Spectroscopic ellipsometry (SE) is the technique of choice to determine material properties of thin films in a fast and non-destructive way. However, its ability to accurately extract the material properties of thin films deposited on rough substrate surfaces still remains a challenge, due to depolarization of specularly reflected light. In this paper we present a method based on SE to determine the properties of thin films on rough surfaces. It is shown that, by analyzing SE data only at discrete photon energies, information such as the film thickness and the refractive index at these photon energies can be extracted. The discrete photon energies selected in this method can be related to destructive interference of light at the thin-film surfaces, which significantly reduces the depolarization problem. The method is demonstrated using thin amorphous hydrogenated silicon nitride (a-SiNx:H) films deposited on both polished and rough silicon wafer substrates. By varying the a-SiNx:H film thickness, it is shown that the depolarization effect of light is strongly dependent on the incident photon energies due to light interference at the surface of the a-SiNx: H film. Based on this observation, energy selective ellipsometry (ESE) is proposed as a technique for analyzing thin films on random rough surfaces. It is shown that a-SiNx: H films with a wide range of thickness and optical properties on rough silicon surfaces can be studied accurately by means of ESE. This technique is expected to have useful practical applications, for example in photovoltaics where films are typically deposited onto textured substrates as a means of enhancing light trapping. (C) 2013 Elsevier B.V. All rights reserved.