Abstract

We propose a method of rotation angle measurement with high precision in machine vision. An area scan CCD camera, imaging lens, and calibration pattern with a spot array make up the measurement device for measuring the rotation angle. The calibration pattern with a spot array is installed at the rotation part, and the CCD camera is set at a certain distance from the rotation components. The coordinates of the spots on the calibration pattern is acquired through the vision image of the calibration pattern captured by the CCD camera. At the initial position of the calibration pattern, the camera is calibrated with the spot array; the mathematical model of distortion error of the CCD camera is built. With the equation of coordinate rotation measurement, the rotation angle of the spot array is detected. In the theoretic simulation, noise of different levels is added to the coordinates of the spot array. The experiment results show that the measurement device can measure the rotation angle precisely with a noncontact method. The standard deviation of rotation angle measurement is smaller than 3  arc  sec. The measurement device can measure both microangles and large angles.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. X. Dai, O. Sasaki, J. E. Greivenkamp, and T. Suzuki, “High accuracy wide range rotation angle measurement by the use of two parallel interference patterns,” Appl. Opt. 36, 6190-6195 (1997).
    [CrossRef]
  2. W. Wang, G. Liu, Z. Pu, and S. Chen, “Measurement of two-dimensional small angle by means of matrix CCD,” Semiconductor Optoelectron. 25, 134-138 (2004).
  3. C. Kuang, Q. Feng, B. Zhang, Z. Zhang, and S. Chen, “Measurement method of the roll angle,” Proc. SPIE 6150, 61502F (2006).
    [CrossRef]
  4. L. Li, Q. Yu, Z. Lei, and J. Li, “High-accuracy measurement of rotation angle based on image,” Acta Opt Sin. 25, 491-496(2005).
  5. Y. N. Kuichin, O. B. Vitrik, and A. V. Dyshlyuk, “Stabilized fiber optic sensor for remote measuring angle of inclination,” Proc. SPIE 6595, 65952G (2007).
    [CrossRef]
  6. C.-H. Liu, W.-Y. Jywe, and S. C. Tzeng, “Simple three-dimensional laser angle sensor for three-dimensional small-angle measurement,” Appl. Opt. 43, 2840-2845 (2004).
    [CrossRef] [PubMed]
  7. J. A. Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131-138 (2005).
    [CrossRef]
  8. Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47, 053604(2008).
    [CrossRef]
  9. X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310-319 (2009).
    [CrossRef]
  10. J. A. Muñoz-Rodríguez, “Shape connection by pattern recognition and laser metrology,” Appl. Opt. 47, 3590-3608 (2008).
    [CrossRef] [PubMed]
  11. J. A. Muñoz-Rodríguez, “Modeling of a mobile setup by networks for object contouring,” Opt. Eng. 47, 053605 (2008).
    [CrossRef]

2009 (1)

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310-319 (2009).
[CrossRef]

2008 (3)

J. A. Muñoz-Rodríguez, “Modeling of a mobile setup by networks for object contouring,” Opt. Eng. 47, 053605 (2008).
[CrossRef]

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47, 053604(2008).
[CrossRef]

J. A. Muñoz-Rodríguez, “Shape connection by pattern recognition and laser metrology,” Appl. Opt. 47, 3590-3608 (2008).
[CrossRef] [PubMed]

2007 (1)

Y. N. Kuichin, O. B. Vitrik, and A. V. Dyshlyuk, “Stabilized fiber optic sensor for remote measuring angle of inclination,” Proc. SPIE 6595, 65952G (2007).
[CrossRef]

2006 (1)

C. Kuang, Q. Feng, B. Zhang, Z. Zhang, and S. Chen, “Measurement method of the roll angle,” Proc. SPIE 6150, 61502F (2006).
[CrossRef]

2005 (2)

L. Li, Q. Yu, Z. Lei, and J. Li, “High-accuracy measurement of rotation angle based on image,” Acta Opt Sin. 25, 491-496(2005).

J. A. Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131-138 (2005).
[CrossRef]

2004 (2)

W. Wang, G. Liu, Z. Pu, and S. Chen, “Measurement of two-dimensional small angle by means of matrix CCD,” Semiconductor Optoelectron. 25, 134-138 (2004).

C.-H. Liu, W.-Y. Jywe, and S. C. Tzeng, “Simple three-dimensional laser angle sensor for three-dimensional small-angle measurement,” Appl. Opt. 43, 2840-2845 (2004).
[CrossRef] [PubMed]

1997 (1)

Asundi, A.

