A microscopy method for producing a high-resolution image of a 2-dimensional sample. The method includes exciting statistically blinking fluorophores in a sample by irradiating the sample with illumination radiation, repeatedly imaging the sample onto a spatially resolving detector in an image field that covers only a part of the sample to thereby obtain a frame sequence, generating an image from the frame sequence, the image having a spatial resolution increased beyond the optical resolution limit using a cumulant function, moving the position of the image field on the sample at least once and repeating the imaging and generating steps to obtain one image for each position of the image field, and combining the resultantly obtained images to form a complete image of the sample.