基于主观式测量人眼波前像差的眼模型研究

通过主观式光线追踪波前像差测量方法得到用Zernike系数描述的人眼波前像差;在Gullstrand-Le Grand眼模型的基础上,引入用医用角膜地形图仪测量并用高次非球面函数拟合的实际人眼角膜形状数据,又引入角膜、前房及玻璃体厚度等个体化的眼结构参数;在光学建模软件Zemax中用所测Zernike系数建立评价函数,并对用Zernike矢高面描绘的晶状体表面进行优化.由此建立了个体化眼模型,并由此模型中可以计算得到与实际测量的波前像差值完全相同的各项Zernike系数值,从而可用于描述实际人眼的光学特性.     

基于个体眼光学结构的角膜与晶状体的像差补偿

研究角膜对晶状体波前像差的影响对现行的个性化视觉矫正手术有-定的参考价值.运用光学设计软件Zemax,根据个体人眼的角膜地形图、眼内各部分轴向间距和全眼波前像差数据,为22只人眼构建了个体眼光学结构.基于个体眼光学结构和衍射光学理论计算了眼内、外不同位置处的波前,获得了角膜对晶状体波前像差的影响.结果表明,角膜和品状体像差存在补偿和叠加两种关系.大多数眼睛,角膜对晶状体像差有一定补偿作用.总体像散的均方根(RMS)值比品状体像散的RMS值减小0.08～1.48μm,相当于10.1%～77.5%.总体高阶像差的RMS值比晶状体高阶像差的RMS值减小了0.06～0.85 μm,相当于3.8%～79.4%,平均减小了50.7%.其中,球差和彗差的Zernike系数绝对值总体比晶状体分别减小了0.02～0.60μm和0.01～0.39μm,相当于4.3%～98.4%和2.5%～91.4%.     

Contributions of the cornea and the lens to the aberrations of the human eye

The relative contributions of optical aberrations of the cornea and the crystalline lens to the final image quality of the human eye were studied. The aberrations of the entire eye were obtained from pairs of double-pass retinal images, and the aberrations of the cornea were obtained from videokeratographic data. Third-order spherical aberration and coma were significantly larger for the cornea than for the complete eye, indicating a significant role of the lens in compensating for corneal aberrations. In a second experiment retinal images were recorded in an eye before and after we neutralized the aberrations of the cornea by having the subjects wear swimming goggles filled with saline water, providing a direct estimate of the optical performance of the crystalline lens.     

Individual eye model based on wavefront aberration

Based on the widely used Gullstrand-Le Grand eye model, the individual human eye model has been established here, which has individual corneal data, anterior chamber depth and the eyeball depth. Furthermore, the foremost thing is that the wavefront aberration calculated from the individual eye model is equal to the eye's wavefront aberration measured with the Hartmann-shack wavefront sensor. There are four main steps to build the model. Firstly, the corneal topography instrument was used to measure the corneal surfaces and depth. And in order to input cornea into the optical model, high-order aspheric surface-Zernike Fringe Sag surface was chosen to fit the corneal surfaces. Secondly, the Hartmann-shack wavefront sensor, which can offer the Zernike polynomials to describe the wavefront aberration, was built to measure the wavefront aberration of the eye. Thirdly, the eye's axial lengths among every part were measured with A-ultrasonic technology. Then the data were input into the optical design software–ZEMAX and the crystalline lens's shapes were optimized with the aberration as the merit function. The individual eye model, which has the same wavefront aberrations with the real eye, is established.     

人眼模型中各折射面对人眼像差的贡献

将计算光学系统各个折射面对系统像差贡献的理论应用于人眼中.用C语言编制光线追迹程序,计算了人眼各个折射面对眼睛像差的贡献及各种像差经过眼睛不同折射面的变化.给出了眼睛中各个折射面对眼睛彗差的贡献,并发现角膜与晶状体对眼睛彗差的贡献有相互补偿的作用.在眼睛中,角膜前表面对人眼像差的贡献最大,晶状体后表面对眼睛像差的贡献次之,这两个折射面比其他两折射面对眼睛像差的贡献大得多.这说明晶状体后表面也是改善人眼像差的参数之一.     

