses a white plate with discrete markers on the surface. Placing the plate at several random positions can determine the relationship of absolute phase and depth, as well as pixel position and X, Y coordinates. Experimental results and performance evaluations show that the proposed calibration method can easily build up the relationship between absolute phase map and 3D shape data in a simple, flexible and automatic way.

© 2013 OSA

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  1. F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000).
    [CrossRef]
  2. F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging13(1), 231–240 (2004).
    [CrossRef]
  3. Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng.50(8), 1097–1106 (2012).
    [CrossRef]
  4. Z. H. Zhang, D. P. Zhang, and X. Peng, “Performance analysis of a 3-D full-field sensor based on fringe projection,” Opt. Lasers Eng.42(3), 341–353 (2004).
    [CrossRef]
  5. Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng.42(2), 487–493 (2003).
    [CrossRef]
  6. P. R. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng.46(4), 043601 (2007).
    [CrossRef]
  7. M. Vo, Z. Wang, T. Hoang, and D. Nguyen, “Flexible calibration technique for fringe-projection-based three-dimensional imaging,” Opt. Lett.35(19), 3192–3194 (2010).
    [CrossRef] [PubMed]
  8. L. Huang, P. S. K. Chua, and A. Asundi, “Least-squares calibration method for fringe projection profilometry considering camera lens distortion,” Appl. Opt.49(9), 1539–1548 (2010).
    [CrossRef] [PubMed]
  9. H. Du and Z. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett.32(16), 2438–2440 (2007).
    [CrossRef] [PubMed]
  10. Z. H. Zhang, H. Y. Ma, S. X. Zhang, T. Guo, C. E. Towers, and D. P. Towers, “Simple calibration of a phase-based 3D imaging system based on uneven fringe projection,” Opt. Lett.36(5), 627–629 (2011).
    [CrossRef] [PubMed]
  11. Z. H. Zhang, H. Y. Ma, T. Guo, S. X. Zhang, and J. P. Chen, “Simple, flexible calibration of phase calculation-based three-dimensional imaging system,” Opt. Lett.36(7), 1257–1259 (2011).
    [CrossRef] [PubMed]
  12. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal.22(11), 1330–1334 (2000).
    [CrossRef]
  13. Jean-Yves Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ .
  14. A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal.21(5), 476–480 (1999).
    [CrossRef]
  15. Z. H. Zhang, S. S. Meng, and S. J. Huang,D. J. Dorantes-Gonzalez, ed., “Simple and flexible calibration method of a 3D imaging system based on fringe projection technique” in Proceedings of 16th International Conference on Mechatronics Technology, Dante J. Dorantes-Gonzalez, ed. (Tianjin Foreign Language Electronic & Audio-Video Publishing House, Tianjin, China. 2012), pp. 101–105.
  16. http://www.ti-times.com/
  17. Z. H. Zhang, C. E. Towers, and D. P. Towers, “Time efficient color fringe projection system for 3-D shape and colour using optimum 3-frequency Selection,” Opt. Express14(14), 6444–6455 (2006).
    [CrossRef] [PubMed]

2012

Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng.50(8), 1097–1106 (2012).
[CrossRef]

2011

2010

2007

H. Du and Z. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett.32(16), 2438–2440 (2007).
[CrossRef] [PubMed]

P. R. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng.46(4), 043601 (2007).
[CrossRef]

2006

2004

Z. H. Zhang, D. P. Zhang, and X. Peng, “Performance analysis of a 3-D full-field sensor based on fringe projection,” Opt. Lasers Eng.42(3), 341–353 (2004).
[CrossRef]

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging13(1), 231–240 (2004).
[CrossRef]

2003

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng.42(2), 487–493 (2003).
[CrossRef]

2000

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000).
[CrossRef]

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal.22(11), 1330–1334 (2000).
[CrossRef]

1999

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal.21(5), 476–480 (1999).
[CrossRef]

Asundi, A.

Blais, F.

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging13(1), 231–240 (2004).
[CrossRef]

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000).
[CrossRef]

Chen, J. P.

Chiang, F. P.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng.42(2), 487–493 (2003).
[CrossRef]

Chua, P. S. K.

Du, H.

English, C.

P. R. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng.46(4), 043601 (2007).
[CrossRef]

Fisher, R. B.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal.21(5), 476–480 (1999).
[CrossRef]

Fitzgibbon, A.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal.21(5), 476–480 (1999).
[CrossRef]

Fu, Q. L.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng.42(2), 487–493 (2003).
[CrossRef]

Guo, T.

Hoang, T.

Hu, Q. Y.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng.42(2), 487–493 (2003).
[CrossRef]

Huang, L.

