Abstract

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

© 2020 Optical Society of America

Frequency sampling strategy for numerical diffraction calculations

Wenhui Zhang, Hao Zhang, and Guofan Jin
Opt. Express 28(26) 39916-39932 (2020)

Sampling analysis for Fresnel diffraction fields based on phase space representation

Jiasheng Xiao, Wenhui Zhang, and Hao Zhang
J. Opt. Soc. Am. A 39(2) A15-A28 (2022)

Numerical solution of nonparaxial scalar diffraction integrals for focused fields

Matthias Hillenbrand, Damien P. Kelly, and Stefan Sinzinger
J. Opt. Soc. Am. A 31(8) 1832-1841 (2014)

Shifted band-extended angular spectrum method for off-axis diffraction calculation

Wenhui Zhang, Hao Zhang, Kyoji Matsushima, and Guofan Jin
Opt. Express 29(7) 10089-10103 (2021)

Controlling the aliasing by zero-padding in the digital calculation of the scalar diffraction

Jung-Ping Liu
J. Opt. Soc. Am. A 29(9) 1956-1964 (2012)