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Pré-Publication, Document De Travail Année : 2023

A Light-Ray Approach to Fractional Fourier Optics

Résumé

A light ray in space is characterized by two vectors: (i) a transverse spatial-vector associated with the point where the ray intersects a given spherical cap; (ii) an angular-frequency vector which defines the ray direction of propagation. Given a light ray propagating from a spherical emitter to a spherical receiver, a linear equation is established that links its representative vectors on the emitter and on the receiver. The link is expressed by means of a matrix which is not homogeneous, since it involves both spatial and angular variables (having distinct physical dimensions). Indeed, the matrix becomes a homogeneous rotation-matrix after scaling the previous variables with appropriate dimensional coefficients. When applied to diffraction, in the framework of a scalar theory, the scaling operation results directly in introducing fractional-order Fourier transformations as mathematical expressions of Fresnel diffraction phenomena. Linking angular-frequency vectors and spatial frequencies results in an interpretation of the notion of a spherical angular-spectrum. Accordance of both inhomogeneous and homogeneous ray-matrices with Huygens-Fresnel principle is examined. The proposed ray-matrix representation of diffraction is also applied to coherent imaging through a lens.
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Dates et versions

hal-04063779 , version 1 (10-04-2023)

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Éric Fogret, Pierre Pellat-Finet. A Light-Ray Approach to Fractional Fourier Optics. 2023. ⟨hal-04063779⟩
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