Linear canonical transformations in phase space: the Gabor frames approach

Patrick Gioia; Antonin Gilles; Antoine Lagrange; Anas El Rhammad; San Vu Ngoc

doi:10.1117/12.3022395

18 June 2024 Linear canonical transformations in phase space: the Gabor frames approach

Patrick Gioia, Antonin Gilles, Antoine Lagrange, Anas El Rhammad, San Vu Ngoc

Proceedings Volume 12998, Optics, Photonics, and Digital Technologies for Imaging Applications VIII; 129980I (2024) https://doi.org/10.1117/12.3022395
Event: SPIE Photonics Europe, 2024, Strasbourg, France

Abstract

Linear Canonical Transformations are phase space deformations that can be used to describe linear optical systems. In geometric optics they correspond to the transformations of the light rays during propagation in arbitrary media, while in wave optics they describe the evolution of the space-frequency components. Although their meaning is non-ambiguous in the former case, in the latter it depends on the specific space-frequency decomposition of the wavefield. In this paper we gather several results from theoretical time-frequency analysis with Gabor Frames and provide a preliminary analysis on the implementation of phase space deformation for linear optical systems.

Conference Presentation

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Patrick Gioia, Antonin Gilles, Antoine Lagrange, Anas El Rhammad, and San Vu Ngoc "Linear canonical transformations in phase space: the Gabor frames approach", Proc. SPIE 12998, Optics, Photonics, and Digital Technologies for Imaging Applications VIII, 129980I (18 June 2024); https://doi.org/10.1117/12.3022395

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