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Dual-update data-driven control of deformable mirrors using Walsh basis functions.

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    We present a new data-driven method for controlling deformable mirrors (DM) that improves mirror surface accuracy. This approach optimizes DM models and control actions, achieving nanometer-level surface errors for advanced optical applications.

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    Area of Science:

    • Optical Engineering
    • Adaptive Optics
    • Control Systems

    Background:

    • Deformable mirrors (DMs) are crucial for adaptive optics systems, but precise control remains challenging.
    • Existing methods often struggle to account for actuator constraints and dynamic model variations.

    Purpose of the Study:

    • To develop a novel data-driven method for deformable mirror control.
    • To improve the accuracy of DM surface shape control by integrating model estimation and feedback control.
    • To explore the application of Walsh basis functions for DM control.

    Main Methods:

    • A data-driven approach that simultaneously updates the DM model and control actions.
    • Coupling a feedback-control algorithm with recursive estimation of DM influence function models.
    • Utilizing Walsh basis functions to reformulate the control problem in the 2D Walsh basis domain.

    Main Results:

    • Experimental verification on a 140-actuator MEMS DM.
    • Achieved root-mean-square surface errors in the 14-40 nanometer range.
    • Demonstrated potential for further improvement through parameter tuning.

    Conclusions:

    • The developed data-driven method offers effective control for deformable mirrors.
    • The approach is robust, accounting for actuator constraints and enabling precise surface shape control.
    • The method is adaptable to various DM types, including segmented mirrors.