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.     

角膜手术后眼模型的构建和人工晶状体设计

根据角膜屈光手术前的角膜地形图、眼内各组分的轴向间距和波前像差,运用ZEMAX光学设计软件,构建了术前的个性化眼模型.结合角膜屈光手术后实际测量的波前像差,建立了术后个性化眼模型.运用该模型,为角膜屈光手术眼设计了双球面人工晶状体.研究表明:对于角膜屈光手术后人眼,用术后个性化眼模型计算的人工晶状体度数可靠.该模型还能够为术后眼设计矫正像散和其他高阶像差的人工晶状体,同时可以用来评估角膜手术联合白内障术后人眼的光学性能,以及手术中各类偏差对视觉质量的影响.     

A new method to calculate corneal ablation depth based on optical individual eye model

The corneal shape, axial lengths and the wavefront aberrations of the eye were all considered to calculate the ablation depth based on the individual eye model. The optimization method for the curves surface replaced the direct calculation from only the optical path difference method (OPD). We analyzed the eye's optical system on its exit pupil and offered the optimum corneal anterior surface. And the ablation depth was the difference between the pre- and post-optimization along the optical axis of the eye. In our experiment, the maximum ablation depth decreases by 8.5% and the mean ablation depth decreases by 8.2% compared with the OPD method.     

考虑视轴方向的个性化眼模型的构建

包含更多人眼解剖学特性的个性化眼模型具有重要的实验和临床意义。由角膜地形图计算了8只人眼视轴与光轴之间的夹角,水平分量平均值为4.23°±1.51°,竖直分量平均值为-0.40°±1.27°。根据视轴与光轴之间的夹角、角膜地形数据、眼内各部分轴向间距和人眼波像差,运用光学设计软件Zemax分别为这8只人眼构建了考虑视轴方向的个性化眼模型。在此基础上,计算了波前引导的个性化角膜切削深度,并与光程差方法计算的切削深度进行了比较。在切削光区中心处,两者相差不大,平均值为(0.09±0.04)μm;随着半径增大,两者之间的差值逐渐增大。对于所研究的实例,光区外围处的最大差值为0.59μm。个性化眼模型为设计波前引导的个性化角膜切削方案提供了一个有效工具。     

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.     

基于个性化人眼模型的大视场波像差特性的研究

大视场波前像差对人眼光学系统的影响不容忽视。运用Zemax光学设计软件分别为8只正常人眼构建了个性化的人眼模型,该人眼模型由实际测量的人眼波前像差数据、角膜地形数据及眼内各部分轴向间距数据优化得来,与个体人眼具有相同的光学特性。在此基础上,分析了人眼颞侧方向0°,10°,20°,30°,40°,50°视场的离轴像差随视场角的变化趋势,得出边缘视觉比中央视觉质量差主要来源在于像散与彗差。四阶以上的高阶像差随着视场角的改变,变化不大。将个性化人眼模型计算得到的大视场波前像差值与用哈特曼夏克(Hartmann-Shack)波前传感器实际测量得到的人眼像差值相比较,两者结果相吻合。     

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.     

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。     

在测量人眼像差中信息融合方法的应用

建立了基于Hartmann-Shack传感器的主客观人眼波前像差测量系统,该系统使用Hartmann-Shack传感器客观测量人眼像差,分别对模拟眼和活体人眼进行了像差测量.同时系统中加入了主观测量人眼像差的部分,该系统能够同时进行客观和主观的像差测量,实现了使用信息融合的方法对测量结果进行数据处理.并结合了客观测量和主观测量的优点,使用信息融合的方法使测量结果更加合理.     

Measurement of Wavefront Aberration of Human Eye Using Talbot Image of Two-Dimensional Grating

The measurement of human ocular aberration is now frequently performed because of the increase in refractive surgery on the human cornea. The Hartmann-Shack (H-S) wavefront sensor is considered to be the most useful wavefront sensor, and a calculation method for wavefront aberration has been established. New methods of measuring wavefront aberrations of human eyes, using the Talbot image of a two-dimensional grating as a wavefront sensor and local shift of the Talbot image to calculate tilt of the wavefront are shown. The shift of the Talbot image was determined by comparing the phases of fundamental spatial frequency between the grating and the local patch of the Talbot image by Fourier transformation. The actual experiment was performed using a modified commercially available wavefront analyzer. Using these methods, Talbot images were obtained from model eyes and a human eye, and wavefront shapes were successfully reconstructed. Wavefront aberrations can be measured even when the obtained image is degraded by defocusing or scattering.     

Achromatic customized intraocular lens based on an individual pseudophakic eye model

Customized hybrid diffractive-refractive intraocular lens (IOL) has been designed based on an individual pseudophakic eye model constructed with the measured corneal topography data and the eye's axial lengths. The detailed designing and optimizing procedure is given. It is found that an eye with achromatic customized IOL would achieve super modulation transfer function (MTF) in both the scotopic and photopic conditions. The variation of MTF as colors is negligible, the chromatic focus shift is no more than 0.1 D, and the depth of focus is 3.0 D with quite high MTF. The achromatic customized IOL provides excellent visual performance for cataract patients. Moreover, individual pseudophakic eye model can be an effective tool for evaluating the optical performance of pseudophakic eye and the influence of clinical surgery deviation.     

