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.     

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。     

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。     

人眼波前像差的动态特性研究

人眼波前像差随时间涨落会引起人眼光学性能和视觉功能的改变.采用改进的HartmannShack波前传感器人眼像差仪对10只屈光度为0D~-5.0D、直径为3mm和6mm的人眼瞳孔的波前像差进行测量,其中每只人眼在5s内连续测量125次,测量频率为25Hz.为确定测量过程中是否引入人为像差,对人造眼3mm和6mm瞳孔的动态波前像差进行测量比对.结果表明:所测量的10只人眼3mm和6mm瞳孔总的Zernike波前像差均方根涨落幅度的平均值分别为0.087μm和0.105μm,均大于Marechal衍射极限;Zernike第3阶到第7阶波前像差均方根涨落幅度随像差阶数的递增而下降,涨落幅度为0.06~0.02μm;人眼波前像差的涨落频率达6Hz.     

人眼大视场波前像差特性研究

应用改进的Hartmann-Shack波前传感器人眼像差仪,测量了5只5.2 mm瞳孔的正常眼,向鼻侧和颞侧两个水平方向50°视场角Zernike第二级到第十级的波前像差. 视场角从鼻侧和颞侧两个水平方向从0°增大到50°时,Zernike第三级波前像差的rms值平均增大2倍；Zernike第四级波前像差的rms值平均增大1.8倍；Zernike第五级到第十级波前像差的rms值平均增大1.7~1.3倍.     

透射波前Zernike系数与波长的函数关系研究

波前像差可以很好地反映光学系统的性能,波前检测结果通常用一组Zernike多项式线性组合表示。透射式光学系统波前需要在特定波长下检测,由于检测仪器的限制,目前只有少数波长的波前可以得到准确检测。提出一种新的思路,通过分析透射波前Zernike系数与波长的函数关系,间接反映波前随波长的变化规律,从而实现任意波长波前的检测。利用Zemax对光学系统建模,采集光学系统在不同波长时的波前Zernike系数,通过Matlab曲线拟合工具寻找Zernike系数与波长曲线可能存在的函数形式,并最终确定了Conrady-Zernike公式。模拟的光学系统使用这种解析式计算所得Zernike系数的最大误差在1%以内。结果表明透射式光学系统的波前Zernike系数与波长之间基本符合Conrady-Zernike公式的关系。     

光学窗口形变对平行光管光学性能影响分析

由于环境工况的多变性,光学窗口设计交叉了光、机、热等多种学科。在压差、轴向温差及径向温差工况下,分析光学窗口形变对某大口径、长焦距平行光管光学性能的影响,建立了光学窗口的有限元模型,与理论结果进行对比,验证了该有限元模型的有效性。以有限元分析得出的光学窗口变形数据为输入数据,带入改进了的Zernike多项式光机分析接口程序,获得了与像差对应的Zernike系数。用得到的Zernike系数表示光学窗口面型,以波像差作为光学系统成像质量评价指标,分析光学窗口变形对大口径、长焦距平行光管系统光学性能的影响。结果表明:光学窗口变形对平行光管系统光学性能的影响可以忽略不计。     

基于模型选择的模式波前重构算法研究

基于Zernike模式的波前重构算法通常忽略实际波前像差构成的差异, 而用一定数量的低阶Zernike模式进行波前重构, 导致模式混淆或耦合等问题, 进而影响波前重构的精度. 根据信息论中的最小描述长度准则对重构模型的阶数进行了选择, 在此基础上应用非线性优化算法计算重构系数, 并最终实现波前重构; 对不同信噪比条件下振幅均匀分布入射光束的波前进行了重构. 结果表明: 该算法不但能够实现相对于现有算法相对较高的波前重构精度, 并且具有优良的噪声适应性, 体现了模型选择在模式法波前重构算法中的意义.     

二次曲面前房型有晶体眼人工晶体的球差矫正特性分析

为探究二次曲面前房型有晶体眼人工晶体的球差矫正特性,进行了球面和二次曲面有晶体眼人工晶体的设计,并利用像差理论对二者的球差矫正特性进行了研究.基于R.Navarro等人提出的模型眼得到屈光不正眼模型,利用ZEMAX光学软件分别设计了可矫正屈光不正人眼的球面与二次曲面前房型有晶体眼人工晶体.通过对光学传递函数和Zernike球差系数的比较,以及对Seidel球差分布系数的计算分析发现:在保证屈光不正矫正至正常水平的前提下,较之传统球面人工晶体,二次曲面的引入仅对远视眼的球差有矫正作用,并使光学传递函数显著改善|而对近视眼而言,二次曲面人工晶体的球差矫正效果与球面人工晶体相当.这一结论对前房型有晶体眼人工晶体的设计和应用具有重要的理论指导意义.     

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%.     

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.     

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.     

