Generalization of the Minkwitz theorem to nonumbilical lines of symmetrical surfaces.

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.

Optical magnification matrix: near objects and strongly oblique incidence.

Purpose: In every day spectacle use relevant parts of a spectacle lens involve large gaze angles and lie outside the paraxial region. The purpose here is to derive a general equation for the local 2 x 2 magnification matrix of an arbitrary K-surface optical instrument in front of an eye for any given gaze direction. The general case comprises a finite object distance as well as astigmatic surfaces and strongly oblique incidence angles of the involved rays.

Optical magnification matrix: near objects in the paraxial case.

Purpose: For appropriate patient management understanding, the problems due to the change of image size in the near magnification matrix of spectacles are important. The purpose here is to derive an equation for the paraxial 2 x 2 magnification matrix of spherocylindrical two-surface optical instruments (spectacles) in front of an eye at a finite object distance.

Methods: A 2 x 2 stepalong method for the contribution factors to the magnification matrix is developed, starting from a definition within a ray-tracing picture before translating it into quadratic-order wave-tracing concepts.

[Spectacle lenses in sports: optimization of the imaging properties based on physiological aspects].

The goal of correction spectacles is to create a sharp image on the retina by the combined optical system of the eye and the spectacle lens for a given ametropia. As a matter of principle, in this optical system an aberration free correction can be achieved in the optical centre of the spectacle lens, but not over the entire range of gaze angles. In spectacle optics large angles play an important role, different from paraxial optics where only rays close to the axis with small angles of incidence are relevant.