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Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter.

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    This study introduces a noise-robust phase unwrapping algorithm using state space analysis and polynomial phase approximation. The method enhances accuracy by employing a linear Kalman filter and adaptive windowing for improved phase retrieval.

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    Area of Science:

    • Signal Processing
    • Image Analysis
    • Optical Metrology

    Background:

    • Phase unwrapping is crucial for reconstructing true phase from wrapped measurements in various imaging techniques.
    • Traditional methods struggle with noise and complex phase distributions, limiting their applicability.
    • State space analysis offers a framework for modeling and estimating dynamic systems, including phase evolution.

    Purpose of the Study:

    • To develop a noise-robust phase unwrapping algorithm.
    • To improve the accuracy and reliability of phase retrieval in the presence of noise.
    • To provide a flexible method adaptable to different phase distributions.

    Main Methods:

    • Polynomial phase approximation of the true phase within local windows.
    • State space representation of spatial phase evolution and wrapped phase measurements.
    • Linear Kalman filter for state estimation using wrapped phase data.
    • Adaptive window width selection based on local fringe density.
    • Line-scanning or quality-guided pixel selection for phase retrieval.

    Main Results:

    • The proposed algorithm demonstrates noise robustness through simulations and experimental validation.
    • Accurate phase and local fringe frequency estimation is achieved.
    • The linear Kalman filter effectively handles wrapped phase measurements.
    • Adaptive windowing balances computational efficiency and noise resilience.
    • Successful phase retrieval for both continuous and discontinuous phase distributions.

    Conclusions:

    • The developed noise-robust phase unwrapping algorithm is effective and applicable in practical scenarios.
    • State space analysis combined with polynomial phase approximation and linear Kalman filtering provides a powerful approach.
    • The adaptive windowing strategy enhances the algorithm's performance across varying noise levels and fringe densities.