title: Direct and inverse discrete Zernike transform.
abstract: An invertible discrete Zernike transform, DZT is proposed and implemented. Three types of non-redundant samplings, random, hybrid (perturbed deterministic) and deterministic (spiral) are shown to provide completeness of the resulting sampled Zernike polynomial expansion. When completeness is guaranteed, then we can obtain an orthonormal basis, and hence the inversion only requires transposition of the matrix formed by the basis vectors (modes). The discrete Zernike modes are given for different sampling patterns and number of samples. The DZT has been implemented showing better performance, numerical stability and robustness than the standard Zernike expansion in numerical simulations. Non-redundant (critical) sampling along with an invertible transformation can be useful in a wide variety of applications.
authors.affiliation: ICMA, Universidad de Zaragoza and Consejo Superior de Investigaciones Científicas, Facultad de Ciencias, Pedro Cerbuna 12, 50009 Zaragoza, Spain. rafaelnb@unizar.es
authors.forename: Rafael
authors.initials: R
authors.lastname: Navarro
authors.forename: Justo
authors.initials: J
authors.lastname: Arines
authors.forename: Ricardo
authors.initials: R
authors.lastname: Rivera
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D017076:Computer-Aided Design; D004867:Equipment Design; D019544:Equipment Failure Analysis; D007909:Lenses; D008027:Light; D008962:Models, Theoretical; D012542:Scattering, Radiation