Acta Optica Sinica, Volume. 40, Issue 14, 1405003(2020)
Point Spread Function Model of Grating Imaging System Based on Boltzmann Function Edge Fitting
Figures & Tables(15)
Fig. 3. Edge image and fitting effects of different functions. (a) Edge image; (b) fitting results of different functions; (c) local enlargement
Fig. 10. Restoration comparison of different fitting functions. (a) Gauss function; (b) Hyperbolic function; (c) Boltzmann function
Table 1. Fitting goodness of different functions on ESF
View tableTable 1. Fitting goodness of different functions on ESF
θ /(°) Gauss Hyperbolic Boltzmann SSE R-square RMSE SSE R-square RMSE SSE R-square RMSE 4 0.0076 0.9988 0.0127 0.0047 0.9991 0.0091 2 0.0180 0.9978 0.0195 0.0130 0.9984 0.0155 0 0.0028 0.9997 0.0085 0.0069 0.9994 0.0110 -34 0.1164 0.9845 0.0492 0.0264 0.9972 0.0215 0.0120 0.9984 0.0147 -36 0.0161 0.9960 0.0206 0.0206 0.9960 0.0164 0.0070 0.9988 0.0111
Table 2. Fitting parameters of curves under different light intensities
View tableTable 2. Fitting parameters of curves under different light intensities
E ω0 /pixel θR /(°) α /(°) 6.5×10-3 20.08 10.45 62.51 1.3×10-2 19.13 10.94 60.24 2.6×10-2 17.85 12.65 54.68 5.2×10-2 14.28 12.36 49.12 1.0×10-1 12.25 15.16 38.94
Table 3. Fitting goodness of curves under different light intensities
View tableTable 3. Fitting goodness of curves under different light intensities
E 6.5×10-3 1.3×10-2 2.6×10-2 5.2×10-2 1.0×10-1 R-square 0.9609 0.9683 0.9723 0.9699 0.9600
Table 4. Quality evaluation before and after image restoration
View tableTable 4. Quality evaluation before and after image restoration
θ /(°) GMG SSIM Before restoration After restoration Increase rate Before restoration After restoration Increase rate 4 0.0086 0.0150 74.42% 44.94% 89.31% 98.73% 2 0.0082 0.0145 76.83% 51.36% 88.63% 72.57% 0 0.0091 0.0157 72.53% 53.31% 91.94% 72.47% -34 0.0088 0.0141 60.23% 53.92% 89.76% 66.47% -36 0.0085 0.0143 68.23% 48.34% 87.49% 80.99%
Table 5. Quality evaluation of different fitting functions
View tableTable 5. Quality evaluation of different fitting functions
Function GMG SSIM Before restoration After restoration Increase rate Before restoration After restoration Increase rate Gauss 0.0091 3.41% 58.29% 8.10% Hyperbolic 0.0088 0.0095 7.95% 53.92% 69.38% 28.67% Boltzmann 0.0141 60.23% 89.76% 66.47%
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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
Paper Information
Category: Diffraction and Gratings
Received: Mar. 9, 2020
Accepted: Apr. 14, 2020
Published Online: Jul. 23, 2020
The Author Email: Lu Quan (luquan@gxu.edu.cn)
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