For multi-dimensional high-resolution imaging a structure marked with fluorescence markers, fluorescence enabling light is focused to illuminate a measurement area in a sample. A partial area of the measurement area is subjected to fluorescence inhibiting light. The partial area omits a center of the measurement area in that an intensity distribution of the fluorescence inhibiting light comprises a line-shaped intensity minimum. A minimal extension of the intensity minimum in a direction through the center area is by a factor k≥2 smaller than a diameter of the measurement area in said direction. Without spatial resolution, fluorescence light emitted out of the measurement area is measured for a plurality of consecutive angle positions of the intensity minimum about the center, while the measurement area, for each angle position, is subjected to the fluorescence enabling light. A value of the measured fluorescence light is assigned to the position of the center.