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    This study introduces a fast, precise method for calculating the frequency spectrum of spatial triangles using 3D affine transformations. This enhances the rapid generation of computer-generated holograms (CGHs) for 3D objects.

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    Area of Science:

    • Optics and Photonics
    • Computational Imaging
    • Computer Graphics

    Background:

    • Efficient generation of computer-generated holograms (CGHs) is crucial for holographic display and optical information processing.
    • Existing methods for holographic computation, particularly those employing affine transformations, have limitations in speed and precision.

    Purpose of the Study:

    • To present a novel, fast, and precise analytical method for calculating the frequency spectrum of spatial triangles.
    • To improve the efficiency of generating computer-generated holograms (CGHs) using the angular spectrum method for propagation.
    • To introduce a refined 3D affine transformation approach for holographic computations.

    Main Methods:

    • Developed a full-analytical frequency spectrum calculation for spatial triangles utilizing 3D affine transformations.
    • Implemented a two-step transformation process: 3D rotation followed by 2D affine transformation.
    • Introduced a modified back-face culling technique based on exterior normals for accurate occlusion.

    Main Results:

    • The proposed method achieves a more precise derivation compared to previous affine transformation-based techniques.
    • Demonstrated successful implementation for complex 3D objects through numerical simulations and optical experiments.
    • Achieved significantly enhanced computational efficiency compared to prior methods.

    Conclusions:

    • The novel 3D affine transformation method offers a faster and more accurate approach for holographic computations.
    • This advancement enables rapid CGH generation with improved precision, benefiting applications in optical information processing and display technology.