In the slow tool servo (STS) turning technology for optical lenses, the D-shaped toolpath can improve the quality of the optical surfaces of off-axis aspheric and cylindrical microlens arrays. However, the traditional D-shaped toolpath has the problem of excessive servo following error in the X-axis. To address this issue, the projection of the D-shaped toolpath in the XZ plane is divided into a cutting zone and a transition zone. In the transition zone, an equation system based on continuity constraints (surface height, feed-rate, acceleration) is established. By solving this system of equations, a toolpath can be obtained along which the feed-rate of the X-axis varies smoothly. An example shows that the acceleration of the X-axis of the lathe is reduced by 84% compared to the traditional D-shaped toolpath. In the XZC interpolation mode, the spindle velocity of the C-axis changes smoothly. An off-axis spherical surface and an integral mirror have been machined using the optimized D-shaped toolpath. The X-axis servo following error of the lathe during processing is within 7 nm, and the surface shape accuracy reaches 0.361λ at 632.8 nm. This method enables high-precision processing of off-axis curved surfaces and cylindrical arrays.

Previous research indicates that modeling progressive addition lens (PAL) surfaces with high precision requires 231 Zernike polynomials, presenting substantial optimization challenges. This study introduces an innovative method for optimizing PALs by utilizing Zernike polynomial coefficients within commercial optical design software, thereby significantly enhancing computational efficiency. The Analytic Hierarchy Process (AHP) is employed to allocate weights within the merit function. Furthermore, a novel technique is introduced to minimize the number of optimization variables, thereby boosting optimization efficiency. In comparison to traditional methods, our approach achieves a 79.6% reduction in computation time. Tests conducted on manufactured lens samples revealed a 17.2% increase in the width of the distance zone and a 15.9% increase in the width of the near zone. Our method offers an effective strategy for optimizing PALs.

A regional optimization design method is proposed to reduce the astigmatism of progressive addition lenses(PAL).This method is used to optimize the near vision and astigmatic zones of PAL.First,the least squares method is used to find the spherical patch that best fits the superposed region.Subsequently,the progressive surface and spherical patch are combined proportionally to reduce the astigmatism of PAL.Finally,the Zernike polynomial regional fitting method is used to smooth the lens surface at the boundary of the superposed region,thereby reducing unnecessary astigmatism due to surface mutations.The test results of the initial design and optimized lens samples demonstrate that the maximum astigmatism of PAL after optimization decreases by 14.3%,area of maximum astigmatism decreases by 30.5%,and range with astigmatism less than 0.06 D in the near vision area increases by 30.4%.This optimization design method significantly reduces astigmatism while maintaining a relatively unchanged focal power distribution,expanding the effective visual range in near vision areas and improving visual experience for wearers.

We present a method for designing a transmissive-reflective combined optical system to generate a focused ring-shaped laser beam. The design aims to achieve a freely adjustable radius for the focused ring-shaped laser beam and ensure uniform beam intensity even after defocusing. Based on the principle of equal energy splitting, the transmissive system establishes mapping functions for the input and output light projection height. It optimizes the lens parameters to shape the incident Gaussian light into a flat-topped circular shape, thus achieving uniformity of beam intensity. On the other hand, the reflective system uses the adjustable diameter range of the focal plane ring-shaped light and working distance parameters. By applying the principle of geometric ray tracing, it calculates the parameters of the conical reflecting mirror, parabolic cylindrical mirror, and dynamic mirror, then the flat-topped circular light is transformed into a ring-shaped light. The experimental results show that when the half-apex angle of the dynamic mirror is 16 degrees, the designed system can achieve a freely adjustable radius for the focused ring-shaped laser beam from 15 mm to 30 mm with a size error not more than 0.05 mm, and the intensity uniformity after defocusing reaches 84%. The design method can achieve both uniformity of intensity and freedom of size adjustment without replacing the system lens. It has good operability and yields higher precision and efficiency in the processing of ring-shaped light.

