The disclosure relates to a microlithographic projection exposure apparatus and a microlithographic projection exposure apparatus, as well as related components, methods and articles made by the methods. The microlithographic projection exposure apparatus includes an illumination system and a projection objective. The illumination system can illuminate a mask arranged in an object plane of the projection objective. The mask can have structures which are to be imaged. The method can include illuminating a pupil plane of the illumination system with light. The method can also include modifying, in a plane of the projection objective, the phase, amplitude and/or polarization of the light passing through that plane. The modification can be effected for at least two diffraction orders in mutually different ways. A mask-induced loss in image contrast obtained in the imaging of the structures can be reduced compared to a method without the modification.