Method of rotation angle measurement in machine vision based on calibration pattern with spot array

Weimin Li; Jing Jin; Xiaofeng Li; Bin Li

doi:10.1364/AO.49.001001

Applied Optics
Vol. 49,
Issue 6,
pp. 1001-1006
(2010)
•https://doi.org/10.1364/AO.49.001001

Method of rotation angle measurement in machine vision based on calibration pattern with spot array

Weimin Li, Jing Jin, Xiaofeng Li, and Bin Li

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Weimin Li, Jing Jin, Xiaofeng Li, and Bin Li, "Method of rotation angle measurement in machine vision based on calibration pattern with spot array," Appl. Opt. 49, 1001-1006 (2010)

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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.

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Standard Deviation of Noise (CCD pixel)	Mean Value of Rotation Angle Error (arc second)	Standard Deviation of Rotation Angle Error (arc second)
0	0	0
0.01	$- 0.013$	0.154
0.02	0.051	0.308
0.03	$- 0.004$	0.453
0.04	0.020	0.663
0.05	0.080	0.731
0.06	$- 0.164$	0.830
0.07	$- 0.290$	1.122
0.08	0.289	1.441
0.09	0.053	1.341
0.10	$- 0.129$	1.451

Standard Deviation of Noise (CCD pixel)	Mean Value of Rotation Angle Error (arc second)	Standard Deviation of Rotation Angle Error (arc second)
0	0	0
0.01	$- 0.005$	0.156
0.02	$- 0.027$	0.286
0.03	$- 0.015$	0.477
0.04	0.031	0.671
0.05	0.100	0.753
0.06	0.105	0.903
0.07	0.010	1.046
0.08	$- 0.102$	1.172
0.09	$- 0.079$	1.330
0.10	0.018	1.767

Rotation Angle	Measurement Error of Rotation Angle (arc second)	Rotation Angle	Measurement Error of Rotation Angle (arc second)	Rotation Angle	Measurement Error of Rotation Angle (arc second)
$00 ° 00^{'} 00^{''}$	$- 0.055$	$22 ° 30^{'} 00^{''}$	$- 0.065$	$45 ° 00^{'} 00^{''}$	0.058
$00 ° 00^{'} {0.2}^{''}$	$- 0.014$	$22 ° 30^{'} {0.2}^{''}$	$- 0.022$	$45 ° 00^{'} {0.2}^{''}$	0.072
$00 ° 00^{'} {0.4}^{''}$	0.115	$22 ° 30^{'} {0.4}^{''}$	0.078	$45 ° 00^{'} {0.4}^{''}$	0.049
$00 ° 00^{'} {0.6}^{''}$	0.005	$22 ° 30^{'} {0.6}^{''}$	0.050	$45 ° 00^{'} {0.6}^{''}$	$- 0.008$
$00 ° 00^{'} {0.8}^{''}$	$- 0.045$	$22 ° 30^{'} {0.8}^{''}$	$- 0.064$	$45 ° 00^{'} {0.8}^{''}$	$- 0.048$
$00 ° 00^{'} {1.0}^{''}$	$- 0.048$	$22 ° 30^{'} {1.0}^{''}$	$- 0.016$	$45 ° 00^{'} {1.0}^{''}$	0.001
$00 ° 00^{'} {1.2}^{''}$	0.012	$22 ° 30^{'} {1.2}^{''}$	$- 0.046$	$45 ° 00^{'} {1.2}^{''}$	0.087
$00 ° 00^{'} {1.4}^{''}$	$- 0.080$	$22 ° 30^{'} {1.4}^{''}$	0.078	$45 ° 00^{'} {1.4}^{''}$	0.056
$00 ° 00^{'} {1.6}^{''}$	$- 0.042$	$22 ° 30^{'} {1.6}^{''}$	$- 0.040$	$45 ° 00^{'} {1.6}^{''}$	0.001
$00 ° 00^{'} {1.8}^{''}$	0.008	$22 ° 30^{'} {1.8}^{''}$	0.004	$45 ° 00^{'} {1.8}^{''}$	0.042
$00 ° 00^{'} {2.0}^{''}$	0.053	$22 ° 30^{'} {2.0}^{''}$	$- 0.037$	$45 ° 00^{'} {2.0}^{''}$	$- 0.112$

Mean Value of Noise (CCD pixel)	Mean Value of Rotation Angle Error (arc second)	Standard Deviation of Rotation Angle Error (arc second)
0	0.043	0.408
0.01	$- 0.048$	0.491
0.02	0.034	0.480
0.03	$- 0.075$	0.483
0.04	0.004	0.493
0.05	0.112	0.460
0.06	0.009	0.441
0.07	$- 0.059$	0.499
0.08	$- 0.042$	0.455
0.09	0.004	0.456
0.10	$- 0.075$	0.420

Mean Value of Noise (CCD pixel)	Mean Value of Rotation Angle Error (arc second)	Standard Deviation of Rotation Angle Error (arc second)
0	$- 0.018$	0.383
0.01	$- 0.089$	0.496
0.02	0.0389	0.483
0.03	$- 0.0069$	0.466
0.04	$- 0.0449$	0.498
0.05	0.0809	0.445
0.06	0.066	0.436
0.07	0.007	0.452
0.08	$- 0.021$	0.478
0.09	0.031	0.480
0.10	0.040	0.477

Rotation Angle	Measurement Error of Rotation Angle (arc second)	Rotation Angle	Measurement Error of Rotation Angle (arc second)
$00 ° 00^{'} 10^{''}$	0.09	$00 ° 02^{'} 10^{''}$	1.20
$00 ° 00^{'} 19^{''}$	$- 1.13$	$00 ° 02^{'} 19^{''}$	$- 1.02$
$00 ° 00^{'} 28^{''}$	$- 2.96$	$00 ° 02^{'} 30^{''}$	$- 0.78$
$00 ° 00^{'} 42^{''}$	0.60	$00 ° 02^{'} 42^{''}$	$- 0.43$
$00 ° 00^{'} 54^{''}$	0.68	$00 ° 02^{'} 52^{''}$	$- 0.76$
$00 ° 01^{'} 03^{''}$	$- 1.20$	$00 ° 03^{'} 01^{''}$	$- 2.73$
$00 ° 01^{'} 15^{''}$	$- 0.67$	$00 ° 03^{'} 11^{''}$	$- 3.11$
$00 ° 01^{'} 27^{''}$	0.59	$00 ° 03^{'} 26^{''}$	0.88
$00 ° 01^{'} 36^{''}$	$- 1.47$	$00 ° 03^{'} 35^{''}$	$- 0.39$
$00 ° 01^{'} 45^{''}$	$- 2.90$	$00 ° 03^{'} 45^{''}$	$- 1.39$
$00 ° 01^{'} 58^{''}$	$- 0.56$	$00 ° 03^{'} 55^{''}$	$- 1.42$

Rotation Angle	Measurement Error of Rotation Angle (arc second)
$5 ° 23^{'} 57^{''}$	2.62
$10 ° 47^{'} 45^{''}$	1.09
$15 ° 17^{'} 44^{''}$	1.89
$20 ° 41^{'} 41^{''}$	1.29
$25 ° 11^{'} 26^{''}$	$- 2.09$
$30 ° 35^{'} 33^{''}$	1.47
$35 ° 05^{'} 21^{''}$	$- 1.86$
$40 ° 29^{'} 12^{''}$	$- 0.04$
$45 ° 53^{'} 01^{''}$	$- 1.47$

Abstract

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Applied Optics