The performance of a dynamical sagittal-focusing monochromator for hard X-rays is described. It consists of a flat first crystal and a diamond-shaped ribbed second crystal which is clamped by its central rib and dynamically bent by applying a force on its two apices. The system has proved to perform very well on the GILDA beamline at the ESRF. The horizontal acceptance varies with energy and with focusing geometry as predicted theoretically; the total available horizontal fan of radiation (3.6 mrad) is in fact collected in the 1:3 geometry. The system is routinely run in a dynamical focusing mode for XAFS spectroscopy in the energy range 5-30 keV with Si(311) crystals, with a constant spot size FWHM ,-~1 mm on the sample and without degradation of energy resolution or reproducibility. Using simple geometrical considerations we calculate the variations of the horizontal profile of the reflected beam during rocking-curve scans in different focusing geometries and find them in agreement with observed ones. Not only is this is a practical aid in alignment but it illustrates the X-ray optics of sagittal focusing in an elegant way.

An experimental demonstration showing that a one-dimensional focus can be produced by using the principle of inclined diffraction from a perfect crystal is presented. By machining a groove with a controlled cross-sectional pro®le it is shown that it is possible to vary the out-of-plane deviations in a controlled manner and hence generate a focus. Also demonstrated is the use of four re¯ections in (À,+,+,À) dispersive geometry resulting in the cancellation of all beam-spreading in the orthogonal direction. The experiment used an energy of 15 keV with a source-to-crystal distance of 13.5 m and crystal-to-focus distance of 4.5 m. A focus of width 0.29 mm was produced from an incident beam of width 2.7 mm. It is clear from the measurements that a better surface ®nish would result in a smaller focal spot.

As de®ned here, the term`inclined lens' means a longitudinal parabolic groove fabricated into a crystal monochromator. If properly designed, it should provide the horizontal (sagittal) focusing of an X-ray beam. The focusing is based on the sagittal deviation of the beam diffracted on the wall of the groove. This effect follows from the dynamical theory of inclined diffraction. The focusing ef®ciency is limited compared with other methods. On the other hand, the simplicity is the main advantage of this device. The exact shape of the groove is calculated and several methods of keeping the vertical dimension of the beam small are proposed.

The main limitation of Laue geometry for the achievement of a small focus size is the focus broadening caused by the intrinsic Darwin width and the spread of the beam in the Borrmann triangle, resulting from propagation inside the crystal. A method, based on dynamical focusing, is suggested that allows improvement of the quality of high‐energy polychromatic focusing by bent crystals in Laue geometry.