1. A microscopy method to create a high-resolution image ( 55 ) of a sample ( 2 ), the microscopy method comprising the steps of: a) using one of a sample that does not emit statistically flashing luminescent radiation after excitation and providing the sample with a marker that emits statistically flashing luminescent radiation after excitation, and a sample that emits locally distributed, statistically flashing luminescent radiation after excitation; b) exciting the sample to a luminescent state through repeated illumination of the sample in various illumination states of structured illumination, each of the various illumination states being implemented using one of: at least three rotational positions of the structured illumination and one of at least three displacement positions in the structured illumination per rotational position; and at least three rotational positions of the structured illumination and one of at least three scan positions in the structured illumination per rotational position; c) repeatedly imaging the luminescent sample onto a detector in each of the various illumination states, to obtain a sequence of images for each of the various illumination states; d) for each of the various illumination states, creating a raw image that has local resolution increased beyond the optical resolution of the image from each sequence of images by employing a cumulant function that evaluates intensity fluctuations in the sequence of images caused by the flashing; and e) using Fourier filtration to convert the raw images created in step d) into a high-resolution image, which has a local resolution higher than that of the raw image created from each sequence of images and a lateral resolution beyond the optical diffraction limit.