The effect of mechanical vibration and drift on the reconstruction of exit waves from a through focus series of HREM images

Experimental HREM images can show a limited resolution as a result of mechanical vibration and drift. In this paper the effect of such mechanical vibrations on the accuracy of the through focus exit wave reconstruction method is investigated for different thicknesses of a test structure of La₃Ni₂B₂N₃. A through-focus series of HREM images for this structure is simulated for different kinds of mechanical vibration corresponding to an information limit g of about 7 nm⁻¹: (1) no mechanical vibration, (2) isotropic mechanical vibration, and (3) several anisotropic mechanical vibrations. From these through-focus series the reconstructed exit wave is calculated (Ultramicroscopy 64 (1996) 109). The above isotropic and anisotropic mechanical vibrations have a large effect on the reconstructed exit waves when compared with the reconstructed exit wave without mechanical vibration, i.e. the range of amplitudes and phases in a reconstructed exit wave decreases and the background intensity increases. The initial thickness and orientation can be obtained using a least-squares refinement procedure (Acta Crystallogr. A 54 (1998) 91) when there is no mechanical vibration present. In the case of isotropic or anisotropic vibration, the refined thickness and orientation are likely to give wrong results depending on the size of the vibrations and on the number of significant reflections (which is related to the size of the unit cell, the thickness and the misorientation).     

Wiener-filter enhancement of noisy HREM images

The use of Wiener filters to restore noisy HREM images is discussed, exploiting the fact that the noise spectrum can be rather simply estimated. Conventional Wiener, Cannon, parametric versions of these and a random-phase form are found to be very effective. Quantitative analysis indicates that the signal-to-noise ratio is improved by a factor of 3-7, with better results for larger pictures. Such filtering techniques should have rather wide applicability in electron microscopy, and could be applied on-line with TV systems.     

High-resolution wave field reconstruction using a through-focus series of images taken under limited electron dose

The three-dimensional Fourier filtering method and Schiske's Wiener filtering method are compared with the aim of high-resolution wave field reconstruction of an unstained deoxyribonucleic acid (DNA) molecular fiber using a through-focus series of images taken under a limited electron dose. There were some definite differences between the two reconstructed images, although the two kinds of processing are essentially equivalent except for the dimension and the filter used for processing. Through theoretical analyses together with computer simulations, the differences were proved to be primarily due to specimen drift during the experiment. Although the observed structure of the DNA molecular fiber was heavily damaged by electron beam irradiation, reconstructed images by the three-dimensional Fourier filtering method provided higher resolution information on the molecular structure even when relatively large specimen drift was included in the through-focus series. In contrast, in Schiske's Wiener filtering method, the detailed information of the structure was lost because of the drift, although the reconstructed image showed a higher signal-to-noise ratio. The three dimensional Fourier filtering method seems to be more applicable for observing radiation-sensitive materials under an extremely low electron dose, because specimen drift cannot be completely avoided.     

Exit wave reconstruction using a conventional transmission electron microscope

Exit wave reconstruction of a focus series of Ge in [110] using the PAMMAL algorithm was performed on a conventional electron microscope. The simulated images using the reconstructed object wave match very well with those obtained experimentally. Amplitudes from the complex wave function were extracted by means of local Fourier transformation. Crystal thickness and tilt were determined locally by quantitative comparison of the reconstructed amplitudes with amplitudes from multislice calculations. Detailed analysis yields the quasicoherent imaging approach used in the PAMMAL algorithm to produce the largest error in the analysis. For the Ge crystal specimen parameters were quantified to spatial frequencies of 5 nm¹. In the case of an object producing strong diffracted beams, the reconstruction may fail because the quasicoherent approximation will not describe correctly the nonlinear image formation.     

Emergence of small defect contrast within HREM images of nonstoichiometric rutile

Calculations of HREM images have been used to define the conditions for which interpretable information may be obtained concerning the nature of small defects (traditionally called “point defects”) and their aggregation to form extended defects in nonstoichiometric rutile. At specific crystal thickness and lens defocus conditions as few as three small defects (aligned along the projection axis) become visible in lattice images. The emergence of stronger contrast, as extended defects develop, should allow the interstitial or vacancy nature of the defects to be distinguished. Experimental HREM images are also presented which show a variety of “small defect contrasts” for [001], [010] and [111] projections of nonstoichiometric rutiles (TiO_2-x; 0.006 ≦ x ≦ 0.02). None of these allow interstitial versus vacancy defects to be distinguished directly, although some show evidence for aggregates of less than 10 small defects.     

The 'through focus plate' : a simple method for obtaining images through focus on a single photographic plate in the electron microscope using a tilting stage.

