A method for high spatial resolution imaging of a structure of interest in a specimen, having the steps: - selecting a substance from a group of substances, - which have a first state with first fluorescent properties and a second state with second fluorescent properties; - which can be excited in the first state by light of one wavelength to spontaneously emit fluorescent light; - which can be converted from the first state into their second state by the light of the one wavelength and - which can return from their second state into their first state; - marking the specimen's structure of interest with molecules of the substance; - imaging the specimen onto a sensor array, wherein a spatial resolution limit of the imaging being greater (i.e. worse) than an average spacing between closest neighboring molecules of the substance in the specimen; - exposing the specimen to the light of the one wavelength in at least one region which has dimensions larger than the spatial resolution limit of the imaging of the specimen onto the sensor array, alternately wherein fractions of the molecules of the substance being in the first state being excited by the light of the one wavelength to spontaneously emit fluorescent light and being converted into their second state, and wherein at least 10% of the molecules of the substance that are respectively in the first state lying at a distance from their closest neighboring molecules in the first state which is greater than the spatial resolution limit of the imaging of the specimen onto the sensor array; - registering an intensity distribution of the fluorescent light which is spontaneously emitted from the region of the molecules of the substance, in a plurality of images recorded by the sensor array during continued exposure of the specimen to the light of the one wavelength; and - determining the position in the specimen of the molecules of the substance that are respectively in the first state, which lie at a distance from their closest neighboring molecules in the first state which is greater than the spatial resolution limit of the imaging of the specimen onto the sensor array, from the images recorded by the sensor array, characterized in that the first state and the second state are different electronic states of the molecules of the substance. - selecting a substance from a group of substances, - which have a first state with first fluorescent properties and a second state with second fluorescent properties; - which can be excited in the first state by light of one wavelength to spontaneously emit fluorescent light; - which can be converted from the first state into their second state by the light of the one wavelength and - which can return from their second state into their first state; - which have a first state with first fluorescent properties and a second state with second fluorescent properties; - which can be excited in the first state by light of one wavelength to spontaneously emit fluorescent light; - which can be converted from the first state into their second state by the light of the one wavelength and - which can return from their second state into their first state; - marking the specimen's structure of interest with molecules of the substance; - imaging the specimen onto a sensor array, wherein a spatial resolution limit of the imaging being greater (i.e. worse) than an average spacing between closest neighboring molecules of the substance in the specimen; - exposing the specimen to the light of the one wavelength in at least one region which has dimensions larger than the spatial resolution limit of the imaging of the specimen onto the sensor array, alternately wherein fractions of the molecules of the substance being in the first state being excited by the light of the one wavelength to spontaneously emit fluorescent light and being converted into their second state, and wherein at least 10% of the molecules of the substance that are respectively in the first state lying at a distance from their closest neighboring molecules in the first state which is greater than the spatial resolution limit of the imaging of the specimen onto the sensor array; - registering an intensity distribution of the fluorescent light which is spontaneously emitted from the region of the molecules of the substance, in a plurality of images recorded by the sensor array during continued exposure of the specimen to the light of the one wavelength; and - determining the position in the specimen of the molecules of the substance that are respectively in the first state, which lie at a distance from their closest neighboring molecules in the first state which is greater than the spatial resolution limit of the imaging of the specimen onto the sensor array, from the images recorded by the sensor array, characterized in that the first state and the second state are different electronic states of the molecules of the substance.