1. A microscopy method to create a high-resolution image ( 55 ) of a sample ( 2 ), the microscopy method comprising the steps of: a) providing the sample with a marker that emits statistically blinking luminescent radiation after excitation, or using a sample that emits locally distributed, statistically blinking luminescent radiation after excitation; b) exciting the sample to a state of luminescence through structured illumination, wherein the sample is repeatedly illuminated in various illumination states of the structured illumination; c) repeatedly reproducing the luminescent sample onto a detector in each of the various illumination states, so that a sequence of images is obtained for each of the various illumination states; d) creating a raw image that has local resolution increased beyond the optical resolution of the reproduction from each sequence of images by employing a cumulant function that evaluates intensity fluctuations in the sequence of images caused by the blinking, so that a high-resolution raw image is obtained for each of the various illumination states; and e) generating the high-resolution image, which has a local resolution higher than that of the raw images, from the raw images obtained through Fourier filtration.