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    A new algorithm enhances absolute phase estimation using Zernike polynomials (ZPs) and an extended Kalman filter (EKF). This method offers robust and practical solutions for fringe demodulation challenges.

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    Area of Science:

    • Optics and Photonics
    • Signal Processing
    • Metrology

    Background:

    • Absolute phase estimation is crucial in optical metrology.
    • Traditional fringe demodulation methods face challenges with noise and convergence.
    • Representing phase using Zernike polynomials (ZPs) offers a structured approach.

    Purpose of the Study:

    • To propose a novel algorithm for closed fringe demodulation and absolute phase estimation.
    • To convert phase estimation into Zernike polynomial coefficient estimation.
    • To improve the performance and robustness of phase estimation algorithms.

    Main Methods:

    • Representing the 2D phase as a weighted linear combination of Zernike polynomials (ZPs).
    • Employing a state space model for ZP coefficient estimation.
    • Utilizing the extended Kalman filter (EKF) for state estimation due to nonlinearities.
    • Incorporating a pseudo-measurement model with sparsity constraints to enhance EKF convergence.

    Main Results:

    • The proposed algorithm successfully performs absolute phase estimation from closed fringes.
    • The method demonstrates robustness against noise in both simulations and experiments.
    • The EKF with the pseudo-measurement model shows improved convergence performance.

    Conclusions:

    • The novel algorithm provides an effective approach for absolute phase estimation in optical systems.
    • The Zernike polynomial representation combined with EKF offers a powerful framework.
    • The method is practically applicable and noise-robust for real-world metrology applications.