A method for high-resolution scanning microscopy of a sample, wherein - the sample is illuminated with illumination light in such a way that the illumination light is focused at a point in or on the sample to form an illumination spot, - the point is imaged in a diffraction image onto an area detector having detector elements, the area detector having a spatial resolution due to its detector elements which resolves a diffraction structure of the diffraction image, - the sample is scanned line by line in a grid of lines and columns by moving the point relative to the sample to different scanning positions with a step size that is smaller than the diameter of the illumination spot, - the area detector is read out and an image of the sample is generated from the data of the area detector and from the scanning positions assigned to these data, said image having a resolution which is increased beyond an image resolution limit, characterized in that - pre-calculated raw line images are calculated for each recorded line by forming Sheppard sums D ̃ r → z = ∑ h D h r → − s → h, z where h is an index denoting a respective detector element, z denotes an axial sample position, r denotes a lateral sample position, s h denotes a lateral displacement, and D̃ h ( r, z) is a signal which is detected at a detector element h and results from a convolution of the point spread function I h ( r, z) of the respective detector element h with the actual sample image O ( r, z), and - the pre-calculated raw line images are combined into a raw image and deconvolved with the point spread function Ĩ ( r) = Σ h I h ( r - s h, z) to create the image of the sample. - the sample is illuminated with illumination light in such a way that the illumination light is focused at a point in or on the sample to form an illumination spot, - the point is imaged in a diffraction image onto an area detector having detector elements, the area detector having a spatial resolution due to its detector elements which resolves a diffraction structure of the diffraction image, - the sample is scanned line by line in a grid of lines and columns by moving the point relative to the sample to different scanning positions with a step size that is smaller than the diameter of the illumination spot, - the area detector is read out and an image of the sample is generated from the data of the area detector and from the scanning positions assigned to these data, said image having a resolution which is increased beyond an image resolution limit, characterized in that - pre-calculated raw line images are calculated for each recorded line by forming Sheppard sums D ̃ r → z = ∑ h D h r → − s → h, z where h is an index denoting a respective detector element, z denotes an axial sample position, r denotes a lateral sample position, s h denotes a lateral displacement, and D̃ h ( r, z) is a signal which is detected at a detector element h and results from a convolution of the point spread function I h ( r, z) of the respective detector element h with the actual sample image O ( r, z), and - the pre-calculated raw line images are combined into a raw image and deconvolved with the point spread function Ĩ ( r) = Σ h I h ( r - s h, z) to create the image of the sample.