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    Area of Science:

    • Optical Engineering
    • Control Systems
    • Signal Processing

    Background:

    • Closed-loop adaptive optics (AO) systems are crucial for correcting optical aberrations.
    • Performance limitations arise from time delays and measurement noise in AO systems.
    • Existing controllers struggle to optimally reject disturbances under these constraints.

    Purpose of the Study:

    • To determine the ideal rejection transfer function for AO systems limited by time delay and noise.
    • To introduce a novel modal linear predictive controller (MLPC) that approaches this ideal.
    • To optimize MLPC parameters using closed-loop data for evolving conditions.

    Main Methods:

    • Derived the ideal rejection transfer function based on wave-front signal-to-noise ratio (SNR).
    • Developed an MLPC with parameters optimized via a modified recursive least-squares algorithm.
    • Validated the controller's performance using numerical simulations.

    Main Results:

    • The ideal rejection transfer function is proportional to the input wave-front SNR.
    • The proposed MLPC effectively approaches this ideal transfer function.
    • Numerical simulations demonstrate significant reduction in residual wave-front error.

    Conclusions:

    • The MLPC offers a substantial improvement for closed-loop AO systems facing time delays and noise.
    • The optimization method allows adaptation to changing environmental conditions like turbulence.
    • This predictive control strategy enhances the precision and stability of adaptive optics.