An illumination system of a microlithographic projection exposure apparatus comprises an optical raster plate having a light entrance surface. An irradiance distribution on the light entrance surface determines an angular light distribution of projection light when it impinges on a mask to be illuminated. The illumination system further comprises a control unit and a spatial light modulator which produces on the light entrance surface of the optical raster plate a plurality of light spots whose positions can be varied. At least some of the light spots have, along a reference direction (X), a spatial irradiance distribution comprising a portion in which the irradiance varies periodically with a spatial period P.