As superconducting niobium radio-frequency (SRF) cavities approach fundamental material limits, there is increased interest in understanding the details of topographical influences on realized performance limitations. Micro- and nano-roughness are implicated in both direct geometrical field enhancements as well as complications of the composition of the 50 nm surface layer in which the super-currents typically flow. Interior surface chemical treatments such as buffered chemical polishing (BCP) and electropolishing (EP) used to remove mechanical damage leave surface topography, including pits and protrusions of varying sharpness. These may promote RF magnetic field entry, locally quenching superconductivity, so as to degrade cavity performance. A more incisive analysis of surface topography than the widely used average roughness is needed. In this study, a power spectral density (PSD) approach based on Fourier analysis of surface topography data acquired by both stylus profilometry and atomic force microscopy (AFM) is introduced to distinguish the scale-dependent smoothing effects, resulting in a novel qualitative and quantitative description of Nb surface topography. The topographical evolution of the Nb surface as a function of different steps of well-controlled EP is discussed. This study will greatly help to identify optimum EP parameter sets for controlled and reproducible surface levelling of Nb for cavity production. (c) 2010 Elsevier B.V. All rights reserved.