Theory of two-dimensional focusing of a spherical X-ray wave by Bragg diffraction by two bent crystals

The dynamical theory of the diffractional Bragg focusing in a system of cylindrically bent crystals is developed. Two-dimensional focusing `point-to-point' is shown to be possible under certain conditions. The influence of geometrical aberrations (astigmatism, spherical aberration) on the focusing is discussed. The influence of X-ray source sizes and temperature on the focusing is treated theoretically. A double-crystal focusing spectrometer is analysed. Focusing of X radiation by crystals with thin epitaxic films is investigated theoretically. Sensitivity of this focusing to the film thickness (∼1 µm) is demonstrated.