Fast ringing artifact reduction in diffraction calculations using Fresnel integrals

Diffraction calculations, which are fundamental in wave optics, can be significantly accelerated using Fourier transforms. However, they often suffer from ringing artifacts, also known as the Gibbs phenomenon, owing to the discontinuous borders of the calculation windows. Various techniques to suppress ringing artifacts have been proposed, but are typically time-consuming and require additional memory resources. This study proposes a fast method for reducing ringing artifacts using Fresnel integrals without necessitating additional memory. A comparison between the proposed and conventional techniques demonstrates that the proposed method achieves comparable image quality to conventional methods. Moreover, it offers the advantages of fast time and low memory usage. This paper demonstrates that the proposed method can be used to efficiently reduce ringing artifacts in reproduced images of two inline holograms optically acquired with laser and light-emitting diode sources.