Huang, P. S.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng.42(2), 487–493 (2003).
[CrossRef]

Jia, P. R.

P. R. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng.46(4), 043601 (2007).
[CrossRef]

Kofman, J.

P. R. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng.46(4), 043601 (2007).
[CrossRef]

Ma, H. Y.

Nguyen, D.

Peng, X.

Z. H. Zhang, D. P. Zhang, and X. Peng, “Performance analysis of a 3-D full-field sensor based on fringe projection,” Opt. Lasers Eng.42(3), 341–353 (2004).
[CrossRef]

Pilu, M.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal.21(5), 476–480 (1999).
[CrossRef]

Song, M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000).
[CrossRef]

Towers, C. E.

Towers, D. P.

Vo, M.

Wang, Z.

Zhang, D. P.

Z. H. Zhang, D. P. Zhang, and X. Peng, “Performance analysis of a 3-D full-field sensor based on fringe projection,” Opt. Lasers Eng.42(3), 341–353 (2004).
[CrossRef]

Zhang, S. X.

Zhang, Z. H.

Zhang, Z. Y.

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal.22(11), 1330–1334 (2000).
[CrossRef]

Appl. Opt.

IEEE Trans. Pattern Anal.

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal.22(11), 1330–1334 (2000).
[CrossRef]

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least square fitting of ellipses,” IEEE Trans. Pattern Anal.21(5), 476–480 (1999).
[CrossRef]

J. Electron. Imaging

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging13(1), 231–240 (2004).
[CrossRef]

Opt. Eng.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng.42(2), 487–493 (2003).
[CrossRef]

P. R. Jia, J. Kofman, and C. English, “Comparison of linear and nonlinear calibration methods for phase-measuring profilometry,” Opt. Eng.46(4), 043601 (2007).
[CrossRef]

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng.50(8), 1097–1106 (2012).
[CrossRef]

Z. H. Zhang, D. P. Zhang, and X. Peng, “Performance analysis of a 3-D full-field sensor based on fringe projection,” Opt. Lasers Eng.42(3), 341–353 (2004).
[CrossRef]

Opt. Lett.

Other

Z. H. Zhang, S. S. Meng, and S. J. Huang,D. J. Dorantes-Gonzalez, ed., “Simple and flexible calibration method of a 3D imaging system based on fringe projection technique” in Proceedings of 16th International Conference on Mechatronics Technology, Dante J. Dorantes-Gonzalez, ed. (Tianjin Foreign Language Electronic & Audio-Video Publishing House, Tianjin, China. 2012), pp. 101–105.

http://www.ti-times.com/

Jean-Yves Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/ .

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Figures (7)

Fig. 1
Fig. 1

A photo image of the manufactured white plate. There are 9x12 black hollow rings on the surface with neighboring separation of 15mm in the horizontal and vertical directions.

Fig. 2
Fig. 2

Automatically locating the center of all the markers on a captured image of the white plate represented by red dots.

Fig. 3
Fig. 3

Schematic of even fringe projection at the projector and uneven fringe pattern on the reference M. M: Reference plane.

Fig. 4
Fig. 4

The hardware setup of the fringe projection imaging system including a DLP projector, a color 3CCD camera and a personal computer.

Fig. 5
Fig. 5

Measured depth along middle row direction for four positions of −18mm, −6mm, 6mm and 18mm in (a), (b) (c) and (d). X-axis represents the pixel positions along row direction with a range 1,2,3…, 1024, the vertical axis is the reconstructed depth to the reference surface.

Fig. 6
Fig. 6

Illustration of the step artifact and the measured 3D shape data. (a) the step artifact with green projected fringe, (b) absolute phase map, and (c) the measured 3D shape.

Fig. 7
Fig. 7

The measured results on a toy having freeform surface. (a) photo of the toy with green projected fringe, (b) absolute phase map, and (c) the measured 3D shape.

Tables (2)

Tables Icon

Table 1 Experimental results on the accurately positioned plate at-18mm, 6mm, −6mm and −18mm (Unit: mm)

Tables Icon

Table 2 The experimental results on the measured step (Unit: mm)

Equations (4)

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z= L 0 2π L 0 2 Lcosθ P 0 Δϕ( x,y ) ( L 0 +xcosθsinθ ) 2 Lcosθsinθ L 0 +xcosθsinθ +1 ,
z( x,y )= n=0 N a n ( x,y )Δϕ ( x,y ) n ,
s [ u v 1 ] T =A [ R T ] [ x w y w z w 1 ] T ,
{ x r = a 0 (u,v) z r 2 + b 0 (u,v) z r + c 0 y r = a 1 (u,v) z r 2 + b 1 (u,v) z r + c 1 ,

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