Processes for producing semiconductor components and/or other finely structured components include providing a projection objective having a mirror that is located within a predetermined proximity to a pupil surface of a projection objective. In one variant, an image of a pattern is projected onto a light-sensitive substrate in multiple exposures, in which a first pupil filter function is set on the mirror during a first exposure and, during a subsequent, second exposure, a different, second pupil filter function is set by local changes of geometric reflective properties of the mirror in a locally resolving manner.