Calibration method of line-structured light sensors based on a hinge-connected target with arbitrary pinch angles

Zhenmin Zhu; Haoran Liu; Jing Zhang; Jing Zhang; Yumeng Zhou

doi:10.1364/AO.483595

Applied Optics
Vol. 62,
Issue 7,
pp. 1695-1703
(2023)
•https://doi.org/10.1364/AO.483595

Calibration method of line-structured light sensors based on a hinge-connected target with arbitrary pinch angles

Zhenmin Zhu, Haoran Liu, Jing Zhang, and Yumeng Zhou

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Zhenmin Zhu, Haoran Liu, Jing Zhang, and Yumeng Zhou, "Calibration method of line-structured light sensors based on a hinge-connected target with arbitrary pinch angles," Appl. Opt. 62, 1695-1703 (2023)

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Table of Contents Category
- Optical Devices, Sensors, and Detectors
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About this Article
History
- Original Manuscript: December 19, 2022
- Revised Manuscript: January 8, 2023
- Manuscript Accepted: January 16, 2023
- Published: February 22, 2023

Abstract

Line-structured light 3D measurement is often used for 3D contour reconstruction of objects in complex industrial environments, where light plane calibration is a key step. In this paper, we propose a calibration method for a line-structured optical system based on a hinge-connected double-checkerboards stereo target. First, the target is moved randomly in multiple positions at any angle within the camera measurement space. Then, by acquiring any one image of the target with line-structured light, the 3D coordinates of the light stripes feature points are solved with the help of the external parameter matrix of the target plane and the camera coordinate system. Finally, the coordinate point cloud is denoised and used to quadratically fit the light plane. Compared with the traditional line-structured measurement system, the proposed method can acquire two calibration images at once; thus, only one image of line-structured light is needed to complete the light plane calibration. There is no strict requirement for the target pinch angle and placement, which improve system calibration speed with high accuracy. The experimental results show that the maximum RMS error of this method is 0.075 mm, and the operation is simpler and more effective to meet the technical requirements of industrial 3D measurement.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Physical Meaning	Parameters	Values
Principal point	( $u_{0}, v_{0}$ )	(912.2818, 624.1680)
Focal length	( $f_{x}, f_{y}$ )	(4754.1626, 4753.7159)
Distortion	( $k_{1}, k_{2}, p_{1}, p_{2}$ )	( $- 0.05308$ , 0.13926,0,0)

Pinch Angles $α$ (°)	Number of Point Clouds	Number of Point Clouds Used for Fitting After Denoising	Confidence Interval	Light Plane Equation	RMSE (mm)
86.3°	1520	1444	( $- 0.2014.0.1867$ )	$z = 6.6929 x + 39.0173 y - 203.7724$	0.0705
90°	1649	1567	( $- 0.1945.0.1745$ )	$z = 6.6837 x + 38.6776 y - 203.5154$	0.0685
105.7°	1581	1502	( $- 0.1968.0.1791$ )	$z = 6.6889 x + 39.9893 y - 203.8395$	0.0671
120°	1565	1487	( $- 0.1812.0.1711$ )	$z = 6.6746 x + 39.3395 y - 204.1487$	0.0645
126.6°	1638	1556	( $- 0.1852.0.1901$ )	$z = 6.7025 x + 39.1341 y - 203.1694$	0.0652
128°	1608	1528	( $- 0.1922.0.1741$ )	$z = 6.7565 x + 39.5234 y - 203.8968$	0.0681
152.2°	1644	1562	( $- 0.1949.0.1782$ )	$z = 6.7326 x + 39.3214 y - 204.4721$	0.0705
156.6°	1501	1426	( $- 0.1918.0.1733$ )	$z = 6.7569 x + 39.4294 y - 203.6671$	0.0670
170°	1691	1606	( $- 0.1892.0.1821$	$z = 6.7382 x + 39.6324 y - 203.6236$	0.0665
${238. 4}^{0}$	1629	1548	( $- 0.1967.0.1804$ )	$z = 6.7268 x + 39.1246 y - 205.2979$	0.0679
${262. 6}^{0}$	1532	1455	( $- 0.2002.0.1884$ )	$z = 6.6975 x + 39.1285 y - 204.3375$	0.0701
${265. 9}^{0}$	1551	1473	( $- 0.1992.0.1928$ )	$z = 6.6845 x + 39.2871 y - 202.5812$	0.0695

	3D Coordinates of the Test Points Calculated with Our Proposed Method			3D Coordinates of the Test Points Calculated by Zhu’s Method			Coordinate Error
Test Points	$X$ (mm)	$y$ (mm)	$z$ (mm)	$X$ (mm)	$y$ (mm)	$z$ (mm)	$Δ x$ (mm)	$Δ y$ (mm)	$Δ z$ (mm)
A	8.3735	26.6347	897.4263	8.1327	26.2341	897.2396	0.2408	0.4006	0.1867
B	23.1274	23.9219	896.5522	22.8941	23.4887	896.3996	0.2333	0.4332	0.1526
C	37.8476	21.3818	895.6522	37.6063	21.0363	895.5102	0.2413	0.3455	0.1420
D	52.6992	19.0137	894.7115	52.4442	18.6857	894.5495	0.2550	0.3280	0.1620
Rms Error								0.2427	0.3792
									0.1619

(Point1 Point2)	Our Method to Obtain the Distance between Test Points $d_{1}$ (mm)	Zhu’s Method to Obtain the Distance between Test Points $d_{2}$ (mm)	Ideal Distance of Test Points dr (mm)	Distance Deviation $Δ d_{1}$ (mm)	Distance Deviation $Δ d_{2}$ (mm)
(A B)	15.026	15.038	15.050	0.024	0.012
(A C)	29.991	29.978	30.100	0.109	0.121
(A D)	45.057	45.031	45.150	0.093	0.119
(B C)	14.964	14.941	15.050	0.086	0.108
(B D)	30.032	29.995	30.100	0.068	0.105
(C D)	15.068	15.0536	15.050	− 0.018	− 0.036
rms				0.0747	0.0943

Physical Meaning	Parameters	Values
Principal point	( $u_{0}, v_{0}$ )	(912.2818, 624.1680)
Focal length	( $f_{x}, f_{y}$ )	(4754.1626, 4753.7159)
Distortion	( $k_{1}, k_{2}, p_{1}, p_{2}$ )	( $- 0.05308$ , 0.13926,0,0)

Abstract

Data availability

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Tables (4)

Equations (14)

Applied Optics