## 4 Results
### OCPSI Mode Simulation  
Assuming that the OCPSI satellite runs on the 500-km circular sun-synchronous orbit, the satellite sub-satellite point velocity \(V_{s}\) is 7.057 km/s from Equation (9). For the camera, we use a single-chip CMOS detector. The detector center is on the optical axis. It is modeled with \(f=360\) mm, \(a=2.5\) um, \([5120\times 5120]\), \(N=10\), \(\alpha=30^{\circ}\). Here \(f\) is the focal length, \(a\) is the pixel size, \([5120\times 5120]\) is the resolution, and \(N\) is the number of imaging frames in the pendulum scanning hoop. According to Equations (6) and (7), we calculate \(r_{N}=546\) km, \(r_{1}=277\) km. To guarantee the stitching is leakless in this mode, we set the overlap rate of the cone scanning hoop, the overlap rate between the pendulum scanning frames, and the overlap rate between the pendulum scanning periods to be 10%. Then, the cone scanning angular velocity is \(\omega_{s}=0.1831\) rad/s, the cone scanning period \(T_{s}=34.3175\) s, the pendulum scanning angular velocity \(\omega_{c}=1.8193\) rad/s, and the pendulum scanning period \(T_{pend}=0.3166\) s. The simulation results are shown in Figure 20. The black box in the figure is valid data, and it can be observed that there is no leakage in the coverage. As shown in Figure 20, the maximum width can reach 1092 km, the effective width can reach 1060 km, and the effective efficiency can reach 97%, but it can be seen that the overlap is very high. According to Equations (26)-(33), we get the exposure time \(t_{e}=3.79\) us. For remote sensing missions, the ground sampling distance (GSD) is an important mission indicator. The \(GSD\) is  
\[GSD=\frac{al}{f} \tag{43}\]  
where \(l\) is the distance between the satellite and the ground sampling point. According to the above indicators, we get the GSD of 4.06-5.28 m. Therefore, it can be seen that the OCPSI mode can reach a coverage width of the order of 1000 km at the ground sampling distance of 5.3 m.  
In order to obtain higher quality images and improve data utilization, a dual-camera variable speed OCPSI mode is designed according to the principle proposed in Section 3.2. According to Equations (34) and (35), we obtain that the cone scanning angular velocity of the dual-camera variable speed OCPSI mode is 0.0915 rad/s and the cone scanning period is 68.635 s. Then, according to Equations (36)-(38), we obtain the pendulum motion angular velocity and exposure time of the dual-camera variable speed OCPSI mode, as shown in Figures 21 and 22. The pendulum motion angular velocity is reduced to 0.63-1.06 rad/s, and the exposure time is increased to 6.4-11.2 us. This imaging mode reduces the overlap of each frame of images by changing the angular speed of the cone scanning to reduce the amount of data and improve the effective coverage of images. Therefore, the ground coverage simulation of this mode is shown in Figure 23.  
Figure 21: Dual-camera variable speed OCPSI mode: pendulum motion angular velocity. Figure 20: Single-camera constant Speed OCPSI mode ground cover simulation. According to Figure 23, it can be seen that the ground coverage overlap is significantly reduced, but the effective width is 966 km, which is 100 km lower than that of the single-camera constant speed OCPSI mode. Table 1 shows that dual-camera variable speed OCPSI mode effectively reduces cone scanning angular velocity and pendulum motion angular velocity. This mode improves the exposure time and image quality. However, it can be seen from Figures 20 and 23 that the ground coverage width of the dual-camera variable Speed OCPSI mode is reduced by 100 km. When the effective coverage along the track direction reaches the same range, single-camera constant speed OCPSI mode requires four cone scanning rings, while dual-camera variable speed OCPSI mode requires six cone scanning rings. Figure 23: Dual-camera variable speed OCPSI mode ground cover simulation. Figure 22: Dual-camera variable speed OCPSI mode: exposure time.