Detection and quantitative assessment of image aberrations from single HRTEM lattice images

For utilizing the full capabilities of quantitative high-resolution transmission electron microscopy in materials characterization, a precise knowledge of the various aberrations blurring the object information is essential. Here, we describe an extended approach to the detection and quantitative assessment of image aberrations from lattice images of crystal samples. The approach is based on a theoretical analysis of five-beam lattice images in the presence of all relevant optical aberrations and for partial beam coherence. Compact analytical expressions for linear and nonlinear image Fourier coefficients as explicit functions of the aberration parameters are derived. In particular, a fundamental relationship between the occurrence of erroneous image symmetries and the simultaneous presence of optical misalignments and partial beam coherence is established. An image analysis procedure is proposed which allows for the detection of even- and odd-order residual aberrations and for the quantitative determination of defocus, two-fold astigmatism and axial coma if the three-fold astigmatism is known. For coma-free images, the three-fold astigmatism can also be determined quantitatively. Moreover, the procedure allows for a reliable detection of crystal misalignment for images of wedge-shaped crystal samples.     

Observation of lens aberrations for very high-resolution electron microscopy. I. Theory

Least-squares fitting methods are described, currently the most accurate known, for determining the imaging aberrations and other important parameters. The data required are either the image displacement or the image diffractogram shape (or both), as a function of injected beam tilt; the analysis is largely common to the two cases. Explicit solutions are given for some simple cases (e.g. coma-free alignment on the basis of three images only) and some promising developments are considered; the relevant aberration theory is set out in detail. Experimental work reported in a companion paper has confirmed the presence of threefold astigmatism at significant levels, but has not shown any evidence of other higher order aberrations.     

A new way of measuring microscope aberrations

Two-fold astigmatism, three-fold astigmatism and misalignment (coma) can be found from the orientations only of the diffractograms of a set of images with injected beam tilts--typically eight images with tilts of equal magnitude and azimuths 45 degrees apart. The spherical aberration must be determined independently, and the defocus is not measured; however, the measurement required is very much simpler than the measurement of image displacements or induced defocus/astigmatism values, and no calibration of the microscope magnification is needed.     

Higher-order aberration corrector for an image-forming system in a transmission electron microscope

We developed a new electron optical system with three dodecapoles to compensate for spherical aberration and six-fold astigmatism, which generally remains in a two-hexapole type corrector. In this study, we applied the corrector for image-forming system in transmission electron microscope. Compensation for higher-order aberration was demonstrated through a diffractogram tableau using a triple three-fold astigmatism field system, which was then compared with a double hexapole field system. Using this electron optical system, six-fold astigmatism was measured to be less than 0.1 mm at an acceleration voltage of 60 kV, showing that the system successfully compensated for six-fold astigmatism.     

The effect of three-fold astigmatism on measurements of grain boundary volume expansion by high-resolution transmission electron microscopy

In the absence of high-order aberrations, the lattice fringe technique should allow measurement of grain boundary rigid-body displacements to accuracies about an order of magnitude better than the point-to-point resolution of the transmission electron microscope. The three-fold astigmatism, however, introduces shifts of the lattice fringe pattern that depend on the orientation of the lattice relative to the direction of the three-fold astigmatism and thus produces an apparent shift between the two grains bordering the grain boundary. By image simulation of grain boundary model structures, the present paper explores the effect of these extraneous shifts on grain boundary volume expansion measurements. It is found that the shifts depend, among others, on zone axis direction and the magnitude of the lattice parameter. For many grain boundaries of interest, three-fold astigmatism correction to better than 100 nm appears necessary to achieve the desired accuracies.     

A method of using the incident beam tilt as a eucentric goniometer in transmission electron microscopy

The principal difficulties in constructing and operating a eucentric specimen tilting goniometer in a transmission electron microscope are discussed, together with the goniometric function of the incident beam tilt. The latter function is found easy to operate in a eucentric manner. The imaging beam then will have a non-axial path, which will increase particularly the field chromatic aberration. Earlier, however, a technique for the compensation of the chromatic aberration during displaced aperture dark field image formation has been developed. In combination with this technique, it proved possible to use the ordinary incident beam tilt as a eucentric goniometer. Image sequences were obtained, with accurately varied diffraction conditions. The tilt angles and the direction of the tilt axis can be very accurately determined from the displacements of the diffraction pattern.     

