Transmission and gain of singly and doubly focusing refractive x-ray lenses

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Abstract
Multiple refractive lenses with a focal length of 1 to 2 m are a new tool for focusing hard x rays to a spot size in the micrometer range. They may be used for microdiffraction, microfluorescence, and coherent imaging. The lenses may be focusing in one or two dimensions. In this article, we have calculated the transmission and the gain for linear lens arrays, for crossed linear arrays and for doubly focusing lenses with parabolic profile. It is essential to minimize the mass absorption coefficient μ/ρ by choosing low Z materials in order to optimize the transmission. The gain of the lenses can be as high as 5000 and more, i.e., the intensity in the focal spot can be 5000 times higher than that behind a pinhole of size equal to the spot size. In real lenses the gain is smaller and the focal spot is blurred by lens imperfections, by Compton scattering, and by small angle x-ray scattering (SAS). In the present investigation different low Z materials have been tested for SAS. Different linear and crossed linear lenses made of beryllium, boron nitride, pyrographite, plexiglass, polycarbonate, polyoxymethylene, Vespel, and aluminium have been tested for focal spot size, gain, and background. The maximum gain obtained up to now was 13. The focal spot size is slightly larger than the value expected from demagnification of the source size. Possibilities for improving the lens performance are discussed.