Abstract

We characterize the errors associated with open-loop control of a microelectromechanical system deformable mirror (DM) using an approach that combines sparse calibration of the electrostatic actuator state space with an elastic plate model of the mirror facesheet. We quantify sources of measurement error and modeling error and demonstrate that the DM can be shaped in a single step to a tolerance of $\sim 8\mathrm{nm}$ of that achievable with iterative feedback-based closed-loop control. Zernike polynomials with up to $2.5\mathrm{\mu m}$ amplitude were made with this approach and yielded a shape error of $<25\mathrm{nm}$ rms in most cases. Residual errors were shown to be due primarily to spatial resolution limits inherent in the DM (e.g., uncontrollable errors).

© 2010 Optical Society of America

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