Optical aberrations of the cornea and the crystalline lens

The wave-front aberrations of the anterior corneal surface, the posterior corneal surface and the complete eye have been measured by a corneal topographic system (Orbscan II) and a Hartmann-Shack wave-front sensor. We have calculated the aberrations for both the corneal surfaces with the discrete set of corneal elevation data, and with which to acquire the aberrations of the whole cornea. The aberrations of the crystalline lens are calculated by subtracting the aberrations of the cornea from that of the complete eye. The aberration combination between the anterior and the posterior corneal surface, between the cornea and the crystalline lens is complicated, either compensation or addition. For individual Zernike terms, astigmatism and quatrefoil in the anterior corneal surface are added by the posterior corneal surface, while some other terms show compensation between the two surfaces. And for complete eye, astigmatism and spherical aberrations in the cornea are partially compensated by the crystalline lens, and other terms show addition between the two parts. Individual eye shows different combinations of compensation and addition across different Zernike terms.     

Modal tomography of aberrations of the human eye

The work is devoted to the research and development of a new method of modal phase tomography for diagnostics of aberrations of the human eye. Implementation of the method is based on a series of eye aberration measurements taken at different angles to the optical axis by means of a wave-front sensor. The technique of restoration permits the contributions of different elements of the eye to the total aberrations to be separated. The results of numerical research and a model experiment are presented.     

Wavefront aberrations in the accommodated human eye based on individual eye model

In this research, we firstly construct individual eye models based on the wavefront and the measured cornea structure of the eyes. Then we analyze the influence of accommodation on the wavefront aberrations based on individual eye model. The individual eye model has the same wavefront aberration as that measured from Hartmann–Shack wavefront sensor. The optical design software ZEMAX is used to construct the individual eye models for 20 normal eyes. Accommodative conditions are from 0 to –4 diopter in steps of one diopter. The variations of the total, the spherical, the coma and the higher-order root-mean-square wavefront aberrations, as accommodations, are illustrated. Influence of accommodation on wavefront aberration varies from individual to individual, and the variation magnitude is independent of the magnitude of the wavefront aberration of the eye.     

Coherence function analysis of the higher-order aberrations of the human eye

We measured the wavefront aberrations of the eyes of five subjects with a Shack-Hartmann sensor sampling at 21.2 Hz and decomposed the measurements into Zernike aberration terms up to and including the fifth radial order. Coherence function analysis was used to determine the common frequency components between the aberrations within subjects. We found the results to be highly subject dependent. The coherence values were typically <0.4. Possible reasons for this are discussed. Coherence function analysis is a useful tool that can be used in future investigations to determine correlations between the aberration dynamics of the eye and other physiological mechanisms.     

A tomographic method for diagnosis of human eye aberrations

A new method using modal phase tomography for diagnosis of human eye aberration was elaborated and investigated. The method enabled the separation of the contributions from the individual elements of the eye into summary aberrations. The forms of the radiation wavefronts from several reference sources being formed on the retina of the eye as initial data for analysis were considered. Distortions of every element of the eye were represented as a Tsernike polynomial expansion. In this work, the theoretical basis of the method, numerical investigation and experimental modeling results confirming the efficiency of the method are presented.     

Detection of wave aberrations in the human eye using a retinoscopy-like technique

The influence of optical aberrations on the retinoscopic reflex is theoretically analyzed from a geometrical point of view. The relationship between the wave aberrations to the ray aberrations is applied to explain the appearance of the retinoscopic patterns for different types of ocular aberrations. Several schematic models of the human eye are tested numerically, showing that a careful retinoscopic examination can detect the usual eye aberrations.     

