This article provides a derivation of the Rayleigh criterion for surface roughness. As a once-flat surface roughens, the specular reflected wave begins to degrade in power as some of it is scattered in different directions. The result is a predictable degradation that is a function of the rough surface statistics. The end result — the Rayleigh criterion — is used throughout science and engineering to describe everything from propagation off of building sides to the specifications for a satellite dish antenna. Download the article here here.