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    Area of Science:

    • Optics and Photonics
    • Signal Processing
    • Image Analysis

    Background:

    • Fringe analysis is crucial for optical metrology.
    • Local polynomial phase modeling offers a robust approach.
    • Accurate phase field identification remains a challenge.

    Purpose of the Study:

    • To develop an algebraic method for relating polynomial phase coefficients to circular harmonic integrals.
    • To enable accurate identification of local phase fields in fringe patterns.
    • To create an efficient algorithm for denoising and recovering wrapped phase fields.

    Main Methods:

    • Formulating an algebraic equation connecting polynomial phase coefficients and circular harmonic integrals.
    • Transforming circular harmonic integrals into 2D kernel convolutions.
    • Deriving a system of equations for estimating local polynomial coefficients across the phase field.

    Main Results:

    • The proposed method accurately identifies local phase fields.
    • An efficient denoising and recovery algorithm for wrapped phase fields is developed.
    • Experimental results show model identification accuracy close to the Cramér-Rao lower bound.

    Conclusions:

    • The developed algebraic approach provides accurate phase field identification.
    • The algorithm demonstrates efficiency, adaptability, and high accuracy in fringe analysis.
    • Preferred parameter settings for the algorithm are identified through experimentation.