大气Refractive Index的气压指数模型：入射光瞳的天顶距和二阶像差
A Barometric Exponential Model of the Atmosphere's Refractive Index: Zenith Angles and Second Order Aberration in the Entrance Pupil
摘要：
本报告模拟了望远镜场地上方大气层的折射率，折射率（磁化率）随高度呈指数衰减。空气被表示为围绕曲面的球形外壳。我们计算（i）差分天顶距--光线到达望远镜时的实际天顶距与没有大气的假设天顶距之间的差--以及（ii）光线到达入射光瞳时的光程长度分布作为到光瞳中心的距离的函数。在这项工作中的关键技术是扩展一些积分-这取决于折射率分布沿着弯曲的路径的每一条射线从一些虚拟平面在恒星的方向上的入射光瞳-在幂级数的小参数。
英文摘要：
This report models the refractive index above a telescope site by an atmosphere with exponential decay of the refractive index (susceptibility) as a function of altitude. The air is represented as a spherical hull around the surface. We compute (i) the differential zenith angle -- the difference between the actual zenith angle at arrival of rays at the telescope and a hypothetical zenith angle without the atmosphere -- and (ii) the optical path length distribution of rays at arrival in the entrance pupil as a function of the distance to the pupil center. The key technique in this work is to expand some integrals -- that depend on the refractive index profile along the curved path of each ray from some virtual plane in the direction of the star up to the entrance pupil -- in power series of small parameters.
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