Scattering from Superquadric Surfaces

Abstract : Electromagnetic reflection from superquadric surfaces in 2-D is examined. A finite number of zero-curvature points on the surface are identified, and Geometrical Optics is shown to fail at these points. A correction for the failure, based on Physical Optics, is derived via an asymptotic approximation of the PO radiation integral. Solutions are obtained for two cases: reflection from the zero-curvature point for all values of the superquadric parameter v, and reflection both near and far from the zero- curvature point when v = 3. The form of the general multiplicative transition (correction) function is postulated heuristically, based on the integral form of a generalized incomplete Airy function. The resulting Uniform Geometrical Optics (UGO) result compares very favorably with Physical Optics and the Method of Moments.