Evaluation of the meridional longitudinal spherical aberration from corneal topography measurements

This paper shows how corneal topographic data can be used to determine the value of the longitudinal spherical aberration. We have obtained the corneal profiles and the values of the longitudinal spherical aberration for the rays propagating within the steepest and flattest meridional planes, by using a real raytracing algorithm. These corneal profiles have been also fitted to conicoids and the asphericity parameter has been calculated. We have found that the longitudinal spherical aberration follows a parabolic dependence for a circular region of 5 mm in diameter. This parabolic dependence has been fitted with a polynomial function. The data provided by commercial topographic systems can be used to obtain the longitudinal spherical aberration along the selected meridians.     

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.     

Effect of spherical aberration on scintillations of Gaussian beams in atmospheric turbulence

The effect of spherical aberration on scintillations of Gaussian beams in weak, moderate and strong turbulence is studied using numerical simulation method. It is found that the effect of the negative spherical aberration on the on-axis scintillation index is quite different from that of the positive spherical aberration. In weak turbulence, the positive spherical aberration results in a decrease of the on-axis scintillation index on propagation, but the negative spherical aberration results in an increase of the on-axis scintillation index when the propagation distance is not large. In particular, in weak turbulence the negative spherical aberration may cause peaks of the on-axis scintillation index, and the peaks disappear in moderate and strong turbulence, which is explained in physics. The strong turbulence leads to less discrepancy among scintillations of Gaussian beams with and without spherical aberration.     

The intensity distribution of hollow Gaussian beams focused by a lens with spherical aberration

We developed an expression that describes the hollow Gaussian beams (HGBs) passing through a spherically aberrated lens by using the Collins formula. The radial intensity distribution in both spherical aberration SA free lens, lens that exhibits relatively large in both positive spherical aberration PSA, and negative spherical aberration NSA is calculated. Numerical calculations are made and the results show that the PSA and NSA have a strong influence on the intensity distribution especially at the focus. The study showed remarkable results for which there is no hollow Gaussian beam at a large NSA along the optical axis at the focus. In addition, we found that the DSS, and w_r of focused hollow Gaussian beams in the focal region depend not only on the beam radius, and beam order; but also on the spherical aberration.     

人工晶体倾斜与偏心对人眼视功能的影响

基于Hwey-Lan Liou人眼生理模型,采用光线追迹的方法,分析了相同孔径下具有不同球差的人工晶体(IOL)在眼内的倾斜和偏心对人眼视功能的影响.IOL在眼内无倾斜和偏心时,负球差IOL对人眼视功能的改善优于无球差IOL和传统的正球差IOL;当IOL在眼内倾斜,偏心程度一定时,负球差IOL球差值越大,其倾斜和偏心对人眼视功能的降低越明显;植入无球差IOL的眼的视功能受其倾斜和偏心的影响较小,在IOL偏心1.0 mm,倾斜10°已使人眼有明显视觉不适的情况下,仍能表现出良好的光学性能,对人眼视功能的改善不仅优于正球差IOL,而且优于负球差IOL.     

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.     

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.     

Aberration correction of a single aspheric lens with particle swarm algorithm

In order to design a single aspheric lens to meet the requirements of spherical aberration, the particle swarm algorithm is applied to the aberration correction for a single aspheric lens. A mathematical model is constructed, and a program code is developed. Merit functions in an optical system are employed as fitness functions, which combined coefficients of a higher order polynomial equation, a reciprocal of radius of curvature, the conic constant, thicknesses among lens surfaces and refractive indices regarding an optical system. By using this function, the automatic correction of spherical aberration is carried out. The example for a single aspheric lens design using particle swarm algorithm shows that PSO as a tool of the spherical aberration correction for a single aspheric lens is simple and effective, and easy to find a series of good design results. The asphere's more complex surface profile can reduce or eliminate easily spherical aberration at different incidence heights at one time. The automatic design and analysis of a single aspheric lens using this method from the view of a particular optical design problem are presented.     

Effect of amplitude modulation on the read-out signal in an optical disc system with a residual aberration

We conducted a numerical calculation for the point spread function and the variation of the read-out signal in optical disc systems using several apodizing filters, taking into account a spherical aberration and the variation in the bump shape. Based on calculations using the scalar diffraction theory, we are able to determine the best bump size and shape giving the maximum read-out signal for each incident beam modulated by an apodizing filter. This work facilitates the fabrication of high density optical disc systems with a spherical aberration and can then be applied to a real optical disc system like a commercial digital video disc (DVD) system.     

