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Framework to trade optimality for local processing in large-scale wavefront reconstruction problems.

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    Minimum variance wavefront estimation problems allow localized, approximate solutions using local slope measurements. This enables efficient computation and decentralized wavefront estimators, balancing optimality and efficiency.

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    Area of Science:

    • Optics
    • Computational Science
    • Signal Processing

    Background:

    • Wavefront estimation is crucial for adaptive optics systems.
    • Accurate wavefront estimation is computationally intensive.
    • Existing methods may lack efficiency and scalability.

    Purpose of the Study:

    • To develop a localized approximate solution for minimum variance wavefront estimation.
    • To enable efficient and decentralized wavefront estimation algorithms.
    • To explore the trade-off between computational efficiency and estimation optimality.

    Main Methods:

    • Formulating wavefront estimation as a minimum variance problem.
    • Developing localized approximation techniques based on neighborhood slope measurements.
    • Implementing sparse matrix-vector multiplication for efficient computation.
    • Numerical validation on Hudgin and Fried wavefront sensor geometries.

    Main Results:

    • Demonstrated that minimum variance wavefront estimation permits localized approximate solutions.
    • Showcased efficient computation via single sparse matrix-vector multiplication.
    • Validated the approach numerically on Hudgin geometries.
    • Results are generalizable to Fried geometries.

    Conclusions:

    • Localized approximation offers an efficient method for wavefront estimation.
    • The approach facilitates the development of decentralized and adaptable wavefront estimators.
    • This work provides a foundation for trading computational efficiency for estimate optimality.