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Laser & Optoelectronics Progress, Volume. 61, Issue 12, 1211002(2024)

Gamma Nonlinear Self-Compensation Based on General Rational Polynomial Model

Xiaomei Xue1,2,3, Lijun Sun1,2,3, Tianfei Chen1,2,3、*, and Pengxiang Fan1,2,3
Author Affiliations
  • 1Key Laboratory of Food Information Processing and Control of Ministry of Education, Henan University of Technology, Zhengzhou 450001, Henan , China
  • 2Zhengzhou Key Laboratory of Machine Perception and Intelligent System, Henan University of Technology, Zhengzhou 450001, Henan , China
  • 3College of Information Science and Engineering, Henan University of Technology, Zhengzhou 450001, Henan , China
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    AbstractGet PDF(in Chinese)
    Figures&Tables (21)
    Equations (20)
    References (28)
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    Figures & Tables(21)
    Digital phase-shifting fringe projection system

    Fig. 1. Digital phase-shifting fringe projection system

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    Simulation of the fringe patterns captured by camera. (a) Standard sinusoidal fringe (γ=1); (b) distorted fringe (γ=1.5)

    Fig. 2. Simulation of the fringe patterns captured by camera. (a) Standard sinusoidal fringe (γ=1); (b) distorted fringe (γ=1.5)

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    Gray value analysis of simulated single stripe curves. (a) Ideal single line fringe curve; (b) distorted single line fringe curve

    Fig. 3. Gray value analysis of simulated single stripe curves. (a) Ideal single line fringe curve; (b) distorted single line fringe curve

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    Single line comparison of ideal phase principal values and distorted phase principal values

    Fig. 4. Single line comparison of ideal phase principal values and distorted phase principal values

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    Variation curves of standard deviation of phase error under different conditions. (a) Standard deviation varies with the number of iterations; (b) standard deviation varies with the order of retained error term

    Fig. 5. Variation curves of standard deviation of phase error under different conditions. (a) Standard deviation varies with the number of iterations; (b) standard deviation varies with the order of retained error term

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    Comparison of phase errors before and after correction

    Fig. 6. Comparison of phase errors before and after correction

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    Comparison of the relative phase before and after compensation of the algorithm. (a) Before compensation; (b) after compensation

    Fig. 7. Comparison of the relative phase before and after compensation of the algorithm. (a) Before compensation; (b) after compensation

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    Curves of the phase error model. (a) Before removing the deviation points; (b) after removing the deviation points

    Fig. 8. Curves of the phase error model. (a) Before removing the deviation points; (b) after removing the deviation points

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    Absolute phase diagrams contrast before and after compensation by different algorithms. (a) Without compensation; (b) with compensation by double four step phase-shifting algorithm; (c) with compensation by gamma precoding algorithm; (d) with compensation by the proposed algorithm

    Fig. 9. Absolute phase diagrams contrast before and after compensation by different algorithms. (a) Without compensation; (b) with compensation by double four step phase-shifting algorithm; (c) with compensation by gamma precoding algorithm; (d) with compensation by the proposed algorithm

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    Phase error curves at line 500 of absolute phase diagrams before and after phase compensation

    Fig. 10. Phase error curves at line 500 of absolute phase diagrams before and after phase compensation

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    Absolute phase diagrams of vase sculpture. (a) Measured object; (b) first raster image acquired by CCD camera; (c) absolute phase diagram without compensation; (d) absolute phase diagram processed by double four step phase-shifting algorithm; (e) absolute phase diagram processed by gamma precoding algorithm; (f) absolute phase diagram processed by the proposed algorithm

    Fig. 11. Absolute phase diagrams of vase sculpture. (a) Measured object; (b) first raster image acquired by CCD camera; (c) absolute phase diagram without compensation; (d) absolute phase diagram processed by double four step phase-shifting algorithm; (e) absolute phase diagram processed by gamma precoding algorithm; (f) absolute phase diagram processed by the proposed algorithm

