Author Affiliations
1School of Electrical Engineering, Guangxi University, Nanning, Guangxi 530004, China2School of Physical Science and Technology, Guangxi University, Nanning, Guangxi 530004, Chinashow less
Fig. 1. Diagram of experimental light path
Fig. 2. Images formed by grating at partial incident angles
Fig. 3. Edge image and fitting effects of different functions. (a) Edge image; (b) fitting results of different functions; (c) local enlargement
Fig. 4. PSF of grating imaging at partial incident angles
Fig. 5. Diagram of sequential PSF
Fig. 6. Schematic of axial horizontal profile energy distribution
Fig. 7. Change of PSF radius under different light intensities
Fig. 8. Images formed by grating system
Fig. 9. Restored images
Fig. 10. Restoration comparison of different fitting functions. (a) Gauss function; (b) Hyperbolic function; (c) Boltzmann function
θ /(°) | Gauss | Hyperbolic | Boltzmann |
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SSE | R-square | RMSE | SSE | R-square | RMSE | SSE | R-square | RMSE |
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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 |
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Table 1. Fitting goodness of different functions on ESF
E | ω0 /pixel | θR /(°) | α /(°) |
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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 |
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Table 2. Fitting parameters 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 |
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R-square | 0.9609 | 0.9683 | 0.9723 | 0.9699 | 0.9600 |
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Table 3. Fitting goodness of curves under different light intensities
θ /(°) | GMG | SSIM |
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Before restoration | After restoration | Increase rate | Before restoration | After restoration | Increase rate |
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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% |
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Table 4. Quality evaluation before and after image restoration
Function | GMG | SSIM |
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Beforerestoration | Afterrestoration | Increaserate | Beforerestoration | Afterrestoration | Increaserate |
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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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Table 5. Quality evaluation of different fitting functions