Progressive addition lenses (PALs) are a specialized type of free-form ophthalmic lens that provide continuously clear vision from distance to near, significantly enhancing the visual experience. Thus, they have become increasingly popular among the elderly. PALs have undergone continuous design improvements and optimization, resulting in a wide variety of lens types. Given the relatively stable focal power changes in the addition zone of PALs and the higher focal power in the near vision area compared to the distance vision area, it is particularly important to accurately and appropriately evaluate the imaging quality of these lenses. We aim to evaluate the optical performance of PALs at various rotational angles using the point spread function (PSF) method in conjunction with an eye model. Due to the unique design of PALs, wearers need to rotate their eyes to adapt to changes in the visual field when viewing distant and near objects, requiring a more comprehensive simulation of visual performance. Additionally, our study will innovatively investigate which type of optical aberration most significantly affects visual blur when observing distant objects through the astigmatic zone of PALs. Our research will provide novel insights into optimizing lens design and evaluating the performance of PALs.

To comprehensively evaluate the optical performance of PALs, we propose a method based on PSF. First, we design an optical system combining the human eye and lenses in Zemax and perform ray tracing for the design of two different lenses, taking into account realistic eye rotation. The rotation angles of the eye are set within a range of ±25° in both the X and Y directions, sampled at 5° interval, generating a total of 121 rotational sampling points. This setup simulates viewing objects at far, intermediate, and near distances, allowing us to extract PSF images across all angles and distances. Next, the extracted PSF images are convolved with an aberration-free image to obtain an initial simulated retinal image. Finally, the weighting coefficients of the PSF components corresponding to each aberration term are calculated to analyze their effect on image quality. The results indicate that accurate evaluation of the optical performance of PALs requires considering the actual rotation of the eye, as the PSF images extracted after rotation provide a more precise assessment. Moreover, by solving the PSF weighting coefficients, we quantify the extent of PSF image dispersion caused by aberrations, revealing the influence of lens-related aberrations on image quality.

The evaluation method for the optical performance of PALs based on the PSF is feasible. In Fig. 5(a), when observing a distant object through Lens 1, the top of the image shows a clear PSF, indicating sharper imaging and better lens performance. However, at the bottom of the image, the PSF blur enlarges, resulting in diminished image clarity. Similarly, in Fig. 5(b), when an object at an intermediate distance is viewed with a rotation angle of (0°, -10°), and in Fig. 5(c), when observing a close object from the bottom of the lens, the lens performance remains optimal. Figure 6 shows the variations in the clarity of the letter “E” after convolution. The PSF image results for Lens 2 are shown in Fig. 7, and the results after convolution of the acquired PSF are presented in Fig. 8. By comparing the simulation results of Lens 1 and Lens 2, it can be observed that the distance vision zone of Lens 2 is significantly more stretched compared to Lens 1. Specifically, Lens 1 reaches its minimum clarity for distance vision at (0°, -5°), while Lens 2 reaches its minimum at (0°, 0°). Moreover, in both intermediate and near vision, the clarity points of Lens 2 are shifted upwards compared to those of Lens 1. Figure 9 illustrates the PSF obtained from Zemax software on the left and the PSF reconstructed using the fitting coefficient Q on the right, with the corresponding coefficient listed in Table 5. Notably, the ±45° astigmatism (j=3, n=2, m=-2) is dominant. As the rotation angle increases, the absolute values of the coefficients for ±45° astigmatism and (0° or 90°) astigmatism (j=5, n=2, m=2) increase, leading to greater PSF dispersion. By combining Fig. 9 with Tables 5 and 7, the accuracy of the calculated aberration coefficient and its applicability in practical applications are confirmed.

In our study, the introduction of ocular rotation significantly enhances the realism and precision of the evaluation process. The PSF images obtained through the proposed method, when convolved with the optical system, offer a comprehensive and intuitive representation of the optical performance advantages of PALs. This method enables detailed comparisons of imaging quality across various lens designs. By comparing the values of the aberration weight coefficients at symmetrical angles, the accuracy and reliability of the evaluation method are further confirmed, allowing for a quantitative assessment of the effect of aberrations on PSF image dispersion. Our study successfully demonstrates how these aberrations affect overall image quality. For future research, reducing the sampling angle intervals can further enhance the precision of visual simulations. However, such reductions will increase the number of samples required, emphasizing the need to explore optimization strategies for calculating weight coefficients efficiently. This improvement will streamline the optical evaluation process, making it more effective for assessing and refining the performance of PALs.