人眼高阶像差校正和视觉分析系统

人眼除具有可用眼镜或接触镜校正的低阶像差(离焦、像散)之外,还普遍存在高阶像差。高阶像差的存在影响着屈光系统的成像质量。为研究高阶像差对视觉功能的影响,利用自适应光学技术,建立了具有校正高阶像差和产生高阶像差双重功能的人眼高阶像差校正和视觉分析系统。介绍了系统实现高阶像差校正和视觉分析的工作原理;阐述了波前校正器、哈特曼波前探测系统、控制系统等关键单元技术;列出了系统对泽尼克模式像差的校正效果,绝大多数像差从0.5λ降低到0.2λ以下;阐明系统功能的实现过程,并给出仿真实验的结果。该系统为进一步研究高阶像差对视功能的影响提供了有效的手段。     

非球面和梯度折射率在眼光学成象中的作用

在Gullstrand-Le Grand眼模型的基础上,构造不同的眼光学模型,分别研究了角膜非球面、晶状体非球面和昌状体折射率在眼光学成象中的作用.通过比较各模型系统的Zernike标准多项式系数,分析了非球面和梯度折射率对眼光光系统各象差的影响.同时研究了不同模型调制传递函数的特性.     

超视力人眼模型的研究

超视力人眼模型对充分发掘人眼视力达到“鹰视”具有重要意义。用Zernike多项式描述角膜前表面，用渐变折射率描述晶状体的折射率分布，同时考虑人眼视轴和光轴的夹角对成像的影响，利用光学设计软件Zemax建立了人眼超视力模型。将Zernike条纹矢高面应用到人眼模型中，能有效改变视轴方向(即5°视场)的成像质量，提高点扩散函数（PSF）值。采用晶状体渐变折射率符合人眼的实际解剖结构，可有效减小人眼像差。通过分析人眼极限分辨能力和人眼模型波像差，得出当空间频率为60周期/度时，该模型对目标高频细节感知的调制度可达到0.55。     

Correcting anterior corneal aberration and variability of lens movements in keratoconic eyes with back-surface customized soft contact lenses

Customized contact lenses are limited in their correction performance, especially on irregular corneas, owing to decentration and rotation of the lenses. To overcome this limitation, we proposed to customize the back surface of soft contact lenses to match the anterior irregular corneal surface. These lenses were designed to correct anterior corneal aberrations and to improve lens stability. Although in keratoconic eyes the anterior corneal aberrations were effectively corrected, significant residual aberrations were observed. The internal optics, especially the posterior surface of the cornea, was the main source of these residual aberrations. Compared with conventional soft contact lenses, lens stability, on average over three eyes, was improved by a factor of 2 for horizontal and vertical decentrations and a factor of 5 in rotational orientation with the back-surface customized lenses.     

Monte Carlo simulations on corneal and total aberrations before and after LASIK

Previous Monte Carlo simulations which manipulate each Zernike coefficient of total aberrations of human eyes indicate that interactions among wave-front aberrations can provide better visual quality for both pre-LASIK eyes and post-LASIK eyes. In this paper, we go a step further for Monte Carlo simulations which are not only on total aberrations but also on corneal aberrations, before and after LASIK, for a set of eyes. The corneal aberrations after LASIK are acquired through a new reliable method. Then a series of Monte Carlo simulations (including sign simulation, value simulation and meridional simulation) are performed by manipulating each Zernike coefficient (second through sixth-order) of total aberrations as well as corneal aberrations. The results are evaluated by modulation transfer function (MTF) ratio. Total aberrations for post-LASIK eyes still show MTF advantage over randomized aberrations, with slightly change as compared to that for pre-LASIK eyes. However, true corneal aberrations before and after LASIK have no MTF advantage over random aberrations. From this research, we draw conclusions: there is apparent advantage for the complete eye's true aberrations over random aberrations, whether pre-LASIK or post-LASIK, which does not exist for any biological optical surfaces in isolation, and the ability of adaptive mechanism of human eyes, increases after LASIK.     

