Progressive addition lenses (PALs) are commonly used to correct presbyopia and prevent pseudomyopia and other visual accommodation disorders in adolescents. Compared with conventional single-vision lenses, bifocal lenses, and trifocal lenses, the focal length of a PAL changes gently from far to near, and the lens has no obvious boundary of imaging distortion. The shape is well-designed, and it only needs one pair of glasses to look far and closely. At present, the design methods of progressive freeform surfaces are mainly divided into two types: direct method and indirect method. The direct method directly calculates the sag distribution of the entire surface based on the mean curvature. However, this method may make peripheral astigmatism become two times the addition power (ADD), which will affect the visual imaging effect. By constructing the model of mean curvature and principal curvature difference and solving a specific high-order partial differential equation to minimize it, the indirect design method obtains the sag value of the PAL indirectly, which can reduce peripheral astigmatism more effectively while ensuring the lens's photo focal quality. At present, the research on the design of the PAL indirect method mainly focuses on surface optimization, and there is less research on the optimization of the weight function design algorithm. Therefore, based on the existing research, this paper realizes the optimization of the PAL by optimizing the weight function and the mean curvature distribution in the construction of the minimization model algorithm, so as to explore their influence on the optical performance optimization of PALs.

According to a PAL minimization model algorithm in the present studies, two groups of weight functions and mean curvature distributions were first designed, and three groups of free-form PALs with different weight functions and mean curvature distributions were calculated respectively. In the next step, an optimization method was proposed to reset the weight distribution of the lenses according to the conformity matrix, and two groups of PALs with different optimization degrees were recalculated under the same parameters. Then, five groups of lenses were machined and evaluated by free-form surface machine tools and testing instruments, and the effects of the optimization method in this paper on the optical power, astigmatism, and other optical properties of PALs were analyzed. In addition, issues such as wearing personalization and comfort were considered.

The channel length can be shortened, and the ADD can be increased by changing the mean curvature distribution to a circular design. The difference in the shape, area, and weight value of the weight function will affect the sizes of the distance area and the near area. The optical power of the distance area is also improved, and the astigmatism is significantly reduced (Table 2). Lenses after recalculation of weights according to the power conformity matrix are further optimized, and the higher weight value and the more concentrated weight distribution make the optical power error of the lenses become almost zero. The weight function combines the advantages of progressive surfaces with hard and soft designs, and the change of astigmatism from the distance area to the blending area increases slowly, which can reduce the imaging distortion when the line of sight switches from left to right. Maximum astigmatism in the blending area decreased to 1.75 D (Fig. 10). In addition, it has a relatively wide and small astigmatism channel, which can reduce the imaging distortion when the line of sight is from far to near. The machining results are basically consistent with the simulation results. This optimization method can optimize the optical properties of free-form PALs.

This paper mainly explores the influence of weight function and mean curvature distribution on PAL design. Five groups of PALs were calculated by designing five groups of different weight functions and mean curvature distributions. The machining and measurement results show that the weight function and mean curvature distribution jointly affect the optical properties of the lenses. The different shapes, areas, and weight values of the weight function can improve the optical performance of the lens in different aspects. The combination of reasonable mean curvature distribution can improve the power accuracy of the PALs. The weight function reset according to the focal power conformity can reduce the lens photometric error and make the astigmatism of the blending area change more gently, so as to bring a better visual experience for wearers. This paper also considers the flexibility of the design under different refractive states, which can meet the individual needs of different wearers. The research results of this paper can be further deepened, and more different groups of weight function and mean curvature distribution can be designed for comparison, so as to achieve a better optimization effect on the optical performance of the lens.