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We use a simplified mechanical/electrostatic model to describe the coupling between mirror and actuator. A WYKO interferometer is used to characterize the electromechanical performance of a MEMS deformable mirror (Boston Micromachines, Inc). We measured the voltage vs. deflection curves for the sample actuator with and without energizing the local adjacent neighbor actuators. This characterization results generated a quadratic and a linear equations to predict required voltage for actuators under different deflection profiles. We incorporated the MEMS mirror into a simple adaptive optics (AO) testbed. The system includes a near infrared superluminescent diode, a MEMS deformable mirror (DM), and a Shack Hartmann wavefront sensor (SHWS). The real time measurements provided by the SHWS (wavefront slopes) were the input to an integral controller. The controller was calibrated in situ by the typical method of determining an influence matrix which poke each actuator separately and measuring the resulting wavefront slopes at each lenslet. The control software then use the error signal between the current SHS positions and the desired positions, applied the characteristic model of the mirror, and determined the appropriate voltage to apply to each actuator, given the desired deflection for the surrounding actuators. The system was able to provide real time aberration compensation at loop gains of 0.3. A set of Zernike polynomial shapes were produced by DM under different loop gains to test the ability of control. A large proportion of the final wavefront shape could be achieved in a single iteration with a loop gain 1.0.
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