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Novel vortex-transform for high frequency modulated patterns.

Daniel Sierra-Sosa, Luciano Angel-Toro, Nestor Bolognini

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    Summary
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    A new vortex transform generates complex-valued functions from intensity patterns, avoiding unstable singularities. This method enables analysis of intensity and pseudo-phase maps without phase retrieval.

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    Area of Science:

    • Optics and Photonics
    • Image Processing
    • Wave Phenomena

    Background:

    • Phase singularities are critical in wave phenomena but their generation can be unstable.
    • Phase retrieval techniques are often necessary for analyzing intensity recordings.
    • Existing methods may struggle to preserve high-frequency modulation details.

    Purpose of the Study:

    • To introduce a novel vortex-transform for generating complex-valued functions.
    • To enable the analysis of intensity patterns without phase retrieval.
    • To preserve high-frequency modulation components and stable phase singularities.

    Main Methods:

    • Development of a new mathematical transform based on vortex properties.
    • Application of the transform to modulated intensity patterns.
    • Generation of complex-valued functions and subsequent analysis of intensity and pseudo-phase maps.

    Main Results:

    • Successfully generated complex-valued functions from modulated intensity patterns.
    • Avoided the generation of unstable phase singularities during the transform process.
    • Obtained intensity and pseudo-phase maps that preserve modulation structure and stable singularities.

    Conclusions:

    • The proposed vortex-transform offers a stable method for analyzing intensity patterns.
    • It eliminates the need for complex phase retrieval techniques.
    • The transform effectively preserves essential wave characteristics, including modulation and singularities.