Abstract

We propose a new calibration method for a laser galvanometric scanning (LGS) system by adapting the camera model to model the LGS system. The similarity between the camera system and the LGS system has been investigated and exploited. The distortion parameters are acquired by solving a nonlinear least squares problem of 12 coefficients using the Levenberg–Marquardt algorithm. The efficiency of the calibration is improved. Experiments are conducted to verify the proposed model.

© 2009 Optical Society of America

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References

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  1. T. Wu, “Characteristics of a double galvanometer deflection system with a distortion lens,” Acta Opt. Sin. 7, 261-268 (1987).
  2. J. R. Weisz, “Software calibration of scan system distortions,” Proc. SPIE 1454, 265-271 (1991).
  3. X. Chen, J. Hong, H. Yan, and B. Lu, “Study on error correction in dual galvanometer scanning system based on Elman recurrent neural network,” J. Xi'an Jiaotong University 40, 587-590 (2006).
  4. J. Xie, S. Huang, Z. Duan, Y. Shi, and S. Wen, “Correction of the image distortion for laser galvanometric scanning system,” Opt. Laser Technol. 37, 305-311(2005).
    [CrossRef]
  5. R. L. Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464-471 (2004).
    [CrossRef]
  6. O. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint (MIT, 1993).
  7. J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965-680(1992).
    [CrossRef]
  8. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330-1334(2000).
    [CrossRef]
  9. J. J. Moré, The Levenberg-Maquardt algorithm: implementation and theory, in Proceedings of Numerical Analysis, G. A. Watson, ed. (Springer, 1978), pp. 105-116.
    [CrossRef]

2006

X. Chen, J. Hong, H. Yan, and B. Lu, “Study on error correction in dual galvanometer scanning system based on Elman recurrent neural network,” J. Xi'an Jiaotong University 40, 587-590 (2006).

2005

J. Xie, S. Huang, Z. Duan, Y. Shi, and S. Wen, “Correction of the image distortion for laser galvanometric scanning system,” Opt. Laser Technol. 37, 305-311(2005).
[CrossRef]

2004

R. L. Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464-471 (2004).
[CrossRef]

2000

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

1992

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965-680(1992).
[CrossRef]

1991

J. R. Weisz, “Software calibration of scan system distortions,” Proc. SPIE 1454, 265-271 (1991).

1987

T. Wu, “Characteristics of a double galvanometer deflection system with a distortion lens,” Acta Opt. Sin. 7, 261-268 (1987).

Bothe, T.

R. L. Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464-471 (2004).
[CrossRef]

Chen, X.

X. Chen, J. Hong, H. Yan, and B. Lu, “Study on error correction in dual galvanometer scanning system based on Elman recurrent neural network,” J. Xi'an Jiaotong University 40, 587-590 (2006).

Cohen, P.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965-680(1992).
[CrossRef]

Duan, Z.

J. Xie, S. Huang, Z. Duan, Y. Shi, and S. Wen, “Correction of the image distortion for laser galvanometric scanning system,” Opt. Laser Technol. 37, 305-311(2005).
[CrossRef]

Faugeras, O.

O. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint (MIT, 1993).

Herniou, M.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965-680(1992).
[CrossRef]

Hong, J.

X. Chen, J. Hong, H. Yan, and B. Lu, “Study on error correction in dual galvanometer scanning system based on Elman recurrent neural network,” J. Xi'an Jiaotong University 40, 587-590 (2006).

Huang, S.

J. Xie, S. Huang, Z. Duan, Y. Shi, and S. Wen, “Correction of the image distortion for laser galvanometric scanning system,” Opt. Laser Technol. 37, 305-311(2005).
[CrossRef]

Juptner, W. P.

R. L. Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464-471 (2004).
[CrossRef]

Lu, B.

X. Chen, J. Hong, H. Yan, and B. Lu, “Study on error correction in dual galvanometer scanning system based on Elman recurrent neural network,” J. Xi'an Jiaotong University 40, 587-590 (2006).

Moré, J. J.

J. J. Moré, The Levenberg-Maquardt algorithm: implementation and theory, in Proceedings of Numerical Analysis, G. A. Watson, ed. (Springer, 1978), pp. 105-116.
[CrossRef]

Saenz, R. L.

R. L. Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464-471 (2004).
[CrossRef]

Shi, Y.

J. Xie, S. Huang, Z. Duan, Y. Shi, and S. Wen, “Correction of the image distortion for laser galvanometric scanning system,” Opt. Laser Technol. 37, 305-311(2005).
[CrossRef]

Weisz, J. R.

J. R. Weisz, “Software calibration of scan system distortions,” Proc. SPIE 1454, 265-271 (1991).

Wen, S.

J. Xie, S. Huang, Z. Duan, Y. Shi, and S. Wen, “Correction of the image distortion for laser galvanometric scanning system,” Opt. Laser Technol. 37, 305-311(2005).
[CrossRef]

Weng, J.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965-680(1992).
[CrossRef]

Wu, T.

