A projection exposure apparatus for microlithography has an illumination system with an EUV light source and an illumination optical unit to expose an object field in an object plane. A projection optical unit images the object field into an image field in an image plane. A pupil facet mirror in a plane of the illumination optical unit that coincides with a pupil plane of the projection optical unit or that is optically conjugate with respect thereto has a plurality of individual facets on which illumination light can impinge. A correction diaphragm is in or adjacent to a pupil plane of the projection optical unit or in a conjugate plane with respect thereto. The correction diaphragm screens the illumination of the entrance pupil of the projection optical unit so that at least some source images assigned to the individual facets of the pupil facet mirror in the entrance pupil of the projection optical unit are partly shaded by one and the same diaphragm edge. The form of the diaphragm edge is predefined for the partial shading of the source images assigned to the pupil facets in the entrance pupil of the projection optical unit for the correction of the telecentricity and the ellipticity of the illumination.