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    This study introduces a novel 2D Hilbert transform method for accurately diagnosing complex optical fields. The approach effectively reconstructs phase distribution and identifies singular points in speckle fields.

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    Area of Science:

    • Optics and Photonics
    • Image Processing
    • Wave Phenomena

    Background:

    • Complex optical fields contain intricate structures crucial for various applications.
    • Diagnosing these structures, particularly the phase information, presents a significant challenge.
    • Existing methods for localizing special points in speckle fields are often limited by discretization and resolution.

    Purpose of the Study:

    • To develop and validate an optimal approach for diagnosing the structure-forming skeleton of complex optical fields.
    • To address the phase problem in localizing special points within speckle fields.
    • To propose a robust method for phase reconstruction and skeleton element identification.

    Main Methods:

    • Analysis of optical field singularity algorithms considering intensity discretization and image resolution.
    • Application of a "window" 2D Hilbert transform for phase distribution reconstruction.
    • Development of an additional algorithm for solving the phase problem in random 2D intensity distributions.

    Main Results:

    • An optimal approach was identified, significantly improving the localization of special points in speckle fields.
    • The proposed 2D Hilbert transform method enables reconstruction of phase distribution and identification of structure-forming elements, including singular and saddle points.
    • Equi-phase lines were reconstructed within a narrow confidence interval, demonstrating the method's accuracy.

    Conclusions:

    • The "window" 2D Hilbert transform offers an effective solution for reconstructing the phase of speckle fields.
    • This method provides invariance to transformation kernel position and accurately identifies key structural elements of optical fields.
    • The developed approach advances the ability to solve the phase problem for complex optical intensity distributions.