Patent Number: 
Section: claims

1. A method for manufacturing a reflector for X-ray ray radiation having a curved substrate and a multi-layer coating deposited on the substrate, the method comprising the steps of:a) determining a first non-circular arc shape for the substrate along a first cross-section, extending in an XZ plane containing an X direction;b) determining, following step a), a d-value dependence that satisfies Bragg's condition in the X direction;c) determining, in a YZ plane containing a Y direction perpendicular to the X direction, a deviation from a uniform coating dependence that results from a method of deposition of the coating, for a circular substrate shape in the YZ plane;d) determining a second non-circular arc shape for the substrate along a second cross section, extending in the Y direction to compensate for the deviation determined in step c) by bringing regions of the reflector where coating deviations in the Y direction occur into Bragg reflection for a desired wavelength; ande) producing the reflector following steps a) to d), wherein the mirror focuses, renders parallel, or otherwise optically aligns the X-ray radiation in both the X and Y directions using one single reflection. 2. The method of claim 1, wherein the second arc shape of the reflector along the second cross section defines focusing properties of the reflector. 3. The method of claim 2, wherein the focusing properties are within the YZ plane. 4. The method of claim 1, wherein the first arc shape is parabolic, hyperbolic, or elliptical along the first cross-section. 5. The method of claim 1, wherein the multi-layer coating comprises a periodically repeating sequence of layers of materials A, B, . . . with different refractive indices, wherein a sum d=dA+dB+. . . of thicknesses dA, dB. . . of successive layers of the materials A, B, . . . changes continuously along the X-direction. 6. The method of claim 5, wherein the sum changes monotonically. 7. The method of claim 6, wherein the sum changes along the second cross-section. 8. The method of claim 7, where the sum changes by more than 2%. 9. The method of claim 7, wherein a curvature of the reflector along the second cross-section compensates for a change in said sum d along the second cross-section by differing from a comparable reflector with a constant sum d and circular curvature along a respective second cross-section thereof for given focusing and reflectivity properties of the reflector. 10. A reflector produced by the method of claim 9, wherein said first non-circular arc shape differs from said second non-circular arc shape. 11. The method of claim 1, wherein the second arc shape has an elliptical curvature of different lengths of semi-axes along the second cross-section. 12. The method of claim 1, wherein the second arc shape has a parabolic curvature along the second cross section. 13. The method of claim 1, wherein the reflector has a reflecting surface width of more than 2 mm as measured perpendicular to the X-direction. 14. The method of claim 13, wherein the width is at least 4 mm. 15. An X-ray analysis device comprising an X-ray source, an X-ray detector, optical shaping and/or delimiting means and the reflector produced by the method of claim 1, wherein said first non-circular arc shape differs from said second non-circular arc shape. 16. The X-ray analysis device of claim 15, wherein X-ray radiation impinges on the reflector at an angle of less than 5° with respect to the X-direction. 17. The X-ray analysis device of claim 15, wherein a curvature of the reflector along the second cross-section is formed such that a reflectivity of the reflector is maximum for a wavelength of radiation generated by said X-ray source. 18. The X-ray analysis device of claim 15, wherein the reflector focuses X-ray radiation impinging thereon to a focal spot. 19. The X-ray analysis device of claim 18, wherein the focal spot is on a sample or on the X-ray detector. 20. The X-ray analysis device of claim 15, wherein the reflector generates parallel rays. 21. A reflector produced by the method of claim 1, wherein said first non-circular arc shape differs from said second non-circular arc shape.