Monte Carlo simulations on corneal and total aberrations before and after LASIK

Previous Monte Carlo simulations which manipulate each Zernike coefficient of total aberrations of human eyes indicate that interactions among wave-front aberrations can provide better visual quality for both pre-LASIK eyes and post-LASIK eyes. In this paper, we go a step further for Monte Carlo simulations which are not only on total aberrations but also on corneal aberrations, before and after LASIK, for a set of eyes. The corneal aberrations after LASIK are acquired through a new reliable method. Then a series of Monte Carlo simulations (including sign simulation, value simulation and meridional simulation) are performed by manipulating each Zernike coefficient (second through sixth-order) of total aberrations as well as corneal aberrations. The results are evaluated by modulation transfer function (MTF) ratio. Total aberrations for post-LASIK eyes still show MTF advantage over randomized aberrations, with slightly change as compared to that for pre-LASIK eyes. However, true corneal aberrations before and after LASIK have no MTF advantage over random aberrations. From this research, we draw conclusions: there is apparent advantage for the complete eye's true aberrations over random aberrations, whether pre-LASIK or post-LASIK, which does not exist for any biological optical surfaces in isolation, and the ability of adaptive mechanism of human eyes, increases after LASIK.     

The aberration and the modulation transfer function in LASEK and LASIK: Pupil size dependence

The wave-front aberrations on the postoperative eyes with two different type of excimer laser surgery have been measured by a Hartmann-Shack wave-front sensor. We have calculated the aberrations for both 3 and 6 mm pupils, and with which to acquire the MTF of the eye. There are no significant differences in wave-front aberrations postoperatively (P>0.05) for 3 mm pupil size, but with 6 mm pupil, LASIK-treated eyes exhibit significant higher aberrations than LASEK-treated eyes for 4th and 5th-order aberrations. For individual Zernike terms, there are significant difference in , and . The MTF for 6 mm pupil is much lower than those for 3 mm pupil across all spatial frequencies. The LASEK curve shows higher than that with LASIK at spatial frequencies less than 60 c/d, which means that the optical quality in LASEK-treated eyes showed better than in LASIK-treated eyes.     

激光原位角膜磨镶手术后不良症状的光学分析

测量了准分子激光原位角膜磨镶(LASIK)手术后人眼的单色像差。并根据术后症状,将所有数据分类为视物星芒状组、单眼复视组、视物雾状组和参考组。视物星芒状组和视物雾状组的三阶和四阶泽尼克(Zernike)像差的均方根(RMS)值明显大于无症状的参考组。术后有不良症状各组的人眼的调制传递函数(MTF)明显低于参考组的调制传递函数。在明视觉条件下,四阶像差特别是对称性的泽尼克球差,对调制传递函数的影响大;而在暗视觉条件下,三阶像差特别是非对称性的泽尼克彗差对调制传递函数的影响大。四阶以上的高阶像差对各有症状组的调制传递函数曲线有影响,而这些高阶像差对参考组的调制传递函数已无明显影响。像差的均方根值和调制传递函数曲线是研究术后不良症状的较有效光学手段。     

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.     

一种新型人眼波前像差测量补偿系统的研究

离焦是人眼中最主要的像差之一,离焦量过大会严重影响人眼波前像差的测量及矫正精度。为了消除离焦在此方面带来的影响,设计了带有补偿装置的人眼波前像差测量及矫正系统。重点分析了该系统的原理、结构和工作流程。运用Hartmann-Shack波前传感器测量了人眼波前像差,并使用变形反射镜对人眼波前像差进行矫正。对模拟人眼矫正离焦前后的光斑点阵图和波前三维重构图进行了对比分析。研究表明,通过离焦补偿系统对模拟人眼的离焦量进行矫正,使被测量人眼的离焦量由2.020D和-2.035D分别减小到0.011D和-0.007D;通过调焦系统,使显示器上显示出的人眼光斑点阵图由模糊变清晰,提高了信标光在人眼眼底的成像质量。     

Closed-loop adaptive optics in the human eye

We have developed a prototype apparatus for real-time closed-loop measurement and correction of aberrations in the human eye. The apparatus uses infrared light to measure the wave-front aberration at 25 Hz with a Hartmann-Shack sensor. Defocus is removed by a motorized optometer, and higher-order aberrations are corrected by a membrane deformable mirror. The device was first tested with an artificial eye. Correction of static aberrations takes approximately five iterations, making the system capable of following aberration changes at 5 Hz. This capability allows one to track most of the aberration dynamics in the eye. Results in living eyes showed effective closed-loop correction of aberrations, with a residual uncorrected wave front of 0.1microm for a 4.3-mm pupil diameter. Retinal images of a point source in different subjects with and without adaptive correction of aberrations were estimated in real time. The results demonstrate real-time closed-loop correction of aberration in the living eye. An application of this device is as electro-optic "spectacles" to improve vision.     

