Implementation of a Point-to-Point Ray Tracer

Most ray tracers treat ionosphere ray tracing as a Hamiltonian optics problem given an index of refraction, where the index of refraction is derived from atmospheric properties. This direct ODE approach works well when tracing rays with a known start point and launch angle. This method is more less effective when tracing a ray between known start and end points with an unknown launch angle. To overcome this hurdle, some have implemented homing methods that trace numerous rays from the start point with a variety of launch angles until one ray intersects the end point. This task is computationally expensive and difficult to converge especially for high-rays. To solve this issue, Dr. Christopher Coleman developed an iterative approach using Fermat's principle for an aniosotropic medium. This approach begins with a initial estimation of the ray's path, and then iteratively mutates this path to find one with a stationary phase angle. In this work, I lay out my implementation of Dr. Coleman's approach. Development of this method may provide a potentially efficient method for determining the linking path between a transmitter receiver pair, given a model ionosphere.