In this work we consider a structure consisting of a dielectric medium characterized by a dielectric constant i in the region x3 > H, a second dielectric medium characterized by a dielectric constant 2 in the region ((Xi) < X3 < H, and vacuum in the region x3 < C(xi). The surface profile function ((x1) is assumed to be a single-valued function of x1 that is differentiable and constitutes a random process. The structure is illuminated from the region x3 > H by s-polarized light whose plane of incidence is the x1x3-plane. By the use of the geometrical optics limit of phase perturbation theory we show how to design the surface profile function C(xi) in such a way that the mean differential transmission coefficient has a prescribed form within a specified range of the angles of transmission, and vanishes outside this range. In particular, we consider the case that the incident s-polarized light is incident normally on this structure, and the mean intensity of the transmitted light is constant within a specified range of the angle of transmission , and vanishes outside it . Numerical simulation calculations show that the transmitted intensity indeed has this property.