The Helmholtz integral theorem for the scattering or radiation of radio waves from surfaces is examined to obtain a more general approximation of the observed field distribution. The resulting new integral expansion is particularly responsive to evaluation by the method of stationary phases, yielding a quantitative solution applicable to a more general class of surfaces and aperture boundaries than was previously feasible. The problem of reflection from finite irregular surfaces, such as terrain or atmospheric layers, is evaluated formally. The result indicates a source of significant reflections not generally treated by ray theory.
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