Ray Tracing Methods for Calculation of Atmospheric Refraction.

摘要

Equations for tracing rays through an atmospheric medium of continuously variable refractive index are obtained in spherical coordinates from Fermat's principle by applying the Euler equation. By introducing canonical variables they are reduced to a set of first order differential equations in normal form, suitable for stepwise numerical integration. Altitude and azimuth angles are introduced and a transformation is derived for determining the refraction errors, including lateral refraction, from the integrated results. The spherically symmetrical case is considered in more detail and leads to an equation for the error in altitude angle expressible as a quadrature over the radial coordinate. A perturbation formula for obtaining the part of the refraction error due to differences between an actual atmospheric profile and some standard atmospheric profile is derived by taking the functional (or variational) derivative. The resulting integral over the radial coordinate has a particularly simple form. (Author)