Subjective evaluation of intraocular lenses by visual acuity measurement using adaptive optics

We present a new method for subjectively evaluating intraocular lenses (IOLs) without implantation surgery. To illustrate the method, three types of single-piece IOL (equispherical monofocal, rotational symmetric aspheric monofocal, and diffractive bifocal) were assembled into a model eye and evaluated using an ocular adaptive optics system by a single subject. To separate the spherical aberration of the crystalline lens, the subject's corneal topography and wavefront aberrations were measured and modeled. Three levels of Zernike spherical aberration were generated and superposed on the IOLs and the subject's eye. The corrected distance visual acuity was measured by psychophysical visual procedure.     

Information fusion method for ocular aberrations measurement based on subjective visual compensation

The human eye is an imperfect refractive system which not only has defocus and astigmatism, but also has spherical aberration, coma and anomalistic high-order aberrations, all of which have certain influence on the imaging quality of retina. What's worse, aberration is further enlarged as a result of mydriasis in dark field and weak light, thus making the vision performance of human eyes far below diffraction limitation. Further research revealed that human eye visual imaging is not only connected with refractive system, but also is closely related to the subjective judgment of human brain and the process of neural system. In order to overcome the deficiencies, wave-front aberration measurement method and system that has subjective visual compensation is proposed and conducted in combination with objective measurement, which ensures more accurate and realistic measuring results. The experimental data revealed that wave-front aberration obtained from subjective visual compensation measuring method is smaller than objective measurement, which is the result of subjects’ adaptive correction when watching sighting targets. In addition, when subjects are watching different sighting targets, the fluctuation value of wavefront aberration is small. Therefore, it is concluded that subjective visual compensation measuring method contributes to aberration measuring improvement and obtains results match with the realistic state by taking into consideration the actual condition of human eyes when watching targets. Hopefully, these discoveries will be of positive and beneficial value to the determination of human eye aberration treatment.     

The aberration and the modulation transfer function in LASEK and LASIK: Pupil size dependence

The wave-front aberrations on the postoperative eyes with two different type of excimer laser surgery have been measured by a Hartmann-Shack wave-front sensor. We have calculated the aberrations for both 3 and 6 mm pupils, and with which to acquire the MTF of the eye. There are no significant differences in wave-front aberrations postoperatively (P>0.05) for 3 mm pupil size, but with 6 mm pupil, LASIK-treated eyes exhibit significant higher aberrations than LASEK-treated eyes for 4th and 5th-order aberrations. For individual Zernike terms, there are significant difference in , and . The MTF for 6 mm pupil is much lower than those for 3 mm pupil across all spatial frequencies. The LASEK curve shows higher than that with LASIK at spatial frequencies less than 60 c/d, which means that the optical quality in LASEK-treated eyes showed better than in LASIK-treated eyes.     

渐进多焦点镜片的逐点定向曲率补偿优化设计

提出一种利用逐点定向曲率补偿法对渐进多焦点镜片初始模型进行整体优化以减小周边散光区（俗称盲区）的优化设计方法。推导出自由曲面任意方向法曲率的计算公式、确定主曲率和主方向的方法,求出镜片初始模型上各点的曲率差和最大曲率方向、最小曲率方向,通过迭加由不同曲率、不同轴向微小柱面构成的自由曲面,来实现逐点定向曲率补偿,使镜片各点的曲率差适当减小,从而减小散光。给出具体优化步骤和一个优化设计实例,并进行实际加工制作与检测。对比优化前后的光焦度和散光度的面形分布图。结果表明,逐点定向曲率补偿法能有效减小渐进多焦点镜片初始模型的最大散光并明显扩大视远区清晰视觉范围。     

The modelling of the influence of a corneal geometry on the pupil image of the human eye

