In this work we consider a structure consisting of vacuum in the region $x_3>zeta(x_1)$; a dielectric film characterized by a real, positive, dielectric constant (epsilon) in the region $-D < x_3 < \zeta(x_1)$; and a vacuum in the region $x_3<-D$. The surface profile function $\zeta(x_1)$ is assumed to be a single-valued funtion of $x_1$, that is differentiable, and constitutes a random process. This structure is illuminated from the region $x_3 >\zeta(x_1)$ by s-polarized light whose plane of incidence is the $x_1x_3$-plane. By the use of the geometrical optics limit of phase perturbation theory we show how to design the surface profile function $\zeta(x_1)$ in such a way that the mean differential transmission coefficient has a prescribed form within a specified range of the angle of transmission, and vanishes outside this range. In particular, we consider the case in which the transmitted intensity is constant within a specified range of the angle of transmission, and vanishes outsides it. Rigorous numerical simulation calculations show that the transmitted intensity indeed has this property.