人眼波前像差客观测量的研究

分析波动光学中人眼像差的产生机理和波前像差的表示方式。运用Zernike多项式表示人眼波前像差函数,研究Zernike多项式与人眼波像差的对应关系以及一些高级像差对人眼成像质量的影响。通过对自适应光学中Zernike多项式重建波前理论的研究,重点分析了应用Hartmann-Shack波前传感器测量人眼客观像差并用变形反射镜矫正人眼像差的解决方案。对提高正常眼睛的视力和人眼屈光矫正手术具有重要的实验和临床价值。     

Measurement of specimen-induced aberrations of biological samples using phase stepping interferometry

Confocal or multiphoton microscopes, which deliver optical sections and three‐dimensional (3D) images of thick specimens, are widely used in biology. These techniques, however, are sensitive to aberrations that may originate from the refractive index structure of the specimen itself. The aberrations cause reduced signal intensity and the 3D resolution of the instrument is compromised. It has been suggested to correct for aberrations in confocal microscopes using adaptive optics. In order to define the design specifications for such adaptive optics systems, one has to know the amount of aberrations present for typical applications such as with biological samples. We have built a phase stepping interferometer microscope that directly measures the aberration of the wavefront. The modal content of the wavefront is extracted by employing Zernike mode decomposition. Results for typical biological specimens are presented. It was found for all samples investigated that higher order Zernike modes give only a small contribution to the overall aberration. Therefore, these higher order modes can be neglected in future adaptive optics sensing and correction schemes implemented into confocal or multiphoton microscopes, leading to more efficient designs.     

Simulation of specimen-induced aberrations for objects with spherical and cylindrical symmetry

Wavefront aberrations caused by the refractive index structure of the specimen are known to compromise signal intensity and three‐dimensional resolution in confocal and multiphoton microscopy. However, adaptive optics can measure and correct specimen‐induced aberrations. For the design of an adaptive optics system, information on the type and amount of the aberration is required. We have previously described an interferometric set‐up capable of measuring specimen‐induced aberrations and a method for the extraction of the Zernike mode content. In this paper we have modelled specimen‐induced aberrations caused by spherical and cylindrical objects using a ray tracing method. The Zernike mode content of the wavefronts was then extracted from the simulated wavefronts and compared with experimental results. Aberrations for a simple model of an oocyte cell consisting of two spherical regions and for a model of a well‐characterized optical fibre are calculated. This simple model gave Zernike mode data that are in good agreement with experimental results.     

采用单位激励影响矩阵数值计算的瑞奇-康芒检测技术

在影响矩阵法瑞奇-康芒检验中,恢复被测面形的关键在于构建被检平面面形误差与系统波像差之间的Zernike系数影响矩阵。为了提高瑞奇-康芒法的检测精度,研究了采用单位激励法来精确计算影响矩阵的方法。分别重构平面镜仅包含某一种Zernike波像差下的系统波像差分布,经Zernike拟合得到该种Zernike像差的影响系数向量;由各Zernike像差的影响系数向量组成影响矩阵,然后用最小二乘拟合出被检平面面形。对口径为90mm的平面镜进行实际检验,在瑞奇角为26.5°与40.6°的情况下进行波前恢复,得到被检平面镜PV值为0.141 3λ,RMS为0.019 4λ。与直接采用平面参考镜检测相比,瑞奇-康芒法检测误差PV值为0.082 8λ,RMS为0.010 9λ。该方法能够精确生成影响矩阵,抑制了影响矩阵法中对大F数的依赖,可用于精确恢复平面镜面形。     

Specimen-induced distortions in light microscopy

Specimen‐induced aberrations affect the imaging properties in optical 3D microscopy, especially when high numerical aperture lenses are used. Studies on aberrations are often properly concerned with the degradation of image quality such as compromised resolution or reduced signal intensity. Apart from these, aberration effects can also introduce geometric image distortions. The effects, discussed here are particularly strong when thick biological specimens are investigated. Using a high numerical aperture interferometer, we measured wavefront aberrations in transmission mode and quantified geometric distortions associated with specimen‐induced aberrations. This assessment for a range of biological specimens allows estimation of the accuracy of spatial measurements. The results show that high‐resolution spatial measurements can be significantly compromised by specimen‐induced aberrations.     

