Analysis of numerical diffraction calculation methods: from the perspective of phase space optics and the sampling theorem

• DOI: 10.1364/josaa.401908
• Publication Date: 2020-09-22T22:33:12Z
• Authors: Wenhui Zhang; Hao Zhang; Colin J. R. Sheppard; Guofan Jin
• Keywords: Optical phase space; Physical optics; Impulse response; Nyquist–Shannon sampling theorem; Fourier optics; Fresnel equations

Diffraction calculations are widely used in applications that require numerical simulation of optical wave propagation. Different diffraction calculation methods have their own transform and sampling properties. In this study, we provide a unified analysis where five popular fast analyzed from the perspective phase space optics theorem: single Fourier transform-based Fresnel transform, transfer function approach, impulse response angular spectrum method, Rayleigh-Sommerfeld convolution. The evolutions an input signal's space-bandwidth product (SBP) during propagation illustrated with help diagram (PSD) ABCD matrix. It is demonstrated all above cannot make full use SBP signal after diffraction; some properties been ignored. Each method has its restrictions applicable range. reason why different ranges explained physical models. After comprehensively studying comparing effect on these methods, suggestions given for choosing proper overcoming corresponding methods. PSD matrix to illustrate intuitively. Numerical results presented verify analysis, potential ways develop new also discussed.