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    Area of Science:

    • Optics and Photonics
    • Computational Physics
    • Signal Processing

    Background:

    • Calculating diffraction integrals in three-dimensional (3D) Fourier domains is computationally intensive.
    • Existing methods struggle with efficiency for complex 3D objects and spherical surfaces.

    Purpose of the Study:

    • To develop a computationally efficient method for calculating diffraction integrals onto spherical surfaces.
    • To express the diffraction integral as a convolution on the sphere for faster computation.

    Main Methods:

    • The diffraction integral is reformulated in the 3D Fourier domain as a convolution.
    • Spherical harmonic transforms are employed instead of traditional Fourier transforms for 2D convolution on the sphere.
    • Analysis of sampling pitch requirements for spherical data handling.

    Main Results:

    • The proposed method accelerates diffraction integral calculations by over 6,000 times compared to direct methods.
    • Successful verification through simulations of Young's interference experiment and complex 3D objects.
    • Detailed derivation and analysis of the diffraction integral and sampling requirements.

    Conclusions:

    • The spherical harmonic transform approach offers a significant speedup for diffraction calculations on spherical surfaces.
    • This method is applicable to various 3D objects and optical phenomena.
    • Efficient computation of diffraction integrals is crucial for advanced optical simulations.