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Parabolic refractive X-ray lenses are optical components, especially suitable for third-generation synchrotron radiation sources. This article describes the status of the development of our lenses and illustrates the possibilities for micrometre and submicrometre focusing and for X-ray imaging in absorption and phase contrast. The parabolic lens profile ensures distortion-free imaging of high quality. First characteristics of Be lenses are given. A microscope based on Be lenses is expected to have a lateral resolution below 80 nm.

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