Abstract

One important step of phase-based three-dimensional imaging system is calibration, which defines the relationship between phase and depth data. Existing calibration methods are complicated and hard to carry out because of using a translation stage or gauge block in a laboratory environment. This Letter introduces a new simple, flexible calibration method by using a checkerboard and a white plate having discrete markers with known separation. The checkerboard determines the internal parameters of a CCD camera. The plate gives phase and depth data of each pixel to establish their relationship. Experimental results and performance evaluation show that the proposed calibration method can reliably build up the accurate relationship between phase map and depth data in a simple, flexible way.

© 2011 Optical Society of America

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References

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  1. F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10(2000).
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2011 (1)

2010 (3)

2007 (1)

P. R. Jia, J. Kofman, and C. English, Opt. Eng. 46, 043601(2007).
[CrossRef]

2006 (1)

2004 (1)

Z. H. Zhang, D. P. Zhang, X. Peng, and X. T. Hu, Opt. Lasers Eng. 42, 341 (2004).
[CrossRef]

2003 (1)

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, Opt. Eng. 42, 487 (2003).
[CrossRef]

2001 (1)

2000 (2)

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10(2000).
[CrossRef]

Z. Zhang, IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330(2000).
[CrossRef]

1999 (1)

A. Fitzgibbon, M. Pilu, and R. B. Fisher, IEEE Trans. Pattern Anal. Mach. Intell. 21, 476 (1999).
[CrossRef]

Asundi, A.

Bouguet, J.-Y.

J.-Y. Bouguet, “Camera calibration toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/.

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10(2000).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10(2000).
[CrossRef]

Chiang, F. P.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, Opt. Eng. 42, 487 (2003).
[CrossRef]

Chua, P. S. K.

English, C.

P. R. Jia, J. Kofman, and C. English, Opt. Eng. 46, 043601(2007).
[CrossRef]

Fernandez, S.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, Pattern Recogn. 43, 2666 (2010).
[CrossRef]

Fisher, R. B.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, IEEE Trans. Pattern Anal. Mach. Intell. 21, 476 (1999).
[CrossRef]

Fitzgibbon, A.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, IEEE Trans. Pattern Anal. Mach. Intell. 21, 476 (1999).
[CrossRef]

Fu, Q. L.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, Opt. Eng. 42, 487 (2003).
[CrossRef]

Guo, T.

Hoang, T.

Hu, Q. Y.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, Opt. Eng. 42, 487 (2003).
[CrossRef]

Hu, X. T.

Z. H. Zhang, D. P. Zhang, X. Peng, and X. T. Hu, Opt. Lasers Eng. 42, 341 (2004).
[CrossRef]

Huang, L.

Huang, P. S.

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, Opt. Eng. 42, 487 (2003).
[CrossRef]

Jia, P. R.

P. R. Jia, J. Kofman, and C. English, Opt. Eng. 46, 043601(2007).
[CrossRef]

Kofman, J.

P. R. Jia, J. Kofman, and C. English, Opt. Eng. 46, 043601(2007).
[CrossRef]

Li, W. S.

Liu, Z. B.

Llado, X.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, Pattern Recogn. 43, 2666 (2010).
[CrossRef]

Ma, H.

Nguyen, D.

Peng, X.

Z. H. Zhang, D. P. Zhang, X. Peng, and X. T. Hu, Opt. Lasers Eng. 42, 341 (2004).
[CrossRef]

Pilu, M.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, IEEE Trans. Pattern Anal. Mach. Intell. 21, 476 (1999).
[CrossRef]

Pribanic, T.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, Pattern Recogn. 43, 2666 (2010).
[CrossRef]

Salvi, J.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, Pattern Recogn. 43, 2666 (2010).
[CrossRef]

Song, M.

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10(2000).
[CrossRef]

Su, X. Y.

Towers, C. E.

Towers, D. P.

Vo, M.

Wang, Z.

Zhang, D. P.

Z. H. Zhang, D. P. Zhang, X. Peng, and X. T. Hu, Opt. Lasers Eng. 42, 341 (2004).
[CrossRef]

Zhang, S.

Zhang, Z.

Zhang, Z. H.

Z. H. Zhang, C. E. Towers, and D. P. Towers, Opt. Express 14, 6444 (2006).
[CrossRef] [PubMed]

Z. H. Zhang, D. P. Zhang, X. Peng, and X. T. Hu, Opt. Lasers Eng. 42, 341 (2004).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Pattern Anal. Mach. Intell. (2)

Z. Zhang, IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330(2000).
[CrossRef]

A. Fitzgibbon, M. Pilu, and R. B. Fisher, IEEE Trans. Pattern Anal. Mach. Intell. 21, 476 (1999).
[CrossRef]

Opt. Eng. (3)

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10(2000).
[CrossRef]

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, Opt. Eng. 42, 487 (2003).
[CrossRef]

P. R. Jia, J. Kofman, and C. English, Opt. Eng. 46, 043601(2007).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

Z. H. Zhang, D. P. Zhang, X. Peng, and X. T. Hu, Opt. Lasers Eng. 42, 341 (2004).
[CrossRef]

Opt. Lett. (2)

Pattern Recogn. (1)

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, Pattern Recogn. 43, 2666 (2010).
[CrossRef]

Other (1)

J.-Y. Bouguet, “Camera calibration toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc/.

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Figures (4)

Fig. 1
Fig. 1

Checkerboard and white plate. (a) Photo of the checkerboard with 15 mm × 15 mm black and white squares, (b) photo of the white plate with 9 × 11 green hollow rings with separation of 15 mm .

Fig. 2
Fig. 2

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

Fig. 3
Fig. 3

Images on the white plate of calibration. (a) Extracted edge and determined center of 99 circle rings, (b) Deformed fringe pattern on the white plate, and (c) absolute phase map on the plate surface.

Fig. 4
Fig. 4

Measured distance along one row near the middle of the white plate. X axis represents the pixel positions along the row direction with a range 1, 2, 3, …, 600, the vertical axis is the reconstructed depth of the surface. (a)  z = 18 mm , (b)  z = 18 mm .

Tables (1)

Tables Icon

Table 1 Absolute Error Along the Top, Middle, and Bottom Lines for the Positions 18 mm and 18 mm

Equations (4)

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

z = L 0 2 π L 0 2 L cos θ P 0 Δ φ ( x , y ) ( L 0 + x cos θ sin θ ) 2 L cos θ sin θ L 0 + x cos θ sin θ + 1 ,
z ( x , y ) = n = 0 N a n ( x , y ) Δ φ ( x , y ) n ,
s [ u v 1 ] T = A [ R T ] [ x w y w z w 1 ] T ,
[ x c y c z c ] = [ R 11 R 12 T x R 21 R 22 T y R 31 R 32 T z ] [ x w y w 1 ] .

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