Theoretical Study on the Conversion of Diopter and Geometric Parameters for Freeform Lenses

Abstract To address the challenge of accurately identifying the geometric parameters causing refractive power deviations when a lens fails refractive power inspection, the interaction between geometric parameters and refractive power is investigated in this study to evaluate lens performance. First, based on theory of lens diopter, a geometric conversion model for diopter is derived by considering the influence of center thickness and the radius of curvature of the front and back surfaces, and by applying the ray transfer matrix method and introducing a correction factor. Next, a simulated point cloud model is generated, and a geometric parameter model is constructed through model slicing. The radius of curvature of the front and back surfaces, as well as the center thickness of the lens, are obtained using RANSAC circle fitting and polynomial fitting. Then, refractive power is derived using the refractive power–geometric parameter transformation model. The accuracy of the parameter calculation method is confirmed through simulations, and experimental validation is performed using a coordinate measuring machine. Comparison with measurements from a focimeter shows an absolute refractive power error of no more than 0.01 D. The research results demonstrate an accurate conversion relationship between geometric parameters and refractive power and provide a theoretical foundation for the industry’s digital transformation in lens geometric parameter optimization and manufacturing quality control.