## 3 The Design of OCPSI Mode
### Dual-Camera Variable Speed OCPSI Mode  
In order to reasonably plan the coverage area, reduce the overlap rate, improve the image utilization rate, reduce the pressure on the onboard data storage subsystem and data transmission subsystem, and, at the same time, reduce the requirements for the attitude control capability of the micro-nanosatellite, the dual-camera variable speed OCPSI mode is proposed. This working mode has the advantages of the single-camera constant speed OCPSI mode, and improves some of its shortcomings. To put it simply, this working mode uses two single-chip CMOS optical cameras to distribute both sides of the satellite with the satellite nadir axis as the center. When the satellite performs cone scanning motion, the two optical cameras simultaneously perform forward or backward pendulum scanning imaging. The sub-satellite velocity of the satellite has been calculated in Section 3.1. Then, we deduce the satellite cone scanning velocity through the dual cameras. At the initial moment, the ground coverage on the left side of the sub-satellite point is Camera 1, and the ground coverage on the right side of the sub-satellite point is Camera 2. The ground coverages of Camera 1 and Camera 2 are shown in Figure 13. The blank part of Camera 1 in the dual-camera variable speed OCPSI mode is filled by Camera 2, as shown in Figure 14.  
Figure 12: The schematic diagram of the OCPSI ground coverage. The advantage of dual-camera variable speed OCPSI mode is that, firstly, it can offset the moment of inertia generated by the camera's swing, helping the micro-nanosatellite to adjust the attitude control. Secondly, the coverage areas of Camera 1 and Camera 2 are filled with each other, which can reduce the cone scanning velocity and the pendulum scanning velocity, thereby increasing the exposure time. At this time, the cone scanning motion period is  
\[T_{s}=\frac{(1-\eta)\times 2(r_{N}-r_{1})}{V_{s}} \tag{26}\]  
The cone scanning angular velocity is reduced to  
\[\omega_{s}=\frac{2\pi}{T_{s}}=\frac{\pi V_{s}}{(1-\eta)\times(r_{N}-r_{1})} \tag{27}\]  
In order to improve the efficiency of the working mode and save the system performance, the mode is optimized by turning off some cameras and variable velocity design for some specific time periods. First, we focus on a period of time after the start of the initial moment, and the ground cover image is shown in Figure 15. As shown, the ground cover on the swing outward is completely overlapped. Therefore, we designed the dual-camera variable speed OCPSI mode when the camera is turned off when it swings inward, and the camera is turned on for imaging when it swings outward. This can reduce the overlapping area and improve the effective utilization of the image. Figure 14: Dual-camera OCPSI mode overlay schematic: merging. Figure 13: Dual-camera OCPSI mode overlay schematic: separate. In Figure 15, zooming in on the coverage area, the ground cover on the right has leaks, while the ground cover on the left has overlap. After the analysis, due to the indeterminate direction of the instantaneous linear velocity generated during the cone scanning, the ground on the left side is covered. That is to say, when the instantaneous linear velocity of the cone scanning is in the same direction as the velocity of the sub-satellite point, it will lead to the leakage of the ground cover during the two cycles of the pendulum scanning imaging, while the ground cover on the right side is the opposite. We have designed the variable speed mode. When the instantaneous linear velocity of the cone scanning is consistent with the direction of the sub-satellite point velocity, we reduce the pendulum scanning speed. When the instantaneous linear velocity of the cone scanning is opposite to the velocity at the sub-satellite point, we increase the sweep velocity. Figure 16 is the ground coverage image at time \(t_{n}\).