Design optimization of bendable x-ray mirrors

Convenience and cost often lead to synchrotron beamlines where the final bendable Kirkpatrick-Baez focusing pair must relay the final image to different samples at different image distances e.g., [Proc. FEL2009, 246-249 (2009)] either for different experimental chambers, or diagnostics. We present an initial analytical approach, starting from, and extending the work of Howells et al. [OE 39(10), 2748-62 (2000)] to analyze the trade-offs between choice of mirror, bending couples and the given, shaped sagittal width of the optic. Both experimentally and in simulation, we have found that after an appropriate re-bending, sagittally shaped optics can perform with high quality at significantly different incidence angles and conjugate distances. We present one successful demonstration from the ALS Optical Metrology Beamline 5.3.1, and review some new closed form analytical solutions with a view towards understanding our results.