Analytical Techniques In Scattering

Summary form only given. There are very few geometries for which exact analytical solutions of a scattering problem are available, and these are almost all limited to bodies whose surface is a complete coordinate surface in one of the six coordinate systems for which the vector wave equation is separable. At the dawn of the last century, the Mie series solution for a homogeneous sphere and the Sommerfeld-Carslaw multiform solution for a perfectly conducting wedge were available, but the ability to extract meaningful information from these was limited, and in England at least, data computed from the Mie series was classified in World War II. With the advent of radar, it became necessary to estimate, and later reduce, the scattering from realistic targets, and this led to significant advances in our analytical capability. This paper presents a personal view of some of the themes that have underlaid scattering work over the past fifty years. Among these are the early computations of the exact eigenfunction expressions for the cone and prolate spheroid; integral equation and transform techniques; the Luneburg-Kline expansion establishing the rigorous connection between geometrical optics and electromagnetic theory, and the introduction by Keller in 1953 of the concept of diffracted rays, leading to the geometrical theory of diffraction; the analogous physical theory of diffraction conceived by Ufuntsev that had physical optics as its base and that, in the hands of Mitzner and others, played a role in stealth technology; and low frequency techniques.