## 3 Analysis of Edge Method Accuracy
### Region of Interest (ROI)  
It is generally believed that the ROI extraction in edge method should ensure the vertical or horizontal edge intersect with the upper-lower sides or the left-right sides of the ROI, respectively, but the position and size of ROI are not considered. In practice, it is found that even when the same edge method is used to measure the same edge image, the MTF results may differ with the size and position of the determined rectangular ROI, which will lead to a lack of robustness. It is necessary to study the accurate constraint conditions of ROI extraction to realize automatic and effective ROI extraction. References [11; 14] verify that extracting any irregular ROI shape with edges does not affect the accuracy of the edge method, thus relaxing the constraint of ROI shape. However, it is more difficult to extract any irregular shape than a rectangle, and the result of irregular extraction is difficult to process, which leads to its limited practicability. Considering the practicality and convenience of data processing, this section still adopts rectangular ROI extraction. According to the analysis results in Sections 3.1 and 3.2, it is necessary to consider the concept of \"the minimum number of effective rows\" (\(R_{min}=1/\tan(\theta)\)) to meet the oversampled binning requirements of edge projection at different angles in order to avoid the empty bin caused by insufficient ROI extraction data. However, in order to ensure the accuracy of the edge method, the height of the actual extracted ROI is usually a multiple of \(R_{min}\). This section mainly analyzes the influence of ROI size, including height (ROI-H) and width (ROI-W) of ROI, on the accuracy of the edge method and provides quantitative suggestions for efficient ROI extraction. In order to analyze the influence of ROI size on the edge method more accurately, the ROI extraction position is determined in the center of the edge image, and the ROI with a specified size is automatically extracted by programming. Since the relevant influencing factors of the edge method have nothing to do with which the improved method is adopted, this section will adopt another improved edge method, OMNI-sin, for fairness. When analyzing the influence of ROI-H, the ratio of ROI-H to the height of the edge image is determined as 0.1-0.99, and the ROI-W is automatically determined according to the intersection of the edge and the upper-lower sides, which extend 5 pixels to both sides, respectively. When analyzing the influence of ROI-W, ensure the same ROI-H, and control the extraction of different ROI-W by the ratio of pixel width extending to both sides to edge image width. In this section, the ROI-H factor is analyzed for 0-45 deg BDE edges (at an interval of 0.5 deg). The measurement results representing different angle types are randomly determined and shown in Figure 11. The simulation results of the influence of ROI-W on the accuracy of the edge method are shown in Figure 12. The MTF(Ref) of the BDE image is as described in Section 3.2. The MTF curves in Figure 11a-f show various intensity divergences in the middle and high frequency, and the higher the frequency, the more obvious the divergence. It proves that the ROI-H has an influence on the accuracy of the edge method. Furthermore, it can be founded that the consistency and accuracy of MTF are relatively higher when the ratio of ROI-H to edge image height is greater than 0.5. The MTF curves in Figure 12a-d show high consistency in all frequency ranges. On the premise of satisfying the minimum width, even if the ROI-W is further increased, the improvement of MTF accuracy will be limited, and the computational cost will be increased. When the uniformity of image quality is poor, the MTFs of different edge regions fluctuate greatly. Multi-MTF measurement can be carried out for multi-regions and multi-ROI-H.