In this work we consider a structure consisting of a dielectric medium characterized by a dielectric constant $\epsilon_1$ in the region $x_3 > H$, a second dielectric medium characterized by a dielectric constant $\epsilon_2$ in the region $\zeta(x_1) < x < H$, and vacuum in the region $x < \zeta(x_1)$. The surface profile function $\zeta(x_1)$ is assumed to be a single-valued function of $x_1$ that is differentiable and constitutes a random process. The structure is illuminated from the region $x_3 > H$ by s-polarized light whose plane of incidence is the $x_1x_3$-plane. By the use of geometrical optics limit of phase perturbation theory we show how to design the surface profile function $\zeta(x1)$ in such a way that the mean differential transmission coefficient has a prescribed form within a specific range of the angles of transmission, and vanishes outside this range. In particular, we consider the case that the incident s-polarized light in incident normally on this structure, and the mean intensity of the transmitted light is constant within a specific range of the angle of transmission, and vanishes outside it. Numerical simulation calculations show that the transmitted intensity indeed has this property.