Analysis of laser spot centroiding errors for laser acquisition system in gravitational wave detection missions

In space-based gravitational wave detection, establishing ultra-long-distance and ultra-high-precision laser links between satellites is achieved through the laser acquisition and tracking system. The laser spot centroid positioning method, which offers low computational complexity and strong adaptability to beam shape, is currently the core measurement method during the laser acquisition phase. However, due to various interference factors encountered in practical tests, this algorithm often falls short of meeting the extremely high requirements. To address this challenge, this paper first defines the specific performance criteria for the centroid positioning method based on the needs of laser acquisition in gravitational wave detection. It then comprehensively analyzes how detector noise, window truncation effects, and beam wavefront aberrations impact the accuracy of angular measurements. Using derived analytical expressions, an improved centroiding algorithm is proposed to mitigate the effects of detector noise and wavefront aberrations simultaneously. Numerical simulations are conducted to design the specific parameters for the algorithm and the system, resulting in the ability to achieve an angular measurement accuracy of 60 nrad at the telescope front end.