A wavefront detection method for large aperture optical system based on the sparse aperture sampling is proposed. The conversion matrix of Zernike coefficients between the sub-aperture and full aperture is derived. The full aperture wavefront is calculated by the wavefront of the subaperture and the conversion matrix. The condition number of the conversion matrix is applied to evaluate the accuracy of the full aperture wavefront. Numerical simulation is employed to verify the accuracy of wavefront detection. The simulation results indicate that the wavefront RMS of the full aperture decreases with increasing the fill factor, sub-aperture number and subaperture baseline length of the sparse aperture. The accuracy of the full aperture wavefront can also be improved by our detection method.

Objective The sparse aperture optical system employs multiple discrete sub-apertures to replace the full aperture and achieves the resolution equivalent to that of the full aperture optical system while reducing the volume, quality, and costs. The sub-aperture's wavefront aberrations of the sparse aperture optical system exert impacts on the imaging performance of the whole system. In most studies, the system's field of view is not taken into account during the analysis of the imaging performance and sub-apertures' wavefronts of the sparse aperture optical system. Starting from the generalized pupil function, this paper develops the sparse aperture imaging model considering the system's field of view, thereby providing a theoretical basis for predicting the imaging performance and image restoration of the sparse aperture optical system under different fields of view. Methods The generalized pupil function of the sparse aperture optical system considering the field of view is derived on the theoretical basis of double Zernike polynomials (DZPs). The modulation transfer function ( MTF) of the system is obtained by the Fourier transform. The Golay3 sparse aperture imaging system designed by the ZEMAX optical software is taken as an example. According to the design results, the coefficients of double Zernike polynomials are fitted. The theoretical calculation results and optical design results are compared to verify the sparse aperture imaging theory considering the field of view. The Wiener filter is constructed according to the optical transfer function (OTF) for image restoration to improve the imaging quality of the system under different fields of view. Results and Discussions According to the theoretical model, the results show that when the field of view is 0 degrees, the imaging of the sparse aperture optical system approaches the diffraction limit as shown in Fig. 3(a). Figs. 3(b)-(e) indicate that under the same field of view, the main lobe and side lobe of MTFs decrease rapidly, and the main lobe shows different divergent directions corresponding to the directions of the incident light. As the field of view rises, the main lobe of MTFs further narrows, and the imaging performance of the optical system decreases significantly. MTFs calculated by DZPs are similar to those obtained by ZEMAX software. The contrasts of each line pair in the image simulated by the sparse aperture optical system are calculated under different fields of view. The images are processed by the Wiener filter, and the contrast curves are drawn, as shown in Figs. 9 (a)-(d). The figures demonstrate that the image contrasts of each field of view in horizontal and vertical directions can be greatly improved by the Wiener filter. Under the same field of view and different directions, the restored image has different contrasts in the horizontal and vertical directions. As shown in Fig. 9(b), when the field of view is ( 0. 05 degrees, 0 degrees), the contrast ranges in the horizontal and vertical directions are 0. 84-0. 99 and 0. 62-0. 99, respectively. In Fig. 9(c), when the field of view is (0 degrees, 0. 05 degrees), the contrast ranges in the horizontal and vertical directions are 0. 44-0. 84 and 0. 890. 99, respectively. As the field of view further increases, the contrasts of the image processed by the Wiener filter gradually decrease. In Fig. 9(d), when the field of view is ( 0. 1 degrees, 0 degrees), the contrast range in the vertical direction of the image before and after restoration is 0. 13-0. 26 and 0. 30-0. 43, respectively. Conclusions The sub-aperture's wavefront of the sparse aperture optical system under a non-zero field of view is represented by the DZP. When the generalized pupil function is constructed, the MTFs of the system under different fields of view are calculated by the Fourier transform, and the optical design of the system is carried out by ZEMAX software. Upon the fitting of the DZPs, the calculated MTFs of the system are proven to be consistent with those of the ZEMAX software, which verifies the method of utilizing DZPs to describe the wavefront of the sparse aperture imaging system under different fields of view. The Wiener filter related to the field of view is constructed on the basis of the OTF of the optical system. The image restoration using the Wiener filter effectively improves the imaging quality of the sparse aperture optical system under different fields of view.

