ZrO₂ films were prepared by reactive sputtering. Elastic light scattering was used to determine the cross correlation of the substrate and film interface roughness. Surface profiles were measured with atomic-force microscopy. The power spectral density functions could be fitted by the K-correlation model, suggesting self-affine fractal surfaces. The roughness of the film front surfaces was of the same order of magnitude as the substrate roughness. We have derived a replication factor from experimental data that gives information on the evolution of the contribution of the substrate roughness.