Method for super-resolution evaluation of microscope images illuminated in a structured manner and microscope having structured illumination. The resolution can be improved laterally by a factor of up to two using conventional linear structured Illumination (SIM). If a non-linear iterative method is used for the purpose of deconvolution, the achievable resolution can be improved beyond the theoretical limit. However, the known methods only achieve a small amount of increase. The novel method is intended to make improved resolution or improved contrast possible. If a PSF/OTF that is manipulated (individually for each order) in the same (or in a corresponding) way as the relevant order spatial frequency spectrum is used during the re-weighting in the spatial frequency domain (for the deconvolution), the actually achievable resolution can be nearly doubled in comparison with the conventional SIM, both in one-stage and in two-stage variants.