Image gray-scale modeling and displacement measurement based on the combination of Fourier series and polynomial

Peng Lei; Jinchun Hu; Yu Zhu; Shengwu Du

doi:10.3788/IRLA20210123

Journals >Infrared and Laser Engineering >Volume 51 >Issue 3 >Page 20210123 > Article

Infrared and Laser Engineering
Vol. 51, Issue 3, 20210123 (2022)

Image gray-scale modeling and displacement measurement based on the combination of Fourier series and polynomial

Peng Lei^1、2, Jinchun Hu^1、2, Yu Zhu^1、2, and Shengwu Du^1、2

Author Affiliations

¹State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

²Beijing Key Lab of Precision/Ultra-Precision Manufacturing Equipment and Control, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

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DOI: 10.3788/IRLA20210123 Cite this Article

Peng Lei, Jinchun Hu, Yu Zhu, Shengwu Du. Image gray-scale modeling and displacement measurement based on the combination of Fourier series and polynomial[J]. Infrared and Laser Engineering, 2022, 51(3): 20210123 Copy Citation Text

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Fig. 1. Schematic diagram of measurement principle

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Fig. 2. Two main factors affecting the measurement model. (a) Target image distortion; (b) Inconsistencies between image sensors unit

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Fig. 3. Model identification results before calibration. (a) The result of least square fitting; (b) Residual distribution of model; (c) Right view of the model residual distribution

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Fig. 4. Model identification results after calibration. (a) The result of least square fitting; (b) Residual distribution of model; (c) Right view of the model residual distribution

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Fig. 5. Measurement results. (a) Measurement results before model correction; (b) Measurement results after model correction

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Fig. 6. Relationship between the number of sensor unit and the standard deviation of measurement error

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Parameter	Value	Parameter	Value
A	79.59	${\tau _{\rm{w}}}$	8.667
B	123.8	$\varphi $	0.6262

Table 1. Results of model parameter identification before model correction

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Parameter	Value	Parameter	Value	Parameter	Value
${a_{10}}$	81	${a_{43}}$	1.323e-06	${b_{32}}$	−0.0002089
${a_{11}}$	0.04654	${a_{50}}$	−0.2038	${b_{33}}$	1.421e-06
${a_{12}}$	−0.0002637	${a_{51}}$	−7.2e-05	${b_{40}}$	0.08277
${a_{13}}$	9.085e-07	${a_{52}}$	0.0001074	${b_{41}}$	0.004726
${a_{20}}$	−6.692	${a_{53}}$	−8.738e-07	${b_{42}}$	−3.146e-05
${a_{21}}$	0.01142	${b_{10}}$	−24.01	${b_{43}}$	1.808e-07
${a_{22}}$	1.84e-06	${b_{11}}$	0.04984	${b_{50}}$	0.301
${a_{23}}$	−2.256e-07	${b_{12}}$	−0.0002796	${b_{51}}$	0.003075
${a_{30}}$	−0.6056	${b_{13}}$	1.659e-06	${b_{52}}$	−0.0001482
${a_{31}}$	−0.001703	${b_{20}}$	−9.865	${b_{53}}$	1.122e-06
${a_{32}}$	−1.555e-05	${b_{21}}$	−0.01589	${B_0}$	129.2
${a_{33}}$	2.462e-07	${b_{22}}$	0.000121	${B_1}$	0.04099
${a_{40}}$	−0.1802	${b_{23}}$	−4.206e-07	${B_2}$	−0.0004571
${a_{41}}$	0.006175	${b_{30}}$	0.5337	${B_3}$	2.644e-06
${a_{42}}$	−0.0001946	${b_{31}}$	0.004793	${\tau _{\rm{w}}}$/mm	8.62

Table 2. Results of model parameter identification after model correction

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