A second-order theory is developed for the reflection and transmission of light by a slightly rough surface. The general results are discussed, especially for a rough interface between vacuum and a free-electron-like metal, where surface-plasma excitation can occur. The influence of the damping of the electron gas and of the shape of the roughness is discussed. Some different previous theories for reflection by a rough surface are shown to be limiting cases of the present theory.
E. Kretschmann and E. Kröger, "Reflection and transmission of light by a rough surface, including results for surface-plasmon effects," J. Opt. Soc. Am. 65, 150-154 (1975)