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    Researchers defined a new class of partially coherent planar sources with structured coherence. This work extends Fourier transforms and Hilbert space kernels, offering new possibilities for optical coherence research.

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    Area of Science:

    • Optics and Photonics
    • Mathematical Physics

    Background:

    • The study builds upon the extension of the Fourier transform (FT) to complex arguments and reproducing kernel theory in Hilbert spaces.
    • Existing models for partially coherent sources have limitations in describing structured coherence properties.

    Purpose of the Study:

    • To introduce a novel class of partially coherent planar sources with a structured degree of coherence.
    • To explore the mathematical framework for defining and characterizing these new sources.

    Main Methods:

    • Extension of the ordinary Fourier transform (FT) to complex arguments.
    • Application of results concerning reproducing kernels in Hilbert spaces.
    • Development of a mathematical definition for the new class of sources.

    Main Results:

    • A new class of partially coherent planar sources with structured coherence has been defined.
    • These sources exhibit Schell-model characteristics in one transverse coordinate and dependence on the average orthogonal coordinate.
    • Specific examples of these sources are detailed.

    Conclusions:

    • The proposed approach provides a novel method for generating and analyzing partially coherent planar sources.
    • The defined sources offer a structured degree of coherence, expanding the toolkit for optical coherence research.
    • The methodology is adaptable for defining a wide range of other partially coherent sources.