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 result is a generalization of the formerly known result for the paraxial magnification matrix for infinite object distance. The effect of the finite object distance correction is small but not negligible. Moreover, the methods for deriving this result serve as a starting point for an even more general treatment of oblique incidence in a future work.

The linear relation between the increase of peripheral astigmatism and the increase of power along an umbilical line was described by Minkwitz and is known as the Minkwitz theorem. However, in many cases, modern progressive addition lenses do not show an umbilical principal line. Therefore, we propose to extend the Minkwitz theorem to nonumbilical lines and higher order terms than the linear term of the increase in the peripheral astigmatism. We were able to derive a "generalized Minkwitz theorem," which holds true for a prescribed astigmatism at the principal line. The derived generalized Minkwitz theorem also indicates that the increase of the astigmatism perpendicular to the principal line depends not only on the power increase, as described by the Minkwitz theorem, but also on the astigmatism increase along the principal line. The Minkwitz theorem itself is a special case of this generalization.

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.

Transverse chromatic aberration (TCA) is one of the largest optical errors affecting the peripheral image quality in the human eye. However, the effect of chromatic aberrations on our peripheral vision is largely unknown. This study investigates the effect of prism-induced horizontal TCA on vision, in the central as well as in the 20° nasal visual field, for four subjects. Additionally, the magnitude of induced TCA (in minutes of arc) was measured subjectively in the fovea with a Vernier alignment method. During all measurements, the monochromatic optical errors of the eye were compensated for by adaptive optics. The average reduction in foveal grating resolution was about 0.032 ± 0.005  logMAR/arcmin of TCA (mean ± std). For peripheral grating detection, the reduction was 0.057 ± 0.012  logMAR/arcmin. This means that the prismatic effect of highly dispersive spectacles may reduce the ability to detect objects in the peripheral visual field.