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Over the past decade, the concept of x-ray Deformable Mirror (DM) has matured from early experimental stages to a standard tool now available at many synchrotron/free-electron laser facilities. Indeed, x-ray active optics has become an integral part of all 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. These DMs mainly are employed to correct wavefront errors or provide variable x-ray beam sizes. Due to the coupling between the N actuators of a DM, it is usually necessary to perform a calibration or training step to be able to control the DM to the right target. To determine the optimum actuators settings in order 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. 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 needed voltages for any desired shape, we make use of the metrology data to directly guide the mirror from current status towards the particular target slope/shape via iterative compensations. The feedback for the iteration process is the discrepancy in curvature determined by height/slope measurement data. Experiments demonstrate the feasibility of this simple approach.
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