[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

These simple considerations demonstrate the principal

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These simple considerations demonstrate the principal possibility of turn- ing X-ray beams to relatively large angles by using multiple reflections on
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94 V. Arkadiev and A. Bjeoumikhov specially curved surfaces at grazing angle incidence and form the theoretical basis of the capillary optics. Main Elements of the Capillary Optics Preparation of a surface for total external reflection reveals itself very often as a very difficult problem. On the one hand, the surface must be very smooth. On the other hand, the form of the surface must guarantee that the incidence angle remains smaller than the critical angle of the total external reflection. The demands on grazing incidence mirrors are so high that these mirrors are usually very expensive. It is no wonder that preparation of a surface form to multiple subsequent reflections could be a much harder problem. The main idea of X-ray capillary optics is to use hollow channels in glass for transporting X-ray radiation [55–57]. Such an approach enables to solve several difficult problems at once. First, the surface of glass is smooth enough for reflections with a high reflection coefficient. Second, the form of the chan- nels usually guarantees that the second and all subsequent reflections take place automatically at incidence angles smaller than the critical angle θ cr if the incidence angle at the first reflection does not exceed θ cr . Third, there is an established technology of manufacturing glass capillaries. The simplest element of the X-ray capillary optics is a straight cylindrical monocapillary. Due to the axial symmetry, after the first reflection at an inci- dence angle θ < θ cr all the subsequent reflections occur also at the same angle θ < θ cr so that the radiation captured at the capillary entrance is transported further along its length with minimum losses. Usually a direct beam from an X-ray source is divergent and its intensity falls down as the inverse square of the source–sample distance. In contrast to it, radiation captured by a capil- lary is confined inside this capillary and can be transported to large distances without spreading. This can result in considerable radiation density increase on a sample. The efficiency of applying a capillary is usually described by the notion “intensity gain” relative to a pinhole collimator of the same diameter placed instead of a capillary at its end. Intensity gain originates from a larger angular aperture of a capillary as compared with a pinhole and can be easily estimated in the following way. The angular aperture of a capillary is 2 θ cr , while the aperture of a pinhole collimator is d / R , where d is a collimator (cap- illary) diameter and R is a source–collimator distance. Neglecting intensity losses at reflections, one can obtain the following simple expression for the intensity gain: gain 2 θ cr R d 2 .
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