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In the hard x-ray range, optics based only on refraction, as in the case of visible optics, require extremely small (a few microns) bending radii of the crystal monochromators, since the deviation of the refraction index (δ = 1-n) from unity is of the order of 10-6. Based on the principle of a series of N refractive lenses, compound refractive lenses provide an appreciable focus at a reasonable distance, but the photon flux is limited by absorption because of the generally high value of N required. As the effect of refraction is very weak, x-rays deviate considerably when diffraction occurs in a crystal in Bragg geometry: this is the base of many crystal optics devices. Focusing with crystal optics is generally achieved bending the crystals to modify the orientation of the lattices planes or modulating the entrance surface of a flat or curved crystal, the so-called Bragg-Fresnel lens. Sagittal focusing can be also obtained using asymmetrically cut crystals. From a general point of view the focusing by means of bent crystals in Laue geometry is interesting when high energies are used, because the absorption due to the transmission in the crystals is very limited. The use of bent crystals has two big advantages: it allows to accept a great divergence of the incoming radiation, thus increasing the flux of the focused radiation and allowing at the same time to select its frequencies, owing to the Darwin width of the considered reflection. Indeed, the crystal bending enables the diffracting planes to be crossed at the Bragg angle corresponding to each ray of the incident beam and, at the same time, the diffraction process produces a monochromatic beam. Actually, a small Bragg angle implies a rather long beam path in the crystal in the case of Bragg geometry, whereas in Laue geometry the incidence is almost normal: the absorption is therefore minimized upon using a suitably thin crystal. We suggest here a method allowing to improve the quality of high energy polychromatic focusing by bent crystals in Laue geometry.
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