An illumination optical unit for EUV microlithography includes a first optical element having a plurality of first reflective facet elements and a second optical element having a plurality of second reflective facet elements. Each first reflective facet element from the plurality of the first reflective facet elements has a respective maximum number of different positions which defines a set—associated with the first facet element—consisting of second reflective facet elements in that the set consists of all second facet elements onto which the first facet element directs radiation in its different positions during the operation of the illumination optical unit. The plurality of second reflective facet element forms a plurality of disjoint groups, wherein each of the groups and each of the sets contain at least two second facet elements, and there are no two second facet elements of a set which belong to the same group. This construction makes it possible to provide an illumination optical unit which can be used to provide a large number of different angle-dependent intensity distributions at the location of the object field.