A Review of Numerical Simulation Methods for Near-Field Diffraction in Computational Imaging: A Geometric Flexibility Perspective

Abstract

High-precision and efficient forward models for near-field diffraction are essential for computational imaging systems. However, achieving a balance among physical accuracy, computational efficiency, and geometric flexibility remains a fundamental challenge. This paper presents a systematic review of numerical simulation methods for near-field diffraction, covering their evolution from classical physical formulations to modern efficient sampling approaches. We begin with the Rayleigh–Sommerfeld (RS) integral as a rigorous physical benchmark, highlighting its high physical fidelity and prohibitive O(N⁴) computational cost. We then review fast Fourier transform (FFT)-based acceleration frameworks, focusing on the angular spectrum method (ASM) and its band-limited variant (BL-ASM), the latter of which effectively suppresses sampling-induced aliasing artifacts. To address the limited geometric flexibility of fixed-grid methods, we further examine adaptive approaches, including Fresnel diffraction, the fractional Fourier transform (FrFT), and the scalable angular spectrum (SAS) method, which enables zoom propagation via sampling decoupling. Finally, we discuss the limitations of current flexible-geometry methods, particularly the degradation of physical accuracy in extreme near-field and wide-angle regimes, which restricts their applicability in high numerical aperture (high NA) scenarios. We conclude by outlining future directions toward high NA vectorial modeling and intelligent operator integration.

Keywords

near-field diffraction / angular spectrum method / sampling optimization / computational imaging / scalable diffraction / high NA