Patent Number: 
Section: claims

1. A mirror comprising: a substrate of crystal,  an amorphous cover layer applied to said substrate,  and a reflecting multilayer that covers said amorphous cover layer. 2. The mirror according to  claim 1 , wherein said substrate comprises at least one of the following materials: diamond, BN, SiC, and silicon. claim 1 3. The mirror according to  claim 1 , wherein said cover layer comprises at least one of the following amorphous materials: quartz glass, SiO 2 , and Al 2 O 3 . claim 1 4. The mirror according to  claim 1 , wherein said amorphous cover layer has a thickness in the range of 1 xcexcm through 100 xcexcm. claim 1 5. The mirror according to  claim 1 , wherein said amorphous cover layer has a micro-roughness in the angstrom range. claim 1 6. The mirror according to  claim 1 , wherein said reflecting layer comprises a multilayer constituted for a wavelength region of 10 nm to 20 nm. claim 1 7. The mirror according to  claim 6 , wherein said multilayer is constituted for a wavelength region of 13 nm. claim 6 8. The mirror according to  claim 1 , wherein said mirror has a curved surface. claim 1 9. A production process for a mirror, comprising the steps of shaping a substrate of crystal close to its final contour,  depositing an amorphous cover layer on a mirror side of said substrate,  optical final polishing, and  applying a reflecting layer. 10. The production process according to  claim 9 , comprising depositing said amorphous cover layer by CVD. claim 9 11. An EUV projection exposure device, comprising: an EUV source,  an illuminating optics,  a mask,  a projection objective,  a wafer, and  at least one mirror comprising a substrate of crystal, an amorphous cover layer applied to said substrate, and a reflecting layer that covers said amorphous cover layer included in said illuminating optics or in said projection objective. 12. A mirror comprising: a substrate of crystal,  an amorphous cover layer applied to said substrate,  and a reflecting layer that covers said amorphous cover layer,  wherein said substrate comprises at least one of the following materials: diamond, BN, and SiC. 13. A mirror comprising: a substrate of crystal,  an amorphous cover layer applied to said substrate,  and a reflecting layer that covers said amorphous cover layer,  wherein said cover layer comprises Al 2 O 3 . 14. A mirror comprising: a substrate of crystal,  an amorphous cover layer applied to said substrate,  and a reflecting layer that covers said amorphous cover layer,  wherein said amorphous cover layer has a micro-roughness in the angstrom range.