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The manufacture and properties of compound refractive lenses (CRLs) for hard X-rays with parabolic pro®le 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 pro®le 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 mm has been achieved and a resolution below 0.1 mm can be expected for beryllium CRLs. The main ®elds of application of the refractive X-ray lenses are (i) microanalysis with a beam in the micrometre range for diffraction,¯uorescence, absorption, scattering; (ii) imaging in absorption and phase contrast of opaque objects which cannot tolerate sample preparation; (iii) coherent X-ray scattering.

Based on nanofocusing refractive x-ray lenses a hard x-ray scanning microscope is currently being developed and is being implemented at beamline ID13 of the European Synchrotron Radiation Facility (Grenoble, France). It can be operated in transmission, fluorescence, and diffraction mode. Tomographic scanning allows one to determine the inner structure of a specimen. In this device, a monochromatic (E=21keV) hard x-ray nanobeam with a lateral extension of 47×55nm2 was generated. Further reduction of the beam size to below 20 nm is targeted.

We present the upgrade and present status of the ultrasmall-angle x-ray scattering ͑USAXS͒ beamline BW4 at the Hamburg Synchrotronstrahlungslabor. In order to extend the accessible scattering vector range, new small-angle setups have been established, making use of the high flux and small divergence of BW4. In standard transmission geometry using a beam size of B = 400 ϫ 400 m 2 ͑horizontalϫ vertical͒, typical small-angle resolution ranges from d max = 90 to 650 nm, depending on sample-to-detector distance. Additionally a new microfocus option has been established. This microfocus option allows reducing the sample size by one order of magnitude. Using parabolic beryllium compound refractive lenses, a new standard beam size of B =65 ϫ 35 m 2 ͑horizontalϫ vertical͒ can be provided. The -SAXS resolution is as high as d max = 150 nm. Using -SAXS in combination with grazing incidence ͑-GISAXS͒ on a standard noble metal gradient multilayer, we prove the feasibility of -GISAXS experiments at a second generation source.