Ray Tracing Problem Research Articles

Ionospheric Electron‐Density ProfiJes With Continuous Gradients and Underlying Ionization Corrections. II. Formulation for a Digital Computer

Details are given of a practical computer formulation of the solution to the ionogram real‐height problem developed at the Institute for Telecommunication Sciences and Aeronomy (ITSA) by A. K. Paul. The method can make full joint or independent use of the ordinary and extraordinary group‐height information available from modern high‐quality radio soundings of the ionosphere. It takes advantage of the strong dependence of group height on the vertical electron‐density gradient at the reflection level to provide a profile with continuous gradients; this is an important feature when applying profile data to radio ray tracing or certain aeronomical problems. Corrections for the “starting” and “valley” portions of the distribution (not directly observed on the soundings) are made by fitting simple models for these regions to portions of the ordinary and/or extraordinary echo data. The problem of numerical convergence of integrals involving the group refractive index infinity is solved by a new expression for the index in which the singular part can be integrated explicitly. The layer maximum is obtained by a parabolic extrapolation which maintains the continuity of gradient to the layer peak and which does not require an independent estimate of the critical frequency.

Refraction Operators and Ray Tracing through Cones of Constant Index

A dyadic representation for Snell’s law of refraction is derived and its properties discussed. Alternate forms are given. The problem of ray tracing through a cone of constant refractive index is formally solved in terms of the refraction dyadic. The class of rays which only pierce the cone once is exhaustively discussed.