主客观结合人眼波前像差测量系统的设计与实验

设计了主客观方法相结合的人眼波前像差测量系统。该系统的控制部分以工控机为中心,实现了对离焦补偿装置、LCD视标显示装置和可变形镜驱动器的控制。使用Hartmann-Shack传感器对人眼出瞳的波前像差进行测量,光路中加入了能够显示各种视标和测试图案的LCD,从而考虑到了主观调节对人眼像差的影响,能够对人眼的视觉质量进行全面衡量,实现了客观测量和主观测量在光路中的结合。使用该系统分别测量得到了模拟眼和活体人眼的波前像差,并对主客观测量结果进行了信息融合,能够为个性化的人眼屈光矫正提供有用的依据。     

人眼波前像差主客观测量的信息融合方法

人眼是一个不完善的屈光系统,存在着各种像差,而且视觉不仅与人眼的屈光系统有关,还与主观的判断和神经系统的处理有密切关系.只有主观测量与客观测量相结合,才能得到最佳的视力矫正数据.本文提出了通过信息融合技术把像差的主观测量和客观测量的结果进行融合处理,给出矫正时所需的唯一数据,并通过实验得到了信息融合后的人眼波前像差.     

Single-pass measurements of the wave-front aberrations of the human eye by use of retinal lipofuscin autofluorescence

We describe a technique for making single-pass measurements of the wave-front aberration of the eye. The technique utilizes the natural fluorescence of the retina that is produced by lipofuscin to form an incoherent pointlike source for conventional Shack-Hartmann sensing.     

Compensation of lens aberrations in digital holography

The possibility of compensating for the aberrations of an imaging lens in digital holography is outlined theoretically. The principle is demonstrated with a Mach-Zehnder arrangement and transilluminated objects. Diffraction-limited resolution can be obtained with a plano-convex lens. Amplitude and phase objects were imaged.     

Chromatic aberrations of thin refractive variable-focus lens

We present an approach to an analysis of the third order chromatic aberrations of thin refractive fluid lenses with a variable focal length. A detailed theoretical analysis is performed for a simple fluidic variable-focus lens and formulas are derived for an optical design of such lenses. Aberration coefficients of the third order of the variable-focus lens can be completely characterized by three parameters which depend only on refractive indices of fluids forming the variable-focus lens. Formulas were derived for the change of the third-order aberration coefficients with the wavelength. Calculations are provided for Varioptic lens Arctic-416.     

MR in vivo imaging of oxygen suppression effect of soft contact lens on the human cornea

The O(2) suppression effect of a soft contact lens on the human cornea was measured using dynamic magnetic resonance imaging (MRI) of the anterior chamber transcorneally exposed to O(2). Dynamic T(1)-weighted fast spin echo imaging of anterior chambers (TR = 2 s, TE = 15 ms, 5-mm slice) was performed both before and during oxygen supply to a full goggle placed on the face of volunteers wearing a soft contact lens on one eye and nothing on the other eye as a control. Within 15 min after O(2) administration, significantly lower intensity changes were obtained in the anterior chambers of the eyes with the contact lens than in those of the eyes without one, suggesting that dynamic MRI of the anterior chamber transcorneally exposed to O(2) can be used to evaluate the O(2) suppression effect of a soft contact lens on the cornea.     

The interpretation of multi-exponential water proton transverse relaxation in the human and porcine eye lens

We report results of 1H NMR transverse relaxation experiments on human and porcine eye lenses. Several authors have reported that transverse relaxation is not mono-exponential when observed by the Carr-Purcell-Meiboom-Gill (CPMG) sequence and have interpreted the results by postulating the presence of "pools" of water molecules in different binding environments that do not exchange rapidly on the NMR timescale. We have compared CPMG data for intact lenses with results for lens homogenates and have combined a CPMG spectroscopic pulse train with NMR micro-imaging to study the nature of the transverse relaxation process in human and porcine lenses. Fast exchange of water protons with the lens proteins (crystallins) leads to an enhanced transverse relaxation rate that varies linearly with protein concentration. At the resolution of NMR micro-imaging the transverse relaxation process is mono-exponential. The results show that the multi-exponential CPMG data observed spectroscopically for whole lenses reflect spatial variations in crystallin content through the lens rather than the presence of distinct "bound" and "free" water pools.     

