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

• We propose a variational-difference numerical method for designing progressive-addition lenses.
• The method can be very easily understood and implemented by optical engineers.
• The method can provide satisfactory designs for optical engineers in several seconds.
• The method can be a powerful candidate tool for designing various free-form lenses.

We propose a variational-difference method for designing the optical free form surface of progressive-addition 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 element method, the essence of the proposed variational-difference numerical method lies in minimizing the functional directly by finite difference method 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.