Uniform surface-to-line integral reduction of physical optics for curved surfaces by modified edge representation with higher-order correction

摘要

The modified edge representation is one of the equivalent edge currents approximation methods for calculating the physical optics surface radiation integrals in diffraction analysis. The Stokes’ theorem is used in the derivation of the modified edge representation from the physical optics for the planar scatterer case, which implies that the surface integral is rigorously reduced into the line integral of the modified edge representation equivalent edge currents, defined in terms of the local shape of the edge. On the contrary, for curved surfaces, the results of radiation integrals depend upon the global shape of the scatterer. The physical optics surface integral consists of two components, from the inner stationary phase point and the edge. The modified edge representation is defined independently from the orientation of the actual edge, and therefore, it could be available not only at the edge but also at the arbitrary points on the scatterer except the stationary phase point where the modified edge representation equivalent edge currents becomes infinite. If stationary phase point exists inside the illuminated region, the physical optics surface integration is reduced into two kinds of the modified edge representation line integrations, along the edge and infinitesimally small integration around the inner stationary phase point, the former and the latter give the diffraction and reflection components, respectively. The accuracy of the latter has been discussed for the curved surfaces and published. This paper focuses on the errors of the former and discusses its correction. It has been numerically observed that the modified edge representation works well for the physical optics diffraction in flat and concave surfaces; errors appear especially for the observer near the reflection shadow boundary if the frequency is low for the convex scatterer. This paper gives the explicit expression of the higher-order correction for the modified edge representation.