A microscopy method for producing a high-resolution image of a sample which includes furnishing the sample with a marker that emits statistically flashing luminescence radiation after excitation, or using a sample that has molecules that emit statistically flashing luminescence radiation after excitation. The sample is excited to luminescence in such a manner that the marker/molecules emit luminescence radiation flashing at a flash rate, wherein—the illumination is structured in such a manner that the flash rate varies locally and—the sample is repeatedly illuminated in different illumination states of the structured illumination. The luminescing sample is repeatedly imaged on a detector in each of the different illumination states.