SUMMARYBackground: All over the world, refractive errors are among the most frequently occuring treatable disturbances of visual function. Ametropias have a prevalence of nearly 70% among adults in Germany and are thus of great epidemiologic and socio-economic relevance.

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.

The designs of the tested personalized lenses were perceived by the subjects as intended. This is a prerequisite to the successful customization of PALs to individual wearing preferences. Possible reasons for the preference of the tested personalized lenses are the optimization with respect to individual wearing conditions and the personalization.

From the literature the analytical calculation of local power and astigmatism of a wavefront after refraction and propagation is well known; it is, e.g., performed by the Coddington equation for refraction and the classical vertex correction formula for propagation. Recently the authors succeeded in extending the Coddington equation to higher order aberrations (HOA). However, equivalent analytical propagation equations for 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 propagation equations of power and astigmatism to the case of HOA (e.g., coma and spherical aberration). This is achieved by local power series expansions. In summary, with the results presented here, it is now possible to calculate analytically 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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Geschützte Warennamen (Warenzeichen) werden nicht besonders kenntlich gemacht. Aus dem Fehlen eines solchen Hinweises kann also nicht geschlossen werden, dass es sich um einen freien Warennamen handelt.

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