钠信标光斑大小及回光数研究

钠信标已经成为地基大口径望远镜自适应光学系统的必要组成部分。钠信标光斑大小和回光数是影响自适应光学系统性能的关键因素，从发射角度考虑，主要由激光到达钠层时功率密度分布和耦合效率共同决定。为了准确估计钠信标光斑大小和回光数，首先建立了激光在大气中传输的模型，通过分析激光发射望远镜口径和上行路径大气湍流对激光到达钠层功率密度分布的影响，得出优化激光发射望远镜口径的普适方法；然后根据激光通过发射望远镜后到达钠层的功率密度与耦合效率的关系，计算钠信标光斑大小和回光数；最后利用探测误差和时域误差作为评价指标，计算了系统的最优采样频率。研究结果表明，针对丽江高美古天文台大气条件（大气相干长度（r0@550 nm）中值为7~9 cm），激光发射望远镜口径最佳值为300 mm，此时产生的光斑最优；当r0为9 cm，激光器采用中国科学院理化技术研究所20 W级百微秒脉冲激光器并利用D2a+D2b双峰泵浦激发钠原子时，产生的钠信标回光数为1.3107 photonss-1m-2，光斑大小为0.6，最优的采样频率为900 Hz。

Study on spot size and photon return of a sodium laser guide star

The sodium laser guide star facility has become one of the most important subsystems of adaptive optics system for large ground-based telescope. Spot size and photon return of the sodium laser guide star are the main factors that affect the performance of an adaptive optics system, both of which depend strongly on the laser power density distribution at the sodium layer and the coupling efficiency of the laser. In order to accurately estimate the photon return and spot size, a model was established for laser propagation in atmosphere and the effect of laser launch telescope's diameter and turbulence in the uplink path on the power density distribution was analyzed. A general technique to optimize the laser launch telescope's design was devised. Then the spot size and photon return according to the relationship between the power density and the coupling efficiency were calculated. By minimizing measurement error and temporal error, an optimal sampling frequency was obtained. The researching results show that, for atmosphere condition at Gaomeigu Lijiang (median value of Fried parameter (r0) is 7 to 9 cm at a wavelength of 550 nm), the minimum spot size occurs when the diameter of the laser launch telescope is 300 mm. For an r0 value of 9 cm and at a laser power of 20 W with D2a+D2b re-pumping, the photon return of the sodium laser guide star is expected to be 1.3107 photonss-1m-2 and the spot size is 0.6. The optimal sampling frequency is around 900 Hz.