Surface curvatures and diffraction profiles of sagittally bent Laue crystals

The performance of a bent Laue crystal monochromator crucially depends on the sagittal and meridional bending curvatures of the crystal. To optimize the design of monochromator crystals, the surface curvatures and diffraction profiles of a set of sagittally bent Laue crystals with different aspect ratios have been studied experimentally by optical metrology and X-ray measurements. The results were confirmed with finite-element analysis using large-deformation theory. The nonlinear relationship between the curvatures necessitates an experimentally determined parameter in the theoretical modeling of the diffraction profiles. By taking into account the local stress and the aspect ratio of the sagittally bent Laue crystal, the modified analytical approach successfully predicts the rocking-curve width and the integrated reflecting power. The effect of extreme sagittal bending on the rocking curve is also discussed. To retain high reflectivity, the bending curvature should not exceed its critical value for the specified crystal geometry. Furthermore, the uniformity of the bending curvatures across the crystal surface has been examined, which suggests that the minimum crystal dimension should be approximately twice the size of the beam footprint.