For spatial high resolution determining a position of a singularized molecule, which is excitable with excitation light for emission of luminescence light, in a sample, the excitation light is provided with an intensity distribution comprising an intensity increasing region with a known strictly monotonic course of an intensity of the luminescence light over a distance of the singularized molecule to a model point of the intensity distribution. The model point is arranged at different preliminary positions such that the intensity increasing region extends over a preliminary local area of the sample including the singularized molecule. From intensity values including intensities of the luminescence light separately registered for the preliminary positions of the model point, a further local area is determined which includes the singularized molecule and which is smaller than the preliminary local area. These steps are repeated using the last further local area as the next preliminary local area.