The disclosure provides an illumination system of a microlithographic projection exposure apparatus, as well as related methods and components. In some embodiments, the illumination system includes an optical element configured so that, when a linearly polarised entry beam which has an angle spectrum is incident on the first optical element, a maximum aperture angle of the entry beam at the first optical element is not more than 35 mrad. A component, which is rotationally symmetric about an optical axis of the system, of a birefringence present in the illumination system can be at least partially compensated by the first optical element.