Accuracy Check of GTD MER with Weighted Fringe Wave Using Fresnel Zone Number for Grazing Incidence and Slope Wave Diffraction

Abstract

The reduction of the surface integration to line integration provides numerical computation time and resource savings. Modified edge representation (MER) is a unique concept for a complete definition of equivalent edge currents (EECs) for arbitrary points on the edge, including ones that do not satisfy the diffraction law. By using classical Keller-type diffraction coefficients in EECs, MER recovers the fringe wave (FW) contribution and has the enhanced accuracy of the order of the geometrical theory of diffraction (GTD). The line integration of MER EEC results in uniform and accurate fields everywhere, including geometrical boundaries at the caustics as inherent advantages and geometrical boundaries, such as the reflection shadow boundary (RSB) and incident shadow boundary (ISB). The authors have developed the applicability of MER and arrived at the advanced form of MER (new MER) in which FW components in EEC are weighted by the Fresnel zone number (FZN). This article demonstrates the higher accuracy and wider applicability of this method over GTD and the uniform geometrical theory of diffraction (UTD) for the canonical problem of a large circular disk where the rigorous solution is available. In grazing incidence as an extreme case, the FZN weighting effectively enhances the accuracy of GTD MER. It is also demonstrated that the inherent advantage of GTD MER over GTD and UTD in slope wave diffraction remain unchanged in new MER with this weighting.