A modified goodman's technique for obtaining rocking-beam type patterns

A new method was developed for convergent beam electron diffraction (CBED) and large angle convergent beam electron diffraction (LACBED) in the JEM-100CXII. This method is obtained in the imaging mode using the defocus objective lens and by re-setting condenser-2. A multi-dark field CBED pattern was achieved in two ways.     

随机模式投影双目测量系统中的单目测量方法

针对基于随机模式投影的双目立体测量系统的特点,提出了一种由单摄像机-投影器构成两个单目测量单元的测量方法。首先给出了一个简洁有效的标定算法,该算法只需从不同角度拍摄随机光场在普通白板上的图像（称为标定图像）,就可以标定纯随机模板上每一点经投影镜头发出的光线。无需标定投影镜头畸变,且精度不受投影镜头畸变的影响。然后将随机光场照射下的被测物体图像与标定图像进行亚像素精度的像点匹配,根据三角测量原理获取物体表面的三维点云数据。最后采用标准平面对该方法进行测量精度验证,并给出了具体的测量实例。实验结果表明：平面度测量精度为0.0175mm,不确定度<0.05mm(3σ)。由于采用单目测量单元进行测量时,空间一点无需在两个摄像机视场内均可见,因此避免了因局部高光、被测物体自身遮挡等原因引起的三维测量数据丢失,有效地弥补了双目测量系统的不足。     

On the peculiarities of CBED pattern formation revealed by multislice simulation

A modified multislice method has been developed for calculations of Convergent Beam Electron Diffraction (CBED) patterns. The validity of the method for HOLZ- and Kikuchi-line calculations has been proofed by comparison to Bloch-wave calculations. The application of the method leads to the new understanding of CBED patterns formation. Dynamical scattering of weak HOLZ reflections plays the key role in the appearance of deficient lines in the central CBED disk. Different HOLZ lines do have significantly different and extended scattering areas; the central 000 CBED disk, consequently, contains structural information from an area around the primary beam which is determined by the Bragg angle of HOLZ reflections and the thickness of the sample. A variation of lattice parameters, if present within this area, results in artificial symmetry violations of the pattern and in changes of line profiles.     

Determination of lattice parameters from multiple CBED patterns: A statistical approach

This study deals with the uncertainty of the measurement of lattice parameters by CBED using the kinematic approximation. The analysis of a large number of diffraction patterns acquired on a silicon sample at 93 K with a LaB₆ TEM without energy filter shows the presence of both the systematic and the random parts of errors. It is established that random errors follow the normal statistical distribution and that the precision quantified by the relative standard deviation is about 3–4×10⁻⁴ for lattice parameter measurements made from single pattern. The error sources are analyzed, different ways of enhancement are reviewed, and a new approach is proposed. It is shown that both accuracy and precision can be simply improved by taking into account multiple patterns analysis for the determination of the actual voltage, the single lattice parameter “a” or the complete set of lattice parameters. The precision of about 1.5–2×10⁻⁴ can be reached using a minimum of three HOLZ line patterns for the single “a” parameter and about 5×10⁻⁴ for the complete set of lattice parameters using six diffraction patterns. The use of multiple patterns also allows overcoming the non-uniqueness of solution linked to the CBED studies.     

Automated identification of symmetry in CBED patterns: a genetic approach

The genetic algorithm has been applied for automated identification of symmetry in CBED patterns. A normalized inner product between an original and its symmetry operated CBED patterns was found to be a good measure of similarity between them, and this inner product was used as the objective function in the genetic algorithm. A real floating number implementation of this genetic approach has been applied successfully in identifying rotation axes and mirror planes in experimental CBED patterns obtained from a single crystal of silicon. In particular a three-fold rotation axis reflecting the true three-dimensional symmetry of silicon is clearly distinguished from a six-fold rotation axis as expected from a two-dimensional crystal in the experimental <1 1 1> zone axis CBED pattern.     

