The disclosure relates to a microlithographic projection exposure apparatus, as well as related components and methods. In some embodiments, a microlithographic projection exposure apparatus includes an illumination system and a projection objective, where the illumination system can illuminate an object plane of the projection objective and the projection objective can produce the image of the object plane on an image plane. A polarization-dependent transmission can be produced in the illumination system such that, for at least one polarization distribution in respect of the light impinging on the object plane, a non-homogeneous intensity distribution in the object plane is obtained. The non-homogeneous intensity distribution can afford a homogeneous intensity distribution in the image plane by virtue of polarization-dependent transmission properties of the projection objective.