The disclosure relates to an illumination system for EUV lithography, as well as related elements, systems and methods. In some embodiments, an illumination system includes a first optical element and a second optical element. The first optical element can include a plurality of first facet elements configured so that, when impinged by respective partial beams of radiation, the plurality of first facet elements produce secondary light sources. The second optical element can include a second optical element including a plurality of second facet elements. Each of the plurality of second facet elements can be assigned to at least one of the plurality of first facet elements. The plurality of second facet elements can be configured to be impinged by the radiation via the first optical element.