Adaptive model of the gradient index of the human lens. I. Formulation and model of aging ex vivo lenses

A simple, parametric adaptive model of the refractive index distribution of the ex vivo crystalline lens is presented. It assumes conicoid (or nonrevolution quadric in 3D) iso-indical surfaces, concentric with the external surfaces of the lens. The model uses a minimum number of internal structural parameters, while the shape of the iso-indical surfaces adapts automatically to the external geometry. In this way, it is able to adapt and fit individual distributions as well as adapt to the changes of the lens shape and structure with age and accommodation. The model is fit to experimental data for individual eyes spanning ages 7 to 82 years, where for each eye the crystalline lens dimensions and iso-indical index data are known. The analysis demonstrates that only one age-dependent structural parameter is needed to replicate the internal iso-indical index structure, given age-dependent models for the external surfaces. An age-dependent-parameter global model is derived and is shown to predict age-dependent changes in the ex vivo lens power and longitudinal spherical aberration with age.     

嵌套效应对单向织物压缩行为的影响

通过分析纤维束受压横截面的变化,并基于经典的纤维束本构关系,建立了任意嵌套状态下两层单向织物压缩厚度与外部载荷、层间偏移量之间关系的理论模型。在此基础上进一步建立了多层织物的压缩响应模型。通过对上述模型数值求解,预测了不同层数织物压缩响应。结果表明:同等受力条件下,织物的平均每层厚度随着偏移率的增加而减小;在一定压力下多层织物的平均每层厚度分布近似符合正态分布,且随着层数的增多,分布将会越来越集中;对于大于10层的织物可直接采用压力与内部层间距的期望的变化曲线表征多层织物的压缩性能。经验证,该模型与实验数据吻合较好,从而验证了模型的正确性。     

Examination of the effect of the fibrous structure of a lens on the optical characteristics of the human eye: a computer-simulated model

We introduce a model of the human eye for which we take into consideration the laminated nature of lens fibers. The thickness of each lamina is 5.6 μm; thus the lens comprises 300 eccentric lenses of minute dimensions. The index gradient of the lens is such that the index of refraction increases exponentially from the lens core to its peripheral zone. A vector ray-tracing technique is employed to study the optical haracteristics of the system. Both paraxial and marginal rays are simulated, and the angles of incidence vary from 0° to ±20°. Special attention is given to the meridional caustic surfaces as well as the wave-front distortion of the refracted rays. A quasi-Newton optimization technique is employed to obtain the best parameters for the system. A computer modeling program, written in FORTRAN 77, is used to simulate a ray's refraction through the multisurfaces of the eye. The results show full agreement with previous data and that the cornea is responsible for eliminating possible spherical aberration of the system.     

Adaptive model of the gradient index of the human lens. II. Optics of the accommodating aging lens

A simple, parametric model of the gradient refractive index distribution (GRIN) of the human lens with conicoid surfaces able to adapt to individual distributions as well as to the changes of the lens shape and structure with age and accommodation is presented. The first part of this work was published in a companion paper [J. Opt. Soc. Am. A24, 2175 (2007)]. It included the development of the mathematical formulation of the adaptive model; the validation of its customization capability by fitting, sample by sample, a set of in vitro refractive index distributions of lenses of different ages, ranging from 7 to 82 years, from the recent literature; and an average model of the (in vitro) aging crystalline lens. Here we extrapolate that in vitro GRIN model by assuming that the same structural parameters are valid for the living lens. Then, recent data of the changes of the shape of the aging lens with accommodation from the literature are used to build an aging and accommodating lens model. This is straightforward since the GRIN model adapts automatically to the chosen external lens geometry. A strong coupling was found between the adaptive GRIN distributions and the conic constants affecting the refractive power. To account for the lens paradox and the reported changes in lens spherical aberration with age and accommodation, age- and accommodation-dependent functions for the anterior and posterior internal conic constants were derived through optimization.     

