  This document takes existing derivations of scattering loss from rough
surfaces, and makes them more accessible as a tool to derive the total
scattering loss from a rough mirror given its true surface profile. It does not
contain any new results and is therefore not intended for submission to a
scientific journal in the near future. A rough mirror will diffusively reflect
part of an incident wave, limiting the effective specular reflectivity of the
mirror. This in turn will limit the finesse of an optical resonator using this
mirror. We ask this reflectivity depends on the roughness, in the limit of
small roughness. The derivation we will use is based off a detailed and
well-written book by JA Ogilvy which is almost always out of the library on
loan, is out of print, and we can't find any second-hand copies on the
internet. Note that nowhere does Ogilvy use the phrase 'Debye-Waller factor'.
We outline how this derivation of scattering loss can be used in practice to
calculate the scattering loss given a high-precision experimental measure of
mirror profile.
