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    This study introduces a novel machine learning method for phase retrieval wavefront sensing using Tchebichef moments to analyze point spread functions (PSFs). This approach enhances efficiency and robustness in optical system aberration analysis.

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    Area of Science:

    • Optics and Photonics
    • Machine Learning Applications
    • Computational Imaging

    Background:

    • Conventional phase retrieval wavefront sensing relies on intensity-based methods, which can be limited in accuracy and robustness.
    • Accurate characterization of optical aberrations is crucial for high-performance imaging systems.

    Purpose of the Study:

    • To propose a feature-based phase retrieval wavefront sensing approach using machine learning.
    • To introduce Tchebichef moments for characterizing point spread function (PSF) features.
    • To develop a robust and efficient method for determining optical system aberration coefficients.

    Main Methods:

    • Utilized Tchebichef moments, orthogonal in discrete image space, to represent PSF features at in-focus and defocus planes.
    • Employed a back-propagation artificial neural network to map Tchebichef moment features to aberration coefficients.
    • Trained the neural network to establish a nonlinear relationship between image features and optical aberrations.

    Main Results:

    • Demonstrated that Tchebichef moments effectively characterize PSF intensity distribution.
    • The trained neural network accurately outputs aberration coefficients using image features as input.
    • Experimental validation confirmed the effectiveness and precision of the proposed method.

    Conclusions:

    • The proposed feature-based phase retrieval wavefront sensing approach offers a feasible and easily implemented solution.
    • This method improves the efficiency and robustness of wavefront sensing compared to conventional techniques.
    • The use of Tchebichef moments and machine learning provides a powerful tool for optical system analysis.