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    Area of Science:

    • Optical Metrology
    • Signal Processing
    • Image Analysis

    Background:

    • Phase derivative estimation is crucial for various optical measurement techniques.
    • Existing methods often require multiple recordings or are sensitive to noise.
    • Accurate and direct phase derivative estimation from single interferograms remains a challenge.

    Purpose of the Study:

    • To develop a direct phase derivative estimation technique from a single complex interferogram.
    • To enhance the accuracy and noise robustness of phase derivative estimation.
    • To enable phase derivative estimation for complex spatial variations.

    Main Methods:

    • Representing the interference field as an autoregressive model with spatially varying coefficients.
    • Utilizing the Kalman filter for coefficient estimation.
    • Applying the Rauch-Tung-Striebel smoothing algorithm to refine coefficient estimates.

    Main Results:

    • Successfully computed the spatially varying phase derivative using estimated model coefficients.
    • Demonstrated noise robustness through simulation and experimental results.
    • Validated the applicability of the method for phase derivative estimation with arbitrary spatial variations.

    Conclusions:

    • The proposed technique enables direct and accurate phase derivative estimation from single interferograms.
    • The method exhibits significant noise robustness and handles complex spatial variations effectively.
    • This approach offers a valuable tool for advanced optical metrology and signal processing applications.