Theory of orthogonal aberrations and its use in lens design

The author introduces a complete set of polynomials that are orthogonal in the three-dimensional region (generalized Zernike polynomials). These polynomials make it possible to obtain orthogonal expansion of the wave aberration in the three-dimensional region of field-pupil 0 ≤ r ≤ 1, 0 ≤ ρ ≤ 1, 0 ≤ φ ≤ 2π. This permits us to determine the orthogonal system of individual aberrations and introduce a classification of individual aberrations depending on the degree of field r and pupil ρ, φ variables. The author shows that orthogonal aberrations have a number of unique properties. The developed approach, describing the aberration properties of optical systems by means of orthogonal aberrations, and its use in the construction of new methods and techniques for the design of optical systems form a new section of lens design, namely, “Theory of orthogonal aberrations and its applications in the design of optical systems”.     

The study of correction for chromatic aberrations of human eye with diffractive–refractive hybrid elements

A chromatic corrector with two refractive–diffractive hybrid elements is designed over a reasonable wide field-of-view of 7° to correct the chromatic aberrations of human eye. We investigate the performance of the corrector using several optical criteria in a comparison with the chromatic corrector with single refractive–diffractive element. Both the correctors can correct the longitudinal chromatic aberration (LCA) fairly. It is demonstrated that the chromatic corrector with single element introduces serious eccentric transverse chromatic aberration (TCA), which deteriorates the image quality at the edge field-of-view. On using the chromatic corrector with two refractive–diffractive elements, not only the LCA but also the TCA can be corrected very well. The designed chromatic corrector can be used to improve the retinal image quality and has potential application in the design of visual instruments.     

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。     

Fourier and power law analysis of structural complexity in cornea and lens

The ordered pattern of type I collagen fibrils in the transparent cornea is an example of specialization in the formation of functional ultrastructure. In contrast, the disordered and amorphous distribution of cytoplasmic proteins in the transparent lens resembles the structure of most cells. While the organization of cytoplasmic proteins is often considered to be random, the compartmentalization of functional proteins in biological cells and the organization provided by cytoskeletal elements suggests that non-random patterns of organization are common. Attempts to quantify disordered, amorphous patterns of ultrastructure in cells and tissues have been unsuccessful, in part, because the cellular organization of structural proteins including collagen, keratin, cytoskeletal and crystallin proteins is complex. Characterization of the complex patterns observed in electron micrographs is a fundamental problem in structural biology. This paper reviews the use of Fourier and power law analyses of electron micrographs of cornea and lens as models for ordered and disordered ultrastructure of cells and tissues.     

Optical performance of the eye with progressive addition lens correction

The aim of this study was to simulate the retinal image of the eye with progressive addition lens (PAL), correction (without cylindrical component) and investigate its quality. The optical design and analysis software was used in simulation. The topographical data of the front surface of PAL were taken from the scanning profilometry. Also the coordinates of the points of the distant and near power measurements were taken from topographical measurements. The back surface was assumed to be spherical with a radius of curvature matched so that the optical power of PAL meets the data given by the manufacturer. In order to describe the retinal image quality, various metrics were calculated in comparison to the eye without correction.     

Schematic eye with a gradient-index lens and aspheric surfaces

A new schematic eye with aspheric surfaces and a radially varying refractive-index distribution lens is proposed. Image quality and spherical aberration are determined by use of ray tracing, and the results are presented as spot diagrams and compared with five existing model eyes. The proposed model provides the best image quality and lowest spherical aberration.     

The study of wavelength-dependent wavefront aberrations based on individual eye model

Theoretical calculations of the wavelength dependence of the ocular wavefront aberrations are performed with individual eye model. Individual eye model, based on the traditional Gullstrand-Le Grand eye model, has been established with measured individual cornea data, eyeball depth and wavefront aberrations. We analyze the wavelength-dependent wavefront aberrations at 12 different visible wavelengths (between 400 and 750 nm) for eight eyes. The change of defocus with wavelength (longitudinal chromatic aberration, LCA) is noticeable, and in good agreement with the results from references. In most cases, the primary spherical aberration changes significantly with wavelength. In comparison with the primary spherical aberration, the other higher-order wavefront aberrations have a smaller change with wavelength. These results have potential applications in those situations where defocus or higher-order wavefront aberrations information in arbitrary wavelength is required.