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Branch-cut algorithm with second-order residues in phase unwrapping.

Meiqi Fang

    Optics Letters
    |February 15, 2024
    PubMed
    Summary

    A new branch-cut algorithm for phase map unwrapping in fringe projection systems identifies phase vortices. This method accurately connects residues, improving surface characteristic analysis.

    Area of Science:

    • Optical Metrology
    • Computational Imaging
    • Phase Measurement

    Background:

    • Phase unwrapping is crucial for 3D surface reconstruction from fringe projection systems.
    • Conventional branch-cut algorithms face challenges with residue handling and accuracy.
    • Existing methods often rely on specific residue charge matching, limiting applicability.

    Purpose of the Study:

    • To introduce a novel branch-cut algorithm for phase map unwrapping.
    • To address limitations in conventional phase unwrapping techniques.
    • To enhance the accuracy of relating phase behavior to surface characteristics.

    Main Methods:

    • Development of a novel branch-cut algorithm for phase map unwrapping.
    • Computation of second-order residues with vortex phase structures from wrapped phase data.

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  • Utilizing a second-order derivative that incorporates the wrap cycle.
  • Identifying consistent vorticity direction in phase vortex structures.

    • Main Results:

    • The algorithm successfully exposes second-order residues with vortex phase structures.
    • A consistent vorticity direction was observed in these vortex structures.
    • The method facilitates branch-cut connections between residues irrespective of charge.
    • Demonstrated high accuracy in simulations and practical experiments.

    Conclusions:

    • The novel branch-cut algorithm offers a significant advancement in phase map unwrapping.
    • It overcomes limitations of traditional methods by connecting residues regardless of charge.
    • The algorithm provides an accurate approach for analyzing phase-to-surface characteristic relationships.