An evaluation of various methods for tracing the propagation of electromagnetic energy through the atmosphere

Electromagnetic energy emitted by radar bends as it propagates through the atmosphere because the index of refraction of the atmosphere is not constant. Variations in the index of refraction are primarily caused by local changes in temperature and humidity. The manner in which electromagnetic ray paths bend in various atmospheric environments is of particular interest to groups involved with the use of radar for risk mitigation associated with unmanned aircraft system operations. Radar can be used to detect a majority of targets entering an unmanned aircraft operations area by detecting reflected electromagnetic energy. The detection and accurate determination of the locations of these targets is enabling to collision avoidance. Determining the locations in space and time of the reflected energy is highly dependent upon knowing the bending of ray paths through the atmosphere.

A myriad of approaches have been used to solve this problem. Known as ray tracing techniques, these approaches range from using spatial transformations to deriving equations from a combination of geometric relations and Snell's law. Other approaches have involved tracing the path of a ray in a stepwise fashion, while still other techniques utilize the numerical integration of equations yielding ground range and height. Each of these methods brings with it strengths and weaknesses due to the assumptions involved in obtaining a solution; some methods are more accurate than others. One challenge is that many of these techniques are only partially documented in the readily available literature.

The aim of this work is to develop a ray tracing algorithm by synthesizing the work of previous researchers in order to accurately trace the path of the center of a beam of electromagnetic energy through the atmosphere. An important goal of this work is to develop a technique that accurately takes into account a current index of refraction profile created from observed and modeled atmospheric conditions. Numerous approaches are tested and compared in the development of this algorithm, and the strengths and weaknesses of each approach are evaluated. Moreover, techniques needed to institute these various approaches are provided. This includes important aspects of these approaches that are not readily available in published literature, such as the proper handling of exceptional situations like reflection and downward propagation.