X-ray spectroscopic examinations require a constant size of the focal spot at the location of the sample, which spot should be less than 1 µm over a wide photon energy range, possibly several keV. For instance, the energy range in EXAFS investigations is approx. 1 keV, in XANES examinations, approx. 0.1 keV. These requirements are met by an X-ray lens which has between 100 and 1000 lens elements, each of them with a quasi-parabolic profile. The quasi-parabolic profile is generated preferably by a periodic function. This ensures that no local radiation peaks other than the intended focal spot occur in adjacent areas. X-ray lenses with quasi-parabolic profile, unlike conventional X-ray lenses with parabolic profile, have a clearly increased focal depth. The constancy of the width of the focal spot over a specific focal depth allows X-ray spectroscopic examinations to be conducted within a broad range of energies, i.e. over several keV, without the illuminated area changing its shape and size. This ensures that the spectroscopic information for all energies within the energy range comes from the same sample volume.