A theory of scalar wave scattering by a circular cylinder and a planar substrate

The problem of scalar wave scattering by a cylinder on or near a planar substrate is analytically solved. The solution is in the form of a coupled set of linear equations relating the coefficients of scattering and transmission of the cylinder and those of reflection and transmission of the planar substrate. The coupling is due to the process of multiple scattering by the two objects. Iterative substitution gives the solution in the form of a set of infinite series, and each term explicitly shows the effect of multiple scattering of increasing order.