Incremental diffraction coefficients for source and observation at finite distances from an edge

Recently, an incremental theory of diffraction (ITD) has been introduced which provides a self-consistent, high-frequency description of a wide class of scattering phenomena within a unified framework. Explicit expressions of the incremental diffracted field contributions have been obtained for a plane-wave illumination of wedge-shaped configurations and observation points at a finite distance from the incremental point. In this paper, this method is extended to treat the case when both the source and the observation point are at finite distance from the local incremental point along the edge. To this end, a spectral-domain approach is used to derive a spectral-integral representation for the incremental field contribution. The latter is asymptotically evaluated to find high-frequency closed-form expressions which are uniformly valid at any incidence and observation aspects, including caustics and shadow boundaries of the corresponding ray-field description. The expressions of the incremental diffraction coefficients explicitly satisfy reciprocity. Numerical results are presented and compared with those obtained from different techniques.