On aberrations in saw‐tooth refractive X‐ray lenses and on their removal

The X‐ray lens, which is composed of opposing canted saw‐tooth structures, originally assembled from cut‐out pieces from long‐playing records, is understood by recognizing that an incident plane X‐ray wave will traverse a varying number of triangular prisms in them. The refraction will deflect any beam towards the prism tips and the variation of the deflection angle, which grows linearly with the number of traversed prisms, can result in X‐ray focusing. The structure offers focusing flexibility by simply changing the taper angle. This report will discuss the aberrations arising in the saw‐tooth structure in its simplest form with identical prisms. It is found that the saw‐tooth structures in low‐ Z materials with focal length below 1 m provide less flux density in the focal spot than stacks of one‐dimensionally focusing refractive lenses with identical transmission function. This is due to excessive aberrations in the regular structure, which are absent in stacks of concave lenses, and which limit the focusing to spot sizes of just submicrometre dimensions, as measured experimentally for some lenses. It will be shown that this limitation can be overcome by appropriately modifying the prism shape. Then the image size could be reduced by about an order of magnitude to the diffraction limit with competitive numbers even below 0.1 µm. Microfabrication techniques are identified as the appropriate means for producing the structures.