We compared different power distributions to design freeform progressive addition lenses (PALs) based on a minimization error function model. We employed straight line, trigonometric, eighth-order polynomial, and directly assigned function curvature laws to process the power distributions over an entire surface and assessed their effects on the PAL design. Four power distribution techniques were constructed to connect far vision and near vision areas. Correspondingly, four PALs were designed, simulated, and machined. The results showed that power distribution from the far vision point to the near vision point, according to the straight line curvature law, caused errors of 0.35 and 0.6 D in the distance and addition power, respectively. The error was reduced by the trigonometric curvature law and further reduced under the eighth-order polynomial curvature law. The assigned curvature law had the lowest error among the four lenses. These results indicate that the outcome of the PAL design is sensitive to different power distributions. The proposed method is expected to help advance the design procedure optimization of PALs in optometry.
Spectacle lens are used to compensate refractive errors of the eyes. Therefore, the properties of human eyes were taken into consideration in our research. We not only designed and optimized the lens with the required optical performance in ZEMAX based on the eye-lens system, but also calculated the sag of the aspherical surface according to the optimized parameters. The back surface of the lens was aspherical surface for the better clinical effects than other types of aspherical lens. The results data were subsequently imported into the freeform verifier software (FFV) for analysis and the optical properties of the lens were calculated. It was found that the power distribution has been improved. The thickness of aspherical lens was much thinner than the spherical lens. Therefore, our research found a balance between thickness and optical performance.
Freeform progressive addition lenses (PALs) are mainly divided into distance vision zone, near vision zone, astigmatism channel and peripheral astigmatism zone. The purpose of this study was to compare the effect of the width of the astigmatism channel by changing the near vision area of PALs on the basis of the minimal model method. The change of the near vision area was mainly achieved by changing the distribution function of the main curvature difference and the average curvature weight. Firstly, two weight distribution matrices of different near vision areas were designed, and the second-order partial differential equations of the minimized model were solved by the finite element method. The surface shape of two PALs was obtained. Secondly, the freeform verifier software (FFV) (ROTLEX, Israel) was used to simulate the shapes of the obtained surfaces, and used computer numerical control machine tools to process two groups of PALs. Finally, the Visionix VM-2500 lens measuring instrument was used to measure the PALs. The simulated and measured power and astigmatism distribution contours showed that the width of the astigmatism channel increased with the increase of the near vision area, however, the peripheral astigmatism was increased. Therefore, the near vision zone with an appropriate area can provide a reference for the optimal design of PALs.
The purpose of this study was to compare the optical properties of different astigmatic optical surfaces by direct physical measurement of their surface shapes. The back-surface heights of different astigmatic optical lenses were measured with a freeform measuring machine (FMM). In order to calculate the function of the part point cloud fitting surface for the dispersed data points of the astigmatic lenses, the measured shape data were modeled through surface fitting of a bicubic spline. The principal curvatures of each point on the surface were calculated, and the optical properties of each surface and their combinations were generated as contour plots using custom MATLAB routines. The fitting surface of the actual measurement points was compared with the design surface to determine the surface error. Analyses showed that this nonoptical method using an FMM can be used to effectively evaluate a cylindrical lens by surface height measurements alone. Compared to the optical measurement method, the optical properties derived directly from the surface shape can provide information not accessible by other methods. Therefore, this approach is potentially useful to clinicians who want to better understand the design of astigmatic optical lenses for making better recommendations to their clients.
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