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

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

Peng Lei1,2, Jinchun Hu1,2, Yu Zhu1,2, and Shengwu Du1,2
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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    Figures & Tables(8)
    Schematic diagram of measurement principle
    Two main factors affecting the measurement model. (a) Target image distortion; (b) Inconsistencies between image sensors unit
    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
    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
    Measurement results. (a) Measurement results before model correction; (b) Measurement results after model correction
    Relationship between the number of sensor unit and the standard deviation of measurement error
    • Table 1. Results of model parameter identification before model correction

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      Table 1. Results of model parameter identification before model correction

      ParameterValueParameterValue
      A79.59${\tau _{\rm{w}}}$8.667
      B123.8$\varphi $0.6262
    • Table 2. Results of model parameter identification after model correction

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      Table 2. Results of model parameter identification after model correction

      ParameterValueParameterValueParameterValue
      ${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
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    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

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    Paper Information

    Category: Photoelectric measurement

    Received: Nov. 25, 2021

    Accepted: --

    Published Online: Apr. 8, 2022

    The Author Email:

    DOI:10.3788/IRLA20210123

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