A reflective optical system is designed for generating annular-focused beams using a conical mirror and a parabolic cylindrical mirror. The parameters of the mirrors are obtained in accordance with the design requirements of the annular beam. The rotation equation of the parabolic cylindrical mirror is derived with the same annular beam diameter, while the apex angle of the conical mirror changes. The uniformity of the annular beam intensity is improved by changing the parabolic cylindrical mirror into a concave–convex parabolic cylindrical integrating mirror, which is designed on the basis of the principles of surface division and beam superposition. The mirrors are processed by single-point diamond turning. An experimental facility is built to analyze the size and uniformity of the beam intensity distribution. The annular beam-width error is less than 3%, and the uniformity is 89%. The surface of the concave–convex parabolic cylindrical integrating mirror is smooth and continuous. The experimental data correspond to the theoretical design.

介绍了渐进多焦点眼用镜片的结构.提出了一种双向拟合设计渐进多焦点眼用镜片子午线的方法,采用两条多项式曲线从镜片视远点和视近点双向拟合,获得满足设计要求的子午线.在此基础上,选择与子午线正交、满足设计要求的曲线簇作为轮廓线,计算镜片上各个点的矢高数据,从而获得整个面形.设计结果表明,与只采用一条高阶多项式曲线描述子午线的方法相比较,双向拟合设计镜片子午线的方法可以灵活地调节子午线上光焦度增加的速率,从而控制镜片视远区、视近区以及渐进通道的光焦度和像散,设计满足眼镜佩戴者个性化需求的渐进多焦点眼用镜片,即当镜片参数相同时,双向拟合子午线不同,可以获得相应视觉需要的渐进多焦点眼用镜片.将设计的镜片进行实际加工,并检测加工结果,结果表明,加工获得的镜片性能与设计结果一致.

An optimized method for the design of progressive addition lens (PAL) is proposed in this study. aiming at the characteristics of the population that experiences a transition from myopia to presbyopia. The height expression of the surface of the PAL is proposed based on an aspherical formula, and a continuously varying conic coefficient is used to adjust the optical power and astigmatism distribution. Two PALs with an additional power of 1.5 dioptres were designed for comparison, using the spherical height and the aspheric height expression, respectively. The optical power and astigmatism distribution are given in the design results, and the free form verifier (FFV) of ROTLEX Ltd. in Israel is used to verify the results obtained via simulation. The results show that the optical power around the assembly centre of the optimized PAL annularly increases. The maximum astigmatism distribution of the lens does not exceed 1.25 dioptres, thereby not exceeding 83% of the additional power. In the area above the assembly centre, the astigmatism at any position is less than 0.5 dioptres. The length of the power stabilization zone in the near zone is approximately 20 mm. The optical power of the distance zone of the optimized PAL is annularly increased, which is beneficial to alleviate the asthenopia of myopia. The maximum astigmatism of the lens is considerably reduced, which is easily accepted by customers whose defect in vision has changed from myopia to preshyopia and wear PALs for the first time.

In pursuit of high imaging quality, optical sparse aperture systems must correct piston errors quickly within a small range. In this paper, we modified the existing deep-learning piston detection method for the Golay-6 array, by using a more powerful single convolutional neural network based on ResNet-34 for feature extraction; another fully connected layer was added, on the basis of this network, to obtain the best results. The Double-defocused Sharpness Metric (DSM) was selected first, as a feature vector to enhance the model performance; the average RMSE of the five sub-apertures for valid detection in our study was only 0.015λ (9 nm). This modified method has higher detecting precision, and requires fewer training datasets with less training time. Compared to the conventional approach, this technique is more suitable for the piston sensing of complex configurations.

