Abstract

System geometrical calibration is a challenging task in fringe-reflection 3D measurement because the fringe displayed on the LCD screen does not lie within the camera’s field of view. Commonly, a flat mirror with markers can accomplish system geometrical calibration. However, the position of the markers must be precisely located by photogrammetry in advance. In this Letter, we introduce a calibration method by use of a markerless flat mirror. Experiments in phase measuring deflectometry demonstrate that the proposed method is simple and flexible.

© 2012 Optical Society of America

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References

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  1. X. Su and Q. Zhang, Opt. Lasers Eng. 48, 191 (2010).
    [CrossRef]
  2. R. Tutsch, M. Petz, and M. Fischer, Opt. Eng. 50, 101507 (2011).
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  5. M. Knauer, J. Kaminski, and G. Hausler, Proc. SPIE 5457, 366 (2004).
    [CrossRef]
  6. M. Petz and R. Tutsch, Proc. SPIE 5869, 58691D (2005).
    [CrossRef]
  7. Y. Tang, X. Su, Y. Liu, and H. Jing, Opt. Express 16, 15090 (2008).
    [CrossRef]
  8. L. Huang, C. Ng, and A. Asundi, Opt. Express 19, 12809 (2011).
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  9. Y. L. Xiao, X. Su, and W. Chen, Appl. Opt. 50, 5630 (2011).
    [CrossRef]
  10. M. I. A. Lourakis and A. A. Arqyros, ACM Trans. Math. Softw. 36, 2 (2009).
    [CrossRef]
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    [CrossRef]
  12. W. Zhao, X. Su, Y. Liu, and Q. Zhang, Opt. Eng. 48, 103603 (2009).
    [CrossRef]
  13. W. Li, T. Bothe, C. V. Kopylow, and W. P. O. Juptner, Proc. SPIE 5457, 300 (2004).
    [CrossRef]

2011 (4)

2010 (2)

2009 (3)

M. I. A. Lourakis and A. A. Arqyros, ACM Trans. Math. Softw. 36, 2 (2009).
[CrossRef]

L. Vincent, F. Moreno-Noguer, and P. Fua, Int. J. Comp. Vis. 81, 155 (2009).
[CrossRef]

W. Zhao, X. Su, Y. Liu, and Q. Zhang, Opt. Eng. 48, 103603 (2009).
[CrossRef]

2008 (1)

2005 (1)

M. Petz and R. Tutsch, Proc. SPIE 5869, 58691D (2005).
[CrossRef]

2004 (2)

W. Li, T. Bothe, C. V. Kopylow, and W. P. O. Juptner, Proc. SPIE 5457, 300 (2004).
[CrossRef]

M. Knauer, J. Kaminski, and G. Hausler, Proc. SPIE 5457, 366 (2004).
[CrossRef]

Angel, R. P.

Arqyros, A. A.

M. I. A. Lourakis and A. A. Arqyros, ACM Trans. Math. Softw. 36, 2 (2009).
[CrossRef]

Asundi, A.

Bothe, T.

W. Li, T. Bothe, C. V. Kopylow, and W. P. O. Juptner, Proc. SPIE 5457, 300 (2004).
[CrossRef]

Burge, J. H.

Campos-Garcia, M.

Chen, W.

Diaz-Uribe, R.

Fischer, M.

R. Tutsch, M. Petz, and M. Fischer, Opt. Eng. 50, 101507 (2011).
[CrossRef]

Fua, P.

L. Vincent, F. Moreno-Noguer, and P. Fua, Int. J. Comp. Vis. 81, 155 (2009).
[CrossRef]

Granados-Agustin, F.

Hausler, G.

M. Knauer, J. Kaminski, and G. Hausler, Proc. SPIE 5457, 366 (2004).
[CrossRef]

Huang, L.

Jing, H.

Juptner, W. P. O.

W. Li, T. Bothe, C. V. Kopylow, and W. P. O. Juptner, Proc. SPIE 5457, 300 (2004).
[CrossRef]

Kaminski, J.

M. Knauer, J. Kaminski, and G. Hausler, Proc. SPIE 5457, 366 (2004).
[CrossRef]

Knauer, M.

M. Knauer, J. Kaminski, and G. Hausler, Proc. SPIE 5457, 366 (2004).
[CrossRef]

Kopylow, C. V.

W. Li, T. Bothe, C. V. Kopylow, and W. P. O. Juptner, Proc. SPIE 5457, 300 (2004).
[CrossRef]

Li, W.

W. Li, T. Bothe, C. V. Kopylow, and W. P. O. Juptner, Proc. SPIE 5457, 300 (2004).
[CrossRef]

Liu, Y.

