Hyperbolic tangential function-based progressive addition lens design.

The diopter distribution is key to the successful design of a progressive addition lens. A hyperbolic tangential function is then introduced to describe well the desired diopter distribution on the lens. Simulation and fabrication show that the astigmia on the whole surface is very close to the addition, exhibiting superior performance than that of currently used high-order polynomials and cosine functions. Our investigations found that once the diopter distribution design is reasonable, both the direct and indirect methods of constructing a progressive addition lens can give consistent results. With this function we are able to effectively control the design of critical areas, the position, sizes of far-view and near-view zones, as well as the channel of the lens. This study would provide an efficient way to customize different progressive lenses not only for presbyopia, but also for anti-fatigue, office progressive usages, etc.