A Light-Ray Approach to Fractional Fourier Optics

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