Coherent reflection from a stationary rough surface (source code)

= Coherent reflection from a stationary rough surface
{title2=$\langle\psi_s(x,0)\rangle=-1+(k/\pi)\int\beta S_h$}

Through second order in height, a normally incident acoustic plane wave has the displayed mean reflected <amplitude> for a Dirichlet boundary. The propagating part of the <power spectrum of surface height> contributes a positive real correction to the negative flat reflection coefficient, while the evanescent part contributes an imaginary correction. The mean linear rough correction is zero.