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CUDO: closed-form universal dwell-time optimization for computer-controlled optical surfacing.

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    We developed CUDO, a new analytical framework for optimizing dwell time in optical surfacing. This method offers faster, more accurate results for creating advanced optical systems.

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    Area of Science:

    • Optical engineering
    • Manufacturing science

    Background:

    • Precision optical figuring requires efficient dwell time optimization for nanometer-level accuracy.
    • Current methods often involve iterative processes with extensive hyperparameter tuning.

    Purpose of the Study:

    • To introduce CUDO (closed-form universal dwell-time optimization), a unified analytical framework for dwell time optimization.
    • To provide a closed-form solution that eliminates the need for iterative methods and parameter tuning.

    Main Methods:

    • Developed a unified closed-form analytical framework supporting both function-form and matrix-form dwell time models.
    • Derived direct analytical solutions without adjustable parameters, unifying existing methods.

    Main Results:

    • CUDO achieves accuracy comparable or superior to iterative solvers.
    • Demonstrated substantial reductions in computation time and enhanced numerical robustness.
    • Comparative studies show equivalent residual error with significantly reduced runtime.

    Conclusions:

    • CUDO offers a practical foundation for deterministic fabrication of high-performance optics.
    • The framework simplifies implementation and enables real-time, scalable deployment for next-generation optical systems.