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.