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.     

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.     

Optical Pickup with a Spherical Aberration Compensator Using a Crossed-Stripe Liquid Crystal Device

To increase recording density in an optical disk system, a two-lens system which enlarge its numerical aperture (NA) has been developed. When NA becomes larger, however, the spherical aberration due to disk thickness error increases. We propose an optical pickup with a spherical aberration compensator using nematic liquid crystal (LC). Our LC device is composed of two LC cells each of which has X and Y stripe electrodes, respectively. We discussed how the spherical aberration due to the disk thickness error can be compensated by combination of two crossed cylindrical phase distributions induced by the LC cells, and confirmed the compensation effect in a design example by simulation. We have also fabricated the crossed stripe LC device actually, and have obtained the experimental result which shows that amount sufficient to compensate the aberration is achieved.     

An anatomically accurate eye model with a shell-structure lens

A human eye model based on anatomically accurate eye model previously proposed by Liou, has been transformed into a new eye model, in which laminated structure of the lens is considered. The crystalline lens is presented in the form of hundreds of shells with rotational symmetry, and with constant index within each shell. The refractive index increases from the cortical shell to the inner one, according to the equation proposed by Smith G. et al. The anterior surface of the lens is prolate, whereas the posterior surface of the lens is oblate which is consistent with the anatomical data. A ray tracing procedure has been applied to study the refractive structure of the eye. The optical characters of the model have been studied. The reason that the wings occur on the spherical aberration curve has been given. And we found that the lens with gradient refractive index and lens with shell structure can give same longitudinal spherical aberration results.     

球差对圆偏涡旋贝塞耳-高斯光束聚焦场的影响

利用理查德-沃耳夫矢量衍射积分,分析了初级球差对圆偏振涡旋贝塞耳-高斯光束聚焦光场的影响,获得不同球差系数下的光强分布.结果表明,当初级球差系数增加,会聚光点偏离系统焦平面,纵向光场发生改变;焦点光强逐渐减小,焦平面光场发生变化;光轴上光强峰值逐渐减小,峰值两侧的旁瓣变化趋势相反,光强由对称分布变成非对称分布;初级球差对贝塞耳-高斯光束聚焦光场的影响不依赖其偏振态;离焦无法完全补偿初级球差对聚焦光场的影响.     

Conditions for identical position of optimal image plane for axial imaging with different values of f-number

By analysis of the dependence of longitudinal spherical aberration on the numerical aperture, it is possible to find such values of the numerical aperture, where spherical aberration is zero. Such values of the numerical aperture are called correction zones. The work theoretically analyses the described problem and equations are given for wave aberration coefficients using correction zones for spherical aberration of the third and the fifth order. Our work presents an analysis of optimal values of correction zones and an optimal position of the center of the reference sphere based on the variance of wave aberration for the image quality evaluation. Relations are described for calculation of correction zones of an optical system having an identical position of the optimal image plane for two values of the f-number. The analysis of optical systems using correction zones is performed on an example.     

磁圆形透镜和磁六极透镜的复合系统的象差

近来磁六极透镜作为球差校正器引起了人们的注意。本文研究了磁圆形透镜和磁六极透镜的场分布叠加形成的复合系统的象差。我们在复数域中定义了内积,采用了复数的表象和微分算符,全面讨论了这种复合系统的高斯光学性质及二、三、四级象差,得出了各级象差所有的象差系数的公式。 关键词：     

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.     

Computational aberration correction for an arbitrary linear imaging system

We show that aberration corrections can be made in any arbitrary linear imaging system provided the aberrations are well characterized and at least one of these aberrations can be independently varied in a well-controlled manner. We derive a generalization of the Schr?dinger equation for wave propagation in aberration space assuming forward scattering. Transport equations in aberration space are derived. A general iterative algorithm which can retrieve the phase, and is robust in the presence of noise, is also derived. This is demonstrated using simulated data pertinent to electron microscopy, from a series of images with differing spherical aberration.     

Tight focusing of linearly and circularly polarized vortex beams; effect of third-order spherical aberration

Tight focusing of linearly and circularly polarized vortex beams is studied in the presence of third-order spherical aberration, using vectorial Debye–Wolf integral. Results for total intensity distribution are presented for both polarizations. In addition, results for x-, y-, and z-polarization components are presented for the circularly polarized beam. Generation of longitudinal optical vortex in the tightly focused left circularly polarized beam has also been demonstrated by plotting its phase distribution. Compensation for the effect of spherical aberration has been studied in the presence of defocusing. Effect of aberration on the dark core of a tightly focused azimuthally polarized beam is also investigated.     

折衍混合单透镜的色球差校正研究

分析研究了小视场折射混合单透镜的设计中，当衍射面同时用于消色差和球差时光焦度分配的最优方案，得到了改进的光焦度分配公式，通过设计实例表明，由该改进公式可得到了较好的初始结构，能够有效地克服了衍射光学透镜校球差时产生的较大的色球差，验证了此改进公式的正确性和有效性，此改进公式对折衍混合系统的设计具有指导意义。     

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.     

Hyperchromats with linear dependence of longitudinal chromatic aberration on wavelength

Optical lens systems that are characterized by a chromatic aberration of a predefined form are called hyperchromats. Our work describes a theory of hyperchromats with a linear dependence of longitudinal chromatic aberration on wavelength. The equations are derived for calculation of basic design parameters of these optical systems and some examples of hyperchromatic optical systems are shown. Mentioned optical systems can be used especially in 3D imaging systems and confocal microscopy.     

