Derivation of analytical refraction, propagation and reflection equations for higher order aberrations of wavefronts

Abstract

Derivation of analytical refraction, propagation and reflection equations for Higher Order Aberrations of wavefronts From literature the analytical calculation of Lower Order Aberrations (LOA) of a wavefront after refraction, propagation and reflection is well-known, it is for local Power and Astigmatism performed by the Coddington equation for refraction and reflection and the classical vertex correction formula for propagation. However, equivalent analytical equations for Higher Order aberrations (HOA) do not exist. Since HOA play an increasingly important role in many fields of optics, e.g. ophthalmic optics, it is the purpose of this study to extend the analytical Generalized Coddington Equation and the analytical Transfer Equation, which deals with second order aberration, to the case of HOA (e.g. Coma and Spherical Aberration). This is achieved by local power series expansions. The purpose of this PhD was to extend the analytical Generalized Coddington Equation and the analytical Transfer Equation, which deals with Lower Order Aberrations (power and astigmatism), to the case of Higher Order Aberrations (e.g. Coma and Spherical Aberration). In summary, with the novel results presented here, it is now possible to calculate analytically the aberrations of an outgoing wavefront directly from the aberrations of the incoming wavefront and the refractive or reflective surface and the aberrations of a propagated wavefront directly from the aberrations of the original wavefront containing both low-order and high-order aberrations.