Reflector antennas with superquadric aperture boundaries

A unified treatment for reflector antennas with elliptical (circular) or rounded-rectangular (rounded-square) aperture boundaries utilizing superquadric functions is presented. Reflector antennas with superquadric aperture boundaries possess unique properties. To reveal these properties and properly implement them in diffraction analysis formulation, important geometrical features of the superquadric aperture, including a closed-form expression for the area, are presented. Parametric representations of the superquadric aperture are investigated, and a superior parameterization is introduced for evaluating the diffraction integrals. Representative results of physical optics (PO) analysis for superquadric reflector antennas are presented, and key features of the radiation pattern characteristics are summarized. Although the focus of this work is on reflector antennas, the main feature of superquadric aperture characteristics and its parametric representations are generally applicable to any aperture type antennas