透镜初级球差的横向剪切干涉条纹研究

利用玻璃平行平板构成简单的横向剪切干涉仪可以观察到单薄透镜形成的准直光束的剪切干涉条纹,由干涉条纹分布求出对应的几何像差和离焦量.用焦距为190 mm的单薄透镜做实验,实验结果与计算机模拟结果符合,说明可以从剪切干涉条纹的分布求出透镜的轴向调整误差和初级球差.     

Designing a plano-convex aspheric lens for fiber optics collimator

A plano-convex aspheric lens is designed to collimate the emitted light of the fiber optics. In this paper even orders of general aspheres are used to describe the aspheric surfaces sag. To determine the aspheric coefficient, the even asphere polynomial are fitted on the computed sag data. The surface sag data is determined using genetic algorithm method. The surface sag was analyzed by the commercial optical software package ZEMAX. For typical fiber optics, the numerical aperture (NA) of 0.22 was assumed. With this specification, the expected output spot diagram of 20 mm and the maximum aperture of 25.4 mm have been obtained. A comparison between here presented lens and the similar type of conventional lens has been carried out; the proposed aspheric lens corrected the spherical aberration, which led to increase in the collimated distance.     

具有层状晶状体的人眼模型的光学性质

为了更加符合眼睛的解剖学结构,用建立的层状结构晶状体模型代替了Hway-Lan Liou眼模型中的折射率连续变化的晶状体模型。从而建立了新的眼睛模型。在这个新的层状晶状体模型中,最外层前后表面的非球面系数与解剖学数据相符。由于层状结构使光线追迹具有特殊性。因此用C语言编制了光线追迹程序,并对此眼睛模型的光学性质进行了研究。结果表明,晶状体层数较少时,眼睛的球差曲线出现翼状结构．即层状晶状体的引入使眼睛具有多焦性．并对这种现象进行了解释;具有层状结构晶状体的眼睛和具有折射率连续变化的晶状体的眼睛能够给出等价的球差结果。     

Considering the effectiveness of 3rd order aberration theory from the view point of sine condition in the presence of spherical aberration

Even though the level of computer simulation for optical designing is becoming powerful, the 3rd order aberration theory is still useful for prospecting optical characteristics and developing optics. Therefore, it is important to confirm its validity even now. Considering the physical meaning of imaging, pupil coordinates should be defined by the direction cosine of the ray. The sine condition in the presence of spherical aberration has been derived by using this coordinate and its validity was later confirmed by practical lens designing. On the other hand, in order to deal with object imaging and pupil imaging equivalently, conventional aberration theory uses the pupil coordinate defined by the slope of the ray. By applying this theory, it had been deduced that no spherical aberration exists when the isoplanatic condition is fulfilled and it was then concluded that the sine condition in the presence of spherical aberration is meaningless. Therefore, one might think that this conventional aberration theory is less useful. However, this time I found that the 3rd order spherical aberration can exist with no 3rd order coma aberration under this aberration theory. As a result, the conventional aberration theory is meaningful at least in the 3rd order region.     

高斯光束经过负球差透镜的聚焦

本文讨论高斯光束经过负球差透镜的聚焦，得到了聚焦光场轴上点的光强分布的表示式，并对其进行数值计算。数值计算结果表明，在负球差的情况下，得到光强的最大点位置（最佳聚焦点）相对于无球差情况，往透镜方向移动，并且，最佳聚焦点的光强较无球差时大，当Ｎｗ＝１，Ｎａ＝５，ｋＳ１＝－０．２时，得到的最佳聚焦点的光强是无球差时的１．３４倍。本文还讨论了透镜的菲涅尔数对聚焦光场分布的影响。结果表明，当透镜的菲涅尔数小于１时，球差对高斯光束的聚焦的影响可以忽略。     

Effect of refractive index mismatch aberration in arsenic trisulfide

We demonstrate compensation for the spherical aberration due to the refractive index mismatch that occurs when a laser beam is focused into a thick arsenic trisulfide (As $_2$ S $_3$ ) film with a high numerical aperture objective. The effects of the aberration at different focal depths on the point spread function have been calculated numerically and the axial response method shown to be a useful measure for compensating the spherical aberration. We show that with the addition of adaptive optics based on a spatial light modulator, the aberration can be significantly reduced, resulting in an increase in peak intensity by a factor of 2.4 and a decrease in axial elongation by a factor of 2.2.     

侧面泵浦主振荡功率放大器中的光束质量提高

报道了一种利用球差补偿效应提高侧面泵浦主振荡功率放大器输出光束质量的实验装置。在理论上提出了一种新的球差补偿方法,利用正球差经过会聚透镜焦点后向负球差转化的现象,补偿下一放大级中的正球差效应。在实验上搭建了两级放大的侧面泵浦Nd:YAG主振荡功率放大器。在连续输出的情况下,从振荡级输出功率为42W、光束质量因子为1.48的种子光,经过一级放大后的功率为74W,光束质量因子恶化为1.80;继续经过二级放大后,光束质量因子提高为1.40。实验结果表明,所提出的球差补偿理论是提高激光放大过程中光束质量的有效手段。