A new method for the determination of the wave aberration function for high resolution TEM 1. Measurement of the symmetric aberrations

A new method for the accurate determination of the symmetric coefficients of the wave aberration function has been developed. The relative defoci and displacements of images in a focus series are determined from an analysis of the phase correlation function between pairs of images, allowing the restoration of an image wave even when focus and specimen drift are present. Subsequently, the absolute coefficients of both defocus and 2-fold astigmatism are determined with a phase contrast index function. Overall this method allows a very accurate automated aberration determination even for largely crystalline samples with little amorphous contamination. Using experimental images of the complex oxide Nb16W18O94 we have demonstrated the new method and critically compared it with existing diffractogram based aberration determinations. A series of protocols for practical implementation is also given together with a detailed analysis of the accuracy achieved. Finally a focal series restoration of Nb16W18O94 with symmetric aberrations determined automatically using this method is presented.     

Practical procedure for coma-free alignment using caustic figure

The practical procedure for coma-free alignment using a single defocused transmission electron microscopy (TEM) image is presented. Caustic figures observed in the defocused TEM image of a focused probe are utilized. Coma-free alignment can be carried out by coinciding a bright-field spot with the center of a caustic curve as observed in an underfocus TEM image. With this method, beam tilt misalignment is reduced to the sub-mrad order (e.g. 0.3mrad for 300kV FEG-TEM). This can be done without intentional beam tilting, an amorphous specimen, high-resolution TEM images, or fast Fourier transform for diffractogram or cross-correlation, which are used in previous methods. Residual coma aberration is detected using the multiple Bragg images of a known crystal. Similarity between the present coma-free alignment and well-known STEM alignment using shadow image is discussed.     

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)     

显微物镜像差测定及其像质评价

介绍了我们研制的多功能显微物镜波差测定仪的各种像差测定方法。测试了国内外显微物镜。平视场物镜的波面像差、轴上<λ/4～λ/8,视场边缘～λ/2;非平场的波面像差、轴上<λ/4,边缘视场～3λ。波面像差作为设计装配检测是-种合适的质量判据。作为像质判据,采用白光传递函数较为合适。     

Influence of the elliptical illumination on acquisition and correction of coherent aberrations in high-resolution electron holography

In high-resolution off-axis electron holography, the interpretable lateral resolution is extended up to the information limit of the electron microscope by means of a correcting phase plate in Fourier space. A plane illuminating electron wave is generally assumed. However, in order to improve spatial coherence, which is essential for holography, the object under investigation is illuminated with an elliptically shaped electron source. This special illumination imposes a variation of beam directions over the field of view. Therefore, due to the interaction of beam tilt and coherent wave aberration, the effective aberrations vary over the field of view yielding a loss of isoplanicity. Consequently, in the past the aberrations were only corrected successfully for a small part of the field of view. However, a thorough analysis of the holographic imaging process shows that the imaging artifacts introduced by the elliptical illumination can be corrected under reconstruction by means of a phase curvature, which models the illuminating wave front. Applied in real space, this phase curvature is seamlessly incorporated into the correction process for coherent wave aberration resulting in an improvement of interpretable lateral resolution up to the information limit for the whole field of view.     

A method for producing hollow cone illumination electronically in the conventional transmission microscope.

An electronic device manipulates the primary beam in the conventional transmission microscope to produce a hollow cone of illumination with its apex located at the specimen. The device uses the existing tilt coils of the microscope, and modulates the D.C. signals to both x and y tilt directions simultaneously with various waveforms to produce Lissajous figures in the back-focal plane of the objective lens. Electron diffraction patterns can be recorded which reflect the manner in which the direct beam is tilted during exposure of a micrograph. In the bright-field imaging mode the device provides a microscope transfer function without zeros in all spatial directions and has been used to obtain high resolution images which are also free from the effect of chromatic aberration. A standard second condenser aperture is employed and the width of the cone annulus is readily controlled by defocusing the second condenser lens. The cone azimuthal angle is also controlled electronically; hence the device can also be used in the dark-field imaging mode. This device has been applied to imaging both amorphous and crystalline materials including biomolecular specimens.     

On-line image processing in high resolution electron microscopy

On-line processing and analysis of high resolution electron microscope (HREM) images has been implemented using a software controlled image processor based on a commercial digital video framestore. It directly digitizes the output from the low light TV camera on the HREM and applies any processing necessary. The conditions under which images from amorphous specimens are being obtained can be established on-line. The fast fourier transforms (FFTs) of 256 times 256 pixels produced in 15 s with the system off-line are comparable to those from diffraction analysis of the same data on a laser optical bench. The precision of analysis of defocus, aberrations and astigmatism on-line is discussed, together with possible approaches to routine analysis of crystalline specimens and for interactive control.     

主次镜系统的计算机辅助装调

为了实现大口径望远镜系统的装调,提高其光学成像质量,研究了望远镜装调像差和计算机辅助装调技术。首先针对RC式望远镜系统,分析了装调过程中由于次镜偏心和倾斜导致系统模型产生的扰动误差。针对实际调整过程中选择零彗差点和曲率中心作为旋转中心进行调整的特点,分析了这两个旋转点的选择对系统像差和指向精度的影响。然后结合计算机辅助装调原理,研究了关于恒定彗差、线性像散与模型相关的灵敏度矩阵的特殊形式,结合波像差理论与光学软件Code V模型仿真来实现装调技术。最后,针对1 m级望远镜系统进行了安装调整。实验结果表明:装调后系统的RMS达到了0.144 5λ,大大优于装调前的1.214λ,证实了该方法具有较好的精度、抗干扰能力和实际应用价值。     

Imaging columns of the light elements carbon, nitrogen and oxygen with sub Angstrom resolution.

It is reported that lattice imaging with a 300 kV field emission microscope in combination with numerical reconstruction procedures can be used to reach an interpretable resolution of about 80 pm for the first time. A retrieval of the electron exit wave from focal series allows for the resolution of single atomic columns of the light elements carbon, nitrogen, and oxygen at a projected nearest neighbor spacing down to 85 pm. Lens aberrations are corrected on-line during the experiment and by hardware such that resulting image distortions are below 80 pm. Consequently, the imaging can be aberration-free to this extent. The resolution enhancement results from increased electrical and mechanical stability of the instrument coupled with a low spherical aberration coefficient of 0.595 + 0.005 mm.     

Prospects for aberration-free electron microscopy

Future aberration-corrected electron microscopes that will enable sub-Angstroem spatial and sub-eV energy resolution are outlined . The sub-Angstroem transmission electron microscope (SATEM) only compensates for the spherical aberration and reduces the chromatic aberration disc by means of a monochromator. In order to correct for both aberrations, two novel correctors, the ultracorrector and the superaplanator are proposed which will yield a resolution limit of about 0.5A and a large field of view of more than 4 x 10(6) image points. The superaplanator is best suited for obtaining an achromatic aplanat required for the realization of the high-performance in situ electron microscope of the TEAM project.     

A simple but precise method for quantitative measurement of the quality of the laser focus in a scanning optical microscope

We report a method for characterizing the focussing laser beam exiting the objective in a laser scanning microscope. This method provides the size of the optical focus, the divergence of the beam, the ellipticity and the astigmatism. We use a microscopic‐scale knife edge in the form of a simple transmission electron microscopy grid attached to a glass microscope slide, and a light‐collecting optical fibre and photodiode underneath the specimen. By scanning the laser spot from a reflective to a transmitting part of the grid, a beam profile in the form of an error function can be obtained and by repeating this with the knife edge at different axial positions relative to the beam waist, the divergence and astigmatism of the postobjective laser beam can be obtained. The measured divergence can be used to quantify how much of the full numerical aperture of the lens is used in practice. We present data of the beam radius, beam divergence, ellipticity and astigmatism obtained with low (0.15, 0.7) and high (1.3) numerical aperture lenses and lasers commonly used in confocal and multiphoton laser scanning microscopy. Our knife‐edge method has several advantages over alternative knife‐edge methods used in microscopy including that the knife edge is easy to prepare, that the beam can be characterized also directly under a cover slip, as necessary to reduce spherical aberrations for objectives designed to be used with a cover slip, and it is suitable for use with commercial laser scanning microscopes where access to the laser beam can be limited.     

柱面系统无畸变指纹采集仪的光学设计

针对以往无畸变指纹采集仪多采用棱镜补偿方案,系统存在棱镜的固有像散,光学系统难以补偿这种像差获得较高成像质量这一问题,提出了一种采用柱面系统结合双远心物镜校正投影畸变的新方案。该方案利用双柱面系统,在棱镜没有压缩图像的方向上压缩图像;利用双远心光路,消除物面和像面存在倾斜时的梯形畸变。采用该方案进行的计算机建模,经过合理调整优化函数,平衡各种像差,获得了比棱镜补偿校正畸变方案更高的成像质量。指纹采集仪得到了指纹采集方(物方)大部分视场的传递函数值在特征频率5 lp/mm(对应像方40 lp/mm)时＞0.377, 在特征频率10 lp/mm(对应像方80 lp/mm)时＞0.139的结果,大部分视场传递函数提高到棱镜补偿方案的1.6倍,同时各视场成像质量都比较均衡。     

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.