# Modeling and Calculation of Limit Magnitude Detection of Orbital Optoelectric Tracking System
## 2 Orbital Optoelectric Tracking System Design  
### Basic Principle of Orbital Optoelectric Tracking System  
The orbital optoelectronic tracking system is mainly composed of the imaging plane of the CCD camera, the optical lens, the camera rotation mechanism, and the image transmission and processing module. The imaging plane of the CCD camera is mainly used to capture the dynamic target information in the optical field-of-view; the optical lens of different focal lengths is mainly used to detect the target at different distances; and the camera rotating mechanism is mainly used to make the camera obtain the target imaging information at each moment on the trajectory, which is connected with the rotating axis of the CCD camera. The camera is controlled by an external clock for synchronization imaging in the process of the target's movement on the predetermined track, and achieves real-time tracking. Figure 1 is the principle schematic diagram of the orbital optoelectric tracking system.  
Assuming that point A is the starting position of the target's movement, point B is the stopping position of the target's movement, and \(AB=s\), \(O\) is the position of the optical center of the tracking system at the initial moment; \(O^{\prime}\) and \(O^{\prime\prime}\) are the positions of the optical centers at two moments in the tracking process, and under ideal conditions, the optical centers of the three moments are the same. The three different moments represent the relationship between the tracking platform and the orbital target. The point \(H\) is the middle position of the tracked track, and \(P_{1}\), \(P_{2}\), and \(P_{3}\) are the camera imaging position relationships between the three states in the tracking process.  
The indexes \(i\) and \(n\) are the serial numbers of the tracked target position. It is assumed that \(\theta_{i}\) and \(\theta_{n}\) are the uniform control angles of the tracking platform from No. \(i\), and \(s_{i}\), \(s_{i-1}\), and \(s_{n}\) are the displacement of the target, which is the tracking location of the rotating optical lens.  
If the speed of the target movement is \(v\), under the premise of the known theoretical trajectory length, the theoretical trajectory is divided into a series of displacements according to equal unit time, i.e., a time-division trajectory is carried out within the orbital distance of \(s\). The functional relationship between the displacements \(s_{i}\) and the total length \(s\) is \(s=\sum\limits_{i=1}^{n}s_{i}\). Assuming that during the unit time \(\Delta t\), the theoretical rotating angle of the target relative to the observation point of the tracking platform is \(\theta_{i}\) for the entire trajectory of the target, the total rotating angle of the optical axis is \(\theta=\sum\limits_{i=1}^{n}\theta_{i}\). Based on the above analysis, in order to meet the target tracking conditions, it is only necessary to make the tracking system rotate to the corresponding theoretical angle in each unit time; the ballistic target can be tracked with time-division, the corresponding moment image of the target on the orbital can be monitored, and the corresponding parameter information can be provided by image processing.  
Figure 1: Schematic diagram of orbital optoelectric tracking system.  
From the principle of orbital optoelectronic tracking, it can be seen that in order to stably track the target under each moment on the entire predicted ballistic line, it is necessary that the detection ability of the optoelectronic detector should be sufficient. Otherwise, it is easy to lose the tracking at the different tracking distances.