Abstract

Phase-based fringe projection metrology systems have been widely used to obtain the shape of 3D objects. One vital step is calibration, which defines the relationship between the phase and depth data. Existing calibration methods are complicated because of the dependence of the relationship on the pixel position. In this Letter, a simple calibration procedure is introduced based on an uneven fringe projection technique, in which the relationship between phase and depth becomes independent of the pixel position and can be represented by a single polynomial function for all pixels. Therefore, given a set of discrete points with a known phase and depth in the measuring volume, the coefficient set of the polynomial function can be determined. A white plate having discrete markers with known separation is used to calibrate the 3D imaging system. Experimental results demonstrate that the proposed calibration method is simple to apply and can build up an accurate relationship between phase and depth data.

© 2011 Optical Society of America

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2010

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J. A. M. Rodríguez, Opt. Eng. 48, 123604 (2009).
[CrossRef]

2007

Z. H. Zhang, C. E. Towers, and D. P. Towers, Appl. Opt. 46, 6113 (2007).
[CrossRef] [PubMed]

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

P. J. Tavares and M. A. Vaz, Opt. Commun. 274, 307 (2007).
[CrossRef]

2006

2005

B. A. Rajoub, D. R. Burton, and M. J. Lalor, J. Opt. A 7, S368 (2005).
[CrossRef]

2004

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

2003

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

2001

2000

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

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

1999

A. Fitzgibbon, M. Pilu, and R. B. Fisher, IEEE Trans. Pattern Anal. 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]

Burton, D. R.

B. A. Rajoub, D. R. Burton, and M. J. Lalor, J. Opt. A 7, S368 (2005).
[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]

Fisher, R. B.

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

Fitzgibbon, A.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, IEEE Trans. Pattern Anal. 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]

Fu, X.

Z. H. Zhang, T. Guo, S. X. Zhang, X. Fu, X. T. Hu, C. E. Towers, and D. P. Towers, Proc. SPIE 7790, 77900D (2010).
[CrossRef]

Guo, T.

Z. H. Zhang, T. Guo, S. X. Zhang, X. Fu, X. T. Hu, C. E. Towers, and D. P. Towers, Proc. SPIE 7790, 77900D (2010).
[CrossRef]

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, T. Guo, S. X. Zhang, X. Fu, X. T. Hu, C. E. Towers, and D. P. Towers, Proc. SPIE 7790, 77900D (2010).
[CrossRef]

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]

Lalor, M. J.

B. A. Rajoub, D. R. Burton, and M. J. Lalor, J. Opt. A 7, S368 (2005).
[CrossRef]

Li, W. S.

Liu, Z. B.

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. 21, 476 (1999).
[CrossRef]

Rajoub, B. A.

B. A. Rajoub, D. R. Burton, and M. J. Lalor, J. Opt. A 7, S368 (2005).
[CrossRef]

Rodríguez, J. A. M.

J. A. M. Rodríguez, Opt. Eng. 48, 123604 (2009).
[CrossRef]

Song, M.

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

Su, X. Y.

Tavares, P. J.

P. J. Tavares and M. A. Vaz, Opt. Commun. 274, 307 (2007).
[CrossRef]

Towers, C. E.

Z. H. Zhang, T. Guo, S. X. Zhang, X. Fu, X. T. Hu, C. E. Towers, and D. P. Towers, Proc. SPIE 7790, 77900D (2010).
[CrossRef]

Z. H. Zhang, C. E. Towers, and D. P. Towers, Appl. Opt. 46, 6113 (2007).
[CrossRef] [PubMed]

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

D. P. Towers, C. E. Towers, and Z. Zhang, “Optical imaging of physical objects,” international patent WO/2008/017878(2008).

Towers, D. P.

Z. H. Zhang, T. Guo, S. X. Zhang, X. Fu, X. T. Hu, C. E. Towers, and D. P. Towers, Proc. SPIE 7790, 77900D (2010).
[CrossRef]

Z. H. Zhang, C. E. Towers, and D. P. Towers, Appl. Opt. 46, 6113 (2007).
[CrossRef] [PubMed]

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

D. P. Towers, C. E. Towers, and Z. Zhang, “Optical imaging of physical objects,” international patent WO/2008/017878(2008).

Vaz, M. A.

P. J. Tavares and M. A. Vaz, Opt. Commun. 274, 307 (2007).
[CrossRef]

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. X.

Z. H. Zhang, T. Guo, S. X. Zhang, X. Fu, X. T. Hu, C. E. Towers, and D. P. Towers, Proc. SPIE 7790, 77900D (2010).
[CrossRef]

Zhang, Z.

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

D. P. Towers, C. E. Towers, and Z. Zhang, “Optical imaging of physical objects,” international patent WO/2008/017878(2008).

Zhang, Z. H.

Z. H. Zhang, T. Guo, S. X. Zhang, X. Fu, X. T. Hu, C. E. Towers, and D. P. Towers, Proc. SPIE 7790, 77900D (2010).
[CrossRef]

Z. H. Zhang, C. E. Towers, and D. P. Towers, Appl. Opt. 46, 6113 (2007).
[CrossRef] [PubMed]

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.

IEEE Trans. Pattern Anal.

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

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

J. Opt. A

B. A. Rajoub, D. R. Burton, and M. J. Lalor, J. Opt. A 7, S368 (2005).
[CrossRef]

Opt. Commun.

P. J. Tavares and M. A. Vaz, Opt. Commun. 274, 307 (2007).
[CrossRef]

Opt. Eng.

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

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]

J. A. M. Rodríguez, Opt. Eng. 48, 123604 (2009).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

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

Opt. Lett.

Proc. SPIE

Z. H. Zhang, T. Guo, S. X. Zhang, X. Fu, X. T. Hu, C. E. Towers, and D. P. Towers, Proc. SPIE 7790, 77900D (2010).
[CrossRef]

Other

D. P. Towers, C. E. Towers, and Z. Zhang, “Optical imaging of physical objects,” international patent WO/2008/017878(2008).

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

Schematic of uneven fringe projection at the projector and the even fringe pattern on the reference plane, R.

Fig. 2
Fig. 2

White calibration plate: (a) photo of the white plate having 9 × 11 hollow black rings with a separation of 15 mm , (b) fringe pattern projected on the white plate, and (c) extracted edge and center of the 99 rings.

Fig. 3
Fig. 3

Measured distance along one row near the middle of the white plate. The X axis represents the pixel positions along the row direction with a range of 20,2,3…, 1004; the vertical axis is the reconstructed depth of the surface: (a)  z = 8 mm and (b)  z = 8 mm .

Fig. 4
Fig. 4

Illustration of the designed step and measured depth: (a) design step, (b) 3D shading display, and (c) measured depth. The X and Y axes represent the pixel positions.

Tables (2)

Tables Icon

Table 1 Experimental Results on the Accurately Positioned Plate (Unit: mm)

Tables Icon

Table 2 Experimental Results on the Step Artifact (Unit: mm)

Equations (4)

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

Δ z = Δ ϕ P 0 L 0 2 π L + Δ ϕ P 0 = L 0 / ( 1 + 2 π L Δ ϕ P 0 ) ,
Δ z = a n Δ ϕ n + a n 1 Δ ϕ n 1 + + a 1 Δ ϕ 1 + a 0 ,
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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