[en] We summarize different uses of the eigenmodes of the Neuberger overlap operator for the analysis of the QCD vacuum, here applied to quenched configurations simulated by means of the Luescher-Weisz action. We describe the localization and chiral properties of the lowest modes. The overlap-based topological charge density (with and without UV-filtering) is compared with the results of UV-filtering for the field strength tensor. The latter allows to identify domains of good (anti-)selfduality. All these techniques together lead to a dual picture of the vacuum, unifying the infrared instanton picture with the presence of singular defects co-existent at different scales. (orig.)