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    Area of Science:

    • Optics and Photonics
    • Quantum Optics
    • Mathematical Physics

    Background:

    • Partially coherent beams are fundamental in various optical applications.
    • Accurate characterization of spatial coherence is crucial for understanding beam propagation and interaction.
    • Existing methods for measuring coherence properties can be complex and time-consuming.

    Purpose of the Study:

    • To develop an efficient and accurate method for measuring the 2x2 correlation matrix of paraxial partially coherent beams.
    • To explore and compare different mathematical representations of the correlation matrix.
    • To investigate alternative definitions of the spatial degree of coherence and their experimental implications.

    Main Methods:

    • Utilizing diffraction phenomena from small apertures and obstacles to probe beam correlations.
    • Developing a measurement technique based on analyzing interference patterns.
    • Implementing and testing the method with experimental setups.

    Main Results:

    • Successfully demonstrated an efficient method for measuring the 2x2 correlation matrix.
    • Presented and discussed various representations of the correlation matrix function.
    • Experimental validation confirmed the effectiveness of the proposed technique and explored alternative coherence definitions.

    Conclusions:

    • The presented diffraction-based method offers an efficient approach for characterizing partially coherent beams.
    • The study provides valuable insights into the mathematical representations and definitions of spatial coherence.
    • This work contributes to the advancement of optical beam metrology and characterization.