Zhao Lei, Fei Wenhui, Li Yuejia, Wang Kaiwei, Bai Jian
Opt Lett. 2022 Aug 1;47(15):3776-3779. doi: 10.1364/OL.462972.
The numerical method based on the fast Fourier transform (FFT) is generally applied to calculate the Fresnel diffraction field, which would suffer from sampling constraints. To break this limit, in this Letter, the semi-analytic Fresnel diffraction calculation method is proposed based on polynomial decomposition. The diffraction field is computed by using properly analytic Fresnel diffraction basis functions (FDBFs) according to the application requirements. Analytic FDBF is calculated based on Legendre or Chebyshev polynomials by using the object-domain frequency division multiplexing method. The proposed method offers arbitrary sampling, high-flexibility, and high-accuracy diffraction calculation in the full Fresnel region. The computational efficiency and accuracy of the proposed method are compared with FFT-based methods. It has potential application in light field analysis, wavefront sensing, and image processing.
基于快速傅里叶变换（FFT）的数值方法通常用于计算菲涅耳衍射场，但该方法会受到采样限制。为突破这一限制，本文提出了基于多项式分解的半解析菲涅耳衍射计算方法。根据应用需求，利用适当的解析菲涅耳衍射基函数（FDBF）来计算衍射场。解析FDBF是通过使用物域频分复用方法基于勒让德多项式或切比雪夫多项式计算得到的。该方法在整个菲涅耳区域提供了任意采样、高灵活性和高精度的衍射计算。将该方法的计算效率和精度与基于FFT的方法进行了比较。它在光场分析、波前传感和图像处理方面具有潜在应用。