用构造光系统实现3-D形貌测量的研究

介绍了一个用构造空间二进制编码进行非接触３Ｄ形貌测量的系统。它以一台ＬＣＤ投影仪为硬件基础,用８幅条纹投影图案对被测物体表面进行空间编码。用ＣＣＤ摄像机获取物体编码信息,用基于单一像素的三角法原理从摄像机图像中获取三维形貌数据。指出了二进制编码图案生成软件及其生成的条纹图案的特点。为了提高３Ｄ形貌测量的精度,分析了由摄像机和投影仪镜头造成的误差,建立了它们的透镜误差矫正公式,并取得了良好的实验结果。     

用构造光系统实现3-D形貌测量的研究

介绍了一个用构造空间二进制编码进行非接触3-D形貌测量的系统。它以一台LCD投影仪为硬件基础,用8幅条纹投影图案对被测物体表面进行空间编码。用CCD摄像机获取物体编码信息,用基于单一像素的三角法原理从摄像机图像中获取三维形貌数据。指出了二进制编码图案生成软件及其生成的条纹图案的特点。为了提高3-D形貌测量的精度,分析了由摄像机和投影仪镜头造成的误差,建立了它们的透镜误差矫正公式,并取得了良好的实验结果。     

基于新的系统数学模型的三维形貌测量法

提出新的测量系统数学模型,将投影仪投射光场视为由相位值唯一标识的光投射面的集合所形成的空间,将摄像机成像模型视为一种由成像点图像坐标确定的成像射线形成的集合,将被测点视为所对应的投射面与成像射线的交点。以此为理论基础,采用逆向求解法建立投影仪的数学模型,避免显示标定投影仪的复杂操作过程。将离心畸变与径向畸变分解为两个独立的过程顺序求解,再使用小孔成像模型建立消除畸变后的摄像机数学模型。采用平面靶标自由移动法采集足够多的标定数据,对标定靶的尺寸与位置要求不严,并且在不要求标定数据充满整个视场空间的情况下仍可获得完整的标定结果。本标定过程对系统位置无任何严格要求,同时摆脱对精密位移装置的需求,并有效地消除摄像机与投影仪镜头畸变所产生的标定误差。     

Investigation of the local Ge concentration in Si/SiGe nanostructures by convergent-beam electron diffraction

SiGe multi quantum well structures were investigated by convergent-beam electron diffraction (CBED) measurements. Detailed layer characterizations were performed by acquiring series of bright field CBED patterns in the form of a line scan across the nanostructures in scanning transmission electron microscopy (STEM) mode. From the higher order Laue zone (HOLZ) lines the local lattice parameters were deduced. The Ge concentration corresponding to these lattice parameters was determined by means of the elasticity theory. In this work it is shown that the lattice constants can be determined locally with an accuracy of about ±0.001 to ±0.003 Å which leads to an accuracy of the corresponding Ge concentration of about 1–2%. The characteristics of the focused electron probe and its influence on the experimental data were used for an estimation of the spatial resolution of the CBED method. For comparison, experimental values regarding the spatial resolution were determined by investigating the abrupt interface between Si(1 1 1) and AlN(0 0 0 1).     

Reproducibility of electron microscope magnifications with digital display of individual lens currents

Quantitative measurements on electron micrographs with less than 10% error require precise calibration of all lenses contributing to the final image magnification. Calibration of the magnification to approximately 1.5% is easily attained by using simple statistical methods and a digital display milliampere meter capable of measuring the objective, intermediate and projector lens currents independently. The method detailed, readily adaptable to other electron microscopes, requires the projector lens current be held constant, with the magnification determined by varying the intermediate lens current and corrections made on the basis of calibrated objective lens current effect. The errors of magnification, approximately 1.5%, are the same range as the test grid variation which appears to be the limiting factor. Even with this limitation, magnifications have been determined reproducible to within less than 0.2% in daily use over a 6 month period.     

