Patent Number: 
Section: claims

1. A method for producing a multilayer coating comprising a plurality of layers for reflecting radiation in the soft X-ray or extreme-ultra-violet wavelength range on an optical element which has an optical surface and is operated at an operating temperature (TOP) of at least 30° C., comprising:determining an optical design for the multilayer coating which defines an optical desired layer thickness (nOP dOP) of the layers of the multilayer coating at the operating temperature (TOP), andapplying the layers of the multilayer coating with an optical actual layer thickness (nB dB) selected such that a layer thickness change (nOP dOP−nB dB) caused by thermal expansion of the layers between a coating temperature (TB) and the operating temperature (TOP) is compensated, wherein at least one of:the optical design of the multilayer coating of the optical element is at least substantially optimized with regard to reflectivity of the optical element for an operating wavelength (λ0) at the operating temperature (TOP) andthe operating temperature (TOP) of the optical element varies at least in one direction along the optical surface and, during the coating of the optical element the layers are applied with actual layer thicknesses (dB,x) which vary along the at least one direction. 2. The method as claimed in claim 1, wherein, for determining the layer thickness change (nOP dOP−nB dB) a linear thermal expansion coefficient of the layers of the multilayer coating is determined or at least one optical property of the optical element is measured at the operating temperature (TOP). 3. The method as claimed in claim 1, wherein the optical actual layer thickness (nB dB) is selected to at least substantially equal the optical desired layer thickness (nOP dOP), and the coating of the optical element is effected at at least substantially the operating temperature (TOP). 4. An optical element comprising: a multilayer coating for reflecting radiation in the soft X-ray or extreme-ultraviolet wavelength range, and provided for operation in a beam path of an optical arrangement at an operating temperature (TOP) of at least 30° C.,wherein an optical design of the multilayer coating is at least substantially optimized with regard to a reflectivity (R) of the optical element for a given operating wavelength (λ0), at the operating temperature (TOP). 5. The optical element as claimed in claim 4, wherein a wavelength (λ) of a maximum value of the reflectivity (R) of the optical element at the operating temperature (TOP) corresponds to the operating wavelength (λ0), the wavelength (λ) of the maximum value of the reflectivity (R) of the optical element at the operating temperature (TOP) being shifted relative to the wavelength (λ) of the maximum value of the reflectivity (R) of the optical element at room temperature (TR) by more than 2 per mille, with respect to the operating wavelength (λ0). 6. The optical element as claimed in claim 4, wherein the reflectivity (R) of the optical element at the operating temperature (TOP) is maximized for an average angle of light incidence which lies between 0° and 30°. 7. An optical arrangement, comprising:an illumination system arranged to illuminate an object plane,a projection system arranged to image a structure in the object plane into an image plane andat least one optical element as claimed in claim 4 and arranged in a beam path of the optical arrangement. 8. The optical arrangement as claimed in claim 7, wherein the at least one optical element is designed such that at least one imaging aberration of the optical arrangement at the operating temperature (TOP) of the optical element is at least substantially optimized. 9. The optical arrangement as claimed in claim 8, wherein the imaging aberration is selected from the group consisting of: telecentricity, uniformity, pupil ellipticity and pupil apodization. 10. The optical arrangement as claimed in claim 9, wherein a gradient, in at least one direction, of layer thicknesses (dOP,x) of layers of the multilayer coating of at least one optical element arranged in the illumination system is selected such that, at the operating temperature (TOP) of the optical element, an absolute value of uniformity (U) in an object plane of the optical arrangement in the at least one direction is less than 5%. 11. The optical arrangement as claimed in claim 7, wherein the at least one optical element comprises a plurality of optical elements which, during operation of the optical elements with respective operating temperature (TOP) for the operating wavelength (λ0), has a maximum total transmission which is increased by at least 2% relative to operation of the optical elements at room temperature (TR). 12. The optical arrangement as claimed in claim 7, wherein at least two optical elements that succeed one another in the beam path have differing respective operating temperatures (TOP) during operation of the optical arrangement. 13. The optical arrangement as claimed in claim 7, further comprising at least one heating element configured to heat an optical surface of the at least one optical element to the operating temperature (TOP). 14. An optical element comprising: a multilayer coating comprising a plurality of layers, for reflecting radiation in the soft X-ray or extreme-ultraviolet wavelength range, and provided for operation in a beam path of an optical arrangement at an operating temperature (TOP) of at least 30° C.,wherein an optical design of the multilayer coating is at least substantially optimized with regard to at least one temperature-dependent optical property,wherein the operating temperature (TOP) varies at least in one direction along an optical surface of the optical element, and wherein the multilayer coating, for optimizing the at least one optical property has a gradient of layer thicknesses (dB,x) of the layers of the multilayer coating in the at least one direction. 15. The optical element as claimed in claim 14, embodied as a facet mirror and further comprising a plurality of individual mirrors, at least one optical property of each of the respective individual mirrors being at least substantially optimized at the operating temperature (TOP). 16. An optical arrangement, comprising:an illumination system arranged to illuminate an object plane,a projection system arranged to image a structure in the object plane into an image plane andat least one optical element as claimed in claim 14 and arranged in a beam path of the optical arrangement.