Optical quality in a myopic population of human eyes

An aberrometer was used to measure the monochromatic aberration of 219 eyes in a population of 113 myopic subjects. The Zernike expansion was used to describe the wavefront aberration of the human eyes. From the distribution of Zernike coefficients, the means of almost all Zernike coefficients are approximately zero, and the mean absolute values of Zernike coefficients convey the level of aberration for our study population. Based on the distribution of Zernike coefficients, the averaged optical quality was computed in different methods. The mean MTF and PSF of individual eyes represent the optical quality for a typical myopic eye. Through the calculation of the visual benefits expected from correcting Zernike modes, a large expected visual benefit can be achieved across all spatial frequencies after correcting 5 Zernike modes. Furthermore, the larger improvement of optical quality can be achieved with correcting more Zernike modes at a higher spatial frequency.     

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.     

基于矢量波像差理论的计算机辅助装调技术研究

在三阶矢量波像差理论的基础上,建立了系统内失调量与系统波像差Zernike系数的关系式,并以共轴三反射光学系统为数学模型进行了仿真分析.结果表明,基于矢量波像差理论的装调技术可行,并可用于大型光学系统的装调.利用该理论对一共轴非球面三反系统进行装调,最终使系统波像差RMS<0.080λ.     

Analysis and demonstration of multiplexed phase computer-generated hologram for modal wavefront sensing

We propose to implement a modal wavefront sensor (MWS) using a multiplexed phase computer-generated hologram (MPCGH). Based on general orthogonal aberration modes, the theoretical treatments of the MWS employing a MPCGH are presented with scalar diffraction approximations and Fourier analysis. Under the small aberration approximations, we give the analytical formula for characterizing the relationship between the sensor signal and the amplitude of the aberration mode. We design several MPCGHs with an effective method of modified off-axis reference beam holograms superposition, and code some common orthogonal Zernike aberration modes into the MPCGH. The numerical simulation is carried out to investigate the performance of MWS to detect particular aberration mode(s). The results exhibit the expected responses of the corresponding symmetric spot pair, and indicate that the wavefront distorted by a special Zernike aberration mode, after modulated by the MPCGH, can be transformed into beams with an intensity-normalized differential signal, which can reflect the change trend of the aberration coefficients in the test wavefront. The experimental demonstration with designed MPCGHs in conjunction with two phase-only spatial light modulators was carried out to test the performance of the MWS.     

米级口径经纬仪保护窗口镜面变形分析

为了精确分析外载荷作用下米级口径经纬仪保护窗口镜面变形,本文基于接触有限元理论建立了米级口径经纬仪保护窗口带摩擦接触的有限元分析模型,对比了线性刚性连接和非线性摩擦接触方法的差异。采用齐次坐标变换法去除刚体位移,得到米级口径经纬仪保护窗口镜面畸变数据,使用Zernike多项式作为光机集成分析的接口工具,并将Zernike多项式系数导入ZEMAX中,以波前像差RMS值衡量镜面变形对成像质量的影响,并与干涉仪检测结果进行比较。考虑摩擦接触条件得到的保护窗口镜面波前像差RMS值为38.095 nm、PV为205.027 nm,使用干涉仪检测得到的保护窗口镜面波前像差RMS值为40.626 nm、PV值为235.654 nm。实验结果表明,考虑摩擦接触条件的仿真实验与干涉仪检测实验的镜面波前像差RMS值偏差为6.23%,能更准确地反映米级口径保护窗口镜面变形。     

Method of reconstructing wavefront aberrations by use of Zernike polynomials in radial shearing interferometers

A novel method of reconstructing wavefront aberrations by use of Zernike polynomials for radial shearing interferometers is discussed. This method uses matrix formalism to calculate the Zernike coefficients of a wavefront under test and shows the validity of reconstructing an arbitrary wavefront aberration from an interferogram taken by a radial shearing interferometer. We also propose a new interferometer setup to determine the shape and the direction (concave or convex) of wavefront aberration in a single measurement.     

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。     

利用离轴三反镜光学系统确定各镜的装调公差

利用条纹泽尼克系数与赛德尔像差的关系,在三反镜光学系统的出瞳面上,用条纹泽尼克系数来表示系统的波像差。通过光学设计软件Zemax计算得到三反镜光学系统各镜的装调公差,以公差要求高的镜面作为装调基面,从而减少要调整的自由度。通过分析泽尼克(Zernike)系数在公差范围内的变化幅度来确定光学系统在出瞳面上各个像差的变化幅度,用该幅度的变化量来决定主次三镜各自由度在各个方向上的敏感度,最终确定各个自由度的优化调整级别。对一大口径无遮拦离轴三反镜光学系统进行了装调,在波长λ=632.8nm的条件下进行了检测。结果表明:整个光学系统全视场波前误差的均方根值RMS=0.108λ。