Evaluation of the focusing performance of bent Laue crystals using wave-optical theory

Quantitative analysis of the focusing performance of bent Laue crystals is carried out using the rigorous wave-optical formalism. Via numerical solution of the Takagi equations and the Fresnel integral, the influence of diffraction on the formation of the image of an X-ray source is analysed. The results are compared with those obtained using a formalism based on the geometrical optics approximation and significant differences are found. A formula for the geometrical aberration of a cylindrically bent crystal is derived. The effect of the aberration on image formation is analysed.