Computation of wave scattering problems from a spheric body: Derivation of the new Sommerfeld-Watson transformation

Abstract

In this paper, the new Sommerfeld-Watson transformation is introduced and a new derivation processing is given. Unlike the original one, this new derivation directly starts from the solution of the traditional Sommerfeld-Watson transformation. The result is instantly reached using the relation between Ql (cos Oθ) and Pl (cos Oθ) which represents travelling wave and standing wave respectively. So the mathematical processing is simpler and faster than the original derivation approach. At last, the simulation results show that the new approach is in good agreement with the traditional solution.