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    Area of Science:

    • Optics and Photonics
    • Computational Imaging
    • Signal Processing

    Background:

    • Wavefront reconstruction is vital for adaptive optics, interferometry, and phase contrast imaging.
    • Traditional Cartesian and Zernike polynomial bases have limitations in representing complex wavefronts and avoiding overfitting.
    • Existing methods struggle with non-standard wavefronts like optical vortices or sharp discontinuities.

    Purpose of the Study:

    • To develop a novel, flexible, and efficient wavefront reconstruction technique.
    • To address the limitations of Cartesian and Zernike bases for complex optical wavefronts.
    • To improve robustness to noise and account for system misalignment.

    Main Methods:

    • Utilized an over-complete phase dictionary incorporating Zernike polynomials and specialized functions for complex modes.
    • Employed sparse representation techniques inspired by compressed sensing and sparse coding.
    • Integrated a trainable rigid transform to compensate for optical system misalignment.

    Main Results:

    • Demonstrated enhanced representation flexibility and efficiency for complex wavefronts.
    • Achieved improved robustness to noise through enforced sparsity in the coefficient space.
    • Successfully accounted for system misalignment using the rigid transform.

    Conclusions:

    • The proposed method offers a superior alternative for wavefront reconstruction, particularly for complex optical phenomena.
    • This approach enhances the performance and applicability of optical systems requiring precise wavefront analysis.
    • Future work may involve further optimization and application to real-time optical systems.