The tuning of a Zernike phase plate with defocus and variable spherical aberration and its use in HRTEM imaging

With the advent of the double-hexapole aberration corrector in transmission electron microscopy the spherical aberration of the imaging system has become a tunable imaging parameter like the objective lens defocus. Now Zernike phase plates, altering the phase of the diffracted electron wave, can be approximated more perfectly than with the lens defocus alone, and the amount of phase change can be adjusted within wide limits. The tuning of the phase change allows an optimum contrast transfer in high-resolution imaging even for thick crystalline objects, thus surpassing the limits of the well-known Scherzer lamda/4 phase plate to the imaging of thin objects. The optimum values for the spherical aberration and the lens defocus are derived, and the limits and imperfections of the approximation explored. A mathematical link to the channelling approximation of high-energy electron diffraction shows how the image contrast of atomic columns can be improved systematically within wide thickness limits. Depending on the specimen thickness different combinations of spherical aberration and defocus are favourable: positive spherical aberration with an underfocus, zero spherical aberration with zero defocus, as well as negative spherical aberration with an overfocus.     

子孔径合成光学成像系统像质评价研究

子孔径合成光学成像系统的出瞳波前是离散的,需要同时引入波象差和衍射光学理论,拟合最佳高斯参考球面,计算出瞳波前和波象差,并通过对像面的衍射积分,评估系统像质。对比了两种像质评估的方法,其一是直接利用干涉仪实测获得的整体出瞳波面参数拟合Zernike多项式衍射直接积分法计算像面复振幅分布,其二是对子出瞳波面衍射直接积分在像面的复振幅的叠加。设计并制造了一个三子镜合成的成像光学系统,在此基础上用ZYGO GPI XP干涉仪验证并对比了使用两种方法的对像质计算的特点。结果表明,子出瞳波面直接衍射积分叠加法的精度更高,但计算量大;在衍射限附近,前者的拟合精度也能满足像质的定性评估要求,且计算量较小。     

Three‐dimensional optical transfer functions in the aberration‐corrected scanning transmission electron microscope

In the scanning transmission electron microscope, hardware aberration correctors can now correct for the positive spherical aberration of round electron lenses. These correctors make use of nonround optics such as hexapoles or octupoles, leading to the limiting aberrations often being of a nonround type. Here we explore the effect of a number of potential limiting aberrations on the imaging performance of the scanning transmission electron microscope through their resulting optical transfer functions. In particular, the response of the optical transfer function to changes in defocus are examined, given that this is the final aberration to be tuned just before image acquisition. The resulting three‐dimensional optical transfer functions also allow an assessment of the performance of a system for focal‐series experiments or optical sectioning applications.     

高数值孔径投影光刻物镜波像差的自动平衡优化

考虑高数值孔径(NA)投影光刻物镜视场较大、波像差分布不均匀,本文提出了一种自动优化设计方法来降低设计过程中出现的全视场最大波像差。该方法通过将一个自动调节采样视场权重的循环程序附加在光刻物镜的局部优化程序之外来自动平衡全视场的波像差,进而降低全视场的最大波像差。设计实例证明,运用该方法后光刻物镜全视场波像差的均匀性显著提高,最大波像差降低为原来的63%。该方法在光学设计软件Code V中有良好的应用效果,应用该方法不但能节省光刻物镜设计者的时间,而且会降低设计对设计者设计经验的依赖性。同时,该方法也可推广应用在其他对成像质量要求较高的光学系统设计中。     

Measurement of lens aberrations by means of image displacements in beam-tilt series

Electron microscope image aberrations are determined by means of the beam tilt/image displacement method with respect to the precision required to obtain a resolution of 1 A. The method simultaneously yields all image aberrations to the fourth order and it is independent of the material used for the procedure. The experimental procedure using amorphous carbon is described and errors in measuring beam-tilt angles, magnifications and image displacements can be kept sufficiently small to achieve the required accuracy. The method is applied to determine aberration constants of a CM300 FEG/UT microscope with correction of the three-fold astigmatism. The coefficient of spherical aberration and the modulus of the three-fold astigmatism were measured to 0.60 (+/- 0.02) mm and 150 (+/- 50) nm, respectively. The beam tilt/image displacement procedure is also computer simulated using an amorphous model structure yielding the same values for the lens aberrations which are used for imaging. However, a coefficient of spherical aberration of 0.67 mm is obtained by applying the focus variation/diffractogram analysis on the same model.     

