论文标题
由于大气折射而导致的横向移位的计算
Computation of the lateral shift due to atmospheric refraction
论文作者
论文摘要
大气折射会改变天空中物体的明显位置。我们计算了用于短距离应用（例如波前传感和流星轨迹）的横向翻译。我们旨在计算每个高度处的横向移位，并根据气象条件和观察部位的位置研究其变异。我们还特别注意这种侧向转移的色谱。我们从光线路径的几何图形跟踪中提取了折射的变化方程。数值方法和干燥的气氛模型使我们能够数值整合耦合方程式系统。除此之外，基于泰勒的扩展，我们还建立了三个横向移位的分析近似，其中之一是文献中已经知道的一个。我们将三个近似值与数值解决方案进行了比较。所有这些估计器都包含在Python 3.2软件包中，该软件包可在线获得。使用数值积分估计器，我们计算了任何天顶角的横向移位值，包括低海拔。该偏移通常在45°的天顶角约为3 m左右，在65°下为10 m，在85°时甚至300 m°。接下来，研究横向移位随波长的函数的变异性显示可见的和近红外的差异高达2％。对每个近似值的误差的分析显示了三个估计值的有效性范围是天顶角的函数。平坦的地球估计器的相对误差小于1％，高达55°，而新的扩展二阶估计器可改善该结果高达75°。平坦的地球估计量足以适用于天顶角低于55°的应用，但是对于低海拔的流星轨迹估算了精制估计器。
Atmospheric refraction modifies the apparent position of objects in the sky. We computed the lateral translation that is to be considered for short-range applications, such as wavefront sensing and meteor trajectories. We aim to calculate the lateral shift at each altitude and study its variation according to meteorological conditions and the location of the observation site. We also pay special attention to the chromatism of this lateral shift. We extracted the variation equations of refraction from the geometric tracing of a light ray path. A numerical method and a dry atmosphere model allowed us to numerically integrate the system of coupled equations. In addition to this, based on Taylor expansions, we established three analytic approximations of the lateral shift, one of which is the one already known in the literature. We compared the three approximations to the numerical solution. All these estimators are included in a Python 3.2 package, which is available online. Using the numerical integration estimator, we calculated the lateral shift values for any zenith angle including low elevations. The shift is typically around 3 m at a zenith angle of 45°, 10 m at 65°, and even 300 m° at 85°. Next, the study of the variability of the lateral shift as a function of wavelength shows differences of up to 2% between the visible and near infrared. The analysis of the errors of each approximation shows the ranges of validity of the three estimators as a function of the zenith angle. The flat Earth estimator achieves a relative error of less than 1% up to 55° while the new extended second-order estimators improves this result up to 75°. The flat Earth estimator is sufficient for applications where the zenith angle is below 55° but a refined estimator is necessary to estimate meteor trajectories at low elevations.
