# Research on Large Divergence Angle Laser Ranging System +
## 1 Introduction  
As of 19 February 2025, there are 13,810 operational satellites in orbit globally--a dramatic increase from just 4852 satellites recorded at the end of 2021. According to a report by Euroconsult, the number of satellites in orbit is projected to grow by 17,000 by 2030, representing a fourfold increase compared to the past decade. Additionally, ABI Research, a global technology intelligence firm, estimates that the total number of active low Earth orbit (LEO) satellites will surge from 7473 in 2023 to approximately 42,600 by 2032. The surge in on-orbit satellites heralds the rapid development of applications such as satellite networking, navigation, exploration, remote sensing, and countermeasures. This growth is shifting the demand for spaceborne ranging from traditional long-distance satellite-to-ground measurement to close-range inter-satellite ranging.  
As a high-precision measurement tool, laser rangefinders play an indispensable role in the aerospace field. The characteristics of high precision, high speed, and non-contact measurement make it a crucial device for precise distance measurement, navigation, detection, and monitoring in aerospace missions. The application of aerospace laser rangefinders is significant in enhancing the navigation accuracy of spacecraft and ensuring the safety of aerospace missions.  
Unlike common applications such as vehicle-mounted, ground-based, or individual use scenarios, laser ranging equipment for aerospace applications often measures targets that are in high-speed motion and have extremely small reflective cross-sections, with a considerable relative velocity between the measuring platform and the target, reachingup to 15 km/s. The entire satellite not only moves around the Earth under the action of the Earth's gravitational force, but its orbit will also be affected by other disturbing forces [1]. The high relative motion between the platform and the target makes alignment challenging during the ranging process. Therefore, how to observe and track targets under such conditions of relatively high-speed motion is a key technical issue that needs to be addressed in the future development of space-based satellites.  
The relationship between the true value of the probability of laser ranging and the illumination probability and detection probability is represented as  
\[p_{ra}=p_{i}\times p_{d} \tag{1}\]  
In the equation, \(p_{ra}\) represents the true probability, which is the probability of accurately measuring the real distance to the target. \(p_{i}\) denotes the illumination probability, which is the probability that the entire target cross-section is illuminated by the laser when aimed and fired at the target. \(p_{d}\) is the detection probability, which is the probability of detecting the target when the entire cross-section is illuminated by the laser. The illumination probability is dependent on the aiming error, which includes both random errors and systematic errors [2]. Detection probability relies on the detection capability of the laser rangefinder and its signal processing performance, while illumination probability is directly related to the system's aiming performance or the size of the laser spot on the target. High-precision aiming and tracking systems tend to be heavier and bulkier; thus, increasing the size of the laser spot on the target and enhancing the divergence angle of the laser beam emitted by the rangefinder is a more cost-effective solution.