On a synthesis of field scattered by a perfectly conducting obstacle and Rayleigh's hypothesis

If one considers the stationary boundary-value problem of wave scattering by an obstacle with an arbitrarily shaped surface, the Rayleigh hypothesis signifies the possibility of representing scattered waves by means of Rayleigh's series everywhere outside the surface of the scatterer. A method of rigorous solution of the scattered-field-synthesis problem is proposed for a 2-D external point-source excited case. The boundary condition corresponds to a perfectly conducting finite obstacle with a smooth analytic boundary. Some simple geometrical restrictions on the location of the analytical continuation's singularities supply the necessary and sufficient conditions for the Rayleigh hypothesis to be valid.<>