利用相位差异技术恢复宽带白光图像

研究了用于扩展目标成像的相位差异技术。该技术利用焦面和离焦面上的两幅图像之间的相位差异来估算波前相位畸变,同时对采集的图像进行恢复。设计了白光目标成像实验系统,用宽带白光作光源,在实验室搭建实验平台,模拟无穷远处目标和波前相位畸变。采用直角梯形分光棱镜将光路分为两个通道,在一台相机上同时采集两个通道像面上的图像,消除了相机不同产生的差异,极大地抑制了噪声对图像恢复的影响,分光后系统抗两个通道独立的高斯白噪声的能力为10%。实验结果显示恢复后的图像分辨率提高了19%,表明该技术是适合光电成像系统的图像恢复技术。     

The resolution of photoelectron microscopes with UV, X-ray, and synchrotron excitation sources

The resolution of emission electron microscopes is calculated by determining the intensity distribution in the image. The object is a small disc of uniform brightness centered on the axis. A finite object, as distinct form a point source, provides a non-zero current in the image without the requirement of infinite object brightness and the consequent infinities in the geometrical intensity distribution. The minimum object size, which in turn affects the resolution of the microscope, depends on the minimum current or contrast required in the image. In photoelectron microscopes with UV illumination just above the threshold for emission the predominant aberrations are the chromatic and spherical aberrations of the accelerating field and the spherical aberration of the objective lens. For higher energies, e.g. in the soft X-ray range, the chromatic aberration of the objective lens must also be taken into account, as the aberration coefficients of the accelerating field are greatly reduced. The intensity distributions in the image are calculated first for single energies. The intensity distribution for a beam with a range of energies is obtained by adding a series of single-energy distribution curves weighted according to the energy distribution function. In the presence of spherical aberration the position of the image formed by the electrons depends on the angle of emission. In image planes between the paraxial and marginal planes the combination of spherical aberration and defocus causes the the image spot to have a retrograde type of behavior as the angle of emission increases. The image spot initially moves away from the axis in the azimuth of emission and then returns to the axis and moves away in the opposite azimuth. As a result the intensity in the central portion of the image plane is enhanced. The single-energy intensity distribution curves calculated as a function of depth in the image reveal the existence of a compact, high-intensity image peak in an image plane located between the paraxial and marginal planes. This peak occurs in the plane in which the image spot has a maximum retrograde displacement equal to its radius. The present analysis shows that the resolution in the high-intensity plane is better than in the plane of least confusion, and the effects of aberrations in these two planes are quite different.(ABSTRACT TRUNCATED AT 400 WORDS)     

干涉图的波面拟合与分析

据干涉图的离散数据,可用多种多项式来对其进行拟合。本文讨论了用Zernike、Chebyshev、Seidel三种多项式拟合波面的原理,在IBM-PC-XT机上对它们的拟合精度进行了计算和分析,并用Zernike多项式,结合实例计算了波面函数、峰谷值和均方根值,并给出相应的三维和二维图,同时还验证了程序的精度,具有一定的实用价值。     

大数值孔径物镜的波像差测量及其特殊问题

设计了基于振幅型棋盘光栅的二维剪切干涉仪,用于测量大数值孔径(NA)物镜的波像差。研究了棋盘光栅剪切干涉仪的基本原理,分析了大数值孔径物镜波像差测量时涉及的几个特殊问题。首先,根据棋盘光栅的远场衍射函数分析了棋盘光栅的衍射效率和衍射级分布,给出了剪切干涉图数据的处理方法。接着,根据球面光瞳坐标与平面探测器坐标的投影关系,分析了光瞳坐标畸变的影响;采用几何光线追迹方法,分析了光栅方程非线性对系统误差的影响。最后,推导了物镜光瞳边缘的相对照度与数值孔径的关系。试验结果表明:采用相同光瞳坐标,NA为0.6的显微物镜的波像差测量重复性(3σ)可达到3.7 mλ。对大数值孔径物镜测量过程中涉及的特殊问题进行了探讨,结果提示:测量大数值孔径物镜的波像差时,需要考虑光瞳坐标畸变、光栅方程引入的系统误差、光瞳边缘照度衰减的影响等。     

