Bendable Kirkpatrick-Baez mirrors for the ALS micro-diffraction beamline 12.3.2: optimal tuning and alignment for multiple focusing geometries

Using an example of Kirkpatrick-Baez mirrors for the micro-diffraction beamline 12.3.2, we present the recent development of bendable x-ray optics and experimental techniques used for focusing of beams of soft and hard x-rays at the Advanced Light Source (ALS). We briefly review the nature of the bending and analyze a generalized solution of the bending equation for a side-profiled elliptically bent mirror substrate. A scaling rule is derived to understand a range of reliable tunability of the bendable optics for different applications (e.g., different focal distances and grazing incidence angles). Original design approaches are developed for assembly of bendable mirrors with minimal spurious stress and misalignment and for final precision compensation of the residual stress, substrate twist, and roll-off misalignment of the mirrors. Procedures used for optimal shaping and alignment of bendable optics at the ALS optical metrology laboratory are also briefly reviewed.