A mirror (1) for a microlithography projection exposure apparatus including a substrate (3) and a reflective coating (5). A functional coating (11) between the substrate (3) and the reflective coating (5) has a local form variation (19) for correcting the surface form of the mirror (1), wherein the local form variation (19) is brought about by a local variation in the chemical composition of the functional coating (11) and wherein a thickness of the reflective coating (5) is not changed by the local variation in the chemical composition of the functional coating (11). The local variation in the chemical composition of the functional coating (11) can be brought about by bombardment with particles (15), for example with hydrogen ions.