Model eyes for evaluation of intraocular lenses

In accordance with the present international standard for intraocular lenses (IOLs), their imaging performance should be measured in a model eye having an aberration-free cornea. This was an acceptable setup when IOLs had all surfaces spherical and hence the measured result reflected the spherical aberration of the IOL. With newer IOLs designed to compensate for the spherical aberration of the cornea there is a need for a model eye with a physiological level of spherical aberration in the cornea. A literature review of recent studies indicated a fairly high amount of spherical aberration in human corneas. Two model eyes are proposed. One is a modification of the present ISO standard, replacing the current achromat doublet with an aspheric singlet cut in poly(methyl methacrylate) (PMMA). The other also has an aspheric singlet cut in PMMA, but the dimensions of it and the entire model eye are close to the physiological dimensions of the eye. They give equivalent results when the object is at infinity, but for finite object distances only the latter is correct. The two models are analyzed by calculation assuming IOLs with different degrees of asphericity to elucidate their sensitivity to variation and propose tolerances. Measured results in a variant of the modified ISO model eye are presented.     

Plasmon Resonances of Nanoshells of Spheroidal Shape

Plasmon resonances are computed for nanoshells of prolate and oblate spheroidal shape. Both longitudinal and transverse resonances are investigated as a function of aspect ratio and shell thickness. Formulas for the surface charge density on the outside and inside shell surfaces are derived.     

眼球系统中关键屈光元件的光学模型研究

角膜和晶状体是人眼光学系统中两个关键的屈光元件,为了理解眼内各介质和整个眼球的屈光状态以及视网膜上的成像,有利于眼科临床方面的应用,需要分别对二者进行光学特性模型的分析与研究。根据角膜和晶状体的光学特性,应用光学设计软件Zemax和有关的数学工具,从光学成像角度,分别对角膜和晶状体模型进行研究:基于结合人眼光学模型的角膜双二次曲面模型的建立方法,统计分析了我国人眼实测角膜参数的数据;通过对晶状体折射率分布特点的分析,分别在轴向和径向上进行了综合分析。最后给出了符合我国人眼特点的角膜面型的统计数值,完善了我国人眼角膜光学模型的建立;获得了形式简单且能够表示晶状体折射率分布一般特征的梯度渐变模型表达式。基于收集的我国人眼实测数据的角膜面型模型和晶状体梯度渐变形式的折射率模型,为解决人眼光学系统研究中的关键问题提供了新的方案和思路。     

Appearance of images through a multifocal intraocular lens

The appearance of images through a multifocal intraocular lens (IOL) was simulated. The optical transfer function (OTF) of a model eye containing the multifocal lens was measured and divided by the OTF of the model eye with a monofocal IOL. This ratio was used to filter digital images, generating simulations that represent the retinal images seen through a multifocal intraocular lens when viewed through an eye with a monofocal lens. A dichoptic side-by-side display was used to present the original image to one eye, implanted with the multifocal lens, while the other eye, implanted with monofocal lens, viewed the simulations and variations on the simulations to derive a point of subjective equivalence. Four subjects with such bilateral lens implants were tested for near and distance vision. The results validate the test methodology and the simulations. Referenced to the nominal theoretical filter, the prediction was within a 0.25-diopter (D) blur for distance simulation and within a 0.50-D blur for the near-vision simulation.     

A Continuum Based Thick Shell Element for Large Deformation Analysis of Layered Composites

A new continuum based thick shell model is presented for modeling orthotropic laminated shell structures undergoing large elastic deformations. An equivalent single-layer model involving seven nodal degrees of freedom is used. In that layered model, there are no restrictions on the number of layers, their thickness and their stacking sequence. The shell model accounts explicitly for the thickness change in the shell, as well as the normal stress and strain states through its thickness. Shear locking is avoided using an assumed natural strain formulation, while thickness locking is avoided using modified displacement interpolation functions. The performance of the layered shell element is tested using several linear and non-linear composite plate and shell problems involving anisotropic, angle and cross-ply laminates, cylindrical and spherical shells.     

