Diffraction at the vertex of a quarter plane

The uniform theory of diffraction (UTD) technique has been thoroughly employed for practical applications such as the prediction of the radar cross section (RCS) of complex targets, or the computation of radiation characteristics of antennas in their operating platform (aircraft, ships, satellites, etc.). The UTD framework is based on a diffraction coefficient constructed via canonical diffraction problems. Among these problems, the quarter plane problem plays an fundamental role. Edge diffracted rays are usually added and higher order contributions, namely vertex and doubly diffracted rays, also need to be added. We focus our attention on the vertex diffracted contribution consisting of dominant and subdominant terms. Exact solutions for the quarter plane (QP) diffraction have been given in literature (Satterwhite, R.S. and Kouyoumjian, R.G., 1970; Smyshlyaev, V.P., 1993), but they are difficult to implement and not well suited for practical asymptotic evaluation. Our solution, although not derived from the exact solution of the QP, is nicely simple and uniformly compensates for the discontinuity of the leading single and double diffraction UTD contribution at their shadow boundaries.