Optical freeform surface components have attracted much attention due to their high degree of design freedom and small size. However, the design and processing difficulty of such components limit its wide application in optics industry. In recent years, diamond turning has been considered an efficient method for processing optical freeform surfaces, but the research on tool path generation of this processing method is not systematic. Progressive addition lens (PAL) is a typical optical freeform surface and is widely used to correct people’s vision problems. Firstly, this paper introduces a method of designing PAL. Then, an optimized tool path generation method for diamond turning of the optical freeform surface is proposed, the equal angle method is used to select the discrete points, and a tool nose radius compensation method suitable for both slow slide servo (SSS) and fast tool servo (FTS) is adopted. Finally, the turning experiment is carried out with a single point diamond lathe, and a PAL surface with a roughness of 0.087 μm was obtained. The power and astigmatism distributions were measured using a Rotlex freeform verifier to verify the rationality of the optical design.

1.减少视网膜周边远视离焦延缓近视加深理论的由来 近年流行的控制视网膜周边远视性离焦有助于延缓近视加深的理论来自两方面的研究:其一,Earl L.Smith教授的恒河猴实验[1]和Lin.Z团队的人群实验[2]均表明,视网膜周边远视离焦诱发眼轴和近视度数增长,而视网膜周边近视性离焦则可以抑制眼轴增长.其二,近年来众多研究表明是调节滞后和调节灵敏度不足而非传统观点认为的调节痉挛加速近视增长.比如Sreenivason等人检测发现近视儿童的调节灵敏度明显低于正视儿童[3],Langaas团队的测量则表明近视儿童的调节滞后重于正视儿童.这两种理论其实是可以相互验证的,因为配戴单焦点近视镜片近距离阅读时的调节滞后将加剧周边远视离焦现象.

We propose an evaluation method to judge the fitting extent to ophthalmic lens for the individual wearer. An Eye-Lens-Object optical system is set according to wearer's visual performance and the characteristic of ophthalmic lens assembly. A visual reference surface is proposed to calculate the object distance. The RMS radius of the spot diagram and MTF average value from optical design software Zemax are regarded as the criterion of assessing the image quality on the retina. Three cases are simulated to verify that our method is effective. The wearers can experience a comfortable wearing feeling when the evaluation method is used during the design of ophthalmic lens. The validity of our method is demonstrated to instruct designing the progressive addition lens with the freeform surface.

We propose a numerical method for the design of a progressive addition lens (PAL) that can accommodate more personal needs as compared to using the analytical solution of the Laplace equation. In our method, the auxiliary function u(x, y) of a PAL is obtained by the numerical solution of the Laplace equation with the boundary and link conditions. The boundary condition is obtained using the genetic algorithm with the input from the individual requirement. The link condition is determined using the finite difference method with a smoother u(x, y) on the meridian. Two examples are given for outdoor and office use. In both cases, the astigmatism area is pushed towards a small area near the edge of the lens. (C) 2017 Optical Society of America

以渐进多焦点镜片的加工为实例,阐述了采用CNC雕刻机(En3d)加工自由曲面光学元件的加工工艺,利用TRACEPRO软件宏语言将点阵数据生成非均匀有理B样条自由曲面,运用精雕机的JDPaint软件生成刀具路径,对自由曲面光学元件进行加工制造.利用自由曲面面形测量仪对加工完成的渐进多焦点镜片进行光焦度分布和散光分布的面形分析.实验结果表明:采用CNC雕刻机加工自由曲面光学元件的加工工艺简单,操作方便,并且加工后的渐进多焦点镜片面形符合设计要求.

根据遗传算法不依赖于具体优化目标且稳健性强的特点,提出运用遗传算法来寻找渐进多焦点眼镜片最优子午线的设计方案.基于子午线平滑方程,用二进制字符串(染色体)表示渐进多焦点眼用镜片子午线曲率变化曲线多项式系数.运用罚函数法和线性加权法将渐进多焦点镜片的光焦度和散光度多目标规划化成单目标函数.根据目标函数进行选择、交叉和变异,产生新一代染色体种群,循环搜索渐进多焦点镜片子午线最优系数.最后通过两个优化实例并加工成镜片样品进行测试分析,结果表明设计结果与实际测试结果基本相符.