Optimal tuning and calibration of bendable mirrors with slope measuring profilers

We describe a technique to optimally tune and calibrate bendable x-ray optics for sub-micron focusing. The focusing is divided between two elliptically cylindrical reflecting elements, a Kirkpatrick-Baez (KB) pair. Each optic is shaped by applying unequal bending couples to each end of a flat mirror. The developed technique allows optimal tuning of these systems using surface slope data obtained with a slope measuring instrument, the long trace profiler (LTP). Due to the near linearity of the problem, the minimal set of data necessary for the tuning of each bender, consists of only three slope traces measured before and after a single adjustment of each bending couple. The data are analyzed with software realizing a method of regression analysis with experimentally found characteristic functions of the benders. The resulting approximation to the functional dependence of the desired shape provides nearly final settings. Moreover, the characteristic functions of the benders found in the course of tuning, can be used for retuning to a new desired shape without removal from the beamline and re-measuring. We perform a ray trace, using profiler data for the finally tuned optics, predicting the performance to be expected during use of the optics on the beamline