title: Derivation of the refraction equations for higher-order aberrations of local wavefronts at oblique incidence.
abstract: From the literature the calculation of power and astigmatism of a local wavefront after refraction at a given surface is known from the vergence and Coddington equations. For higher-order aberrations (HOAs) equivalent analytical equations do not exist. Since HOAs play an increasingly important role in many fields of optics, e.g., ophthalmic optics, it is the purpose of this study to extend the "generalized Coddington equation" to the case of HOA (e.g., coma and spherical aberration). This is done by local power series expansions. In summary, with the results presented here, it is now possible to calculate analytically the local HOA of an outgoing wavefront directly from the aberrations of the incoming wavefront and the refractive surface.
authors.affiliation: Research and Development Ophthalmic Lenses, Rodenstock GmbH, Isartalstr. 43, 80469 München, Germany. gregor.esser@rodenstock.com
authors.forename: G
authors.initials: G
authors.lastname: Esser
authors.forename: W
authors.initials: W
authors.lastname: Becken
authors.forename: W
authors.initials: W
authors.lastname: Müller
authors.forename: P
authors.initials: P
authors.lastname: Baumbach
authors.forename: J
authors.initials: J
authors.lastname: Arasa
authors.forename: D
authors.initials: D
authors.lastname: Uttenweiler
mesh_terms: D000465:Algorithms; D015350:Contrast Sensitivity; D003941:Diagnostic Techniques, Ophthalmological; D006801:Humans; D008027:Light; D015233:Models, Statistical; D008962:Models, Theoretical; D009799:Ocular Physiological Phenomena; D055095:Optics and Photonics; D011680:Pupil / Q000502:physiology*; D012029:Refraction, Ocular; D014785:Vision, Ocular