基于温度场理论的望远镜主镜视宁度及“气刀”效应分析

Telescope Primary Mirror Seeing and Air Knife Effect Analysis Based on Theoretical Calculation of Temperature Field

综合考虑非线性气温环境和主镜视宁度表面"气刀"强制对流换热,对地基望远镜主镜瞬态温度场理论模型进行研究,结合分离变量法和格林函数法求解出温度场的解析表达式。以4m主镜为例,运用温度场理论模型解析解,对主镜视宁度进行了分析计算。分析了"气刀"对主镜视宁度的改善效果;讨论了"气刀"风速与主镜视宁度的关系;分析了不同径厚比对主镜视宁度的影响。利用有限元方法分析4m主镜温度场,与所推导的温度场理论结果进行比较,二者获得了较好的一致性。主镜温度场理论解在望远镜主镜设计中具有普适的应用价值。

The theoretical model in temperature field based on primary mirror of ground based telescope with the condition of non-linear ambient temperature and forced air flow upon the optical surface is analyzed. The analytical solution is gotten by separation of variables and Green function method. Take 4-m primary mirror as an example, the value of mirror seeing is caculated and anylised by using analytical solution of temperature field theory model. The effect of air flow upon the primany mirror seeing is discussed. The relationship between mirror seeing and air flow velocity upon the primary mirror is studied. Primary mirror seeing is analyzed with different ratios of mirror′s diameter to thickness. The temperature field of primary mirror of 4-m diameter is also studied by finite element method. The analytical solution is highly consistent with the solution of finite element method. The analytical solution of temperature field model has universal application value in designing telescope primary mirror.