## 5 Experiments and Discussion
### Deviation Analysis of Simplified Method  
Equations (18) and (21) provide the exact solution and the small-angle approximated solution for non-coaxial image motion compensation, respectively. Simulation calculations are required to compare and verify the compensation accuracy and deviation of the simplified approximation method. As the roll axis of the platform rotates from \(-45^{\circ}\) to \(+45^{\circ}\), the camera pitch planning angle \(\theta_{N}\) ranges from \(32^{\circ}\) to \(45^{\circ}\), as determined by the LOS path planning model in Equation (4). Considering attitude disturbances and scanning speed, the roll variation \(\Delta\phi\) during the exposure period remains below \(1^{\circ}\). When the aircraft is aligned with the nadir point, the initial camera pitch angle \(\theta_{start}\) is \(45^{\circ}\). As the roll variation angle \(\Delta\phi\) increases from \(0^{\circ}\) to \(1.5^{\circ}\), planning curves of the compensation angle \(2x\) and pitch angle \(\theta\) for the simplified approximation algorithm and the exact compensation algorithm are shown in Figure 7a,b, while the compensation deviation are shown in Figure 7c,d. As shown in Figure 7, after applying the simplified approximation algorithm, the maximum compensation deviation of the compensation mirror during the roll motion is \(6\times 10^{-5}\), corresponding to \(1\)\(\upmu\)rad. With an instantaneous field of view of \(250\)\(\upmu\)rad, the calculated compensation deviation is better than \(0.004\) pixels, meeting the compensation requirements. Since the simplified compensation algorithm assumes that the camera pitch angle remains equal to its initial value, there exists a certain approximation deviation in the pitch angle during the compensation period. When the deviation reaches \(0.5\) pixels, equivalent to \(0.07^{\circ}\), the roll motion angle is \(1.28^{\circ}\). Therefore, as long as the roll motion remains below \(1.28^{\circ}\) during exposure, the simplified algorithm can achieve effective image motion compensation. Figure 7: Comparison of \(45^{\circ}\) camera pitch angle: (**a**) compensation angle; (**b**) pitch angle; (**c**) compensation angle deviation; (**d**) pitch angle deviation. Figure 7 shows that when the initial pitch angle is fixed, the approximation deviation of the compensation mirror and pitch mirror is positively correlated with the roll variation angle. Therefore, we further analyze the effect of the initial camera pitch angle \(\theta_{start}\) on the simplified compensation algorithm when the roll variation angle \(\Delta\phi\) is fixed. When \(\Delta\phi\) = 1.28\({}^{\circ}\) and \(\theta_{start}\) varies from 30\({}^{\circ}\) to 45\({}^{\circ}\), planning curves of the compensation angle 2\(\kappa\) and pitch angle \(\theta\) for the simplified approximation algorithm and the exact compensation algorithm are shown in Figure 8a,b, while the compensation deviation curves are shown in Figure 8c,d. As shown in Figure 8, when the roll variation angle is fixed, the approximation deviation of the compensation mirror and pitch mirror is positively correlated with the absolute value of the initial pitch angle, although the variation is small. The compensation deviation of the compensation mirror remains around 3 \(\times\) 10\({}^{-5\circ}\), corresponding to an accuracy better than 0.002 pixels, while the compensation deviation of the pitch mirror is approximately 7 \(\times\) 10\({}^{-3\circ}\), corresponding to an accuracy better than 0.5 pixels. In summary, during camera scanning imaging, the maximum compensation deviation occurs when imaging at a 45\({}^{\circ}\) squint view of the ground point. However, as long as the roll variation angle remains below 1.28\({}^{\circ}\) during image motion compensation, the simplified approximation compensation method can be applied to achieve backward-squint image motion compensation.