## 5 Experiments and Discussion
### Image Motion Compensation Simulation
This is due to the fact that the scanning speed at this time is 40\({}^{\circ}\)/s (0.7 rad/s), while the speed-to-height ratio is 0.04 rad/s. Under such conditions, rotational motion is identified as the primary cause of boundary point displacement. Even with compensation, a certain degree of image rotation still occurs. This issue is inherent in two-axis cameras during the scanning process and is discussed in detail in Section 5.5. The time-varying ground projection coordinates of each boundary point during the compensation period were recorded at 5 ms intervals, as listed in Table 1.  
Based on these coordinates, the deviations at each time step were calculated, and the root mean square (RMS) deviations were summarized in Table 2. The maximum RMS deviation within the 5 ms intervals was 1.4445 m, and the minimum was 1.0950 m. The average deviation per millisecond was 1.26 m/ms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Time (s)** & **Point (a)** & **Point (b)** & **Point (c)** & **Point (d)** \\ \hline
0 & (2571.311, 240.951) & (3500.160, 281.122) & (2571.311, \(-\)240.951) & (3500.160, \(-\)281.122) \\
0.005 & (2572.030, 241.769) & (3501.352, 280.310) & (2570.436, \(-\)240.173) & (3499.182, \(-\)281.998) \\
0.010 & (2572.752, 242.586) & (3502.542, 279.495) & (2569.562, \(-\)239.393) & (3498.199, \(-\)282.872) \\
0.015 & (2573.481, 243.406) & (3503.734, 278.673) & (2568.688, \(-\)238.609) & (3497.209, \(-\)283.748) \\
0.020 & (2574.222, 244.234) & (3504.936, 277.839) & (2567.807, \(-\)237.814) & (3496.202, \(-\)284.632) \\
0.025 & (2574.955, 245.049) & (3506.120, 277.015) & (2566.940, \(-\)237.029) & (3495.207, \(-\)285.502) \\
0.030 & (2575.683, 245.855) & (3507.291, 276.196) & (2566.083, \(-\)236.252) & (3494.219, \(-\)286.362) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ground projection trajectories of boundary points over the compensation period. Figure 15: Ground projection positions of boundary points: (**a**) upper; (**b**) right; (**c**) left; (**d**) lower. The ground displacement deviations of each boundary point were converted into angular deviations and then projected onto the image plane based on the focal length. The residual image motion deviations after compensation are summarized in Table 3. At a scanning speed of 40\({}^{\circ}\)/s and a speed-to-height ratio of 0.04 s\({}^{-1}\), during backward-squint imaging at a 45\({}^{\circ}\) viewing angle, the maximum image motion deviation speed on the sensor plane was 3.06 \(\upmu\)m/ms. If the image motion permitted was one-half the size of one pixel, the maximum allowable integration time was 1.96 ms. Considering a total scanning field of view of 90\({}^{\circ}\), the scanning interval was set from \(-\)40\({}^{\circ}\) to 40\({}^{\circ}\). Figure 16 shows the ground-projected FOV corresponding to scanning angles from 0\({}^{\circ}\) to 40\({}^{\circ}\). It can be observed that the central viewing line remains aligned along the same horizontal direction, demonstrating stable pointing performance. To further analyze the compensation performance at different scanning angles under the given pitch tilt condition, the same method was applied to evaluate the compensation \begin{table}
\begin{tabular}{c c c c c} \hline
**Time (s)** & **Point (a)** & **Point (b)** & **Point (c)** & **Point (d)** \\ \hline
0.005 & 1.0891 & 1.4426 & 1.1712 & 1.3131 \\
0.010 & 1.0906 & 1.4422 & 1.1705 & 1.3148 \\
0.015 & 1.0970 & 1.4478 & 1.1747 & 1.3225 \\
0.020 & 1.1112 & 1.4630 & 1.1866 & 1.3399 \\
0.025 & 1.0958 & 1.4425 & 1.1692 & 1.3214 \\
0.030 & 1.0859 & 1.4288 & 1.1573 & 1.3097 \\ \hline
**RMS (m)** & 1.0950 & 1.4445 & 1.1716 & 1.3203 \\ \hline \end{tabular}
\end{table} 
Table 2: RMS deviations of ground projection boundary points. Figure 16: Ground-projected field of view at roll angles from 0\({}^{\circ}\) to 40\({}^{\circ}\). effect at each angle. The image-plane motion deviation speeds of the four ground boundary points were plotted, as shown in Figure 17a.