Near-field line-integral representation of the Kirchhoff-type aperture radiation for a parabolic reflector

A line-integral representation is presented for a linearly polarized Kirchhoff-type aperture radiation from a parabolic reflector antenna. The main purpose of this result is concerned with the acceleration of the numerical integration for calculating the near field of large reflector antennas. The formulation, which is rigorous for a uniform aperture field, is based on the application of the equivalence principle to a projecting surface, which allows the analytical evaluation in a closed form of a twofold surface integral which defines the radiated field at any space point; the extension to a slowly varying primary feed pattern is based on an asymptotic approximation, which is proved to be accurate in the proximity of the aperture to -30 dB of amplitude edge illumination. The present formulation is well suited to be improved by fringe diffraction contributions in the framework of edge-wave theories such as the physical theory of diffraction (PTD) and the incremental theory of diffraction (ITD).