5. The Minkwitz Rüssel
This simple design is sometimes mentioned in the litterature as elephant's trunk. It consists of an involute of a circle as umbilical main meridian and circles as orthogonal sections. So the surface can be totally represented by analytical functions and give an umbilical line and isolines- graphs with high precision and regularity.
The design with a continuous power increase from the top to the bottom of the lens offers almost horizontal isopower-lines, but also a rather high amount of peripheral astigmatism deteriorating the optical quality of the far vision (FV)- and near vision (NV)-zones. This underlines the need for a main meridian with stabilized sections in the FV- and NV-part. The Minkwitz theorem is demonstrated qualitatively and quantitatively.
5.1 The coordinate system
5.2 The principal meridian
5.3 Geometry and equations of the progressive surface
5.4 Analysis of design and calculations