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    A new hybrid optimization algorithm, EPSO-BFGS, effectively addresses large-scale wave-front sensing challenges in phase diversity phase retrieval (PDPR). It combines evolutionary particle swarm optimization (EPSO) with BFGS for efficient and accurate wave-front sensing.

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    Area of Science:

    • Optics and Photonics
    • Computational Science
    • Wavefront Sensing and Adaptive Optics

    Background:

    • Phase diversity phase retrieval (PDPR) is crucial for wave-front sensing.
    • Existing optimization algorithms struggle with large-scale wave-front sensing, often getting trapped in local minima or exhibiting low convergence.
    • There is a need for efficient and reliable optimization methods for large-scale wave-front sensing applications.

    Purpose of the Study:

    • To develop a practicable optimization algorithm for large-scale wave-front sensing in PDPR.
    • To overcome the limitations of existing local and global optimization algorithms.
    • To enhance the accuracy and efficiency of wave-front sensing.

    Main Methods:

    • A two-step hybrid global optimization algorithm, EPSO-BFGS, was constructed.
    • It combines evolutionary particle swarm optimization (EPSO) for global search with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for local refinement.
    • EPSO identifies a rough global minimum, followed by BFGS for precise convergence.

    Main Results:

    • Numerical examples demonstrated the feasibility and reliability of EPSO-BFGS for various scales of wave-front sensing.
    • Two numerical cases validated its effectiveness for large-scale wave-front sensing.
    • A verification experiment further affirmed the algorithm's performance.

    Conclusions:

    • EPSO-BFGS is a viable and effective optimization algorithm for large-scale wave-front sensing in PDPR.
    • The hybrid approach balances global exploration and local exploitation for improved accuracy and speed.
    • This method offers a significant advancement for wave-front sensing technologies.