Optimizing the location of multiple laser guide stars in ground layer adaptive optical systems

At present, the ground layer adaptive optical systems are using multiple laser guide stars arranged in regular polygons as reference targets to measure the effects of atmospheric turbulence. Obtaining the optimal position of laser guide stars becomes an interesting problem to analyze. This paper proposes a method to obtain the optimal position of laser guide stars by using a genetic algorithm as the optimization algorithm and a simplified geometry model of the ground layer adaptive optic system as the evaluation function. Furthermore, multi-process, Numba library, and multi-thread techniques methods are used to accelerate calculation speed. Based on these methods, real atmospheric turbulence profiles are used to analyze the relationship between the optimal position of laser guide stars with different numbers and the different atmospheric turbulence profiles from the same site, through an example of a ground layer adaptive optics system with 14 arcmin field of view. The results show that the optimal position of laser guide stars in the same site is almost the same and their statistically optimal positions are all regular polygon. Besides, we also find that the spatial resolution of turbulence profiles has strong effects to positions of laser guide stars, showing that the more equivalent layers in the measurement results, the closer the position distribution of laser guide stars is to the regular polygon.