A projection exposure apparatus for microlithography comprises illumination optics for illuminating object field points of an object field in an object plane is disclosed. The illumination optics have, for each object field point of the object field, an exit pupil associated with the object point, where sin(γ) is a greatest marginal angle value of the exit pupil. The illumination optics include a multi-mirror array that includes a plurality of mirrors to adjust an intensity distribution in exit pupils associated to the object field points. The illumination optics further contain at least one optical system to temporally stabilize the illumination of the multi-mirror array so that, for each object field point, the intensity distribution in the associated exit pupil deviates from a desired intensity distribution in the associated exit pupil in the case of a centroid angle value sin(β) by less than 2% expressed in terms of the greatest marginal angle value sin(γ) of the associated exit pupil and/or, in the case of ellipticity by less than 2%, and/or in the case of a pole balance by less than 2%.