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.     

渐进多焦点镜片波前像差的扩束测量方法

利用波前传感器测量自由曲面镜片时,由于自由曲面镜片的直径通常大于波前传感器的接收孔径,主要采用子孔径拼接技术测量镜片的波前像差。针对子孔径拼接技术测量中存在着操作繁琐、数据处理量大等问题,提出渐进多焦点镜片波前像差的扩束测量方法,得到渐进多焦点镜片中央直径为22 mm圆形区域内的波前像差。为了验证试验的可靠性,将测量得到的波前像差泽尼克表述中的离焦项转换为球镜度,与条纹偏折法测量得到镜片的球镜度进行对比实验,实验结果证明了渐进多焦点镜片波前像差的扩束测量方法可以用于渐进多焦点镜片波前像差的检测。     

Studies of transverse chromatic aberration based on individual eye model

Two kinds of individual eye models, with and without involving the angle between visual axis and optical axis, are constructed according to the measurements of the corneal surfaces, the optical axis lengths and wavefront aberrations. The constructed eye models are then used to investigate the properties of the transverse chromatic aberration (TCA) and its influence on visual performance. The statistical distributions of the horizontal TCA, vertical TCA and the absolute magnitude of the TCA over the spectrum from 470 to 650 nm are provided, respectively. The variations of TCA with wavelength as referring to the central wavelength of 555 nm for five subjects are also provided. Then we evaluate the impact of TCA on image performance in comparison with longitudinal chromatic aberration (LCA). It is shown that LCA is more detrimental than foveal TCA in image quality. It is found that, while LCA was corrected well, the foveal TCA is simultaneously corrected. Finally, we investigate the correction of peripheral TCA with an achromatizing element. The correction of peripheral TCA of human eye strongly depends on the location of the achromatizing element, and with the element in front of the eye, the peripheral TCA cannot be corrected.     

基于矢量波像差理论的两反光学系统装调研究

 为了实现对两反光学系统的精密装调,提出一种基于矢量波像差理论和波像差检测技术对失调量精确求解的装调方法。使用矢量波像差理论,将已设计的两反光学系统参数、失调量和失调光学系统的波像差之间建立方程;然后通过干涉测量法得到某一个视场的干涉图,利用条纹分析软件得到表征失调系统三阶彗差和三阶像散的泽尼克项系数,将泽尼克项系数代入方程从而求解出失调量。运用此方法对4 m口径RITCHEY-CHR-TIEN结构的天文望远镜进行模拟装调,最终求解的失调量与引入的失调量结果相互吻合,说明该装调方法正确。     

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%.     

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.     

Model-based adaptive non-null interferometry for freeform surface metrology

A model-based adaptive non-null interferometry(MANI) is proposed for steep optical freeform surfaces in situ testing. The deformable mirror(DM) affording the flexible compensation is monitored with the beam in the interferometer by a wavefront sensor. The residual wavefront aberration in the non-null interferogram is eliminated by the multi-configuration ray tracing algorithm based on the system model, especially the DM surface model. The final figure error can be extracted together with the surface misalignment aberration correction.Experiments proving the feasibility of the MANI are shown.     

A modified phase diversity diffraction wavefront sensor with a grating

The phase diversity wavefront sensor is one of the tools used to estimate wavefront aberration, and it is often used as a wavefront sensor in adaptive optics systems. However, the performance of the traditional phase diversity wavefront sensor is limited by the accuracy and dynamic ranges of the intensity distribution at the focus and defocus positions of the CCD camera. In this paper, a modified phase diversity wavefront sensor based on a diffraction grating is proposed to improve the ability to measure the wavefront aberration with larger amplitude and higher spatial frequency. The basic principle and the optics construction of the proposed method are also described in detail. The noise propagation property of the proposed method is also analysed by using the numerical simulation method, and comparison between the diffraction grating phase diversity wavefront sensor and the traditional phase diversity wavefront sensor is also made. The simulation results show that the diffraction grating phase diversity wavefront sensor can obviously improve the ability to measure the wavefront aberration, especially the wavefront aberration with larger amplitude and higher spatial frequency.     

A mathematical model of Schmidt corrector plate with defocus in variable for quick F ratio and large aperture systems

To make it easier for designing Schmidt optical systems, based on wavefront aberration functions, a mathematical model of the corrector plate aspheric surfaces varies as a function of defocusing amount is established. It corrects not only the third-order spherical aberration, but also the 5th-order spherical aberration for the system. A series of Schmidt optical systems were designed as examples to evaluate the mathematical model of the aspherics. Results show that the mathematical model is precisely in fitting the needed shape of the corrector, and can be used for the systems for quick F ratio and large aperture. A mathematical model for reflective correctors shape is also established.