A variational-difference numerical method for designing progressive-addition lenses

We propose a variational-difference method for designing the optical free form surface of progressiveaddition lenses (PALs). The PAL, which has a front surface with three important zones including the far-view, near-view and intermediate zones, is often used to remedy presbyopia by distributing optical powers of the three zones progressively and smoothly. The problem for designing PALs could be viewed as a functional minimization problem. Compared with the existing literature which solved the problem by the B-spline finite elementmethod, the essence of the proposed variational-difference numerical method lies inminimizing the functional directly by finite differencemethod and/or numerical quadratures rather than in approximating the solution of the corresponding Euler–Lagrange equation to the functional. It is very easily understood and implemented by optical engineers, and the numerical results indicate that it can produce satisfactory designs for optical engineers in several seconds. We believe that our method can be a powerful candidate tool for designing various specifications of PALs. © 2013 Elsevier Ltd. All rights reserved.