J. A. Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131-138 (2005).
[CrossRef]

Chen, S.

C. Kuang, Q. Feng, B. Zhang, Z. Zhang, and S. Chen, “Measurement method of the roll angle,” Proc. SPIE 6150, 61502F (2006).
[CrossRef]

W. Wang, G. Liu, Z. Pu, and S. Chen, “Measurement of two-dimensional small angle by means of matrix CCD,” Semiconductor Optoelectron. 25, 134-138 (2004).

Chen, X.

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310-319 (2009).
[CrossRef]

Dai, X.

Dyshlyuk, A. V.

Y. N. Kuichin, O. B. Vitrik, and A. V. Dyshlyuk, “Stabilized fiber optic sensor for remote measuring angle of inclination,” Proc. SPIE 6595, 65952G (2007).
[CrossRef]

Feng, Q.

C. Kuang, Q. Feng, B. Zhang, Z. Zhang, and S. Chen, “Measurement method of the roll angle,” Proc. SPIE 6150, 61502F (2006).
[CrossRef]

Greivenkamp, J. E.

Jin, Y.

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310-319 (2009).
[CrossRef]

Jywe, W.-Y.

Kuang, C.

C. Kuang, Q. Feng, B. Zhang, Z. Zhang, and S. Chen, “Measurement method of the roll angle,” Proc. SPIE 6150, 61502F (2006).
[CrossRef]

Kuichin, Y. N.

Y. N. Kuichin, O. B. Vitrik, and A. V. Dyshlyuk, “Stabilized fiber optic sensor for remote measuring angle of inclination,” Proc. SPIE 6595, 65952G (2007).
[CrossRef]

Lei, Z.

L. Li, Q. Yu, Z. Lei, and J. Li, “High-accuracy measurement of rotation angle based on image,” Acta Opt Sin. 25, 491-496(2005).

Li, J.

L. Li, Q. Yu, Z. Lei, and J. Li, “High-accuracy measurement of rotation angle based on image,” Acta Opt Sin. 25, 491-496(2005).

Li, L.

L. Li, Q. Yu, Z. Lei, and J. Li, “High-accuracy measurement of rotation angle based on image,” Acta Opt Sin. 25, 491-496(2005).

Li, Z.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47, 053604(2008).
[CrossRef]

Liu, C.-H.

Liu, G.

W. Wang, G. Liu, Z. Pu, and S. Chen, “Measurement of two-dimensional small angle by means of matrix CCD,” Semiconductor Optoelectron. 25, 134-138 (2004).

Muñoz-Rodríguez, J. A.

J. A. Muñoz-Rodríguez, “Shape connection by pattern recognition and laser metrology,” Appl. Opt. 47, 3590-3608 (2008).
[CrossRef] [PubMed]

J. A. Muñoz-Rodríguez, “Modeling of a mobile setup by networks for object contouring,” Opt. Eng. 47, 053605 (2008).
[CrossRef]

J. A. Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131-138 (2005).
[CrossRef]

Pu, Z.

W. Wang, G. Liu, Z. Pu, and S. Chen, “Measurement of two-dimensional small angle by means of matrix CCD,” Semiconductor Optoelectron. 25, 134-138 (2004).

Rodriguez-Vera, R.

J. A. Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131-138 (2005).
[CrossRef]

Sasaki, O.

Shi, Y.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47, 053604(2008).
[CrossRef]

Sun, J.

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310-319 (2009).
[CrossRef]

Suzuki, T.

Tzeng, S. C.

Vitrik, O. B.

Y. N. Kuichin, O. B. Vitrik, and A. V. Dyshlyuk, “Stabilized fiber optic sensor for remote measuring angle of inclination,” Proc. SPIE 6595, 65952G (2007).
[CrossRef]

Wang, C.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47, 053604(2008).
[CrossRef]

Wang, W.

W. Wang, G. Liu, Z. Pu, and S. Chen, “Measurement of two-dimensional small angle by means of matrix CCD,” Semiconductor Optoelectron. 25, 134-138 (2004).

Wang, Y.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47, 053604(2008).
[CrossRef]

Xi, J.

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310-319 (2009).
[CrossRef]

Yu, Q.

L. Li, Q. Yu, Z. Lei, and J. Li, “High-accuracy measurement of rotation angle based on image,” Acta Opt Sin. 25, 491-496(2005).

Zhang, B.

C. Kuang, Q. Feng, B. Zhang, Z. Zhang, and S. Chen, “Measurement method of the roll angle,” Proc. SPIE 6150, 61502F (2006).
[CrossRef]

Zhang, Z.

