Microscope for high-resolution scanning microscopy of a specimen, having - an illumination device for illuminating the specimen, - an imaging device for scanning at least one point or line spot over the specimen for imaging the point or line spot in a diffraction-limited, stationary individual image into a detection plane at an imaging scale, - a detector device for capturing the individual image in the detection plane for different scanning positions with a spatial resolution that, taking account of the imaging scale, is at least twice as large as a full width at half maximum of the diffraction-limited individual image, - an evaluation device for evaluating a diffraction structure of the individual image for the scanning positions from the data of the detector device and for producing an image of the specimen, said image having a resolution that is increased beyond the diffraction limit, wherein - the detector device has: - a detector array that has pixels and that is larger than the individual image, characterized in that the detector device furthermore has: - a non-imaging redistribution element (20-21; 30-34; 30-35) that is disposed upstream of the detector array and that distributes the radiation from the detection plane in a non-imaging fashion onto the pixels of the detector array, - wherein the redistribution element comprises a bundle of optical fibres, said bundle having an entrance arranged in the detection plane and an exit at which the optical fibres end at the pixels of the detector array in a geometric arrangement that differs from that of the entrance, and - wherein the pixels of the detector array are larger than what is necessary for the diffraction-limited resolution. - an illumination device for illuminating the specimen, - an imaging device for scanning at least one point or line spot over the specimen for imaging the point or line spot in a diffraction-limited, stationary individual image into a detection plane at an imaging scale, - a detector device for capturing the individual image in the detection plane for different scanning positions with a spatial resolution that, taking account of the imaging scale, is at least twice as large as a full width at half maximum of the diffraction-limited individual image, - an evaluation device for evaluating a diffraction structure of the individual image for the scanning positions from the data of the detector device and for producing an image of the specimen, said image having a resolution that is increased beyond the diffraction limit, wherein - the detector device has: - a detector array that has pixels and that is larger than the individual image, characterized in that the detector device furthermore has: - a non-imaging redistribution element (20-21; 30-34; 30-35) that is disposed upstream of the detector array and that distributes the radiation from the detection plane in a non-imaging fashion onto the pixels of the detector array, - a detector array that has pixels and that is larger than the individual image, characterized in that the detector device furthermore has: - a non-imaging redistribution element (20-21; 30-34; 30-35) that is disposed upstream of the detector array and that distributes the radiation from the detection plane in a non-imaging fashion onto the pixels of the detector array, - a non-imaging redistribution element (20-21; 30-34; 30-35) that is disposed upstream of the detector array and that distributes the radiation from the detection plane in a non-imaging fashion onto the pixels of the detector array, - wherein the redistribution element comprises a bundle of optical fibres, said bundle having an entrance arranged in the detection plane and an exit at which the optical fibres end at the pixels of the detector array in a geometric arrangement that differs from that of the entrance, and - wherein the pixels of the detector array are larger than what is necessary for the diffraction-limited resolution.