ITD formulation for the currents on a plane angular sector

Approximate high-frequency expressions for the currents induced on a perfectly conducting plane angular sector are derived on the basis of the incremental theory of diffraction (ITD). These currents are represented in terms of those predicted by physical optics (PO) plus fringe contributions excited by singly and doubly diffracted (DD) rays at the two edges of the angular sector. For each of these two contributions, additional currents associated to vertex diffracted rays are introduced that provide continuity at the relevant shadow boundary lines. The transition region of DD rays is described by a transition function involving cylinder parabolic functions. The asymptotic solution presented here is constructed in such a way to satisfy far from the vertex the expected edge singularities, which tend to be the same as those predicted by the exact solution of the half plane. Numerical results are compared with the exact solution of the same problem and with moments method results for scattering from polygonal plates.