Weimin Li,1,*
Jing Jin,1
Xiaofeng Li,1
and Bin Li1
1Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, 96#, Jing Zhai Road, Hefei, Anhui Province, China
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)
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 . The measurement device can measure both microangles and large angles.
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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
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
0.154
0.02
0.051
0.308
0.03
0.453
0.04
0.020
0.663
0.05
0.080
0.731
0.06
0.830
0.07
1.122
0.08
0.289
1.441
0.09
0.053
1.341
0.10
1.451
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
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
0.156
0.02
0.286
0.03
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
1.172
0.09
1.330
0.10
0.018
1.767
Table 3
Simulation Experiment of the Resolution of Rotation Angle Measurement
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)
0.058
0.072
0.115
0.078
0.049
0.005
0.050
0.001
0.012
0.087
0.078
0.056
0.001
0.008
0.004
0.042
0.053
Rotation angle measurement error when the measurement error of the image coordinates of the spot array is 0.03 pixel.
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)
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
0.491
0.02
0.034
0.480
0.03
0.483
0.04
0.004
0.493
0.05
0.112
0.460
0.06
0.009
0.441
0.07
0.499
0.08
0.455
0.09
0.004
0.456
0.10
0.420
Table 5
Rotation Measurement Errors When there is Noise with Different Mean Value in the Theoretical Simulation, under the Condition of Large Rotation Angle ()
Mean Value of Noise (CCD pixel)
Mean Value of Rotation Angle Error (arc second)
Standard Deviation of Rotation Angle Error (arc second)
0
0.383
0.01
0.496
0.02
0.0389
0.483
0.03
0.466
0.04
0.498
0.05
0.0809
0.445
0.06
0.066
0.436
0.07
0.007
0.452
0.08
0.478
0.09
0.031
0.480
0.10
0.040
0.477
Table 6
Detection Results of Tiny Rotation Angle
Rotation Angle
Measurement Error of Rotation Angle (arc second)
Rotation Angle
Measurement Error of Rotation Angle (arc second)
0.09
1.20
0.60
0.68
0.59
0.88
Table 7
Detection Results of Large Rotation Angle
Rotation Angle
Measurement Error of Rotation Angle (arc second)
2.62
1.09
1.89
1.29
1.47
Tables (7)
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
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
0.154
0.02
0.051
0.308
0.03
0.453
0.04
0.020
0.663
0.05
0.080
0.731
0.06
0.830
0.07
1.122
0.08
0.289
1.441
0.09
0.053
1.341
0.10
1.451
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
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
0.156
0.02
0.286
0.03
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
1.172
0.09
1.330
0.10
0.018
1.767
Table 3
Simulation Experiment of the Resolution of Rotation Angle Measurement
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)
0.058
0.072
0.115
0.078
0.049
0.005
0.050
0.001
0.012
0.087
0.078
0.056
0.001
0.008
0.004
0.042
0.053
Rotation angle measurement error when the measurement error of the image coordinates of the spot array is 0.03 pixel.
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)
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
0.491
0.02
0.034
0.480
0.03
0.483
0.04
0.004
0.493
0.05
0.112
0.460
0.06
0.009
0.441
0.07
0.499
0.08
0.455
0.09
0.004
0.456
0.10
0.420
Table 5
Rotation Measurement Errors When there is Noise with Different Mean Value in the Theoretical Simulation, under the Condition of Large Rotation Angle ()
Mean Value of Noise (CCD pixel)
Mean Value of Rotation Angle Error (arc second)
Standard Deviation of Rotation Angle Error (arc second)