On the universal behavior of scattering from a rough surface for small grazing angles

It is shown that for scattering from a plane of an average rough surface, the scattering cross section of the range of small grazing angles of the scattered wave demonstrates a universal behavior. If the angle of incidence is fixed (in general, it should not be small), the diffuse component of the scattering cross section for the Dirichlet problem is proportional to θ² where θ is the (small) angle of elevation and for the Neumann problem it does not depend on θ. For the backscattering case, these dependencies correspondingly become θ⁴ and θ⁰. The result is obtained from the structure of the equations that determine the scattering problem rather than the use of an approximation