Method for examining a sample with spatially highly resolved luminescence microscopy, said sample being marked by marker molecules that are activatable by way of a switching signal such that only then are they excitable to emit certain luminescence radiation, wherein the method comprises the following steps: a) introducing the switching signal to the sample in such a way that only a subset of the marker molecules present in the sample are activated, wherein there are portions in the sample in which activated marker molecules have a distance from their next closest activated marker molecule which is greater than or equal to an optical resolution of a detection of luminescence radiation, b) exciting (S1, S2) the activated molecules to emit luminescence radiation, c) detecting the luminescence radiation with the optical resolution and d) producing image data from the luminescence radiation recorded in step c), said luminescence radiation specifying the geometric locations of the luminescence-radiation-emitting marker molecules with a spatial resolution that is increased beyond the optical resolution, characterized in that e) the detection of the luminescence radiation in step c) or the production of the image data in step d) comprises a nonlinear amplification (S4, S5) of recorded luminescence radiation, said amplification preferring higher intensities, in order to sharpen the spatial resolution beyond the optical resolution and steps a)-e) are iterated a number of times in order to produce an overall image of the sample, wherein individual images are produced in each case, wherein image data of the individual images obtained after step e) are superposed on image data from preceding iterations in each case in order to form the overall image such that the overall image has been completed after the final iteration. a) introducing the switching signal to the sample in such a way that only a subset of the marker molecules present in the sample are activated, wherein there are portions in the sample in which activated marker molecules have a distance from their next closest activated marker molecule which is greater than or equal to an optical resolution of a detection of luminescence radiation, b) exciting (S1, S2) the activated molecules to emit luminescence radiation, c) detecting the luminescence radiation with the optical resolution and d) producing image data from the luminescence radiation recorded in step c), said luminescence radiation specifying the geometric locations of the luminescence-radiation-emitting marker molecules with a spatial resolution that is increased beyond the optical resolution, e) the detection of the luminescence radiation in step c) or the production of the image data in step d) comprises a nonlinear amplification (S4, S5) of recorded luminescence radiation, said amplification preferring higher intensities, in order to sharpen the spatial resolution beyond the optical resolution and steps a)-e) are iterated a number of times in order to produce an overall image of the sample, wherein individual images are produced in each case, wherein image data of the individual images obtained after step e) are superposed on image data from preceding iterations in each case in order to form the overall image such that the overall image has been completed after the final iteration.