Apparatus for the light-induced scanning-microscope display of specimen parameters and of their distribution, in which apparatus the specimen is scanned on the illumination side by a beam of light, and radiation emitted by the specimen and not contained in the illumination-side spectral region is detected in phase with the scanning raster, characterized by the fact that, between the source of light and the specimen (4, 24, 44, 119) there are, first a splitting mirror (5, 22, 104), and then means (3, 23, 120) for the raster-like deflection of the beam of light, and then an objective (17, 25, 113) for focusing the light beam on the specimen, and further characterized by the fact that radiation coming from the specimen is focused on at least one stationary detector (13, 29, 47, 116), the latter focus being via the objective (17, 25, 113), the deflection means (3, 23, 120), and the splitter mirror (5, 22,104).