11. Varilux Comfort, natural vision by large viewing zones and a soft periphery
Varilux Comfort is characterized by a geometry combining the advantages of a "hard" and a "soft" progressive design. The research work to create an ergonomically correct meridian is laid down in the patents US 5 270 745 and US 5 272 495, which define the meridian consisting of three line segments. US 5 488 442 contains the conditions for the surface with a short progression zone and a soft periphery for good peripheral and dynamic vision.
In order to design a geometry, combining these almost contradictory conditions, bicubic tensor B-spline surfaces offer the necessary flexibility. The control points of this spline surface are determined by the minimization of an error functional, with the surface function as input argument. Assuming, that in a first approximation the first derivatives are constant, the problem is reduced to the minimization of a quadratic functional, which is equivalent to the solution of a linear equation system. The input parameters are the weight functions and for penalizing surface astigmatism and deviation from the prescribed power and the prescribed power Hsoll. These parameters are calculated from the data of US 5 488 442.
The program and the process steps of an approximate optimization are disccussed. The isoplots for power increase and surface astigmatism show a design with large viewing zones for far and near vision, a short power progression and low peripheral astigmatism and gradients.
11.1 Freeform surfaces built with splines
11.2 Establishing the Merit Function
11.3 Minimizing the error functional
11.4 The bicubic tensor product B-spline surface
11.5 Establishing the linear equation system (LES)
11.6 Optimization Method
11.7 Results and analysis
Annex : Matlab program for minimizing the error functional