In normal conditions, a pupil of the eye is observed through the optical system of the cornea. The cornea is the anterior surface of the eye and is the major refractive element of the human eye. The influence of the corneal shape should not be neglected in measurements of the pupil size. The purpose of this study was to estimate the influence of the corneal geometry, the diameter of the pupil and its position in the anterior chamber on the magnification and position of the image of the pupil. The numerical calculations presented in the paper assume infinitely thin cornea, and the corneal topography was approximated by the elongated ellipsoid. The ray tracing procedure was used in our numerical modelling. The magnification of the pupil image amounted to about 10% and increases with decrease of radius of curvature and eccentricity of the corneal profile and decreases for the largest pupil. The results show also that the pupil image is placed nearer the corneal apex than the real pupil. The image of the pupil is always blurred, which limits the sharp observation of the pupil.     

Changes in corneal asphericity after laser refractive surgery,including reflection losses and nonnormal incidence upon the anterior cornea

We tested the effects on laser ablation of reflection losses and nonnormal incidence on the anterior cornea. We measured presurgical and postsurgical corneal asphericity in 94 myopic eyes, comparing it with the corneal asphericity predicted by the Munnerlyn formula, modified or not, with an adjustment factor that takes into account the two effects mentioned above. The predictive power of the experimental results was stronger when we considered the adjustment factor. We propose to modify ablation algorithms by taking this adjustment factor into account, especially in customized corneal ablation, which needs high accuracy for correcting eye aberrations.     

基于波前像差的个性化人工晶体设计

在个性化人眼光学结构的基础上,运用ZEMAX软件的优化功能,设计了符合实际人眼光学特性的个性化人工晶体。该人工晶体不仅可以矫正离焦和像散,还引入了非球面可以矫正人眼的球差。文中将个性化人工晶体优化后得到的屈光度与经验公式计算得到的屈光度作了比较,在经验公式0.25D精确度的基础上有了提高,并直观地描述了个性化人工晶体植入前后人眼调制度和分辨率的变化情况。对样本人眼矫正后人眼分辨率最大变化由28 L/mm提高到118 L/mm,调制度由0.02提高至0.51。分析结果表明,个性化植入人工晶体的方法可以提高人眼矫正的精确度,不同人眼的波前特性不同,矫正效果也有相应的差异。     

Curvature sensor for the measurement of the static corneal topography and the dynamic tear film topography in the human eye

A system to measure the topography of the first optical surface of the human eye noninvasively by using a curvature sensor is described. The static corneal topography and the dynamic topography of the tear film can both be measured, and the topographies obtained are presented. The system makes possible the study of the dynamic aberrations introduced by the tear film to determine their contribution to the overall ocular aberrations in healthy eyes, eyes with corneal pathologies, and eyes wearing contact lenses.     

基于反转光楔和泽尼克多项式的共形光学设计

采用一对反向旋转的累斯莱棱镜可以实现对目标视场的动态扫描,并应用一对内表面为泽尼克边缘矢高表面的透镜对共形光学整流罩引入的主要像差进行校正,剩余像差则由累斯莱棱镜内表面进行补充校正.设计实例中,通过比较光学系统校正前后的成像质量以验证这种校正方法的有效性.     

Fresnel-based analysis of Kasprzak's crystalline model: statistical results and individual predictions

We present a new modelization technique of the human eye based on the calculation of light distributions inside the eye. The method is applied to the study of the crystalline model proposed by Kasprzak and Popiolek. We obtain corneal surface data and axial lengths for two groups of real eyes. With these data, we construct a diffractive model of a human eye, which permits calculation of propagated light distributions at any distance inside the eye. The real crystalline lens is substituted by Kasprzak's model, thus obtaining a realistic model eye. From calculated patterns, we obtain the Strehl ratio and the modulation transfer functions of 44 eyes, divided in two groups according to the age. We compare our results with those in the bibliography. Finally, we check the performance of the method through individual comparison of the calculated image positions with respect to the retina with the refractive data for the each subject. We have observed good agreement between our method and results from other authors. We also find reasonable correlation between calculated refraction and subjective exams.