A comparison of techniques for obtaining convergent beam electron diffraction patterns with a JEOL 200CX

Three different techniques for obtaining convergent beam electron diffraction (CBED) patterns using a JEOL 200CX transmission electron microscope will be described and compared. The first technique, described by Goodman, will be shown to yield clear, undistorted patterns, but only with relatively large camera length, and a limited field of view. A second technique, which is a modification of Goodman's technique, will be shown to yield CBED patterns of both large camera length and small camera length with a much larger angular coverage, but the magnitude of the beam convergence is limited by distortion in the pattern. A third technique will then be presented which permits the formation of small camera length, relatively undistorted CBED patterns with large angular coverage and greatly increased beam convergence; high quality large camera length CBED patterns can also be obtained by simply increasing the strengths of the diffraction lenses.     

基于市售设备的结构光系统模型及标定

在射影几何矩阵模型和三角法解析模型的基础上,结合市售数码相机和投影仪内部结构参数精度高、工作稳定的特点建立了结构光三维测量系统的实用数学模型。提出一种借助数码相机赋予投影仪"视觉"功能,向标定模板投射正交格雷码图案,从而确定DMD像面点和空间标准点对应关系的投影仪标定方法。作为上述数学模型的基础,设计了基于共线特征的校正模板,采用图像法将数码相机镜头畸变参数分离于系统参数之外单独标定。文中具体给出了数学模型、标定公式及校正模板,最后进行了标定、测量实验。仿真系统验证了方法的可行性,测量相对误差约为0.2%;实际系统平面测量相对误差小于0.7%,重构的复杂表面具有良好视觉效果。     

Computer programs for unit-cell determination in electron diffraction experiments

A set of computer programs for unit-cell determination from an electron diffraction tilt series and pattern indexing has been developed on the basis of several well-established algorithms. In this approach, a reduced direct primitive cell is first determined from experimental data, in the means time, the measurement errors of the tilt angles are checked and minimized. The derived primitive cell is then checked for possible higher lattice symmetry and transformed into a proper conventional cell. Finally a least-squares refinement procedure is adopted to generate optimum lattice parameters on the basis of the lengths of basic reflections in each diffraction pattern and the indices of these reflections. Examples are given to show the usage of the programs.     

Demonstration of a tunable two-frequency projected fringe pattern with acousto-optic deflectors

We report on a fringe projector for three-dimensional shape measurement. The developed instrument is able to project a two-frequency fringe pattern, each frequency is independently controlled by electronics. Moreover, each phase of the two fringe patterns is also independently adjusted. The projection system is based on the use of a pair of custom large bandwidth (40 MHz) and high efficiency (60%) TeO2 deflectors. The developed instrument offers the combined advantages of a static two-frequency fringe projector and of a tunable single frequency fringe projector.     

Effect of electron beam parameters on simulated CBED patterns from edge-on grain boundaries

Convergent beam electron diffraction (CBED) at vertical grain boundaries (parallel to the electron beam) can be applied to determine the symmetry of bicrystals. It can also be used to investigate the structure of the boundary region itself when subnanometre probe sizes are employed. In this paper it is shown that (sub)nanometre-probe CBED patterns are largely influenced by the electron-beam geometry. In particular, simulations of coherent CBED patterns based on the multislice algorithm show that the CBED pattern of an edge-on interface depends on the defocus distance between the probe position and the specimen midplane, the probe size and the beam-convergence angle. The pattern symmetry may be lower than the theoretically predicted symmetry in case of large spherical aberration. This effect increases with smaller accelerating voltages. An increase in the beam-convergence angle also increases the possibility of a non-optimum symmetry due to spherical aberration of a coherent probe. Thus, for the determination of an interface structure using subnanometre (coherent) probes, the imaging conditions play an important role.     

