Microscopy method for producing a high-resolution image of a sample with a lateral resolution above the optical diffraction limit, wherein the method comprises the following steps: a) the sample is provided with a marker which emits statistically flashing luminescence radiation after excitation, or use is made of a sample which emits locally distributed, statistically flashing luminescence radiation after excitation, wherein the markers, on their own in each case and independently of adjacent markers, constantly change between two luminescence radiation states at a flash frequency, b) the sample is excited to luminescence by structured illumination, wherein the sample is repeatedly illuminated in different illumination states (.o1/.o9) of the structured illumination, c) the luminescing sample is repeatedly imaged onto a detector in each of the different illumination states such that an image sequence (44.o1-44.o9) is obtained for each of the different illumination states (.o1-.9), d) a raw image which has a spatial resolution that was increased above the optical resolution of the image is produced from each image sequence (44.o1-44.o9) by means of a cumulant function in accordance with the SOFI microscopy method, which evaluates intensity fluctuations in the image sequence caused by the flashes, such that a high-resolution raw image (53.o1-53.o9) is obtained for each of the different illumination states (.o1-.o9), characterized in that, in step c), the different illumination states are at least three rotational positions and, for each rotational position, at least three displacement positions of the structured illumination and the structured illumination is effectuated by means of a grating, a variably adjustable stripe modulator or a DMD with frequencies close to the optically transmissible limit frequency of the microscope, and e) the high-resolution image which has a spatial resolution that is increased in relation to the raw images (53.o1-53.o9) is produced from the obtained raw images (53.o1-53.o9) by computational processing that comprises Fourier filtering in accordance with the SIM microscopy method. a) the sample is provided with a marker which emits statistically flashing luminescence radiation after excitation, or use is made of a sample which emits locally distributed, statistically flashing luminescence radiation after excitation, wherein the markers, on their own in each case and independently of adjacent markers, constantly change between two luminescence radiation states at a flash frequency, b) the sample is excited to luminescence by structured illumination, wherein the sample is repeatedly illuminated in different illumination states (.o1/.o9) of the structured illumination, c) the luminescing sample is repeatedly imaged onto a detector in each of the different illumination states such that an image sequence (44.o1-44.o9) is obtained for each of the different illumination states (.o1-.9), d) a raw image which has a spatial resolution that was increased above the optical resolution of the image is produced from each image sequence (44.o1-44.o9) by means of a cumulant function in accordance with the SOFI microscopy method, which evaluates intensity fluctuations in the image sequence caused by the flashes, such that a high-resolution raw image (53.o1-53.o9) is obtained for each of the different illumination states (.o1-.o9), characterized in that, in step c), the different illumination states are at least three rotational positions and, for each rotational position, at least three displacement positions of the structured illumination and the structured illumination is effectuated by means of a grating, a variably adjustable stripe modulator or a DMD with frequencies close to the optically transmissible limit frequency of the microscope, and e) the high-resolution image which has a spatial resolution that is increased in relation to the raw images (53.o1-53.o9) is produced from the obtained raw images (53.o1-53.o9) by computational processing that comprises Fourier filtering in accordance with the SIM microscopy method.