Differentiable design of progressive-addition lens using NURBS surface

Presbyopia is an age-related condition that gradually reduces the eye's ability to focus on nearby objects, affecting over a billion people globally. The progressive-addition lens (PAL), commonly used for presbyopia correction, struggles to eliminate inherent astigmatism in the lateral areas of the progressive corridor. In this paper, we propose an efficient method for designing PAL using a differentiable optimization approach based on non-uniform rational B-spline (NURBS) surface, with an initial estimate derived through a modified variational-difference numerical method. Our method focuses on addressing a nonlinear error function without local approximations. In the two design examples, the high-level astigmatism areas near the intermediate transition zone are pushed toward the edge of the lens, demonstrating the effectiveness of our method.