Method of manufacturing an X-ray optical element for an X-ray analysis apparatus

A method of manufacturing an X-ray optical element. The element consists of a body of a material having a shape memory. At a high temperature, i.e. a temperature beyond the transition temperature of the material, the body is pressed so as to impart a first, desired shape. A surface of the body is thus shaped for example, as a logarithmic spiral or as another curved shape. After cooling to a low temperature, i.e. a temperature below the transition temperature of the material, a second, machinable shape is imparted to the body, preferably a flat surface. A number of precision operations can be performed on this second, machinable shape, for example polishing to a surface roughness of 0.5 nm RMS. Subsequent to this precision operation, the body is heated and resumes its first, desired shape which is retained after cooling. The body can be provided, if desired, with a comparatively thin surface layer which is also polished in the flat shape and which bends when the body resumes the desired shape. This layer can be chosen on the basis of desired mechanical (polishability) or X-ray optical properties. The X-ray optical element may comprise notably a multilayer mirror for X-ray purposes, thus forming a high- precision crystal for wavelength analysis.