The Uniform Geometrical Theory of Diffraction and Some of Its Applications

Keller introduced his Geometrical Theory of Diffraction (GTD) in the 1950s. The Geometrical Theory of Diffraction development was revolutionary, in that it explained the phenomena of wave diffraction entirely in terms of rays for the first time, via a systematic generalization of Fermat's principle. In its original form, the Geometrical Theory of Diffraction exhibited singularities at and near ray-shadow boundaries and caustics. For practical applications, it is necessary to patch up the Geometrical Theory of Diffraction in such regions. Uniform asymptotic high-frequency methods overcome the failure of the Geometrical Theory of Diffraction inside those regions, and outside those regions they generally reduce to the Geometrical Theory of Diffraction. One such highly developed approach happens to be the Uniform Geometrical Theory of Diffraction (UTD). The present article focuses on some key Uniform Geometrical Theory of Diffraction developments in a semi-historical fashion, with a few typical applications to illustrate the power and utility of the Geometrical Theory of Diffraction/Uniform Geometrical Theory of Diffraction concept to solve practical problems.