In high spatial resolution imaging, a structure in a specimen is marked with a substance which, in a first electronic state, is excited by light of one wavelength to emit fluorescent light, which is also converted from its first into a second electronic state by that light, and which returns from its second into its first electronic state. The specimen is imaged onto a sensor at a spatial resolution not resolving an average spacing between neighboring molecules of the substance, and exposed to the light at such an intensity that the molecules in the first state are alternately excited to emit fluorescent light and converted into their second state, and that at least 10% of the molecules presently in their first state lie at a distance from their closest neighboring molecules in their first state which is greater than the spatial resolution of the imaging onto the sensor.