# Modeling and Calculation of Limit Magnitude Detection of Orbital Optoelectric Tracking System
## 1 Introduction  
The optoelectric tracking system is complex, integrating optical imaging technology, precision mechanical technology, electronic technology, precision tracking and control technology, image recognition technology, etc. [1; 2; 3; 4]. It is capable of realizing the rapid detection and recognition of the target and completing its tracking and measurement. With the increasing development of optoelectric imaging technology and the highly automated test technology, it has a wide range of applications in the military, aerospace, industrial monitoring, and other fields [5; 6; 7]. In the shooting range test, it is an important piece of equipment in the testing of parameters for guns and other weapons, and it plays an important role for dynamic target detection and recognition under a complex environment. The optical detection capability constrains its accuracy and the reliability of the tracking, so the evaluation of that is an important component [8; 9; 10]. The evaluation methods can be categorized into the model method, simulation method, and test method. Researchers have carried out some basic discussions and research on the model method, mainly focusing on optoelectric imaging detectors, but there is relatively little research on the influence of the environment, etc. [11; 12]. Based on the basic knowledge of radiance and  
measurement accuracy, strong performance stability, good intuition, and good resistance to ground clutter interference, countries around the world have researched optoelectronic tracking devices since the 1940s. The world's first optoelectronic tracking device of KTH-41 theodolite was successfully developed at the Peenemuende shooting range in Germany in 1940, and was used for the external ballistic trajectory measurement of missiles. The United States from the 1970s on began the study of optoelectronic detection systems, and the White Sands Missile Range developed an intelligent TV tracking system for multi-target tracking in 1974. China developed the first large-scale movies theodolite model 150-1 in 1974, which was successfully tested and approved by the Commission for Science, Technology, and Industry for National Defense. Optoelectric theodolite model 778 was developed in 1985, which is the fourth-generation product of the optical measuring device in the shooting range. Its comprehensive performance has reached a new level of the same kind of instruments in China. This research has provided effective means for the mission of launch, measurement and control, and observation and attitude control in the launch phase of the spacecraft, such as missiles and satellites in the shooting range; at the same time, it can be used for weapon accuracy identification and performance detection in a conventional shooting range. For the detection performance estimation of the optoelectric imaging system, a variety of evaluation theories and models have been proposed [13; 14; 15], which can be mainly classified into three categories. One is based on the [PERSON] criterion [16], without considering the nature of the target and the defects of the image; the corresponding capabilities of the photoelectric imaging system, such as the detection and recognition of the target, are determined by the resolution method of the target equivalent fringe. In order to make up for the shortcomings of the single frequency of [PERSON]'s criterion, various evaluation methods and parameters have also been proposed, such as the modulation transfer function area (MTFA), which considers the image quality relating to the integral of the difference between the modulation transfer function (MTF) and the contrast of the human eye; the integral contrast sensitivity (ICS), which considers the image quality to be a function of the integrals of the quotient for the MTF and the contrast transfer function (CTF); and the square of root integral (SORI), which considers that the image quality is related to the integral of the quotient for the MTF and CTF.