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Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.

Yu Xiao, Xiahui Tang, Yingxiong Qin

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |November 10, 2016
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    This study introduces a new diffraction simulation method using the nonuniform fast Fourier transform (NUFFT) to accurately model tilted planes without interpolation errors. This approach enhances calculation accuracy for all rotation angles, improving diffraction simulation for tilted planes.

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    Area of Science:

    • Optics and Photonics
    • Computational Physics
    • Signal Processing

    Background:

    • Diffraction simulation between tilted planes typically uses angular spectrum rotation in the frequency domain.
    • Conventional fast Fourier transform (FFT)-based methods require spectrum interpolation due to uneven sampling after rotation, leading to accuracy degradation with increasing angles.
    • Numerical errors from spectrum interpolation limit the accuracy of diffraction simulations for significantly tilted planes.

    Purpose of the Study:

    • To develop a precise and efficient method for simulating diffraction propagation between tilted planes.
    • To overcome the accuracy limitations of conventional FFT-based methods caused by spectrum interpolation.
    • To enable accurate diffraction simulations for large rotation angles, including those near π/2.

    Main Methods:

    • The study transforms the diffraction propagation problem into a discrete Fourier transform on unevenly sampled points.
    • The nonuniform fast Fourier transform (NUFFT) method is employed to evaluate this transform accurately and efficiently.
    • Avoidance of spectrum interpolation is a key methodological advantage.

    Main Results:

    • The NUFFT-based method effectively handles diffraction simulation between tilted planes without spectrum interpolation.
    • High calculation accuracy is maintained across various rotation angles, even approaching π/2.
    • The computational efficiency of the NUFFT method is comparable to conventional FFT-based approaches.

    Conclusions:

    • The NUFFT method provides a significant improvement in accuracy for diffraction simulations involving tilted planes.
    • This approach eliminates interpolation errors, ensuring reliable results for large rotation angles.
    • The NUFFT method offers a computationally efficient and accurate alternative for simulating diffraction between tilted planes.