A useful decomposition for the Green's functions of cylinders and spheres

A method is presented for improving the convergence of the near field evaluation of Green's functions for cylinders and spheres. The slow convergence of the scattered field which occurs when both the field point and source point approach the surface of the scatterer is shown to be due to the presence of an image inside the scatterer, thus giving physical insight into the method. The method involves the subtraction of this image field term by term from the scattered field expression, leaving a series which converges quickly. The image field is restored by using closed form expressions. This special image term is shown to be analogous to the image which occurs in electrostatics problems where a charge is in the presence of a cylinder or sphere.