## 5 Comparative Experiments and Discussion  
### Simulation: Proposed Method vs. Other Methods  
The Mod edge method is compared with the four representative edge methods used in the previous simulation analysis. The 0-45 deg BDE images are used for testing, and the MTF results of five methods at 0, 0.1, 0.2, 0.3, 0.4, and 0.5 lp/pix are compared. The simulation results are shown in Figure 17.  
Figure 17: Simulation comparison: proposed method vs. other methods at specific SF points: (**a**) when SF is 0 lp/pix, (**b**) when SF is 0.1 lp/pix, (**c**) when SF is 0.2 lp/pix, (**d**) when SF is 0.3 lp/pix, (**e**) when SF is 0.4 lp/pix, (**f**) when SF is 0.5 lp/pix (Nyquist frequency).  
It can be seen from Figure 17a-f that the robustness of Mod, ISO, and ISO-cos edge methods in all frequency ranges is better than that of OMNI and OMNI-sin edge methods. However, the performance superiority of Mod is not obvious compared with ISO-cos because the test image is noiseless and the image quality uniformity in different areas is high. On the premise of ensuring the accuracy of MTF measurement, the Mod edge method mainly solves the problem of weak robustness caused by the complicated image quality. In addition, it can be clearly observed from Figure 17 that the data volatility of MTF results measured by the OMNI edge method is the greatest; that is, the possibility of abnormal measured values is the greatest. This also indirectly verifies the analysis conclusion in the second paragraph of Section 2.3 and Figure 1; that is, the accuracy of ISO-cos projection binning strategy is superior to OMNI projection binning strategy in principle. However, the data volatility of OMNI-sin measurement results is lower than that of the OMNI method because the variable OSR model with stronger adaptability improves the stability of MTF measurement to some extent.  
Referring to the simulation process in Figure 6e-h, the simulation results according to the Mod edge method are shown in Figure 18. Comparing the smoothness and continuity of the polar coordinate curves of Figures 18 and 6e-h, it can be seen that the multidirectional MTF measurement of the Mod edge method is more robust.  
The analysis in Section 3.5 shows that when the SNR of the edge image is greater than 10 dB, the MTF result is reliable. Therefore, in order to further verify the performance of the Mod edge method, the simulated BNDE image with an SNR of 12.6 dB is used for MTF measurement, and the simulation result is shown in Figure 19.  
It can be seen from Figure 19a-d that when there is noise in the image, the MTF measurement robustness of the Mod edge method in the whole frequency ranges is higher than that of ISO, ISO-cos, OMNI, and OMNI-sin edge methods, especially in the high frequency ranges, which proves that Mod edge method has certain anti-noise ability and stronger engineering practicability. When the image SNR is less than 10 dB, how to ensure the effectiveness of MTF measurement by edge method remains unsolved, and further research is needed to expand the application scope of the edge method.  
Figure 18: MTF for different tilt angle BDE images vary from 0.20 deg to 44.5 deg (the angle interval is 0.50 deg) in polar coordinates using Mod edge method.