## 5 Experiments and Discussion
### Image Motion Compensation Simulation
It can be observed that the image motion deviations of the upper boundary point a and the lower boundary point d increased with the scanning angle, while those of the left point c and right point b decreased. The residual image motion deviation after compensation ranged from 1.9 \(\upmu\)m/ms to 3.1 \(\upmu\)m/ms. Figure 17b illustrates the relationship between the maximum allowable exposure time and the scanning angle. Influenced by the residual image motion of boundary points a and d, the maximum exposure time at a scanning angle of 45\({}^{\circ}\), with a scanning speed of 40\({}^{\circ}\)/s and a speed-to-height ratio of 0.04, was determined to be 1.7 ms. Overall, the variation in scanning angle introduced a residual deviation fluctuation of approximately 0.6 \(\upmu\)m/ms. In the previous analysis, the rotational component of the scanning motion was identified as the primary contributor to the compensation deviation. Figure 18 further illustrates the impact of different scanning speeds on the performance of the proposed compensation method. As shown in the figure, the residual image motion on the focal plane gradually decreases with reduced scanning speed, allowing for longer exposure durations. Figure 18e shows that when the scanning speed is 20\({}^{\circ}\)/s, the maximum residual image motion on the focal plane is 1.9 \(\upmu\)m/ms, allowing for a maximum exposure time of 3.2 ms. At a reduced scanning speed of 10\({}^{\circ}\)/s, as illustrated in Figure 18g, the residual further decreases to about 1 \(\upmu\)m/ms, extending the maximum exposure time to approximately 6 ms. These results demonstrate that lower scanning speeds significantly improve the compensation effect by reducing residual image motion and extending allowable exposure time. Figure 17: Focal plane compensation residuals and maximum exposure time under varying scanning angles: (**a**) residual image motion velocity; (**b**) maximum exposure duration. Through the above analysis, it can be concluded that the aircraft platform velocity also has a certain impact on the proposed compensation method. Under fixed tilt angle and scanning speed conditions, simulations were conducted across a typical range of speed-to-height ratios (0-0.1) commonly used in airborne imaging. The variations in residual image motion compensation deviations on the focal plane with respect to the speed-to-height ratio are shown in Figure 19. As the ratio increases, the residual deviations of the right boundary point b and the left boundary point c gradually increase, while those of the upper point a and the lower point d gradually decrease. The overall variation remains within 0.3 \(\upmu\)m/ms, indicating that the influence of platform speed on compensation performance is relatively small when the scanning speed is high. These results demonstrate the robustness of the proposed method in compensating for forward motion-induced image shifts. Further investigation into the impact of the pitch tilt angle on the effectiveness of image motion compensation, simulations were conducted within the typical range of 20\({}^{\circ}\) to 45\({}^{\circ}\), under identical parameter conditions and a fixed scanning speed of 40\({}^{\circ}\)/s. Figure 20 illustrates the variation of focal plane residual deviation and maximum exposure time with respect to the pitch tilt angle under different scanning angles. As shown in the figure, the residual deviation on the focal plane exhibits noticeable changes with varying pitch tilt angles. When the pitch tilt angle is 20\({}^{\circ}\), the residual deviation across different scanning angles is approximately 1.2 \(\upmu\)m/ms, allowing for a maximum exposure time of about 4.5 ms. As the pitch tilt angle increases to 45\({}^{\circ}\), the residual deviation  
Figure 19: Variations in focal plane residual compensation deviation under different scanning speeds and speed-to-height ratios: (**a**) \(\omega=40^{\circ}\)/s; (**b**) \(\omega=30^{\circ}\)/s; (**c**) \(\omega=20^{\circ}\)/s; (**d**) \(\omega=10^{\circ}\)/s.