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    This study introduces an analytical method to significantly reduce computation time and memory for cylindrical computer-generated holograms. The new approach uses Bessel function expansion for faster, more efficient hologram calculations.

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    Area of Science:

    • Optics and Photonics
    • Computational Imaging
    • Holography

    Background:

    • Calculating cylindrical computer-generated holograms (CGH) traditionally demands substantial computational resources, including time and memory.
    • Existing numerical methods, often relying on Fast Fourier Transform (FFT), present limitations in efficiency for complex holographic wavefronts.

    Purpose of the Study:

    • To develop and present an analytical method for calculating cylindrical CGH that minimizes computational cost.
    • To demonstrate significant reductions in calculation time and memory usage compared to conventional numerical techniques.

    Main Methods:

    • Representing the wavefront on a cylindrical surface as a convolution integral in the 3D Fourier domain.
    • Analytically performing the Fourier transformation of the convolution kernel using a Bessel function expansion.
    • Implementing an efficient calculation of Bessel function series and conducting numerical simulations.

    Main Results:

    • The proposed analytical solution drastically reduces calculation time and memory requirements for cylindrical CGH.
    • The method achieves these efficiencies without compromising accuracy, offering a significant advantage over FFT-based numerical approaches.
    • Comparative analysis confirms the substantial performance gains in both speed and memory footprint.

    Conclusions:

    • The analytical method based on Bessel function expansion provides a highly efficient alternative for generating cylindrical holograms.
    • This approach is crucial for advancing real-time holographic display and other computational imaging applications requiring reduced resource utilization.