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.

Contents

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

> 5. The Minkwitz Ruessel