An illumination optical unit includes a collector mirror which produces a polarization distribution that is applied to the first faceted optical element during the operation of the illumination optical unit. There are at least two first facet elements to which radiation having a differing polarization is applied. The first faceted optical element has at least one first state in which the normal vectors of the reflective surfaces of the first facet elements are selected so that a first predetermined polarization distribution results at the location of the object field during the operation of the illumination optical unit.