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    Area of Science:

    • Optics and Photonics
    • Digital Imaging
    • Computational Science

    Background:

    • Single-shot interferogram analysis is crucial for complex object wave recovery.
    • Traditional Fourier filtering methods lack full pixel resolution.
    • Optimization approaches offer potential but are hindered by parameter tuning.

    Purpose of the Study:

    • Introduce a novel, parameter-free optimization method for single-shot interferogram analysis.
    • Simplify object wave recovery without critical empirical tuning.
    • Achieve full pixel resolution in complex object wave reconstruction.

    Main Methods:

    • Developed Mean Gradient Descent (MGD), a new optimization approach.
    • MGD balances data consistency and constraint terms without cost function minimization.
    • Iteratively progresses solutions by bisecting descent directions of error and constraint terms.

    Main Results:

    • Successfully recovered a step phase object from simulated interferograms (off-axis and on-axis) with various noise levels.
    • Achieved full pixel resolution, demonstrated by accurate phase step recovery.
    • Exhibited excellent root-mean-square (RMS) phase accuracy compared to ground truth.

    Conclusions:

    • MGD provides a simple, effective, and parameter-free solution for single-shot interferogram analysis.
    • The method achieves full pixel resolution and high accuracy in object wave recovery.
    • MGD's concept may extend to broader optimization problems.