Tilting the specimen in an electron -icroscope by a relatively small angle can provide a continuous through focal series on a single plate, as the displacement of the object at the edge of the field can be adjusted to be of the same order of magnitude as the alteration of focal point by the fine lens controls. This simple rapid manoeuvre could have applicaitons in the microscopy of uniform preparations, particularly if the specimen is subject to beam damage, and in assessing microscope performance rapidly.     

Fuzzy logic approaches to the analysis of HREM images of III–V compounds

It is known that high-resolution electron microscopy (HREM) can provide quantitative information on the properties of crystalline materials. The HREM patterns of layered structures of III–V semiconductors vary with the chemical composition of the latter within the sublattices, which is also influenced by interdiffusion. Local variations of the crystal cell similarity are recorded for image analysis and compared with templates of known material composition.
Of the advanced theories of data interpretation, the now well-established fuzzy logic is highly suited for corresponding image processing techniques. Combining neighbouring image cell similarities, the underlying chemical composition is evaluated by applying fuzzy logic criteria of inference to masks of about 1 nm × 1 nm in size.
The new approach can be used to localize regions of significant changes in composition, i.e. edge detection, and to determine the composition across the interface region. The methods introduced prove successfully applicable to simulated as well as to experimental images of AlAs/Al _x Ga_{1− x} As. Similarity/composition relations of nonlinear as well as nonmonotonic characteristics are studied to establish an alternative fuzzy logic approach.     

Calculations of HREM image intensity using Monte Carlo integration

We have developed a numerical approach for the accurate and efficient calculation of HREM image intensity formed using a partially coherent source. The approach is based on Monte Carlo integration, and is suitable for use in general image restoration methods using a series of images. The accuracy of this approach is compared with calculations based on the transmission cross coefficient (TCC) for strong scattering objects, as a function of the number of sampling points, defocus, atomic number and specimen thickness. Its efficiency is compared with that of exact TCC calculations based on equally-spaced sampling of the beam divergence and focal spread distributions. The results indicate that the Monte Carlo approach is particularly advantageous for nonlinear image restoration algorithms.     

Structure projection retrieval by image processing of HREM images taken under non-optimum defocus conditions

A direct method for retrieval of the projected potential from a single HREM image of a thin sample is presented. Both out-of-focus and astigmatic images can be restored. The defocus and astigmatism values are first determined from the Fourier transform of the digitised HREM image. Then a filter is applied which reverts the phases of those Fourier components which have been reversed by the Contrast Transfer Function (CTF). The method has been incorporated into the CRISP image processing system. It can be applied on any sample, crystalline or amorphous. From thin crystalline areas the projected symmetry can be determined and a further improvement achieved by imposing the symmetry exactly. This compensates for the effects of crystal tilt. Five HREM images of a thin crystal of K(8-x)Nb(16-x)W(12+x)O80 (x = 1), taken with different defocus and astigmatism values, were processed. Only one, taken near Scherzer defocus, was directly interpretable before image processing. After processing, all images showed the projected potential of the structure. Using data to 2.77 angstroms resolution, all heavy (Nb/W) atom positions were found in every image, within on average 0.15 angstroms of the positions determined by single crystal X-ray diffraction. In the HREM images taken under non-optimum defocus conditions, also the potassium atoms in the tunnels of the structure were found.     

Computer simulation of HREM images of network models of SiO2 glass

The possibilities and limitations of HREM for evaluating structural details in amorphous silica were investigated by computer simulation. The calculated defocus series of HREM images for an unstrained and a linearly strained network model of vitreous SiO₂ have shown that microvoids, density fluctuations as well as strained regions can be interpretably imaged for thin specimens (t < 5 nm).     

HREM structure characterization of interfaces in semiconducting multi-layers using molecular-dynamics-supported image interpretation

Multi-layer structures in binary systems, for example InAs/AlSb and AlSb/GaSb, as well as ternary InGaAs/AlGaAs quantum wells grown by molecular beam epitaxy (MBE) are investigated by high-resolution electron miscroscopy (HREM). Interpretation of the micrographs requires methods of image analysis and the computer simulation of the HREM contrast. The relaxed atomic structure of the interfaces is modelled by molecular dynamics (MD) and energy minimization. The importance of strain relaxations to the image interpretation will be demonstrated and compared with the image spread and shift caused by the microscope aberrations. The possibility of revealing the compositional variations and the elastic deformations at the interfaces by HREM imaging under special defocus and sample thickness conditions will be discussed.     

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.     

Optimized HREM imaging of objects supported by amorphous substrates using spherical aberration adjustment

High Resolution Electron Microscopy (HREM) is often used to characterize objects supported by amorphous substrates, usually amorphous carbon. HREM is currently undergoing step change in performance due to aberration correctors. This paper examines the aberration corrected imaging of objects supported by amorphous substrates. In particular, we show that a substantial increase in the ratio of the object contrast to the substrate contrast can be achieved by utilizing the strong variation of phase contrast with height, which is present when the spherical aberration has been adjusted to a small value. This variation is examined using the familiar Weak Phase Object Approximation model from which it is determined that the contrast ratio achieves a maximum at a small nonzero value of the spherical aberration. This result is confirmed by multislice modelling which allows for deviations from the Weak Phase Object Approximation and delocalization effects. One important practical result of this study is the need to place the object of interest on the correct side of the amorphous carbon substrate.     

Projected potential profiles across interfaces obtained by reconstructing the exit face wave function from through focal series

An iterative method for reconstructing the exit face wave function from a through focal series of transmission electron microscopy image line profiles across an interface is presented. Apart from high-resolution images recorded with small changes in defocus, this method works also well for a large defocus range as used for Fresnel imaging. Using the phase-object approximation the projected electrostatic as well as the absorptive potential profiles across an interface are determined from this exit face wave function. A new experimental image alignment procedure was developed in order to align images with large relative defocus shift. The performance of this procedure is shown to be superior to other image alignment procedures existing in the literature. The reconstruction method is applied to both simulated and experimental images.     

基于时变图像序列的脉搏信息提取

为获取全面客观的脉诊信息,本文提出一种全新的脉搏信息检测方法-脉搏触觉图像化法。本系统模拟中医脉诊实际,采用软性薄膜加压探头,由单一CCD摄像头采集得到脉搏动态时变图像序列。在算法实现上,从图像整体灰度变化入手,应用图像相关性和图像灰度重心变化分别提取脉搏波形图,并利用图像重心法分析得出不同人在不同取脉压力下的部分脉搏特征。研究结果表明,基于时变图像序列的方法能够有效提取脉搏波的幅度、形态和脉搏频率、节律等信息,为脉搏信息的检测和表征提供了新的手段和方法。     

Averaging of periodic images using a microcomputer

A system based on a commercial microcomputer and a commercial image-capturing TV interface is described which carries out both real space and conventional Fourier transform-based image averaging procedures. Various real space manipulations are described for handling images with either one-dimensional or two-dimensional periodic features. In certain cases, real space averaging procedures have many advantages and are recommended to those not familiar with the mathematics of methods based on Fourier transformation. In other cases Fourier transformation processes are necessary and these also have been implemented on the microcomputer. They can be used to determine periodicities, to produce two-dimensional average images or as a basis for three-dimensional reconstruction. Examples showing the principles of application of these methods use appropriate images from electron micrographs of muscle and collagen.     

Analysis of scanning probe microscope images using wavelets

The utility of wavelet transforms for analysis of scanning probe images is investigated. Simulated scanning probe images are analyzed using wavelet transforms and compared to a parallel analysis using more conventional Fourier transform techniques. The wavelet method introduced in this paper is particularly useful as an image recognition algorithm to enhance nanoscale objects of a specific scale that may be present in scanning probe images. In its present form, the applied wavelet is optimal for detecting objects with rotational symmetry. The wavelet scheme is applied to the analysis of scanning probe data to better illustrate the advantages that this new analysis tool offers. The wavelet algorithm developed for analysis of scanning probe microscope (SPM) images has been incorporated into the WSxM software which is a versatile freeware SPM analysis package.     

Enhancement of confocal microscopy images using Mueller-matrix polarimetry

A simplified procedure based on Mueller-matrix polarimetry has recently been reported as a method of retinal image improvement in a confocal ophthalmoscope [J. M. Bueno et al ., J. Opt. Soc. Am. A 24, 1337 (2007)]. Here, we have applied the technique to imaging static samples providing well-defined reflection properties. The method uses a generator of polarization states in the illumination pathway of a confocal scanning laser system. From the calculated four elements of the Mueller matrix of any sample and instrument combination, the best images defined by different metrics were constructed. For samples with specular, diffuse and mixed reflections, the best-constructed images showed an enhancement in both objective and subjective image quality compared to the original images and those obtained from frame averaging. This technique could improve microscopic imaging in many diverse fields, particularly in biomedical imaging.     

The interpretation of EBIC images using Monte Carlo simulations

Charge collection microscopy, usually known by the acronym EBIC (Electron Beam Induced Current) imaging, is a powerful technique for the observation and characterization of semiconductor materials and devices in the scanning electron microscope. Quantitative interpretation of EBIC images is often difficult because of the problem of accurately representing the electron-beam interaction with the semiconductor. This paper uses a Monte Carlo technique to simulate the electron-beam interaction, and it is shown that this permits simple analytical point-source solutions to be generalized to fully represent the experimental situation of an extended, non-uniform, carrier source. The model is demonstrated by application to EBIC imaging in the Schottky barrier geometry.