T. Wu, “Characteristics of a double galvanometer deflection system with a distortion lens,” Acta Opt. Sin. 7, 261-268 (1987).

Xie, J.

J. Xie, S. Huang, Z. Duan, Y. Shi, and S. Wen, “Correction of the image distortion for laser galvanometric scanning system,” Opt. Laser Technol. 37, 305-311(2005).
[CrossRef]

Yan, H.

X. Chen, J. Hong, H. Yan, and B. Lu, “Study on error correction in dual galvanometer scanning system based on Elman recurrent neural network,” J. Xi'an Jiaotong University 40, 587-590 (2006).

Zhang, Z.

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

Acta Opt. Sin.

T. Wu, “Characteristics of a double galvanometer deflection system with a distortion lens,” Acta Opt. Sin. 7, 261-268 (1987).

IEEE Trans. Pattern Anal. Mach. Intell.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965-680(1992).
[CrossRef]

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

J. Xi'an Jiaotong University

X. Chen, J. Hong, H. Yan, and B. Lu, “Study on error correction in dual galvanometer scanning system based on Elman recurrent neural network,” J. Xi'an Jiaotong University 40, 587-590 (2006).

Opt. Eng.

R. L. Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 464-471 (2004).
[CrossRef]

Opt. Laser Technol.

J. Xie, S. Huang, Z. Duan, Y. Shi, and S. Wen, “Correction of the image distortion for laser galvanometric scanning system,” Opt. Laser Technol. 37, 305-311(2005).
[CrossRef]

Proc. SPIE

J. R. Weisz, “Software calibration of scan system distortions,” Proc. SPIE 1454, 265-271 (1991).

Other

O. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint (MIT, 1993).

J. J. Moré, The Levenberg-Maquardt algorithm: implementation and theory, in Proceedings of Numerical Analysis, G. A. Watson, ed. (Springer, 1978), pp. 105-116.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic of the LGS system.

Fig. 2
Fig. 2

Distortions of the LGS system (a) when the f θ lens is not used and (b) when the f θ lens is used.

Fig. 3
Fig. 3

Model of the camera system.

Fig. 4
Fig. 4

Schematic of the arrangement of the test objects.

Fig. 5
Fig. 5

HGLS used in the experiment.

Fig. 6
Fig. 6

(a), (b), (c) Marked images on the test plane of three different positions. (d), (e), (f) Coordinates of the marked points (where the lines intersect) extracted from marked images.

Fig. 7
Fig. 7

(a) Rectified lines marked on the plane and (b) marked points extracted from the corresponding plane.

Fig. 8
Fig. 8

(a) Residuals of the desired and marked points and (b) direction and amplitude of the residuals. The circles indicate the desired points, and the crosses indicate the marked points.

Equations (12)

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{ x = f tan 2 θ x / cos 2 θ y + d tan 2 θ x y = f tan 2 θ y ,
{ x = f tan 2 θ x / cos 2 θ y y = f tan 2 θ y .
{ x = f sin 2 θ x cos 1 ( cos 2 θ x cos 2 θ y ) / ( 1 cos 2 2 θ x cos 2 2 θ y ) 0.5 y = f sin 2 θ y cos 2 θ x / ( 1 cos 2 2 θ x cos 2 2 θ y ) 0.5 .
X c = R * X w + T ,
X I = f c z c X c ,
δ u ( u , v ) = ( g 1 + g 3 ) u 2 + g 4 u v + g 1 v 2 + k 1 u ( u 2 + v 2 ) + k 2 u ( u 2 + v 2 ) 2 + k 3 u ( u 2 + v 2 ) 3 , δ v ( u , v ) = g 2 u 2 + g 3 u v + ( g 2 + g 4 ) v 2 + k 1 v ( u 2 + v 2 ) + k 2 v ( u 2 + v 2 ) 2 + k 3 v ( u 2 + v 2 ) 3 ,
u d = u + δ u ( u , v ) , v d = v + δ v ( u , v ) .
u p = u d d u + u 0 , v p = v d d v + v 0 ,
u = f u z c x c , v = f v z c y c ,
δ u ( u , v ) = k 1 u ( u 2 + v 2 ) + k 2 u ( u 2 + v 2 ) 2 + k 3 u ( u 2 + v 2 ) 3 + k 4 u 2 + k 5 u v + k 6 v 2 , δ v ( u , v ) = k 7 v ( u 2 + v 2 ) + k 8 v ( u 2 + v 2 ) 2 + k 9 v ( u 2 + v 2 ) 3 + k 10 u 2 + k 11 u v + k 12 v 2 ,
m = g ( p , θ , Θ ) .
J ( φ ) = i N j M m i j g ( p i j , θ , Θ i ) 2 ,

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