壳层厚度对核-壳结构PS-SiO_2杂化颗粒压缩弹性模量的影响

基于正负电荷间的静电作用制备了具有核-壳结构的聚苯乙烯-氧化硅(PS-SiO2)杂化颗粒,通过调节正硅酸乙酯的用量对样品的SiO2壳层厚度进行控制。利用原子力显微镜(AFM)在微观尺度上测定杂化颗粒的力-位移曲线,根据Hertz接触模型和Sneddon接触模型,考查了SiO2壳层厚度对样品压缩弹性模量的影响。扫描电子显微镜(SEM)和透射电镜(TEM)结果显示,杂化颗粒中PS内核尺寸为(197±9)nm,壳层由SiO2纳米颗粒组成,在本试验范围内杂化颗粒样品的壳厚为11~16nm。在Hertz接触模型条件下,PS微球的弹性模量为(2.2±0.5)GPa,其数值略低于PS块体材料。当SiO2壳厚由11nm增至16nm时,杂化颗粒的弹性模量从(4.4±0.6)GPa增至(10.2±1.1)GPa,其数值明显低于纯SiO2,且更接近于PS内核。     

Corneal changes induced by laser ablation: study of the visual-quality evolution by a customized eye model

This study focuses on the changes induced in both the asphericity and homogeneity of the cornea for a group of myopic eyes undergoing LASIK surgery. Eyes were characterized by a Kooijman-based customized eye model in which changes were introduced in the form of Gaussian-distributed refractive-index variations of given correlation length for the inhomogeneities and in the form of an expression, based on the modified Munnerlyn's paraxial formula, for the post-LASIK asphericity. Visual quality was evaluated in terms of the Modulation Transfer Function and the Point-Spread Function. The results show that, on average, the evolution of visual acuity is consistent with the change in corneal asphericity, while the evolution of contrast sensitivity requires a loss in corneal homogeneity in order to be explained. By including both effects in the model, the overall model performance in predicting visual quality is improved.     

Non-rotational aspherical models of the human optical system

The aim of this work was to define three-dimensional (3D) non-rotational aspherical parametric models for the human cornea and lens using computational geometry and CAD representations. The hyperbolic cosine based function is used for the cornea and a parametric model is used for lens modeling. Data analysis and visualization of 3D non-rotational models were made using the Rhinoceros CAD software and MATLAB software was used for numeric computation. We combined, implemented, and evaluated these models with a 3D ray-tracing in order to fully analyze the human eye model. It was found that 3D non-rotational aspherical models for the human eye could be more accurately modeled and rendered for analysis with finite element method. The objective of this study is to present and analyze mathematical models of the cornea and lens and to highlight the potential of optical applications of the eye models containing astigmatic surfaces, which are more close to the real eye than spherosymmetric eye models.     

An experimental study of frost formation on a horizontal cylinder under cross flow

Frost layers formed on the front and rear surfaces of a horizontal cylinder during cross flow are found to be thicker than those at the top and bottom surfaces where the flow separation is nearly initiated. This observation was obtained in an experimental study carried out to examine frost formation on a horizontal cylinder given a cross flow condition. The thickness of the frost layer and the temperature distribution in the cylinder were measured for various experimental conditions. The local heat flux around the cylinder and the effective thermal conductivity of the frost layer were likewise evaluated, while thickness and surface temperature of the frost layer around the cylinder were measured periodically. These measurements were obtained by varying the Reynolds number, temperature, and humidity. The dew point temperature of the inlet air, however, was kept below the freezing point throughout the experiment. Results also reveal that inlet air velocity, temperature, and humidity affect thickness and thermal conductivity of the frost layer.     