Spherical aberration from trajectories in real and hard-edge solenoid fields

For analytical, real and hard-edge solenoidal axial magnetic fields, the low-energy electron trajectories are obtained using the third-order paraxial ray equation. Using the particle trajectories, it is shown that the spherical aberration in the hard-edge model is high and it increases monotonously with hard edginess, although the focal length converges, in agreement with a recent field and spherical aberration model. The model paved the way for a hard-edge approximation that gives correct focal length and spherical aberration, which is verified here by the trajectory method. In essence, we show that exact hard-edge fields give infinite spherical aberrations.     

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.     

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.     

用粒子群算法进行单个非球面透镜的球差校正

为设计出符合球差要求的单个非球面透镜,把粒子群算法应用到单个非球面透镜的球差校正中,构造相应的数学模型,并编程实现算法.设计关于非球面高次多项式的顶点曲率半径,高次多项式各项系数,透镜面之间的距离和玻璃折射率等光学系统结构参数的适应度函数,用这个函数作为评价函数,实现对球差的自动校正.给出用粒子群算法进行单个非球面透镜设计的实例,结果证明:粒子群算法用于非球面透镜的球差校正简单有效,能同时校正不同入射高处的球差,且容易发现一系列好的设计结果.从实际光学设计角度呈现使用这种方法进行单个非球面透镜的自动设计分析.     

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.     

Precise multipass Herriott cell design: derivation of controlling design equations

Multipass Herriott cells are often designed using the thin lens approximation, which results in approximate dimensions or imperfect patterns due to both spherical aberration and the finite width of the optic. We derive the design equations for exact solutions to the Herriott cell problem. We also show that Herriott cells using spherical mirrors cannot be designed such that multiple concentric beam patterns all meet their reentrant condition. We derive a solution for elliptical mirrors that allows this condition to be met simultaneously for many beams.     

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.     

The study of the effects of higher-order aberrations on human contrast sensitivity with white-light retinal aerial image modulation (AIM)

The impact of higher-order aberrations on contrast sensitivity function (CSF) is calculated using individual white-light retinal aerial image modulation (AIM). Wavefront aberrations of 26 eyes are measured with Hartmann-Shack sensor, and the CSFs in natural light are acquired through a range of 2-48 c/deg. The white-light AIM is computed as the ratio of modulation transfer function (MTF) in white-light to CSF. Through manipulating the higher-order aberrations, the affected CSF is predicted by employing the white-light AIM. We find that coma aberration mainly influences CSF at higher spatial frequency and spherical aberration affects CSF in the whole spatial frequency range non-selectively. Additionally, it is spherical aberration rather than coma that impacts the CSF more substantially. Furthermore, the maximum value of area under CSF (AUCSF) is obtained without full correction of higher-order aberration, which indicates that there is compensatory mechanism among aberrations.     

球差透镜聚焦部分相干光束获得局域空心光束

基于Collins公式,研究了空间相干度为零阶贝塞耳函数的部分相干光通过球差透镜后在几何焦平面附近的光强分布情况.研究表明,通过改变部分相干光的光谱相干度,球差系数可以得到平顶光束和局域空心光束.球差系数决定了最佳聚焦点的位置.当球差系数为正时,最佳聚焦点随着球差系数的增大向远离透镜的方向运动,甚至超过几何焦点;当球差系数为负时,最佳聚焦点随着球差系数绝对值的增大向靠近透镜方向移动.另外,在正负球差绝对值相等时,光强分布以几何焦点相对称.     

高库仑量大电流两电极气体火花开关研究

设计了一个两电极气体火花开关，开关的主体部分仅包括阴极、阳极两个主电极，以及金属外壳和绝缘支撑外壳，两电极结构取消了触发极，消除了由于触发极烧蚀影响开关寿命的问题。开关设计工作电压23 kV，单脉冲能量1.2 MJ，峰值电流300 kA，单次脉冲电荷转移量110 C。初步试验阶段开关工作电压达到15 kV，开关的通流180 kA，电荷转移量为47.85 C。开关触发性能可靠，电极烧蚀均匀。     

偏心和倾斜光学系统初级象差理论的研究

在共轴光学系统波象差的基础上,推导出了光学元件的偏心和倾斜分别对主要象差的影响.得出了除了球差外,每一种象差由于偏心和倾斜都引入了它同种类的象差;小量的偏心和倾斜并不改变系统的球差的结论;如果球差并不为零,将会产生与象高无关的彗差,即轴向彗差等等.