C. Kuang, Q. Feng, B. Zhang, Z. Zhang, and S. Chen, “Measurement method of the roll angle,” Proc. SPIE 6150, 61502F (2006).
[CrossRef]

Acta Opt Sin. (1)

L. Li, Q. Yu, Z. Lei, and J. Li, “High-accuracy measurement of rotation angle based on image,” Acta Opt Sin. 25, 491-496(2005).

Appl. Opt. (3)

Opt. Eng. (2)

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47, 053604(2008).
[CrossRef]

J. A. Muñoz-Rodríguez, “Modeling of a mobile setup by networks for object contouring,” Opt. Eng. 47, 053605 (2008).
[CrossRef]

Opt. Laser Technol. (1)

J. A. Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131-138 (2005).
[CrossRef]

Opt. Lasers Eng. (1)

X. Chen, J. Xi, Y. Jin, and J. Sun, “Accurate calibration for a camera-projector measurement system based on structured light projection,” Opt. Lasers Eng. 47, 310-319 (2009).
[CrossRef]

Proc. SPIE (2)

Y. N. Kuichin, O. B. Vitrik, and A. V. Dyshlyuk, “Stabilized fiber optic sensor for remote measuring angle of inclination,” Proc. SPIE 6595, 65952G (2007).
[CrossRef]

C. Kuang, Q. Feng, B. Zhang, Z. Zhang, and S. Chen, “Measurement method of the roll angle,” Proc. SPIE 6150, 61502F (2006).
[CrossRef]

Semiconductor Optoelectron. (1)

W. Wang, G. Liu, Z. Pu, and S. Chen, “Measurement of two-dimensional small angle by means of matrix CCD,” Semiconductor Optoelectron. 25, 134-138 (2004).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic diagram of in-plane angle measurement device with machine vision based on spot array.

Fig. 2
Fig. 2

Schematic diagram of the calibration pattern with spot array.

Fig. 3
Fig. 3

Schematic of the rotation of the calibration pattern spot array.

Fig. 4
Fig. 4

Average of measurement error of angle in the simulation experiment, when the rotation angle is 1 ° 360 ° .

Fig. 5
Fig. 5

Standard deviation of the measurement error of angle in the simulation experiment, when the rotation angle is 1 ° 360 ° .

Tables (7)

Tables Icon

Table 1 Measurement Error of Angle under the Circumstance that the Object Coordinates of the Spot Array are Blurred with Noises of Different Standard Deviation When the Rotation Angle is 1 arc sec

Tables Icon

Table 2 Measurement Error of Angle under the Circumstance that the Object Coordinates of the Spot Array are Blurred with Noises of Different Standard Deviation when the Rotation Angle is 45 °

Tables Icon

Table 3 Simulation Experiment of the Resolution of Rotation Angle Measurement

Tables Icon

Table 4 Rotation Measurement Errors When there is Noise with Different Mean Value in the Theoretical Simulation, under the Condition of Tiny Rotation Angle (1 arc sec)

Tables Icon

Table 5 Rotation Measurement Errors When there is Noise with Different Mean Value in the Theoretical Simulation, under the Condition of Large Rotation Angle ( 45 ° )

Tables Icon

Table 6 Detection Results of Tiny Rotation Angle

Tables Icon

Table 7 Detection Results of Large Rotation Angle

Equations (6)

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

X c = i , j f ( i , j ) · i i , j f ( i , j ) ,
Y c = i , j f ( i , j ) · j i , j f ( i , j ) .
u = a 0 + a 1 x + a 2 y + a 3 x 2 + a 4 y 2 + a 5 x y + a 6 x 3 + a 7 y 3 + a 8 x 2 y + a 9 x y 2 + a 10 x 4 + a 11 y 4 + a 12 x y 3 + a 13 x 3 y + a 14 x 2 y 2 ,
v = b 0 + b 1 x + b 2 y + b 3 x 2 + b 4 y 2 + b 5 x y + b 6 x 3 + b 7 y 3 + b 8 x 2 y + b 9 x y 2 + b 10 x 4 + b 11 y 4 + b 12 x y 3 + b 13 x 3 y + b 14 x 2 y 2 .
u 2 i u 20 = ( u 1 i u 10 ) × cos α ( v 1 i v 10 ) × sin α ,
v 2 i v 20 = ( u 1 i u 10 ) × sin α + ( v 1 i v 10 ) × cos α ,

Metrics