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A Fresnel-like X-ray lens can be constructed by a triangular array of identical prisms whose base corresponds to the 2\pi-shift length. Each column of prisms is progressively shifted from the optical axis by an arbitrary fraction of the prism height. Similarly to the multi-prism lens, quasi-parabolic profiles are formed by a superposition of straight-line segments. The resulting projected lens profile is approximately linear with a Fresnel-lens pattern superimposed on it to provide the focusing. This geometry exhibits a significantly larger effective aperture than conventional parabolic refractive lenses. Prototype lenses were fabricated by deep reactive ion etching of silicon. These one-dimensionally focusing lenses were tested at a synchrotron beamline and provided focal line-widths down to 1.4 µm FWHM and an intensity gain of 39 at a photon energy of 13.4 keV. Fabrication imperfections gave rise to unwanted interference effects resulting in several intensity maxima in the focal plane. The presented design allows the focal length to be shortened without decreasing the feature size of the lens. Furthermore, this feature size does not limit the resolution as for real Fresnel optics.

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