Fig. 1. Point source imaging system
Fig. 2. Schematic of point source method
Fig. 3. Schematic of star point method reconstructionPSF process
Fig. 4. Simulation results of few pixels star point images. (a) Image1; (b) image2; (c) image3; (d) image4
Fig. 5. Simulation results of multi-pixel star point images. (a) Image1; (b) image2; (c) image3; (d) image4
Fig. 6. Scatter plots of star point images. (a) Scatter plot of single star point image; (b) encrypted scatter plot of 4 star point images registration
Fig. 7. Scatter plots of star point images registered with different number of images. (a) Single image; (b) 4 images; (c) 6 images; (d) 8 images; (e) 10 images
Fig. 8. Normalized MSE of PSF and MTF under different number of registered images. Few pixels star point images, (a) MSE after PSF normalization, (b) MSE after MTF normalization; multi-pixel star point images, (c) MSE after PSF normalization; (d) MSE after MTF normalization
Fig. 9. MTF obtained by LSF through different processing methods under different images. (a) Few pixels star point simulation images; (b) multi-pixel star point simulation images
Fig. 10. Schematic of optimized star point method
Fig. 11. MSE curves of MTF under different noise standard deviations
Fig. 12. Star point simulation diagram with different radius. (a) 0.4 pixel; (b) 0.6 pixel; (c) 0.8 pixel; (d) 0.9 pixel; (e) 1.0 pixel; (f) 2.0 pixel; (g) 3.0 pixel; (h) 4.0 pixel
Fig. 13. MSE curves of MTF under different radius
Fig. 14. Point source image sequences with different defocus. (a) -0.2 mm; (b) -0.1 mm; (c) 0 mm; (d) +0.1 mm; (e) +0.2 mm
Fig. 15. Overfocus curves of traditional point source method and proposed method
Step | Method |
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Detect star point center position | Centroid method, centroid weighting method, Gaussian fitting method, edge circle fitting method | Reconstruct PSF | 2D Gaussian fitting of single image, 2D Gaussian fitting of reconstructed image | Obtain MTF by Fourier transform | Gaussian fitting Fourier transform, window Fourier transform |
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Table 1. Processing method of each step in star point method
Image | MSE/pixel |
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Centroidmethod | Centroidweightingmethod | Gaussianfittingmethod |
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4(a) | 0.03788 | 0.02577 | 0.01596 | 4(b) | 0.04262 | 0.01927 | 0.00790 | 4(c) | 0.03020 | 0.01688 | 0.00725 | 4(d) | 0.02464 | 0.01197 | 0.01545 | Mean ofMSE /pixel | 0.04721 | 0.01930 | 0.01415 | Runningtime /(10-4 s) | 0.16043 | 0.32019 | 221.09170 |
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Table 2. Comparison of center positioning error and running time of few pixels simulation star point images
Image | MSE /pixel |
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Centroid method | Centroidweighting method | Gaussianfitting method | Edge circlefitting method |
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5(a) | 0.04726 | 0.01988 | 0.00949 | 0.00483 | 5(b) | 0.01066 | 0.01743 | 0.02492 | 0.07244 | 5(c) | 0.02679 | 0.00866 | 0.01578 | 0.08593 | 5(d) | 0.04648 | 0.03029 | 0.01526 | 0.08104 | Mean of MSE /pixel | 0.10909 | 0.09542 | 0.08943 | 0.13456 | Running time /(10-4 s) | 0.96031 | 1.07636 | 793.21601 | 24.89920 |
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Table 3. Comparison of center positioning error and running time of multi-pixel simulation star point images
Image number | MSE /pixel |
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Few pixels star point simulation image | Multi-pixel star point simulation image |
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Hanningwindow method | Gaussianfitting method | Hanningwindow method | Gaussianfitting method | 1 | 0.007805 | 0.006289 | 0.001138 | 0.000619 | 2 | 0.008302 | 0.006626 | 0.001198 | 0.000674 | 3 | 0.008248 | 0.006569 | 0.001136 | 0.000624 | 4 | 0.008812 | 0.007468 | 0.001070 | 0.000578 | 5 | 0.007217 | 0.004632 | 0.001087 | 0.000583 | 6 | 0.008427 | 0.006347 | 0.001115 | 0.000599 | 7 | 0.008521 | 0.006649 | 0.001087 | 0.000582 | 8 | 0.007563 | 0.006480 | 0.001158 | 0.000623 | 9 | 0.009912 | 0.008139 | 0.001122 | 0.000595 | 10 | 0.008378 | 0.006821 | 0.001175 | 0.000645 | Mean of MSE /pixel | 0.008319 | 0.006602 | 0.001129 | 0.000612 |
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Table 4. MSE of MTF obtained by different LSF processing methods under different number of images
Standard deviation of noise | 5 | 10 | 15 | 20 | 25 | 30 | 40 |
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MSE/(10-6 pixel) | 0.008362 | 0.046330 | 0.333800 | 1.075700 | 6.760600 | 31.104400 | 345.573100 |
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Table 5. MSE of MTF under different noise standard deviations
Radius /pixel | 0.9 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 |
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MSE /pixel | 0.185050 | 0.159630 | 0.051070 | 0.021300 | 0.010530 | 0.006654 |
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Table 6. MSE of MTF under different radius of dispersion circles
Device | Parameter | Value |
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Light source | Center wavelength/ nm | 550 | CMOS detector | Cell size/ mm | 0.00345 | Lens | Focal length/ mm | 50 |
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Table 7. Parameters of imaging system
Method | Sharpnessratio | Sensitivity | Mean value /(cycles·pixel-1) |
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Traditional | 5.2758 | 0.3938 | 0.05885 | Proposed | 5.3120 | 0.7322 | 0.06560 |
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Table 8. Index evaluation results