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.     

轴位移法测定GRIN透镜的折射率分布系数

本文对GRIN透镜的精确光线追迹公式作了推导,介绍了轴位移法对透镜折射率分布的测量方法及相应的数据处理,并对测量误差进行了分析和计算,从而对测定GRIN透镜折射率分布提供了一种精确而且实用的方法。     

Single dispersive gradient-index profile for the aging human lens

We provide a single gradient-index (GRIN) profile for the crystalline lens in an updated age-dependent emmetropic-eye model. The parameters defining the GRIN profile include their variation with age and the dispersion of the refractive index in order to account for the increase in the positive-wave spherical aberration, for the constant chromatic difference in the refraction of the human eye, as well as for the decrease in the retinal-image quality with aging. In accounting for these ocular properties, the results show that first, the value of the dispersion parameters are invariant with age. Second, those parameters defining the distribution of the lens index cause the lens-center-index value to decrease slightly, and its position along the lens axis changes with age. Furthermore, these findings are in agreement with the lens paradox.     

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。     

Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens

In the first part of this paper we presented a tomographic method to reconstruct the refractive index profile of spherically symmetrical lenses. Here we perform the generalization to lenses that are rotationally symmetrical around the optical axis, as is the ideal human lens. Analysis of the accuracy and versatility of this method is carried out by performing numerical simulations in which different magnitudes of experimental errors and two extreme case scenarios for the likely shape of the refractive index distribution of the human lens are considered. Finally, experimental results for a porcine lens are shown. Conceptually simple and computationally swift, this method could prove to be a valuable tool for the accurate retrieval of the gradient index of a broad spectrum of rotationally symmetrical crystalline lenses.     

Optical coherence tomography of glass reinforced polymer composites

Optical coherence tomography (OCT) is a nondestructive and noncontact technique to image microstructure within scattering media. The application of OCT to highly scattering materials such as polymer composites is especially challenging. In this work, OCT is evaluated as a technique to image fiber tows and voids in two materials: an epoxy E-glass-reinforced composite and a vinyl-ester E-glass-reinforced composite. Features detected using OCT are compared with optical microscopy. Fiber architecture and voids of glass-reinforced polymer composites can be successfully imaged using OCT. The quality of the OCT image is strongly affected by the refractive index mismatch between the fibers and reinforcement. The largest sources of noise in the images arise from fiber lens effects, interference from within the sample, and a very large reflection at the surface.     

线聚焦光学相干层析术的研究

提出了一种高速光学相干层析(OCT)成像技术方案。利用柱面镜的成像特性将传统OCT的点聚焦成像模式改变为线聚焦成像模式,从而降低二维OCT图像的扫描维数,达到提高成像速度的目的。利用ZEMAX光学软件对系统进行光线追迹获得光束经过柱面镜后的聚焦情况。随后采用635nm的激光光源和柱面镜构建了实验系统,实验结果很好地验证了光线追迹仿真结果。     

The effect of pressure on GRIN lenses

The changes of the optical power of Gradient Index (GRIN) lenses occurring in hydrostatic pressures of the range of 0-2 GPa are investigated. The measurements of the position of the waist of the semiconductor laser beam revealed the increase of the optical power of the lenses with increasing pressure. The use of the special plano-concave lenses insensitive to the changes of the refractive index of the pressure medium allowed to attribute the changes to the increasing index gradient in GRIN material. The effect has been explained within the frame of Mueller’s theory of photoelasticity. The findings have been then confirmed in experiments with the plano-planar and plano-convex lenses of the same materials.     

用于OCT动态聚焦的液晶菲涅尔波带透镜研究

提出了利用液晶菲涅尔波带透镜实现光学相干层析成像(OCT)动态聚焦的方法.根据扭曲相液晶空间光调制器(TN-LCSLM)的光学特性,设计了适用于OCT动态聚焦的菲涅耳波带透镜.利用TN-LCSLM型菲涅耳波带透镜进行了变焦控制实验,焦距实测结果与设计值比较吻合.此外,本文讨论了采用TN-LCSLM型菲涅耳波带透镜实施动态聚焦涉及到的一些问题.     

Foundations for low-loss fiber gradient-index lens pair coupling with the self-imaging mechanism

A fiber-optic collimator that emits a Gaussian beam with its beam waist at a certain distance after the exit face of the lens is labeled a self-imaging collimator. For such a collimator, the waist of the emitted Gaussian beam and its location are partly dependent on the properties of the gradient-index (GRIN) lens. Parameters for the self-imaging collimator are formulated in terms of the parameters of a GRIN lens (e.g., pitch, core refractive index, gradient index, length) and the optical wavelength. Next, by use of the Gaussian beam approximation, a general expression for the coupling power loss between two self-imaging-type single-mode fiber (SMF) collimators is, for the first time to our knowledge, derived as a function of three types of misalignment, namely, separation, lateral offset, and angular tilt misalignment. A coupling experiment between two self-imaging collimators with changing separation distance is successfully performed and matches the proposed self-imaging mechanism coupling loss theory. In addition, using a prism, lateral offset, as well as angular tilt, misalignments are experimentally simulated for a two self-imaging collimator coupling condition by a single collimator reflective test geometry. Experimental results agree well with the proposed loss formulas for self-imaging GRIN lenses. Hence, for the first time to our knowledge, the mathematical foundations are laid for employing self-imaging-type fiber collimators in SMF-based free-space systems allowing optimal design for ultra-low-loss coupling.     

