## 5 Conclusions  
In this paper, we address the limitations of existing sub-pixel edge detection and ESF curve extraction algorithms, specifically their low accuracy and high error rates. Through simulation experiments, we generate ideal computer-generated slanted-edge images and introduce varying levels of noise to assess the algorithms' performance. We focus on comparing the accuracy and stability of different methods for calculating the angle in the slanted-edge technique. Furthermore, we examine the impact of the OSR on the method's measurement accuracy and propose an adaptive model based on the optimal OSR. This  
Figure 19: Nyquist MTF at different angles in laboratory testing.  
Figure 18: Images of slanted-edge targets at different angles: (**a**) slanted-edge angle of 3\({}^{\circ}\); (**b**) slanted-edge angle of 7\({}^{\circ}\); (**c**) slanted-edge angle of 8\({}^{\circ}\); (**d**) slanted-edge angle of 10\({}^{\circ}\); (**e**) slanted-edge angle of 14\({}^{\circ}\); (**f**) slanted-edge angle of 20\({}^{\circ}\).  
model adjusts the sampling rate according to the edge angle, enhancing its applicability across a broader range of angles. Additionally, we employ higher-order polynomial edge fitting to mitigate the effects of spatial aberrations and image noise more effectively.  
This paper subsequently analyzes the image factors influencing the slanted-edge method's calculations. Specifically, it analyzes how the slanted-edge angle, ROI, contrast, and SNR impact the method's accuracy. These factors are quantitatively assessed as constraints of the slanted-edge method through simulation experiments. The simulation results show that when the slanted-edge angle is between 6\({}^{\circ}\) and 12\({}^{\circ}\), the relative error between the calculated value and the theoretical value is within 0.01, which indicates that when the slanted-edge angle is between 6\({}^{\circ}\) and 12\({}^{\circ}\), the slanted-edge method has the best stability in the solving results, and it is a more ideal range of the slanted-edge angle. The ROI of slanted-edge height is at least 30 pixels, and the slanted-edge width is selected based on the principle of including as large a bright and dark area as possible. The SNR of the slanted-edge image significantly influences the results of MTF calculations. As the SNR decreases, there is a rapid decline in calculation accuracy. Conversely, contrast has a minimal impact on MTF calculation accuracy, with results maintaining a high level of precision even when the contrast ratio decreases to 0.3. To ensure optimal calculation results, it is imperative to maintain an SNR greater than 30 dB for the slanted-edge image, along with a contrast ratio exceeding 0.3.  
At present, the selection of the ROI for slanted-edge images remains a manual process in this paper. Future advancements may involve the integration of neural networks or feature recognition techniques to intelligently automate the selection of the effective ROI. Factors such as atmosphere and motion blur that cause MTF attenuation in photoelectric imaging systems can be added to the subsequent analysis to make it more universally applicable, further improve the algorithm, and increase the computational accuracy. In this paper, we use both simulation and laboratory experiments for algorithm validation and accuracy analysis, which can be followed by on-orbit experiments using real on-orbit image data for further evaluation.  
Conceptualization, J.Y. and Y.Z.; methodology, J.Y.; software, J.Y. and B.Q.; validation, J.Y., X.B. and W.W.; formal analysis, H.L.; data curation, J.Y.; writing--original draft preparation, J.Y.; writing--review and editing, Y.Z., B.Q. and X.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data Availability Statement: Data is contained within the article.  
The authors declare no conflict of interest.