Asymptotic solution for the reflectivity of a very rough surface

Asymptotic solutions for the reflectivity of a very rough surface are obtained in closed form up to second order in variance of slope. The zeroth-order solution gives the reflectivity of a specular surface and the sum of the higher-order terms yields the net effect of the rough surface. Within the common regions of validity of small rms slope and incident angle not close to grazing, the result agrees very well with those obtained with numerical methods.