1. A method for high-resolution luminescence microscopy of a sample marked with marking molecules that can be activated and subsequently excited to emit particular luminescent radiation, wherein the method comprises: a) repeated activation and excitation of a subset of the marking molecules to emit luminescent radiation, at least some of the luminescent marking molecules being at least at a distance from the luminescent marking molecules immediately adjacent thereto greater than or equal to a length which results from a predetermined optical resolution; b) repeated imaging of the sample along a depth direction and with the predetermined optical resolution; c) production of individual images from the imaging operations from step b), wherein geometrical locations of the luminescent marking molecules in the individual images are determined with a spatial resolution which is increased above the predetermined optical resolution; and wherein d) the activation and/or excitation in step a) is effected with radiation which is introduced into at least two regions, the regions each extending along a plane substantially perpendicular to the depth direction, the regions having a predetermined extent in the depth direction, and the regions, when seen in the depth direction, arranged in such a manner that said regions are behind one another and overlap only partially, and wherein e) separate images of the sample are recorded in step b) for activation and/or excitation of each of the at least two regions in order to obtain a depth information relating to the luminescent marking molecules from the separate images.