Design of progressive addition lenses for myopia control

Myopia has become an increasingly serious global public health issue, particularly among adolescents. Progressive Addition Lenses (PALs), characterized by a continuously varying optical power across the lens surfaces, have been widely applied in the correction and management of myopia. However, traditional PALs design methods often rely on fixed-form mathematical models to describe the optical power distribution. These models typically lack sufficient flexibility in controlling the power transition, especially within the critical intermediate zone, making it difficult to achieve a smooth shift between distance and near vision. To overcome this limitation, this paper proposes a meridional optical power modeling method based on a dual logistic function. This approach offers greater parameters tunability, enabling precise control over key features such as the location, steepness, and smoothness of the power transition, thereby supporting more personalized lens designs. Additionally, the lens sag profile is represented using Legendre orthogonal polynomials, and the gradient descent algorithm is employed to optimize the lens surface, effectively reducing astigmatism and improving overall optical performance. Two typical design examples, tailored for outdoor activities and office work respectively, are presented to validate the adaptability and effectiveness of the proposed method under different visual demands, demonstrating its potential to enhance wearer visual comfort.