Comparison of uniform asymptotic theory and Ufimtsev's theory of electromagnetic edge diffraction

High-frequency asymptotic solutions of electromagnetic edge diffraction by two different theories are studied. One is the uniform asymptotic theory which is a refinement of Keller's geometrical theory of diffraction. The other is Ufimtsev's theory of the edge wave, representing an improvedment over the classical physical optics theory. These two theories are summarized, their features compared, and their relations discussed. When the observation point is away from shadow boundaries and caustics, both uniform asymptotic theory and Ufimtsev's theory, up to (and including) orderk^{-1/2}, agree with Keller's theory. Near or on shadow boundaries, uniform asymptotic theory gives an explicit field solution, while Ufimtsev's result contains a physical optics integral. The evaluation of that integral is not a trivial task. In a two-dimensional test problem, it is shown that both theories do give, up to orderk^{-1/2}, an identical field solution everywhere including the edge, shadow boundaries, and transition regions.