Derivation of the Reflection Equations for Higher-Order Aberrations of Local Wave Fronts by Oblique Incidence

Esser, Gregor; Becken, Wolfgang; Müller, Werner; Baumbach, Peter; Arasa, Josep; Uttenweiler, Dietmar

doi:10.1016/b978-0-12-394297-5.00001-5

Cited by 3 publications

(3 citation statements)

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“…In the present thesis we have developed a general method for generating refraction, propagation and reflection equations for local wavefront aberrations of any order under arbitrarily oblique incidence conditions, which are published in [25,26,27]. The main advantage of the approach presented in this thesis is that it is based exclusively on analytical formulas which are novel.…”

Section: Discussionmentioning

confidence: 99%

“…A direct consequence is that if only aberrations of one single order are present, then the generalization of the Coddington equation will be exact for that order , which reads for the two-dimensional problem in case of refraction and in case of reflection , and in the three-dimensional case the vector-valued version of which reads for refraction and for reflection. These results include as a special case the well-known scalar Vergence equation as well as the Coddington equation (order ), but extend these refraction equations to aberrations of any arbitrary higher order which is done for the first time and published in [25,27]. It is important to note that the formalism presented in this work in general allows to determine each of the three surfaces (incoming wavefronts, refractive or reflective surface, outgoing or reflected wavefront) up to an order , provided that the two other surfaces are given up to the same order .…”

Section: Discussionmentioning

confidence: 99%

“…Am. A "Derivation of the propagation equations for higher order aberrations of local wavefronts" by Esser et al [26] and in Advances in Imaging and Electron Physics "Derivation of the reflection equations for higher order aberrations of local wavefronts by oblique incidence" by Esser et al [27].…”

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confidence: 99%

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

Esser

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%