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    This study introduces a 3D angular spectrum method to derive Fourier diffraction formulas. This approach simplifies the analysis of forward-propagating waves in optical systems.

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    Area of Science:

    • Optics
    • Mathematical Physics

    Background:

    • The Rayleigh-Sommerfeld and Kirchhoff diffraction formulas are fundamental in optics.
    • Existing formulations often require complex mathematical treatments.
    • A unified, three-dimensional approach is needed for advanced diffraction analysis.

    Purpose of the Study:

    • To develop novel three-dimensional Fourier representations of classical diffraction formulas.
    • To utilize the angular spectrum method for a more comprehensive diffraction analysis.
    • To simplify the mathematical description of diffraction phenomena.

    Main Methods:

    • Employing a three-dimensional angular spectrum representation.
    • Deriving three-dimensional Fourier forms of the first and second Rayleigh-Sommerfeld diffraction formulae.
    • Deriving the three-dimensional Fourier form of the Kirchhoff diffraction formula.

    Main Results:

    • Successfully developed three-dimensional Fourier representations for the Rayleigh-Sommerfeld and Kirchhoff diffraction formulas.
    • Demonstrated that these representations simplify to three-dimensional Fourier representations for forward-propagating waves.
    • Provided a unified framework for analyzing diffraction in the forward half-space.

    Conclusions:

    • The angular spectrum method offers a powerful tool for developing 3D Fourier diffraction theories.
    • The derived formulas provide a simplified and unified approach to forward diffraction.
    • This work advances the mathematical understanding of wave propagation and diffraction.