Potential of a beryllium x-ray lens

The use of refractive lenses for focusing x-ray beams has been the subject of publications since the early 1980s. Detailed calculations have been made for different shapes for the refractive lens: cylindrical, spherical, parabolic, and for a Fresnel-type refractive lens. The main drawback to the use of a single refractive lens to focus x-rays is that the index of refraction (n = 1 {minus} {delta}) is very close to 1, which results in a lens with a very long focal length. Recently Snigerov and others have suggested and experimentally demonstrated, using cylindrical-shaped lenses, that this problem of long focal lengths can be overcome by using many lenses in series. Each lens refracts the photon through a small angle, but the sum of these sequential changes in direction can be moderately larger. This increase in effective refraction angle reduces the focal length of the lens to a few meters or less and makes the multi-element lens a much more useful instrument for focusing x-rays. This paper, annualizes the expected performance of a lens consisting of a series of aligned hollow spheres in a beryllium substrate. The use of hollow spheres rather than hollow cylinders produces focusing of the x rays into a small focal spot in contrast to the single-directional focusing of the hollow cylinders, which produces a line focus. Two multi-element lenses have been constructed: one with 20 1-mm-diameter hollow spheres in an aluminum substrate, and one with 50 hollow spheres, 1 mm in diameter, in a beryllium substrate. Some construction details and calculations of the expected performance, are given for these two multi-element lenses.