Crystal thickness and extinction distance determination using energy filtered CBED pattern intensity measurement and dynamical diffraction theory fitting

A new method for measuring thickness and extinction distance of single crystals based on computed adjustment of measured and calculated CBED pattern intensity profiles is presented and discussed. The experimental beam intensity distribution is measured from an energy filtered CBED pattern recorded on a CCD camera. The calculated profile is based on dynamical diffraction theory, and with the two-beam approximation the analytical expression contains only two free parameters: specimen thickness t and extinction distance xig. Parameter refinement through minimization of the difference between experimental and calculated intensity profiles is carried out using Origin 5.0 software from Microcal. The iterative procedure always converges to a unique solution in a few seconds, yielding an accurate value for both thickness and extinction distance. The method is extensively tested on silicon using the (0 0 4) Bragg reflection. On specimens in the usual TEM thickness range, the method gives result similar to the conventional (P.M. Kelly et al., Phys. Stat. Sol. A31 (1975) 771; S.M. Allen, Philos. Mag. A 43 (1981) 325) graphical methods, both based on the measurement of fringe spacing. Moreover, it is shown that the calculation matches perfectly both the positions of the minimums and maximums as well as the amplitude of maximums. For any single intensity profile, specimen thickness and extinction distance can be determined with a precision of about 0.2%. A statistical comparison of our method with the Kelly and Allen techniques, based on more than 50 experiments, shows an improvement in measured extinction distance dispersion. Using 197 keV electrons, and liquid-nitrogen cryo-holder, the new technique yields an experimental value of 161+/-3 nm for the extinction distance for silicon with the (0 0 4) Bragg reflection. The equivalent tabulated value at 0 K is about 156 nm. Using the Kelly and Allen methods, the extinction distance is found to be 162+/-6 nm. The improvement in precision is a direct consequence of matching the intensity profile envelope, which contains information on the extinction distance. Also the accuracy of thickness determination is improved and is around 0.5 to 1% for common specimen thickness. The minimum measurable sample thickness is shown to be two to three times thinner than with the Kelly and Allen methods (0.3 xig, as opposed to 0.8 xig). With no independent calculation of the extinction distance needed, the method is also applicable on unknown crystals. The method is fast, simple and can be easily automated.     

投影仪内参数的标定新方法

基于编码结构光的自标定三维重构技术中需将投影仪视为一个逆向的摄像机,而且需要标定其在针孔模型下的内参数矩阵。本文提出的投影仪内参数新标定方法,不需要精密移动的机械装置或精密标定模块就可以实现投影仪内参数的标定。该方法首先提取图像中的特征点坐标,依据伪随机编码原理求出特征点在投影平面上的坐标,利用几何原理求得特征点在靶标平面上的二维坐标,再通过张氏标定法完成对投影仪的内参数标定。实验表明该方法可操作性好,结果准确可靠。     

基于层次化算法在欧氏空间不标定重构三维场景

研究一种由彩色编码投影仪及数码摄像机组成的不标定三维场景重构技术,在三维场景重构过程中,只有投影仪的参数需事先标定,而摄像机的内外参数在三维重构过程中不需标定且可随场景的不同而变化。基于层次化算法,仅需单幅三维图像就可实现对三维未知场景进行不标定欧氏重构。详细地叙述了该种不标定算法,并进行了实验验证。     

基于CATIA二次开发的微透镜阵列仿真

汽车灯具的发展日新月异,近年来出现的新型灯种Logo灯逐渐流行。Logo灯可根据客户要求投射出各种图案,其原理是将光源发出的光通过灯内微透镜阵列投射至地面,但由于地面与光源透镜不平行,图像倾斜投影时会产生畸变失真现象,因此光学设计需要对光源图形进行修正才能避免失真。详细介绍如何通过CATIA二次开发对Logo灯的微透镜阵列进行仿真。     

Translation symmetries in convergent-beam electron diffraction

The interpretation of the CBED pattern symmetries derived from the specimen symmetry has been given by Goodman and by Buxton, Eades, Steeds and Rackham. The former paper deals with the effect of the translation components of symmetries, which are normal to the incident surface, while the latter paper ignores the presence of these translation components. The graphical method proposed by Buxton et al. cannot be applied to the symmetry with translation. The Ewald construction method used by Goodman is also not applicable to the symmetry with translation. A simple interpretation of the CBED pattern symmetries can be obtained based on the multiple-scattering formula, where the translation component is also taken into account.