GTD ray tracing by mapping

Ray tracing is an important part in field computation when applying geometrical optics (GO) and geometrical theory of diffraction (GTD). Tracing of specific rays may be carried out in two different ways, often denoted forward and backward ray tracing. In both of these, rays are conveniently distinguished by their type stating the scattering surfaces and edges in the order in which these occur along the ray. In forward ray tracing a ray is launched from the source and followed through its reflections and diffractions until a field point is reached. With sufficiently many rays from the source all field points are reached by every possible ray type. In backward ray tracing the user determines which ray types are to be included. Then, for these types the ray path(s) fulfilling Fermat's principle shall be found. For simple surfaces and edges this may be done analytically and the method is simple to implement and fast to execute. For a general and automatic procedure the forward ray tracing is best suited, but if a given field point is to be hit with sufficient accuracy a very large number of rays needs to be launched from the source. The present paper describes a hybrid method in which the rays are launched from the source with a coarse spacing of primary search rays. These rays are used to identify the ray types reaching the region of a given field point. Next a mapping technique is applied as backward ray tracing for finding the precise ray path to the requested field point.