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The manufacture and properties of compound refractive lenses (CRLs) for hard X-rays with parabolic profile are described. These novel lenses can be used up to ∼60 keV. A typical focal length is 1 m. They have a geometrical aperture of 1 mm and are best adapted to undulator beams at synchrotron radiation sources. The transmission ranges from a few % in aluminium CRLs up to about 30% expected in beryllium CRLs. The gain (ratio of the intensity in the focal spot relative to the intensity behind a pinhole of equal size) is larger than 100 for aluminium and larger than 1000 for beryllium CRLs. Due to their parabolic profile they are free of spherical aberration and are genuine imaging devices. The theory for imaging an X-ray source and an object illuminated by it has been developed, including the effects of attenuation (photoabsorption and Compton scattering) and of the roughness at the lens surface. Excellent agreement between theory and experiment has been found. With aluminium CRLs a lateral resolution in imaging of 0.3 µm has been achieved and a resolution below 0.1 µm can be expected for beryllium CRLs. The main fields of application of the refractive X-ray lenses are (i) microanalysis with a beam in the micrometre range for diffraction, fluorescence, absorption, scattering; (ii) imaging in absorption and phase contrast of opaque objects which cannot tolerate sample preparation; (iii) coherent X-ray scattering.
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