The reflective optical element for the EUV wavelength range, method for production and for the correction of such an element, projection objective for microlithography having such a member and the projection exposure system for microlithography with a projection lens such

The invention relates to a reflective optical element 39 for the EUV wavelength range having a coating applied on the surface of a substrate layer arrangement, wherein the layer arrangement comprises at least one layer portion of system 37, which consists of a periodic sequence of at least one period of individual layers, wherein the period of two individual layers comprises different refractive index in the EUV wavelength range, wherein the substrate at least along an imaginary surface 30 with a fixed distance between 0 microns and 100 microns from the surface has a variation of density of more than 1% by volume, and wherein the substrate either by a protective layer is protected by a protective layer or sub-system of the layer arrangement or by a suitably compacted surface region 35 of the substrate prior to a long-term aging or compaction by EUV radiation. Moreover, the invention relates to a method for generating such a reflective optical element. Furthermore, the invention relates to a method for the correction of such a reflective optical element, and a projection lens having such an optical element, as well as a projection exposure apparatus comprising such a projection lens.