title: Expressions for aberration coefficients using nonlinear transforms.
abstract: A matrix method to do nonlinear calculations is described. This is possible only under the special condition when a transformation maps a zero vector onto a zero vector. Geometrical optics conform to this condition and hence matrix methods can be applied to calculate aberrations. Methods to reduce computational complexities using symmetry arguments are provided. The formalism is applied to study refraction by a conic surface. Aberration coefficients, up to fifth order, are obtained as functions of eccentricity and the latus rectum of the conic surface. The method can be used to model corneal aberrations.
authors.affiliation: School of Optometry, University of Missouri-St. Louis, USA.
authors.forename: V
authors.initials: V
authors.lastname: Lakshminarayanan
authors.forename: S
authors.initials: S
authors.lastname: Varadharajan
mesh_terms: D003315:Cornea / Q000033:anatomy & histology*; D006801:Humans; D017711:Nonlinear Dynamics; D055095:Optics and Photonics; D012029:Refraction, Ocular; D013499:Surface Properties