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Numerical diffraction propagation by Haar wavelet transform.

Yu Xiao, Changcheng Duan, Hao Peng

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    |September 23, 2025
    PubMed
    Summary

    This study introduces a new Haar wavelet transform-based method (HWTM) for optical simulations. HWTM overcomes sampling limitations in FFT-based techniques, enhancing accuracy and computational efficiency in diffraction modeling.

    Area of Science:

    • Optics and Photonics
    • Computational Physics
    • Digital Signal Processing

    Background:

    • Fast Fourier Transform (FFT)-based numerical diffraction methods are crucial for optical simulations like digital holography.
    • These methods suffer from sampling limitations due to the chirp function, impacting precision, propagation distance, and observation area size.
    • Existing plane wave basis methods, such as the angular spectrum method, face aliasing issues.

    Purpose of the Study:

    • To develop a novel numerical diffraction method that overcomes the sampling limitations of FFT-based techniques.
    • To enhance accuracy and computational efficiency in optical simulations within the Fresnel diffraction range.
    • To adapt the method for broader applications, including Rayleigh-Sommerfeld diffraction and off-axis scenarios.

    Main Methods:

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    • Utilizing the Haar wavelet basis for input wave modeling, offering an efficient and naturally discrete representation.
    • Implementing the Haar wavelet transform-based method (HWTM) to eliminate sample aliasing issues associated with the chirp function.
    • Enabling flexible sampling of the output field for improved accuracy and efficiency.

    Main Results:

    • HWTM effectively eliminates sample aliasing issues inherent in FFT-based chirp function sampling.
    • The method demonstrates enhanced accuracy and computational efficiency for Fresnel diffraction.
    • Simulation experiments confirm the advantages of HWTM over traditional FFT-based approaches.

    Conclusions:

    • The Haar wavelet transform-based method (HWTM) provides a superior alternative to FFT-based techniques for numerical diffraction.
    • HWTM offers improved accuracy, computational efficiency, and flexibility in sampling for optical simulations.
    • The method's adaptability extends its utility to various diffraction regimes and configurations.