纯相位液晶空间光调制器拟合泽尼克像差性能分析

纯相位液晶空间光调制器作为波前校正器构成的高分辨率、低能耗、价格低廉、易于控制的自适应光学系统受到越来越多的关注.作为一种新型波前校正器件,它对波前像差的校正能力是反映其在自适应光学系统中应用的一个重要的指标,因此有必要仔细地研究它对各种像差的校正能力,以确定其可能的应用范围.波前校正器对各阶泽尼克像差的拟合效果有效地反映了该器件对不同像差的校正能力.利用256×256像素的纯相位液晶空间光调制器(LC-SLM)产生不同系数的前36项泽尼克像差分析LC-SLM对不同像差的校正能力.讨论了填充因子、离散像素 关键词： 液晶空间光调制器 相位调制 自适应光学 泽尼克多项式     

自适应光学随机并行梯度下降算法波前整形规律仿真

本文首先介绍了基于Zernike模式的SPGD算法对大气湍流畸变波前的整形原理,通过推导得到了关于性能指标的简明表达式,使SPGD算法收敛速率得到明显提升。然后建立了自适应光学随机并行梯度下降算法波前整形系统模型,主要对SPGD算法收敛速率、整形能力和整形效果随波前畸变量和变形镜模型的变化规律作了较为详细的仿真研究,整体定性结果表明：三者的变化规律有一定的相似性,同时利用最小二乘法得到了关于整形能力和整形效果变化规律的定量表达式,若从自适应光学波前整形系统的实时性和简单性考虑,在保证一定整形效果的情况下,选择37单元变形镜对畸变波前的3~27（25）阶Zernike像差进行整形即可。     

Information fusion method for ocular aberrations measurement based on subjective visual compensation

The human eye is an imperfect refractive system which not only has defocus and astigmatism, but also has spherical aberration, coma and anomalistic high-order aberrations, all of which have certain influence on the imaging quality of retina. What's worse, aberration is further enlarged as a result of mydriasis in dark field and weak light, thus making the vision performance of human eyes far below diffraction limitation. Further research revealed that human eye visual imaging is not only connected with refractive system, but also is closely related to the subjective judgment of human brain and the process of neural system. In order to overcome the deficiencies, wave-front aberration measurement method and system that has subjective visual compensation is proposed and conducted in combination with objective measurement, which ensures more accurate and realistic measuring results. The experimental data revealed that wave-front aberration obtained from subjective visual compensation measuring method is smaller than objective measurement, which is the result of subjects’ adaptive correction when watching sighting targets. In addition, when subjects are watching different sighting targets, the fluctuation value of wavefront aberration is small. Therefore, it is concluded that subjective visual compensation measuring method contributes to aberration measuring improvement and obtains results match with the realistic state by taking into consideration the actual condition of human eyes when watching targets. Hopefully, these discoveries will be of positive and beneficial value to the determination of human eye aberration treatment.     

人眼高阶像差校正和视觉分析系统

人眼除具有可用眼镜或接触镜校正的低阶像差(离焦、像散)之外,还普遍存在高阶像差。高阶像差的存在影响着屈光系统的成像质量。为研究高阶像差对视觉功能的影响,利用自适应光学技术,建立了具有校正高阶像差和产生高阶像差双重功能的人眼高阶像差校正和视觉分析系统。介绍了系统实现高阶像差校正和视觉分析的工作原理;阐述了波前校正器、哈特曼波前探测系统、控制系统等关键单元技术;列出了系统对泽尼克模式像差的校正效果,绝大多数像差从0.5λ降低到0.2λ以下;阐明系统功能的实现过程,并给出仿真实验的结果。该系统为进一步研究高阶像差对视功能的影响提供了有效的手段。     

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.     

