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    The van Cittert-Zernike theorem now applies to vector fields, linking source properties to far-field coherence and polarization. Experiments validate this extension using spatial averaging for Gaussian stochastic fields.

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    Area of Science:

    • Optics and Photonics
    • Classical Electrodynamics

    Background:

    • The van Cittert-Zernike theorem traditionally relates scalar source properties to far-field coherence.
    • Extending this to the vectorial regime is crucial for understanding complex light fields.

    Purpose of the Study:

    • To extend the van Cittert-Zernike theorem to the vectorial domain.
    • To experimentally demonstrate the vectorial van Cittert-Zernike theorem.
    • To connect vectorial source structure with far-field coherence and polarization.

    Main Methods:

    • Spatial averaging over the observation plane was employed as a replacement for ensemble averages.
    • The study utilized Gaussian stochastic fields.
    • Analytical and experimental results were obtained for a rectangular aperture.

    Main Results:

    • Successful extension of the van Cittert-Zernike theorem to the vectorial regime.
    • Demonstration of the theorem's ability to link complex vectorial source structure to far-field coherence and polarization.
    • Quantitative agreement between analytical predictions and experimental outcomes.

    Conclusions:

    • The vectorial van Cittert-Zernike theorem provides a robust framework for analyzing partially coherent polarized light.
    • Spatial averaging is a viable method for experimental validation in the vectorial domain.
    • The findings are applicable to various vectorial source structures and optical systems.