Flexible and simple telecentric camera calibration method

Yu Duan; Pengyu Hu; Huiwen Deng; Chuanxiang Li; Xing Qu; Guofeng Zhang; Shuming Yang

doi:10.1364/AO.474235

Applied Optics
Vol. 61,
Issue 32,
pp. 9625-9633
(2022)
•https://doi.org/10.1364/AO.474235

Flexible and simple telecentric camera calibration method

Yu Duan, Pengyu Hu, Huiwen Deng, Chuanxiang Li, Xing Qu, Guofeng Zhang, and Shuming Yang

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Yu Duan, Pengyu Hu, Huiwen Deng, Chuanxiang Li, Xing Qu, Guofeng Zhang, and Shuming Yang, "Flexible and simple telecentric camera calibration method," Appl. Opt. 61, 9625-9633 (2022)

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Abstract

The measurement accuracy of telecentric imaging technique straightforwardly depends on the calibration of the telecentric camera. We present a flexible and simple calibration method based on a telecentric imaging model and orthogonality of rotation matrix. First, we use the orthogonality of rotation matrix to solve the magnification. Second, the external parameters are solved by the imaging model, and the ambiguity of sign is solved. Finally, we use the LM nonlinear optimization method to solve the distortion parameters. Experimental results show that the reprojection error is 0.7 pixels, which represents the actual dimension of 6.37 µm. In addition, the standard measuring block and real objects are measured, and the results verify the measurement accuracy and robustness of the proposed method.

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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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Item	Yao’s Method [11]	Proposed Method	LM Optimizer
m	0.3791067	0.3790631	0.37899285
R	$(\begin{matrix} - 0 .24509 & 0.96950 & 0 .00075 \\ 0 .96915 & 0 .24502 & - 0 .02679 \\ - 0 .02616 & - 0 .00583 & - 0 .99964 \end{matrix})$	$(\begin{matrix} - 0.24513 & 0.96967 & - 0.01305 \\ 0.96932 & 0.24506 & - 0.02190 \\ - 0.01802 & - 0.01802 & - 0.99967 \end{matrix})$	$(\begin{matrix} - 0.245 08 & 0.969 49 & - 0 .00096 \\ 0.96 914 & 0.2450 1 & - 0.0 2760 \\ - 0.0 2652 & - 0.0 0769 & - 0.9996 2 \end{matrix})$
T	$(\begin{matrix} 22 .31896 \\ 9 .060392 \\ n o n \end{matrix})$	$(\begin{matrix} 22.32299 \\ 9.0620327 \\ n o n \end{matrix})$	$(\begin{matrix} 22. 31885 \\ 9.06 03509 \\ n o n \end{matrix})$
K	$(\begin{matrix} 1 .62304 e - 07 \\ - 2 .42138 e - 11 \end{matrix})$	$(\begin{matrix} 1 .61373 e - 07 \\ - 2 .40762 e - 11 \end{matrix})$	$(\begin{matrix} 1 .59271 e - 07 \\ - 2 .47352 e - 11 \end{matrix})$

	Halcon (mm)	Proposed Method (mm)	Yao’s Method [11] (mm)
Gauge Block, Level 0, Nominal size 20 mm	19.98561	19.9998	19.99697
	19.98704	20.00139	19.99791
	19.98574	19.99969	19.9954
	19.99322	20.0098	20.00858
	19.99484	20.00886	20.005
	19.9864	20.00052	19.99642
	19.986	19.99988	19.99458
	19.98783	20.00168	19.99638
	19.992	20.006	19.99388
Average	19.98874	20.00307	19.99835

	Halcon	Proposed Paper	Yao’s Method [11]
MAE	−0.01126	0.00288	0.00165
MSE	0.00018	8.99e-5	9.79e-5
RMSE	0.0134	0.00948	0.00989

(mm)	Upper Left	Upper Right	Lower Left	Lower Right
Vernier caliper	3.83	3.79	3.87	3.91
Proposed method	3.83008	3.7955	3.86784	3.91872

Item	Yao’s Method [11]	Proposed Method	LM Optimizer
m	0.3791067	0.3790631	0.37899285
R	$(\begin{matrix} - 0 .24509 & 0.96950 & 0 .00075 \\ 0 .96915 & 0 .24502 & - 0 .02679 \\ - 0 .02616 & - 0 .00583 & - 0 .99964 \end{matrix})$	$(\begin{matrix} - 0.24513 & 0.96967 & - 0.01305 \\ 0.96932 & 0.24506 & - 0.02190 \\ - 0.01802 & - 0.01802 & - 0.99967 \end{matrix})$	$(\begin{matrix} - 0.245 08 & 0.969 49 & - 0 .00096 \\ 0.96 914 & 0.2450 1 & - 0.0 2760 \\ - 0.0 2652 & - 0.0 0769 & - 0.9996 2 \end{matrix})$
T	$(\begin{matrix} 22 .31896 \\ 9 .060392 \\ n o n \end{matrix})$	$(\begin{matrix} 22.32299 \\ 9.0620327 \\ n o n \end{matrix})$	$(\begin{matrix} 22. 31885 \\ 9.06 03509 \\ n o n \end{matrix})$
K	$(\begin{matrix} 1 .62304 e - 07 \\ - 2 .42138 e - 11 \end{matrix})$	$(\begin{matrix} 1 .61373 e - 07 \\ - 2 .40762 e - 11 \end{matrix})$	$(\begin{matrix} 1 .59271 e - 07 \\ - 2 .47352 e - 11 \end{matrix})$

Abstract

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Equations (29)

Applied Optics