Patent Number: 
Section: claims

1. A method for producing a mirror element that has a substrate and a reflective coating for extreme ultraviolet wavelength radiation, comprising:pre-compacting the substrate by hot isostatic pressing,applying the reflective coating to a surface region of the pre-compacted substrate, and further compacting the pre-compacted substrate by irradiating the pre-compacted substrate with at least one of ions and electrons in a surface region of the substrate,wherein the pre-compacted substrate is irradiated until a density in the surface region is at least 0.5% higher than a density of a remainder of the substrate that is not in the irradiated region. 2. The method according to claim 1, wherein the pre-compacted substrate is irradiated homogeneously before the coating is applied in the surface region. 3. The method according to claim 1, wherein the coating is applied before the pre-compacted substrate is irradiated homogeneously. 4. The method according to claim 1, further comprising selecting a doped glass material or a glass ceramic as the material for the substrate. 5. The method according to claim 1, wherein the temperature during the hot isostatic pressing is selected to be between 1100° C. and 1300° C. 6. The method according to claim 5, wherein the temperature during the hot isostatic pressing is selected to be between 1150° C. and 1250° C. 7. The method according to claim 1, wherein the pressure during the hot isostatic pressing is selected to be between 20 MPa and 250 MPa. 8. The method according to claim 7, wherein the pressure during the hot isostatic pressing is selected to be between 50 MPa and 150 MPa. 9. The method according to claim 1, wherein the holding time during the hot isostatic pressing is selected to be between 0.5 hour and 5 hours. 10. The method according to claim 9, wherein the holding time during the hot isostatic pressing is selected to be between 2 hours and 4 hours. 11. The method according to claim 1, wherein the substrate is compacted by the hot isostatic pressing by at least 1%, preferably by at least 1.5%, in particular by at least 3%. 12. The method according to claim 11, wherein the substrate is compacted by the hot isostatic pressing by at least 3%. 13. The method according to claim 1, wherein at least one of:(a) the ions have an energy of between 0.2 MeV and 10 MeV at a total particle density of from 1014 to 1016 ions per cm2, and(b) the electrons have a dose of between 10 J/mm2 and 1000 J/mm2 at energies of between 10 KeV and 20 KeV. 14. The method according to claim 1, further comprising: carrying out the irradiation until there is obtained in the surface region a density that is at least 1% higher than the density of the remainder of the substrate. 15. The method according to claim 14, wherein the irradiation is carried out until there is obtained in the surface region a density that is at least 1.5% higher than the density of the remainder of the substrate. 16. The method according to claim 14, wherein the surface region extends to a depth of 5 μm from the surface of the substrate.