A variational approach to progressive lens design

The ability of the human eye to accommodate (i.e. to see both near and far objects sharply) decreases with age. In order to correct this defect, so-called progressive-addition lenses (PALs) have been developed.This paper presents a new method for the design and quality control of PALs. The desired properties of the PAL are combined in an error functional, involving curvature properties of the front surface of the lens. It is shown how to efficiently minimize this error functional iteratively and we prove quadratic convergence. We also present an efficient method for reconstructing the geometry of a manufactured PAL based on sensor data obtained by measuring devices.The combination of geometry reconstruction and optimization provides a useful tool for the main design loop of PALs. The system has been developed and implemented in close cooperation with the optical industry.