On the optimum probe in aberration corrected ADF-STEM

New aberration correctors present new challenges in optimizing (minimizing) the probe size in the STEM (Scanning Transmission Electron Microscope). A small probe is important for high resolution imaging and analytical microscopy. Some effects of aperture size, corrector accuracy, and higher order aberrations on probe size and image artifacts are calculated. Accumulated small errors in the aberration corrector can produce a significant decrease in image contrast, which may be important in quantitative image comparisons of theory and experiment. It is important to match the objective aperture to the accuracy of the corrector instead of just the (third order) spherical aberration of the objective as in the commonly used Scherzer conditions.     

On the importance of fifth-order spherical aberration for a fully corrected electron microscope

Next generation aberration correctors will not only eliminate the third-order spherical aberration, but also improve the information limit by correction of chromatic aberration. As a result of these improvements, higher order aberrations, which have largely been neglected in image analysis, will become important. In this paper, we concern ourselves with situations where sub-A resolution can be achieved, and where the third-order spherical aberration is corrected and the fifth-order spherical aberration is measurable. We derive formulae to explore the maximum value of the fifth-order spherical aberration for directly interpretable imaging and discuss the optimum imaging conditions and their applicable range.     

Correction of the spherical aberration of the CTEM objective lens using a foil lens

A foil lens has been applied to the objective lens of a conventional transmission electron microscope and its characteristics in correcting the spherical aberration have been investigated experimentally. Special polepieces of the objective lens were designed so that the foil lens can easily be inserted into them. The spherical aberration of a compound lens consisting of the objective lens and the foil lens was measured from the displacement of the {200} dark field image of a magnesium oxide crystal from its bright field image for various voltages of the foil lens. The experiment has shown that the spherical aberration of the objective lens, being excited at $\text{NI}\text{√V}\text{= 19.6 A V}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ at 100 kV, is reduced and becomes negative as the foil lens voltage is increased. The experimental result is in good agreement with calculations involving the third- and fifth-order spherical aberrations.     

Zemax软件在离轴三反射镜系统计算机辅助装调中的应用

利用Zemax光学设计软件与自编计算机辅助装调软件,实现了对大口径、长焦距、无中心遮拦离轴三反射镜光学系统的装调.通过Zemax软件模拟光学系统的失调模式,得到整个光学系统的波前像差,把波前像差代入到自编的复杂光学系统计算机辅助装调软件中,计算出光学系统的失调量,与引入的失调量对比,证明了其正确性.在实际的装调过程中,用小型球面干涉仪分别收集3个视场的干涉图,得到失调光学系统的失调量,用Zemax软件验证失调量数据的正确性,从而指导装调.按此方法,在波长λ=632.8nm时,得到离轴三反射镜光学系统的全视场波像差RMS值为0.108λ.该方法也可以运用到其他光学系统中.     

基于阻尼最小二乘算法的计算机辅助装调方法

对于具有中心遮拦的光学系统装调,需要将获得的波前进行拟合求取低阶像差。但是Zernike圆多项式在环域上已不具有正交性,不能正确的计算低阶像差。而Zernike环多项式在环域上具有正交性,可以解决这个问题。基于阻尼最小二乘法的算法原理,运用MatLab实现了计算机辅助装调。文中对卡塞格林光学系统进行了模拟实验,验证了使用Zernike环多项式进行拟合的辅助装调程序的正确性。同时,对于辅助装调程序的应用范围也做出了分析。     

制作平面全息光栅的离轴抛物镜/洛埃镜干涉系统

设计和制作具有较高波前平面度和结构稳定的干涉曝光系统是研制高质量平面全息光栅的首要条件.对离轴抛物镜/洛埃镜系统、单透镜/洛埃镜系统、球面反射镜/洛埃镜系统和双分离透镜/洛埃镜系统等4种单反射镜干涉曝光系统产生的干涉条纹直线度进行了光线追迹.在干涉场中放置标准光栅,使用于曝光的两束平行光入射到光栅上,从而衍射光相干叠加...