The sagittal-bent Laue monochromator can provide an ideal way to focus high-energy X-ray beams. However, the anticlastic curvature induced by sagittal bending has a great influence on the crystal performance. Thus, characterizing the bent-crystal shape is very important for predicting the performance of the bent-crystal monochromator. In this paper the crystal profile is measured by off-line optical metrology and on-line X-ray experiments. The off-line results showed that the bent-crystal surface could be well fitted to a saddle surface apart from a redundant cubic term which was related to the different couples applied on the crystal. On-line characterization of the meridional and the sagittal radius of the bent crystal includes double-crystal topography and ray-tracing measurement. In addition, the double-crystal topography experiment could be used as a quick diagnostic method for the bending condition adjustment. The sagittal radius of the bent crystal was characterized through a ray-tracing experiment by using a particularly designed tungsten mask. Moreover, rocking curves under different bending conditions were measured as well. The results were highly consistent with analytical results derived from the elastic theory. Furthermore, radii along different vertical positions under various bending conditions were measured and showed a quadratic relationship between the vertical positions and the meridional radii.
An approximate point-based alternative for the estimation of variance under big BAF sampling