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    Area of Science:

    • Optics and Photonics
    • Statistical Optics
    • Mathematical Physics

    Background:

    • The far-field intensity distribution of light beams is crucial for applications in optical imaging and communication.
    • Controlling the spatial coherence of light sources offers a pathway to engineer beam characteristics.

    Purpose of the Study:

    • To establish a fundamental relationship between source coherence properties and far-field intensity patterns.
    • To introduce and analyze novel random light sources with engineered coherence properties.
    • To explore the potential of coherence modulation for far-field beam shaping.

    Main Methods:

    • Mathematical modeling of the source degree of coherence using convolution operations.
    • Employing Gaussian Schell-model and multi-sinc Schell-model correlation functions.
    • Analysis of the resulting far-field intensity distributions in polar and Cartesian coordinates.

    Main Results:

    • An inherent relationship was established between the source's degree of coherence and its invariant far-field intensity pattern.
    • Two new classes of random sources were introduced based on coherence convolution.
    • The novel sources generate far-field intensity patterns exhibiting multi-sinc Schell-model transverse distributions enveloped by a Gaussian profile.

    Conclusions:

    • The study demonstrates that manipulating source coherence through convolution can precisely shape far-field beam profiles.
    • These findings highlight the significant potential of coherence modulation for advanced beam shaping applications.
    • The generated beams resemble multi-sinc Schell-model beams filtered by a soft-edge Gaussian aperture.