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    Curves of phase error model. (a) Before removing the deviation points; (b) after removing the deviation points

    Fig. 12. Curves of phase error model. (a) Before removing the deviation points; (b) after removing the deviation points

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    Single line phase error analysis diagram of vase sculpture under different phase error compensation algorithms

    Fig. 13. Single line phase error analysis diagram of vase sculpture under different phase error compensation algorithms

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    Absolute phase diagrams of a triangular pyramid sculpture. (a) Measured object; (b) first raster image acquired by CCD camera; (c) absolute phase diagram without compensation; (d) absolute phase diagram processed by double four step phase-shifting algorithm; (e) absolute phase diagram processed by gamma precoding algorithm (f) absolute phase diagram processed by the proposed algorithm

    Fig. 14. Absolute phase diagrams of a triangular pyramid sculpture. (a) Measured object; (b) first raster image acquired by CCD camera; (c) absolute phase diagram without compensation; (d) absolute phase diagram processed by double four step phase-shifting algorithm; (e) absolute phase diagram processed by gamma precoding algorithm (f) absolute phase diagram processed by the proposed algorithm

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    Curves of phase error model. (a) Before removing the deviation points; (b) after removing the deviation points

    Fig. 15. Curves of phase error model. (a) Before removing the deviation points; (b) after removing the deviation points

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    Single line phase error analysis diagram of triangular pyramid sculpture under different phase error compensation algorithms

    Fig. 16. Single line phase error analysis diagram of triangular pyramid sculpture under different phase error compensation algorithms

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    • Table 1. Experimental equipments in grating fringe projection measurement system

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      Table 1. Experimental equipments in grating fringe projection measurement system

      Experimental facilityModel parameter
      Digital projectorEPSON CH-TW610（800 pixel × 600 pixel）
      CCD cameraGUPPY PRO GPF 201C IPC
      Lens of the cameraMVL-KF5024M-6MP
      Computeri59400F，NVIDIA GeForce GTX 1050

    • Table 2. Phase errors in absolute phase diagrams with and without compensation

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      Table 2. Phase errors in absolute phase diagrams with and without compensation

      Phase error compensation algorithmMaximum error valueStandard deviation
      Without compensation0.19950.1098
      Double four step phase-shifting0.08260.0219
      Gamma precoding0.04690.0167
      Proposed algorithm0.02990.0137

    • Table 3. Running times of different phase error compensation algorithms

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      Table 3. Running times of different phase error compensation algorithms

      Phase error compensation algorithmRunning time /s
      Gamma precoding9.9423
      Double four step phase-shifting79.0058
      Proposed algorithm6.6480

    • Table 4. Phase errors of vase sculpture under different phase error compensation algorithms

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      Table 4. Phase errors of vase sculpture under different phase error compensation algorithms

      Phase error compensation algorithmMaximum error valueStandard deviation
      Without compensation0.15390.0846
      Double four step phase-shifting0.07430.0351
      Gamma precoding0.05190.0262
      Proposed algorithm0.03960.0164

    • Table 5. Phase error of triangular pyramid sculpture under different phase error compensation algorithms

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      Table 5. Phase error of triangular pyramid sculpture under different phase error compensation algorithms

      Phase error compensation algorithmMaximum error valueStandard deviation
      Without compensation0.17870.1182
      Double four step phase-shifting0.08640.0208
      Gamma precoding0.05860.0184
      Proposed algorithm0.04460.0177
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    Xiaomei Xue, Lijun Sun, Tianfei Chen, Pengxiang Fan. Gamma Nonlinear Self-Compensation Based on General Rational Polynomial Model[J]. Laser & Optoelectronics Progress, 2024, 61(12): 1211002

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    Paper Information

    Category: Imaging Systems

    Received: Jun. 12, 2023

    Accepted: Aug. 10, 2023

    Published Online: May. 20, 2024

    The Author Email: Tianfei Chen (chen_tianfei@163.com)

    DOI:10.3788/LOP231502

    CSTR:32186.14.LOP231502

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology