A pattern recognition method for lattice distortion measurement from HRTEM images

The idea of the method is to analyse a crystal lattice by creating a grid of quadrilaterals corresponding to repeated cells that are visible in the image. This approach combines image processing elements with a continuum field theory, to create a distortion-independent similarity measure that is used to select the most appropriate among possible lattice configurations. Subsequently, displacement and distortion fields are computed from individual cell positions. The method allows one to obtain these fields even for images where a periodic cell does not necessarily appear as a single dot of intensity in a high-resolution transmission electron microscopy (HRTEM) image, which results in a lower accuracy of commonly used approaches, namely geometric phase and peak finding. The results obtained from this method are verified quantitatively by comparison with known distortion tensor distributions and Burgers vector values on both simulated and real images.     

An expanded approach to noise reduction from high-resolution STEM images based on the maximum entropy method

An expanded use of the maximum entropy method (MEM) is suggested to reduce noise from an experimental high-angle annular dark-field (HAADF) scanning transmission electron microscope (STEM) image. The MEM is combined with an estimate of the standard deviation of noise from an experimental HAADF STEM image and low-pass filtering using the information limit for an incoherent STEM image. Consequently, the present method has just one parameter of a Lagrange multiplier. It is demonstrated that the present method can reduce noise efficiently in high-resolution HAADF STEM images.     

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.     

One method for restoration of blurred images

A new method is proposed to reduce image distortions caused by random noise and rectilinear uniform motion of the object or recording system. The of a restoration model is based on a statistical regularization method, and the obtained system of linear equations and inequalities is solved using a multistep support vector method. An advantage of this approach is that the iterative nature of the algorithm makes it possible to take into account the a priori information on the solution represented by the inequalities. The results of numerical experiments showing the efficiency of the algorithm are given.     

Measurement of effective source distribution and its importance for quantitative interpretation of STEM images

We review the manner in which lens aberrations, partial spatial coherence, and partial temporal coherence affect the formation of a sub-Å electron probe in an aberration-corrected transmission electron microscope. Simulations are used to examine the effect of each of these factors on a STEM image. It is found that the effects of partial spatial coherence (resulting from finite effective source size) are dominant, while the effects of residual lens aberrations and partial temporal coherence produce only subtle changes from an ideal image. We also review the way in which partial spatial and temporal coherence effects are manifest in a Ronchigram. Finally, we provide a demonstration of the Ronchigram method for measuring the effective source distribution in a probe aberration-corrected 300 kV field-emission gun transmission electron microscope.     

Upper limits for the residual aberrations of a high-resolution aberration-corrected STEM

The development of correctors for electron optical systems has already brought the improvement of resolution for a low-voltage scanning electron microscope and a commercially available transmission electron microscope and is anticipated in the near future for a dedicated scanning transmission electron microscope (STEM). The resolution attainable especially of a probe-forming system at 200 kV cannot only be estimated from calculations ignoring all non-rotationally symmetric axial aberrations in an electron optical system. For a certain resolution, one would like to attain, the influence of the deviations from the ideal, aberration-free system has to be investigated. Therefore, in the following we have carried out the evaluation of the required accuracy for the compensation of the various residual aberrations in order to achieve a resolution in the sub-Angstrom regime with a probe-forming system.     

Restoration of confocal images for quantitative image analysis

Quantitative studies of three-dimensional (3-D) structure of microscopic objects have been made possible through the introduction of microscopic volume imaging techniques, most notably the confocal fluorescence microscope (CFM). Although the CFM is a true volume imager, its specific imaging properties give rise to distortions in the images and hamper subsequent quantitative analysis. Therefore, it is a prerequisite that confocal images are restored prior to analysis. The distortions can be divided into several categories: attenuation of areas in the image due to self-absorption, bleaching effects, geometrical effects and distortions due to diffraction effects. Of these, absorption and diffraction effects are the most important. This paper describes a method aimed at the correction of diffraction-induced distortions. All the steps necessary in restoring confocal images are discussed, including a novel method to measure instrumental properties on a routine basis. To test the restoration procedure an image of a fluorescent planar object was restored. The results show a considerable improvement in the z-resolution and no ringing artefacts. The relevance of the method for image analysis is demonstrated by a comparison of results of applying 3-D texture analysis to restored and unrestored images of a synthetic object. Furthermore, the method can be successfully applied to noisy fluorescence images of biological objects, such as interphase cell nucei.     

The Peak Pairs algorithm for strain mapping from HRTEM images

Strain mapping is defined as a numerical image-processing technique that measures the local shifts of image details around a crystal defect with respect to the ideal, defect-free, positions in the bulk. Algorithms to map elastic strains from high-resolution transmission electron microscopy (HRTEM) images may be classified into two categories: those based on the detection of peaks of intensity in real space and the Geometric Phase approach, calculated in Fourier space. In this paper, we discuss both categories and propose an alternative real space algorithm (Peak Pairs) based on the detection of pairs of intensity maxima in an affine transformed space dependent on the reference area. In spite of the fact that it is a real space approach, the Peak Pairs algorithm exhibits good behaviour at heavily distorted defect cores, e.g. interfaces and dislocations. Quantitative results are reported from experiments to determine local strain in different types of semiconductor heterostructures.     

Simulation of a hollow cone-shaped probe in aberration-corrected STEM for high-resolution tomography

In a simulation study, we found that focal depth extension using a hollow cone-shaped probe with an annular aperture is useful for three-dimension (3D) tomography of aberration-corrected scanning transmission electron microscopy (STEM). Our calculations showed that, for 200 kV STEM, a sub-angstrom sized probe could extend the focal depth from a few to more than several tens nm. We also examined the influence of obstructing bridges, including actual fabricated annular apertures, on focused probe intensity distribution. We found that, to avoid any distortion of probe intensity, the width of the bridges should be narrow. Quantitative evaluation showed that the ratio of obstructing area of the bridges to the area of the annular slit should be less than 0.11.     

Biostatistical analysis of quantitative immunofluorescence microscopy images

Semiquantitative immunofluorescence microscopy has become a key methodology in biomedical research. Typical statistical workflows are considered in the context of avoiding pseudo‐replication and marginalising experimental error. However, immunofluorescence microscopy naturally generates hierarchically structured data that can be leveraged to improve statistical power and enrich biological interpretation. Herein, we describe a robust distribution fitting procedure and compare several statistical tests, outlining their potential advantages/disadvantages in the context of biological interpretation. Further, we describe tractable procedures for power analysis that incorporates the underlying distribution, sample size and number of images captured per sample. The procedures outlined have significant potential for increasing understanding of biological processes and decreasing both ethical and financial burden through experimental optimization.     

Formation of a high-resolution image from a series of mutually shifted images using optimal linear prediction

A high-resolution image is constructed by joint interpolation of a series of low-resolution images differing in mutual shifts which are not multiples of the sampling interval. Interpolation coefficients are determined by using correlations between the readings of the initial images. Results of experiments showing the efficiency of the proposed approach are given.     

The S-state model: a work horse for HRTEM

The S-state model describes the dynamical scattering of electrons in a specimen foil, consisting of atom columns parallel to the beam direction, such as a crystal or a particular crystal defect. In this model the electrons are considered to be trapped in the electrostatic potential of an atom column, in which it scatters dynamically. This picture allows physical insight, and it explains why a one-to-one correspondence is maintained between the exit wave and the projected structure, even in case of strong dynamical scattering. Furthermore the model can be parameterised in a simple closed analytical form. Apart from the computational advantages, the S-state model proves to be very useful to deduce the projected structure directly from the exit wave, so as to "invert" the dynamical scattering. In this paper the validity of the S-state model, is evaluated in much depth by a proper quantum mechanical treatment. The analytical parameterisation of the 1S eigenfunction and eigenenergy is discussed. It is shown that the method, even in case of small tilts, is valid for most thicknesses, currently used in HRTEM studies. Even for closely spaced atom columns, such as the dumbbells in Si [1 1 0], Sn [1 1 0] and GaN [1 1 0], the positions of the atom columns can be deduced with an accuracy of a few pm.     

Discussions on the multiple-input maximum a-posteriori wave-function restoration method in high-resolution electron microscopy

The multiple-input maximum a-posteriori (MIMAP) wave-function restoration method in high-resolution electron microscopy proposed by Kirkland (1984) is further discussed. A modified MIMAP criterion that considers likely correlations between individual micrographs in a series of micrographs taken at different imaging conditions is presented. By performing wave-function restoration for a multislice method-simulated defocus series of MgO[110], the convergent properties of this modified MIMAP method are also described.     

一种磁记忆检测定量分析的新方法

金属磁记忆检测技术是利用磁记忆效应对铁磁性材料的应力集中区进行无损检测的新方法.磁记忆效应的特征是应力集中部位表面的漏磁场的切向分量最大、法向分量存在过零现象.在目前的研究工作中,研究方法主要是以测量磁记忆法向信号过零点位置来判断应力集中,从而割裂了切向与法向之间内在的关系.探讨了采用法向切向联合检测的方法,利用一种新型的磁阻传感器HMC1002,设计组装了高精度的二维弱磁场测量传感器.通过对拉伸试件进行2种方法检测的对比实验,结果表明,此方法比单一的法向磁场分量过零值点的检测更有效,可望在磁记忆检测定量分析研究中有很好的实际应用价值.     

A quantitative method for analysing AFM images of the outer surfaces of human hair

Cuticle step height is an important parameter for the quantitative assessment of human hair. This paper describes a novel, computational method for the rapid calculation of step heights from atomic force microscope images obtained from large numbers of specimens. Such an approach is necessary to allow a statistical analysis of the inherently wide distribution of cuticle step heights characteristic of a single hair sample. The method described will be of use to cosmetic formulation chemists and forensic scientists and also to dermatologists in the field of disease diagnosis.     

Quantitative structural analysis of twin boundary in alpha-Zn7Sb2O12 using HAADF STEM method

The structure and composition of the 1/4{110} twin boundary in alpha-Zn7Sb2O12 have been determined by using quantitative high-angle annular dark field scanning transmission electron microscopy (HAADF STEM) analysis. The noise in the experimental HAADF STEM images is reduced by using the maximum entropy method and average processing, and the parameters used in dynamical simulations are experimentally determined. From the analysis, it has been found that octahedral sites in the twin boundary slightly shift parallel to the [110] direction, and a reduction of the Sb concentration at the octahedral sites on the plane adjacent to the twin boundary was detected. The reduction was measured from three regions in the same twin boundary, and the Sb concentrations were 4 +/- 3, 8 +/- 3 and 19 +/-2 at% from 33 at%.     

Two-phase flow in porous media: obtaining sharp digitized images of serial sections for subsequent quantitative analysis

Microscopic studies of the distributions of oil and aqueous phases within the pore space of reservoir rocks, at various relative saturations, are of fundamental importance in understanding migration, distribution, mobilization and recovery of oil in the context of a particular (enhanced) oil recovery method. The most effective approach to use for these studies is three-dimensional computer reconstruction with the data for the three-phase system (rock, oil, aqueous phase) entered by video digitization of a set of serial sections. A novel technique for creating accurate three-phase digitized images from the serial section data is described. By use of appropriate pore cast materials and lighting conditions, three different two-phase video images are created and digitized. In each image, a different one of the three phases in the pore cast is one of the two distinguishable phases. The two best two-phase digitized images are combined to give the three-phase digitized image.     

Wave field restoration using three-dimensional Fourier filtering method.

A wave field restoration method in transmission electron microscopy (TEM) was mathematically derived based on a three-dimensional (3D) image formation theory. Wave field restoration using this method together with spherical aberration correction was experimentally confirmed in through-focus images of amorphous tungsten thin film, and the resolution of the reconstructed phase image was successfully improved from the Scherzer resolution limit to the information limit. In an application of this method to a crystalline sample, the surface structure of Au(110) was observed in a profile-imaging mode. The processed phase image showed quantitatively the atomic relaxation of the topmost layer.