Evaluation of a fundamental integral in rough-surface scattering theory

An algorithm is presented for the numerical evaluation of a fundamental but intractable integral that occurs in the physical theory of scattering from random rough surfaces. It is based on a rational-function approximation to an integrand factor, augmented with techniques for excluding poles and zeros from the path of integration. Examples, complete with error analysis, are provided for cases relevant to acoustic sea-floor and sea-surface scattering.