Radiation by directive sources over a rough planar surface is considered. It is shown that image theory can be used for computing the expected value of the scattered power density, in spite of the essentially incoherent nature of the scattering process, provided that a region of sufficient extent around the specular point, Fermat's region, is illuminated by the primary sources. This result resembles the case of reflection over a smooth plane; its mathematical derivation is also supported by a physical model.