The disclosure relates to an illumination system of a microlithographic projection exposure apparatus. The illumination system can include a depolariser which in conjunction with a light mixing system disposed downstream in the light propagation direction at least partially causes effective depolarisation of polarised light impinging on the depolariser. The illumination system can also include a microlens array which is arranged upstream of the light mixing system in the light propagation direction. The microlens array can include a plurality of microlenses arranged with a periodicity. The depolariser can be configured so that a contribution afforded by interaction of the depolariser with the periodicity of the microlens array to a residual polarisation distribution occurring in a pupil plane arranged downstream of the microlens array in the light propagation direction has a maximum degree of polarisation of not more than 5%.