Esser Gregor, Becken Wolfgang, Müller Werner, Baumbach Peter, Arasa Josep, Uttenweiler Dietmar
Research and Development Ophthalmic Lenses, Rodenstock GmbH, Munich, Germany.
J Opt Soc Am A Opt Image Sci Vis. 2011 Dec 1;28(12):2442-58. doi: 10.1364/JOSAA.28.002442.
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.