Properties of microlenses produced on a layer of tot'hema and eosin sensitized gelatin

Gelatin sensitized with tot'hema and eosin (compounds used in medical therapy) appears to be an excellent material for microlens fabrication. Lenses are produced by irradiation with a 532 nm laser beam. Aspheric concave lenses are formed rapidly with low power radiation. The lens profile is analyzed, as well as imaging properties. Physics of lens formation is also proposed. All material constituents are nonpoisonous, resulting in an environmentally safe, low toxicity material.     

激光起爆器光学窗口的研究

文章设计了平面透镜、单凸透镜、双凸透镜组及格林透镜等几种光学窗口,并通过发火试验详细讨论了几种窗口的优劣。研究结果表明,自聚焦透镜发火阈值要远低于其它光学透镜结构发火能量,是目前最为理想的窗口透镜。     

基于矩阵方法的共轴球面系统屈光特性研究

基于眼科屈光学理论,运用矩阵方法建立了单个球镜片及多个球镜片组合的复杂共轴球面系统的精确屈光特性模型,并与简化模型进行比较,分析镜片间距及放置顺序对组合后屈光特性的影响。基于该精确屈光特性模型,对影响球镜度的各项不确定度分量进行分析。组成镜片的前、后表面曲率半径是影响屈光特性的主要不确定度分量,其次是镜片材料折射率和镜片间距引入的不确定度分量,中心厚度引入的不确定度分量最小。     

Single-mode fiber coupling efficiency with graded-index rod lenses

Losses are calculated for the single-mode graded-index- (GRIN-) lens coupler. The main advantage of this coupling system is large separation between fibers with small power loss. The excess loss of the GRIN-lens coupler is due primarily to the misalignments of the GRIN lenses and is most sensitive to angular tilt rather than lateral offset or end separation. The excess loss is calculated from the overlap of two differently sized or misaligned Gaussian beams. Experimental results show that this method is adequate for predicting losses that are due to misalignments of the GRIN lenses.     

Correction of chromatic aberrations in GRIN endoscopes

A gradient-index (GRIN) endoscope can be constructed by substituting for the usual objective and relay sections suitable cylindrical index-distribution rod lenses. Currently available GRIN lenses exhibit large amounts of chromatic aberration. Axial color arises mostly from the relay lens, while lateral color is due to the objective lens. A negative lens cemented to a shortened GRIN relay lens can simultaneously correct axial and lateral chromatic aberrations with commercially available components. This correction system reduces the requirements for mechanical centration better than do color correctors that are incorporated into the ocular design. Monochromatic aberrations are also considered.     

Micro gradient-index conical lenses: simulation and fabrication methods

In this paper, a micro gradient-index conical lens, which has a larger acceptance angle than a conventional microlens, is presented. Methods on how to simulate these lenses in commercial optical design software CodeV are introduced, and the effects of several index profiles and cone shapes are compared in simulation. Results show that a micro gradient-index conical lens has a four times larger acceptance angle compared with a microlens. Additionally, conical lenses with a Gaussian-index profile show a larger acceptance angle than those with a solid refractive index. Fabricated conical lenses show an acceptance angle of more than 27 degrees for a detection threshold of 50%, which agrees with the simulation result.     

Graded-index fiber lens proposed for ultrasmall probes used in biomedical imaging

The quality and parameters of probing optical beams are extremely important in biomedical imaging systems both for image quality and light coupling efficiency considerations. For example, the shape, size, focal position, and focal range of such beams could have a great impact on the lateral resolution, penetration depth, and signal-to-noise ratio of the image in optical coherence tomography. We present a beam profile characterization of different variations of graded-index (GRIN) fiber lenses, which were recently proposed for biomedical imaging probes. Those GRIN lens modules are made of a single mode fiber and a GRIN fiber lens with or without a fiber spacer between them. We discuss theoretical analysis methods, fabrication techniques, and measured performance compared with theory.     

Spherical gradient-index polymer lens with low spherical aberration

A sphere lens with a spherical gradient index (GRIN) was prepared by the modified suspension polymerization technique. GRIN spheres with quadratic- and linear-index distributions were obtained by two different methods to confirm the effect of the GRIN profile on the focusing property of the sphere lens. It was confirmed in both theory and experiment that the spherical aberration of such GRIN spheres was remarkably decreased compared with that of a homogeneous sphere.     

Waveguiding Fresnel Lenses: Modelling and Fabrication

Abstract

This paper examines the methods, problems and results of modelling Fresnel lenses, and the progress towards fabricating experimental devices that has resulted from these evaluations. The computer model used ray-tracing through phase-weighted two-dimensional Fresnel lenses overlaid onto optical waveguide structures. Several types of lenses were considered, digital phase shift, analogue and photolithographically optimized forms being selected for particular study. The evaluation was directed to determining the effect on performance of changes in dimensions, selected focal length and materials. Negative form lens structures were included, as were a range of fabrication methodologies, so that substrate anisotropy and overlayer refractive index were necessarily surveyed. The lens fabrication will ultimately employ three main technologies: dilute-melt proton-exchange in LiNbO₃, GaAlAs and Nb₂O₅ layers as the guiding films, with lens overlays in a range of deposited films with refractive indices up to 3·85. We report preliminary experimental results leading towards such lenses. For a typical lens, aberration and optical power transfer efficiency were measured and examined in relation to the expected coupling efficiency of the lens overlay to the optical waveguide (the ‘overlap’ integral).