Among other things, an illumination device (10) is described for one, two or more observation beam paths, each with an observation device having an observation beam bundle, in particular for an operating microscope, having at least one light source (12) for producing at least one illumination beam bundle for illuminating an object to be observed (13), in particular, an eye to be observed, wherein the at least one illumination beam bundle runs coaxially to an observation beam bundle. It is provided according to the invention, in order to be able to suppress disruptive reflections, that illumination device (10) has an illumination optics (11) that is constructed according to the Köhler principle of illumination, and in which at least one reflection diaphragm (18) is provided in order to avoid light reflected from the surface of an objective element (19). In addition, a correspondingly improved observation device is described.