An illumination system for EUV microlithography includes an EUV light source which generates EUV illumination light with an etendue that is higher than 0.01 mm2. The EUV light source generates a sequence of EUV light pulses having a pulse sequence frequency. An illumination optics of the illumination system is used to guide the illumination light from the light source to an object field. At least one optical modulation component of the illumination system is preferably modulatable synchronously with the pulse sequence frequency. The result is an illumination system where a homogeneity of an object field illumination is improved.