• Acta Optica Sinica
  • Vol. 40, Issue 14, 1405003 (2020)
Quan Lu1、*, Zehao Zhang1, Weiping Zhang2, and Yirong Liu2
Author Affiliations
  • 1School of Electrical Engineering, Guangxi University, Nanning, Guangxi 530004, China
  • 2School of Physical Science and Technology, Guangxi University, Nanning, Guangxi 530004, China
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    DOI: 10.3788/AOS202040.1405003 Cite this Article Set citation alerts
    Quan Lu, Zehao Zhang, Weiping Zhang, Yirong Liu. Point Spread Function Model of Grating Imaging System Based on Boltzmann Function Edge Fitting[J]. Acta Optica Sinica, 2020, 40(14): 1405003 Copy Citation Text show less
    Diagram of experimental light path
    Fig. 1. Diagram of experimental light path
    Images formed by grating at partial incident angles
    Fig. 2. Images formed by grating at partial incident angles
    Edge image and fitting effects of different functions. (a) Edge image; (b) fitting results of different functions; (c) local enlargement
    Fig. 3. Edge image and fitting effects of different functions. (a) Edge image; (b) fitting results of different functions; (c) local enlargement
    PSF of grating imaging at partial incident angles
    Fig. 4. PSF of grating imaging at partial incident angles
    Diagram of sequential PSF
    Fig. 5. Diagram of sequential PSF
    Schematic of axial horizontal profile energy distribution
    Fig. 6. Schematic of axial horizontal profile energy distribution
    Change of PSF radius under different light intensities
    Fig. 7. Change of PSF radius under different light intensities
    Images formed by grating system
    Fig. 8. Images formed by grating system
    Restored images
    Fig. 9. Restored images
    Restoration comparison of different fitting functions. (a) Gauss function; (b) Hyperbolic function; (c) Boltzmann function
    Fig. 10. Restoration comparison of different fitting functions. (a) Gauss function; (b) Hyperbolic function; (c) Boltzmann function
    θ /(°)GaussHyperbolicBoltzmann
    SSER-squareRMSESSER-squareRMSESSER-squareRMSE
    40.00760.99880.01270.00470.99910.0091
    20.01800.99780.01950.01300.99840.0155
    00.00280.99970.00850.00690.99940.0110
    -340.11640.98450.04920.02640.99720.02150.01200.99840.0147
    -360.01610.99600.02060.02060.99600.01640.00700.99880.0111
    Table 1. Fitting goodness of different functions on ESF
    Eω0 /pixelθR /(°)α /(°)
    6.5×10-320.0810.4562.51
    1.3×10-219.1310.9460.24
    2.6×10-217.8512.6554.68
    5.2×10-214.2812.3649.12
    1.0×10-112.2515.1638.94
    Table 2. Fitting parameters of curves under different light intensities
    E6.5×10-31.3×10-22.6×10-25.2×10-21.0×10-1
    R-square0.96090.96830.97230.96990.9600
    Table 3. Fitting goodness of curves under different light intensities
    θ /(°)GMGSSIM
    Before restorationAfter restorationIncrease rateBefore restorationAfter restorationIncrease rate
    40.00860.015074.42%44.94%89.31%98.73%
    20.00820.014576.83%51.36%88.63%72.57%
    00.00910.015772.53%53.31%91.94%72.47%
    -340.00880.014160.23%53.92%89.76%66.47%
    -360.00850.014368.23%48.34%87.49%80.99%
    Table 4. Quality evaluation before and after image restoration
    FunctionGMGSSIM
    BeforerestorationAfterrestorationIncreaserateBeforerestorationAfterrestorationIncreaserate
    Gauss0.00913.41%58.29%8.10%
    Hyperbolic0.00880.00957.95%53.92%69.38%28.67%
    Boltzmann0.014160.23%89.76%66.47%
    Table 5. Quality evaluation of different fitting functions
    Quan Lu, Zehao Zhang, Weiping Zhang, Yirong Liu. Point Spread Function Model of Grating Imaging System Based on Boltzmann Function Edge Fitting[J]. Acta Optica Sinica, 2020, 40(14): 1405003
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