可诱导人眼自主调节的动态像差测量仪

研究了人眼在近视力状态下自动调节产生的动态像差。采用哈特曼-夏克(Hartmann-Shack,H-S)原理研制了一套可诱导人眼屈光调节,并能测量不同调节状态下人眼像差的测量仪。诱导原理为用视标在人眼近距离范围内移动以诱发人眼屈光调节,哈特曼-夏克传感器同时进行像差的测量,可以获得人眼调节时的视觉信息。与干涉仪测量同一像差板进行相比,像差仪的测量精度均方根(RMS)值为λ/50,重复性为λ/500,具有较好的测量精度和重复性。在测量的10人19只眼中,最大的诱发调节幅度为8.6D,一般可诱发调节幅度为3~8D之间,占总人数的84%。     

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.     

Eye models for the prediction of contrast vision in patients with new intraocular lens designs

Theoretical calculations of the polychromatic modulation transfer function (MTF) and wave-front aberration were performed with physiological eye models. These eye models have an amount of spherical aberration that is representative of a normal population of pseudophakic eyes implanted with two different types of intraocular lens (IOL) made from high-refractive-index silicone. These theoretical calculations were compared with the measured contrast sensitivity function (CSF) under mesopic lighting conditions and with wave-front aberration (obtained with a Hartmann-Shack wave-front sensor) collected from 37 patients bilaterally implanted with the same types of lens. The relationships between the ocular wave-front aberration and the MTF predicted by the eye models and the CSF and the ocular wave-front aberration measured in eyes implanted with IOLs were investigated. The predicted improvements in MTF and wave-front aberration correlated well with the improvements measured in practice. Physiological eye models are therefore useful tools for IOL design.     

Statistical description of wave-front aberration in the human eye

The wave aberration of the human eye has been measured by means of a Hartmann-Shack wave-front sensor in a population of normal subjects. The set of data has been used to compute the phase distribution, the power spectrum, and the structure function for the average eye to analyze the statistics of the ocular aberration considered as a phase screen. The observed statistics fits the classical Kolmogorov model of a statistically homogeneous medium. These results can be of use in understanding the average effect of aberrations on the retinal image and can serve as a tool to analyze the consequences of ocular-aberration compensation by adaptive optics, customized ophtalmic elements, or refractive surgery.     

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.     

用SVGA1薄膜晶体管液晶显示器矫正人眼波像差

在研究了SVGA1薄膜晶体管液晶显示器（TFT LCD）的位相调制特性的基础上,用它作为眼波像差的矫正器件,在用哈特曼-夏克波前传感器的眼像差测量系统中对眼波像差进行了成功的矫正.对于5.2 mm的瞳孔,矫正后人眼波像差的PV值降低了3倍多,并接近瑞利判据的像差容限.对系统的光学传递函数(MTF)的分析说明,经波像差矫正后眼的空间分辨率由17 c/deg提高到38 c/deg.     

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.     

Phase contrast, phase retrieval and aberration balancing in shift-invariant linear imaging systems

We treat the problems of phase-contrast image formation, deterministic phase retrieval and aberration balancing, in the imaging of weak objects using two-dimensional shift-invariant linear imaging systems. Three classes of model sample are considered: weak phase objects, weak phase-amplitude objects and single-material weak phase-amplitude objects. For each class of sample we show how the various aberration coefficients, which characterise a given imaging system, contribute to the structure of the associated phase-contrast image. The corresponding inverse problem, of obtaining a closed-form expression for the input wave-field given one or more aberrated phase-contrast images of the same, is then examined. Two sample applications are considered: analyser-crystal phase-contrast imaging of weak objects using hard X-rays, and Zernike-type phase-contrast imaging. We close with a discussion of how coherent and incoherent aberrations may be “balanced” against one another, briefly mentioning the applications of this idea to both “deblur by defocus” and proximity-corrected X-ray lithography.     

LASIK手术对人眼波前像差的影响

采用主观光线追迹的像差仪测量人眼波前像差,比较3mm和6mm 瞳孔直径下,LASIK手术前与术后四个月的29只人眼波像差情况.数据比较分析表明,手术后人眼高阶像差一般会大于术前,且像差增大量随术前屈光度数的增大和瞳孔直径的增大而增加,如3 mm瞳孔直径下86%的人眼高阶像差的RMSH<0.12 μ,>0.4μ.比较人眼波像差的Zernik展开式中各项发现球差Z04无论在3 mm还是6 mm孔径下术后改变都最大;其中,当比较3阶,4阶和5至7阶时可看出对于3 mm孔径第三阶术后改变比例较大,为1.87,6 mm时第四阶改变较大,比例为2.21.