Cross-point calibration method for the Scheimpflug measurement system

Bin Cui; Qinwei Fu; Hao Sun; Wei Tao; Na Lv; Hui Zhao

doi:10.1364/AO.401350

Applied Optics
Vol. 59,
Issue 28,
pp. 8618-8627
(2020)
•https://doi.org/10.1364/AO.401350

Cross-point calibration method for the Scheimpflug measurement system

Bin Cui, Qinwei Fu, Hao Sun, Wei Tao, Na Lv, and Hui Zhao

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Bin Cui, Qinwei Fu, Hao Sun, Wei Tao, Na Lv, and Hui Zhao, "Cross-point calibration method for the Scheimpflug measurement system," Appl. Opt. 59, 8618-8627 (2020)

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Table of Contents Category
- Instrumentation and Measurements
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About this Article
History
- Original Manuscript: June 29, 2020
- Revised Manuscript: August 31, 2020
- Manuscript Accepted: August 31, 2020
- Published: September 25, 2020

Abstract

The Scheimpflug measurement system has broad application prospects in the fields of tomographic particle image velocimetry (PIV), ophthalmology, and three-dimensional reconstruction. Additionally, its special imaging structure makes the theoretical model of other traditional calibration methods no longer applicable. A cross-point calibration method in which the real-world coordinate system is transferred from an in-kind calibrator to displacement, achieving great improvements in the quantity and accuracy of the feature points, is proposed. This method, which makes up for the defects introduced by the distorted imaging plane, also in turn simplifies the calibration process. Finally, the proposed method is tested via both simulation and calibration experiments. The high calibration accuracy verifies that the method is feasible.

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Calibration Results of the Fitting Algorithm		LM Algorithm	GA
Intrinsic parameters	$f$ (mm)	22.09	22.12
	$k_{1}$	7.34e-6	7.56e-6
	$k_{2}$	8.01e-8	8.27e-8
	$p_{1}$	8.13e-3	8.55e-3
	$p_{2}$	3.31e-5	3.36e-5
	$d_{x}$ (mm)	0.0050	0.0048
	$d_{y}$ (mm)	0.010	0.011
	$u_{0}$	890.05	890.02
	$v_{0}$	779.92	779.87
Extrinsic parameters	$α$ (rad)	−0.98	−0.92
	$β$ (rad)	0.091	0.108
	$θ_{x}$ (rad)	0.59	0.54
	$θ_{y}$ (rad)	−0.081	−0.097
	$θ_{z}$ (rad)	−0.024	−0.019
	$t_{x}$ (mm)	0.012	0.023
	$t_{y}$ (mm)	0.107	0.115
	$t_{z}$ (mm)	99.97	99.81

Index	Cross-Point Calibration Method	Zhang’s Calibration Method	RMM	GNIM	Zhu’s Calibration Method
$f$ (mm)	22.09	22.24	22.18	22.20	22.11
$k_{1}$	7.34e-6	7.83e-6	8.25e-6	7.76e-6	7.48e-6
$k_{2}$	8.01e-8	8.31e-8	8.77e-8	8.51e-8	8.27e-8
$p_{1}$	8.13e-3	8.68e-3	9.01e-3	8.62e-3	8.77e-3
$p_{2}$	3.31e-5	3.40e-5	3.55e-5	3.51e-5	3.24e-5
$d_{x}$ (mm)	0.0050	0.0052	0.0058	0.0056	0.0047
$d_{y}$ (mm)	0.010	0.014	0.016	0.021	0.015
$u_{0}$	890.05	890.23	890.28	891.13	890.11
$v_{0}$	779.92	778.96	780.13	780.26	779.14
$α$ (rad)	−0.98	−0.87	−1.02	−0.92	−0.85
$β$ (rad)	0.091	0.125	0.103	0.119	0.097
$θ_{x}$ (rad)	0.59	0.63	0.66	0.67	0.60
$θ_{y}$ (rad)	−0.081	−0.107	−0.092	−0.112	−0.093
$θ_{z}$ (rad)	−0.024	−0.025	−0.033	−0.030	−0.027
$t_{x}$ (mm)	0.012	0.031	0.018	0.025	0.010
$t_{y}$ (mm)	0.107	0.129	0.114	0.118	0.112
$t_{z}$ (mm)	99.97	100.53	100.86	100.53	100.25
Maximum deviation(mm)	0.036	0.078	0.044	0.067	0.051
RMSE (mm)	0.023	0.052	0.027	0.044	0.032

Calibration Results of the Fitting Algorithm		LM Algorithm	GA
Intrinsic parameters	$f$ (mm)	22.09	22.12
	$k_{1}$	7.34e-6	7.56e-6
	$k_{2}$	8.01e-8	8.27e-8
	$p_{1}$	8.13e-3	8.55e-3
	$p_{2}$	3.31e-5	3.36e-5
	$d_{x}$ (mm)	0.0050	0.0048
	$d_{y}$ (mm)	0.010	0.011
	$u_{0}$	890.05	890.02
	$v_{0}$	779.92	779.87
Extrinsic parameters	$α$ (rad)	−0.98	−0.92
	$β$ (rad)	0.091	0.108
	$θ_{x}$ (rad)	0.59	0.54
	$θ_{y}$ (rad)	−0.081	−0.097
	$θ_{z}$ (rad)	−0.024	−0.019
	$t_{x}$ (mm)	0.012	0.023
	$t_{y}$ (mm)	0.107	0.115
	$t_{z}$ (mm)	99.97	99.81

Index	Cross-Point Calibration Method	Zhang’s Calibration Method	RMM	GNIM	Zhu’s Calibration Method
$f$ (mm)	22.09	22.24	22.18	22.20	22.11
$k_{1}$	7.34e-6	7.83e-6	8.25e-6	7.76e-6	7.48e-6
$k_{2}$	8.01e-8	8.31e-8	8.77e-8	8.51e-8	8.27e-8
$p_{1}$	8.13e-3	8.68e-3	9.01e-3	8.62e-3	8.77e-3
$p_{2}$	3.31e-5	3.40e-5	3.55e-5	3.51e-5	3.24e-5
$d_{x}$ (mm)	0.0050	0.0052	0.0058	0.0056	0.0047
$d_{y}$ (mm)	0.010	0.014	0.016	0.021	0.015
$u_{0}$	890.05	890.23	890.28	891.13	890.11
$v_{0}$	779.92	778.96	780.13	780.26	779.14
$α$ (rad)	−0.98	−0.87	−1.02	−0.92	−0.85
$β$ (rad)	0.091	0.125	0.103	0.119	0.097
$θ_{x}$ (rad)	0.59	0.63	0.66	0.67	0.60
$θ_{y}$ (rad)	−0.081	−0.107	−0.092	−0.112	−0.093
$θ_{z}$ (rad)	−0.024	−0.025	−0.033	−0.030	−0.027
$t_{x}$ (mm)	0.012	0.031	0.018	0.025	0.010
$t_{y}$ (mm)	0.107	0.129	0.114	0.118	0.112
$t_{z}$ (mm)	99.97	100.53	100.86	100.53	100.25
Maximum deviation(mm)	0.036	0.078	0.044	0.067	0.051
RMSE (mm)	0.023	0.052	0.027	0.044	0.032

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Applied Optics