A very simple method of sagittal focusing of X-ray synchrotron radiation is presented. A special ray-tracing program which utilizes the diffraction-refraction effect is developed. It is demonstrated both by ray-tracing simulations and by an experiment whereby a reasonably good sagittal concentration of 8 keV synchrotron radiation may be achieved by diffraction on the walls of a cylindrical hole drilled into an Si crystal. The holes were drilled parallel to the (111) planes and their diameter, 1 mm, was chosen so that the focusing distance fits the geometrical arrangement of beamline BM5 at the ESRF. Two such crystals have been used in a dispersive and non-dispersive arrangement. The better result was achieved using the dispersive arrangement. The intensity at the centre of the focus is increased by five times with respect to unfocused radiation. Excellent agreement exists between the ray-tracing simulations and experimental results.

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Ray-tracing simulations of mistuned sagittal diffractive-refractive X-ray lenses (DRXL) are presented. In this article, firstly the characteristic aberrations for various types of crystal misalignments within one-crystal and four-crystal DRXLs are considered, and the sensitivity of such an optical system to the mutual misalignment of its components is discussed. The simulations reveal that a DRXL is not too sensitive to the adjustment of its components. In the second part of this article the performance of such lenses with ideal and approximate profiles is examined. Comparative analysis of parabolic and cylindrical DRXLs showed that, in the case when the linear source size is comparable with the acceptance of the lens, the performances of parabolic and cylindrical DRXLs are practically the same.

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