• Acta Optica Sinica
  • Vol. 41, Issue 14, 1412002 (2021)
Fuqian Li and Wenjing* Chen
Author Affiliations
  • Department of Optic-Electronic, College of Electronics and Information Engineering, Sichuan University, Chengdu, Sichuan 610065, China
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    DOI: 10.3788/AOS202141.1412002 Cite this Article Set citation alerts
    Fuqian Li, Wenjing* Chen. Phase Error Analysis and Correction for Phase Shifting Profilometry Using Crossed Grating[J]. Acta Optica Sinica, 2021, 41(14): 1412002 Copy Citation Text show less
    Schematic of measurement for crossed grating projection profilometry
    Fig. 1. Schematic of measurement for crossed grating projection profilometry
    Spectrum of grating with nonlinear response. (a) Spectrum of horizontal grating; (b) spectrum of vertical grating; (c) spectrum of crossed grating
    Fig. 2. Spectrum of grating with nonlinear response. (a) Spectrum of horizontal grating; (b) spectrum of vertical grating; (c) spectrum of crossed grating
    STD of phase error distribution for crossed grating PSP with different phase shifting steps
    Fig. 3. STD of phase error distribution for crossed grating PSP with different phase shifting steps
    Phase error distribution of crossed grating PSP. (a) Horizontal phase error; (b) vertical phase error
    Fig. 4. Phase error distribution of crossed grating PSP. (a) Horizontal phase error; (b) vertical phase error
    Comparison of phase error distribution. (a) Horizontal phase error; (b) vertical phase error
    Fig. 5. Comparison of phase error distribution. (a) Horizontal phase error; (b) vertical phase error
    Experimental setup
    Fig. 6. Experimental setup
    Experimental results. (a) Captured grating image; (b) STD of phase errors distribution for crossed grating PSP with different phase shifting step
    Fig. 7. Experimental results. (a) Captured grating image; (b) STD of phase errors distribution for crossed grating PSP with different phase shifting step
    Phase error distribution. (a) Horizontal phase error; (b) vertical phase error
    Fig. 8. Phase error distribution. (a) Horizontal phase error; (b) vertical phase error
    Phase error distribution of four methods. (a) Horizontal phase error; (b) vertical phase error
    Fig. 9. Phase error distribution of four methods. (a) Horizontal phase error; (b) vertical phase error
    Measurement results of a heart-shaped object. (a) Heart-shaped object; (b)(e)(g)(j) five-step PSP; (c)(h)(k) double five-step PSP; (d)(f)(i)(l) five-step PSP with Gamma correction
    Fig. 10. Measurement results of a heart-shaped object. (a) Heart-shaped object; (b)(e)(g)(j) five-step PSP; (c)(h)(k) double five-step PSP; (d)(f)(i)(l) five-step PSP with Gamma correction
    CaseHorizontal sinusoidal gratingVertical sinusoidal grating
    11.7011.698
    21.6971.689
    31.6801.673
    Table 1. Pre-encoded Gamma values calculated by horizontal sinusoidal grating and vertical sinusoidal grating
    MethodSTD of the horizontal phase errors /radSTD of the vertical phase errors /rad
    Five-step0.2760.276
    Fifteen-step0.2470.123
    Double five-step0.0500.050
    Table 2. Simulation results of the STD of phase errors for crossed grating PSP
    MethodSTD of the horizontal phase errors /radSTD of the vertical phase errors /radNumber of grating patterns
    Five-step0.2760.2765
    Double five-step0.0500.05010
    Five-step with single carrier0.0020.00210
    Table 3. Simulation results of the STD of phase errors by three methods
    MethodSTD of the horizontal phase errors /radSTD of the vertical phase errors /rad
    Five-step0.1930.215
    Thirteen-step0.1810.093
    Double five-step0.0300.038
    Table 4. Experimental results of the STD of phase errors for crossed grating PSP
    MethodSTD of the horizontal phase errors /radSTD of the vertical phase errors /radNumber of grating patternsTime /s
    Five-step0.1930.21552.413
    Double five-step0.0300.038102.927
    Gamma correction0.0170.02052.441
    Five-step with single carrier0.0160.018102.518
    Table 5. Experimental results of the STD of phase errors by four methods
    Fuqian Li, Wenjing* Chen. Phase Error Analysis and Correction for Phase Shifting Profilometry Using Crossed Grating[J]. Acta Optica Sinica, 2021, 41(14): 1412002
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