Gibbs ringing and the Fresnel transform

Yue Wang; John J. Healy

doi:10.1117/12.2621362

27 May 2022 Gibbs ringing and the Fresnel transform

Yue Wang, John J. Healy

Proceedings Volume 12138, Optics, Photonics and Digital Technologies for Imaging Applications VII; 121380T (2022) https://doi.org/10.1117/12.2621362
Event: SPIE Photonics Europe, 2022, Strasbourg, France

Conference Poster

Abstract

Gibbs ringing is an artefact that occurs when a discontinuous signal is truncated in the Fourier domain. It is a phenomenon which occurs frequently in optics as apodization - the action of an aperture - and which can be interpreted as an idealised low pass filtering process. Diffraction can be approximately modelled using the Fresnel transform. The spectral method of calculating the Fresnel transform, a workhorse in digital holography and other fields, interprets the Fresnel transform as an all-pass filter. In this paper, we analyse the relationship between these phenomena and propose how to use this interpretation to improve image quality.

Citation Download Citation

Yue Wang and John J. Healy "Gibbs ringing and the Fresnel transform", Proc. SPIE 12138, Optics, Photonics and Digital Technologies for Imaging Applications VII, 121380T (27 May 2022); https://doi.org/10.1117/12.2621362

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