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After years of development from a concept to early experimental stage, X-ray Deformable Mirrors (XDMs) are used in many synchrotron/free-electron laser facilities as a standard x-ray optics tool. XDM is becoming an integral part of the present and future large x-ray and EUV projects and will be essential in exploiting the full potential of the new sources currently under construction. The main objective of using XDMs is to correct wavefront errors or to enable variable focus beam sizes at the sample. Due to the coupling among the N actuators of a DM, it is usually necessary to perform a calibration or training process to drive the DM into the target shape. Commonly, in order to optimize the actuators settings to minimize slope/height errors, an initial measurement need to be collected, with all actuators set to 0, and then either N or 2N measurements are necessary learn each actuator behavior sequentially. In total, it means that N+1 or 2N+1 scans are required to perform this learning process. When the actuators number N is important and the actuator response or the necessary metrology is slow then this learning process can be time consuming. In this work, we present a fast and accurate method to drive an x-ray active bimorph mirror to a target shape with only 3 or 4 measurements. Instead of sequentially measuring and calculating the influence functions of all actuators and then predicting the voltages needed for any desired shape, the metrology data are directly used to “guide” the mirror from its current status towards the particular target slope/height via iterative compensations. The feedback for the iteration process is the discrepancy in curvature calculated by using B-spline fitting of the measured height/slope data. In this paper, the feasibility of this simple and effective approach is demonstrated with experiments.
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