三角帆蚌贝壳的微结构及尺寸变化特征

天然生物经历了亿万年的不断进化,已经形成了近乎完美的结构。天然生物材料结构的研究是仿生研究的基础,本文以三角帆蚌贝壳为研究对象,利用SEM和AFM,描述了三角帆蚌贝壳的微结构特征,包括其角质层、棱柱层、珍珠层及界面和晶带的形貌,揭示文石晶片及各层间的尺寸变化规律。研究表明:角质层内部分布大量裂纹,珍珠层与棱柱层无明显过渡界面,珍珠层内发现条状晶带结构缺陷;贝壳壳体和珍珠层厚度随0生长线向外呈现先增大后减小的变化趋势,且单层文石晶片的厚度不均,最厚处可达最薄处的2倍多。对三角帆蚌贝壳的结构进行了深入研究,为其优异的力学性能提供了理论依据,为未来的仿生结构设计提供了新思路和新想法。      

Mechanism of compensation of aberrations in the human eye

We studied the mechanism of compensation of aberrations within the young human eye by using experimental data and advanced ray-tracing modeling. Corneal and ocular aberrations along with the alignment properties (angle kappa, lens tilt, and decentration) were measured in eyes with different refractive errors. Predictions from individualized ray-tracing optical models were compared with the actual measurements. Ocular spherical aberration was, in general, smaller than corneal spherical aberration without relation to refractive error. However, horizontal coma compensation was found to be significantly larger for hyperopic eyes where angle kappa tended to also be larger. We propose a simple analytical model of the relationship between the corneal coma compensation effect with the field angle and corneal and crystalline shape factors. The actual shape factors corresponded approximately to the optimum shapes that automatically provide this coma compensation. We showed that the eye behaves as an aplanatic optical system, an optimized design solution rendering stable retinal image quality for different ocular geometries.     

An analysis of stresses in a model of the periodontal ligament

The writers analyze the stresses in a model of the periodontal ligament of a maxillary central incisor. The model is assumed to be of paraboloidal shape, uniform thickness, and of a homogeneous, isotropic, and linearly elastic material. The inside surface of this paraboloidal shell is subject to rigid body displacement while the outside surface is assumed rigidly supported and stationary. The edge of the model is assumed to be stress free.

A system of paraboloidal coordinates is developed, and this system is fitted to the shape of the root of a typical maxillary central incisor. The displacement functions obtained by solving the differential equations of equilibrium are used to determine the stresses at the inside and outside surfaces of the model ligament. These stresses are subject to superposition so that the stresses associated with any combination of applied forces and couples may be determined.     

鸡蛋品质特性的有限元分析方法

目的研究鸡蛋品质物性参数与结构动力学响应特征参数间的关联特性,构建鸡蛋品质检测的动力学相关性模型。方法以敲击响应检测技术为基础,引入结构动力学分析方法,应用有限元仿真技术定量分析鸡蛋品质物性参数(蛋形参数、蛋壳厚度、蛋壳刚度、蛋液密度)与其一阶共振频率间的对应变化规律,获取鸡蛋品质相关的动力学特征参数。结果鸡蛋品质物性参数中蛋形参数、蛋壳厚度、蛋壳刚度、蛋液密度与其结构一阶共振频率关联性显著;蛋壳厚度与蛋体结构一阶共振频率间符合较好的线性规律。相较而言,蛋壳密度、气室高度对结构一阶共振频率的影响较小。结论鸡蛋品质特性相关参数(蛋形参数、蛋壳厚度、蛋壳密度和蛋液密度)与其结构动力学响应特性具有较强的关联性。     

A higher-order shear deformation theory of laminated elastic shells

A higher-order shear deformation theory of elastic shells is developed for shells laminated of orthotropic layers. The theory is a modification of the Sanders' theory and accounts for parabolic distribution of the transverse shear strains through thickness of the shell and tangential stress-free boundary conditions on the boundary surfaces of the shell. The Navier-type exact solutions for bending and natural vibration are presented for cylindrical and spherical shells under simply supported boundary conditions.