The Hermite-Gauss basis functions have been extensively employed in classical and quantum optics due to their convenient analytic properties. A class of multivariate Hermite-Gauss functions, the anisotropic Hermite-Gauss functions, arise by endowing the standard univariate Hermite-Gauss functions with a positive definite quadratic form. These multivariate functions admit useful applications in optics, signal analysis and probability theory, however they have received little attention in literature. In this paper, we examine the properties of these functions, with an emphasis on applications in computational optics.
Hermite functions orthogonal basis computational optics linear canonical transform Fourier transform Wigner-Vile distribution eigenfunctions
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Mathematics |
Authors | |
Early Pub Date | August 15, 2023 |
Publication Date | April 23, 2024 |
Published in Issue | Year 2024 Volume: 53 Issue: 2 |