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Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
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    This study introduces a novel 2D phase unwrapping method using residue theory to balance phase jumps. The approach aims to reduce processing time and improve residue connection for branch-cut algorithms.

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    Area of Science:

    • Optics and Photonics
    • Image Processing
    • Computational Science

    Background:

    • Two-dimensional phase unwrapping is crucial for reconstructing 3D profiles from interferometric data.
    • Existing branch-cut algorithms face challenges with processing time and residue connection.

    Purpose of the Study:

    • To present a new 2D phase unwrapping method based on residue theory.
    • To minimize processing time and simplify residue connection in phase unwrapping algorithms.

    Main Methods:

    • Utilizing the theory of residues to balance phase jump charges in wrapped phase maps.
    • Applying a phase unwrapping algorithm to modified wrapped maps.
    • Generating wrapped maps via Fourier transform profilometry and real-time dynamic holography.

    Main Results:

    • Demonstrated a method to balance residue charges using shifted phase jumps.
    • The proposed approach aims to reduce computational complexity.
    • Successfully applied the algorithm to reconstruct 3D profiles from experimental data.

    Conclusions:

    • The residue theory-based approach offers a promising solution for efficient 2D phase unwrapping.
    • This method has implications for improving 3D profilometry and holographic imaging techniques.