We present two methods for generating numerically a one-dimensional random surface, defined by the equationx3=&zgr;(x1),that has a prescribed probability density function of slopes. This problem arises in the design of a diffuser that scatters light uniformly within a range of scattering angles and produces no scattering outside this range. Numerical calculations of the scattering of light from random surfaces generated by these approaches show that the scattered intensity, indeed, has a rectangular distribution as a function of the scattering angle. ©1998 American Institute of Physics.