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    Area of Science:

    • Optics and Photonics
    • Statistical Field Theory
    • Wave Propagation

    Background:

    • Stochastic fields often lack Fourier transforms, complicating second-order statistics calculations via fourth-order stochastic wave equations.
    • Wolf's coherent mode decomposition addressed this for wide-sense stationary fields, enabling space-frequency statistics propagation.

    Purpose of the Study:

    • To develop a simplified framework for calculating second-order statistics of wide-sense statistically homogeneous and stationary fields.
    • To demonstrate efficient propagation of spatial coherence and temporal correlations using a novel wavevector-frequency representation.

    Main Methods:

    • Utilized monochromatic plane waves as an eigenfunction basis for cross-spectral density when fields are wide-sense stationary and statistically homogeneous.
    • Introduced a deterministic signal framework, analogous to the complex analytic signal, with identical autocorrelation to the random field.
    • Employed a second-order deterministic wave equation for simplified propagation calculations in the wavevector-frequency domain.

    Main Results:

    • Showed that the spatiotemporal power spectrum fully describes the second-order statistics of these fields.
    • Demonstrated efficient propagation of second-order statistics in the wavevector-frequency representation.
    • Calculated spatial coherence in the far zone of incoherent sources and coherence effects in biological tissues.

    Conclusions:

    • The wavevector-frequency representation, using monochromatic plane waves and deterministic signals, significantly simplifies the analysis of stochastic fields.
    • This approach provides an efficient method for propagating spatial and temporal correlations, applicable to various optical phenomena.