W. Zhao, X. Su, Y. Liu, and Q. Zhang, Opt. Eng. 48, 103603 (2009).
[CrossRef]

Y. Tang, X. Su, Y. Liu, and H. Jing, Opt. Express 16, 15090 (2008).
[CrossRef]

Lourakis, M. I. A.

M. I. A. Lourakis and A. A. Arqyros, ACM Trans. Math. Softw. 36, 2 (2009).
[CrossRef]

Moreno-Noguer, F.

L. Vincent, F. Moreno-Noguer, and P. Fua, Int. J. Comp. Vis. 81, 155 (2009).
[CrossRef]

Moreno-Oliva, V. I.

Ng, C.

Parks, R. E.

Petz, M.

R. Tutsch, M. Petz, and M. Fischer, Opt. Eng. 50, 101507 (2011).
[CrossRef]

M. Petz and R. Tutsch, Proc. SPIE 5869, 58691D (2005).
[CrossRef]

Santiago-Alvarado, A.

Su, P.

Su, X.

Y. L. Xiao, X. Su, and W. Chen, Appl. Opt. 50, 5630 (2011).
[CrossRef]

X. Su and Q. Zhang, Opt. Lasers Eng. 48, 191 (2010).
[CrossRef]

W. Zhao, X. Su, Y. Liu, and Q. Zhang, Opt. Eng. 48, 103603 (2009).
[CrossRef]

Y. Tang, X. Su, Y. Liu, and H. Jing, Opt. Express 16, 15090 (2008).
[CrossRef]

Tang, Y.

Tutsch, R.

R. Tutsch, M. Petz, and M. Fischer, Opt. Eng. 50, 101507 (2011).
[CrossRef]

M. Petz and R. Tutsch, Proc. SPIE 5869, 58691D (2005).
[CrossRef]

Vincent, L.

L. Vincent, F. Moreno-Noguer, and P. Fua, Int. J. Comp. Vis. 81, 155 (2009).
[CrossRef]

Wang, L.

Xiao, Y. L.

Zhang, Q.

X. Su and Q. Zhang, Opt. Lasers Eng. 48, 191 (2010).
[CrossRef]

W. Zhao, X. Su, Y. Liu, and Q. Zhang, Opt. Eng. 48, 103603 (2009).
[CrossRef]

Zhao, W.

W. Zhao, X. Su, Y. Liu, and Q. Zhang, Opt. Eng. 48, 103603 (2009).
[CrossRef]

ACM Trans. Math. Softw. (1)

M. I. A. Lourakis and A. A. Arqyros, ACM Trans. Math. Softw. 36, 2 (2009).
[CrossRef]

Appl. Opt. (3)

Int. J. Comp. Vis. (1)

L. Vincent, F. Moreno-Noguer, and P. Fua, Int. J. Comp. Vis. 81, 155 (2009).
[CrossRef]

Opt. Eng. (2)

W. Zhao, X. Su, Y. Liu, and Q. Zhang, Opt. Eng. 48, 103603 (2009).
[CrossRef]

R. Tutsch, M. Petz, and M. Fischer, Opt. Eng. 50, 101507 (2011).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

X. Su and Q. Zhang, Opt. Lasers Eng. 48, 191 (2010).
[CrossRef]

Proc. SPIE (3)

M. Knauer, J. Kaminski, and G. Hausler, Proc. SPIE 5457, 366 (2004).
[CrossRef]

M. Petz and R. Tutsch, Proc. SPIE 5869, 58691D (2005).
[CrossRef]

W. Li, T. Bothe, C. V. Kopylow, and W. P. O. Juptner, Proc. SPIE 5457, 300 (2004).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Reflection projection model.

Fig. 2.
Fig. 2.

(a) Robustness of the linear solution and (b) robustness of the bundle adjustment.

Fig. 3.
Fig. 3.

(a) Reference points on LCD screen and (b), (c), (d) reference points and reprojection on the mirror image: +, reference points on the mirror image; O, reprojection based on the linear algorithm; □, reprojection after bundle adjustment.

Fig. 4.
Fig. 4.

(a) 3D shape and (b) error distributions to the fitting shape.

Equations (7)

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

[p1]=[I2nnT2dn01×31][RT01][p1],
q=R(p).
{R^=(I2nnT)RT^=(I2nnT)T+2dn.
R^jR^jTmjj=(I2njnjT)(I2njnjT)Tmjj=mjj.
n1=m13×m12m13×m12n2=m21×m23m21×m23n3=m13×m23m13×m23,
[(In1n1T)2n100(In2n2T)02n20(In3n3T)002n3][Td1d2d3]=[T^1T^2T^3].
f=ij[R(pi,j)qi,j]2pi,j=(I2vjvjTvjTvj)Rpi,j+(I2vjvjTvjTvj)T+2vj.

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