Automated high-throughput electron tomography by pre-calibration of image shifts

Electron tomography is a versatile method for obtaining three‐dimensional (3D) images with transmission electron microscopy. The technique is suitable to investigate cell organelles and tissue sections (100–500 nm thick) with 4–20 nm resolution. 3D reconstructions are obtained by processing a series of images acquired with the samples tilted over different angles. While tilting the sample, image shifts and defocus changes of several µm can occur. The current generation of automated acquisition software detects and corrects for these changes with a procedure that incorporates switching the electron optical magnification. We developed a novel method for data collection based on the measurement of shifts prior to data acquisition, which results in a five‐fold increase in speed, enabling the acquisition of 151 images in less than 20 min. The method will enhance the quality of a tilt series by minimizing the amount of required focus‐change compensation by aligning the optical axis to the tilt axis of the specimen stage. The alignment is achieved by invoking an amount of image shift as deduced from the mathematical model describing the effect of specimen tilt. As examples for application in biological and materials sciences 3D reconstructions of a mitochondrion and a zeolite crystal are presented.     

Automatic focus correction for spot-scan imaging of tilted specimens.

The variation in defocus within an image of a highly tilted specimen can be a serious source of artifact. Spot-scan imaging can be combined with dynamic focusing to greatly reduce this range of defocus. A protocol is described for determining the parameters required for the automatic focus compensation during the recording of a spot-scan image. Images of a gold test specimen demonstrate the efficacy of this procedure in extending the area of the image that contains high-quality data. In case the tilt angle or resolution is high enough that the height difference of the specimen within each small illuminated area is larger than the depth of field, the image must be treated to compensate for the focus variation. The same principle is used as was developed for compensation of conventional images of tilted specimens.     

Microscopic tomography with ultra-HVEM and applications

The ultra-HVEM with an accelerating voltage of 3 MV at Osaka University is capable of achieving excellent penetration and resolution for thick specimens. We obtained images of 5-microm-thick slices tilted at angles of up to 70 degrees for biological samples and observed stick-shaped samples of Si devices free from missing zone. These features make the ultra-HVEM an invaluable extension of 3D observation by electron tomography. In this paper, we introduce aspects of ultra-HVEM tomography; specifically, the magnification, the amount of image blurring for thick samples and the electron staining method. Finally, we give some typical applications in the fields of cell biology, pathology and electrical engineering.     

Multiscale iterative voting for differential analysis of stress response for 2D and 3D cell culture models

Focused ion beam-scanning electron microscope (FIB-SEM) tomography is a powerful application in obtaining three-dimensional (3D) information. The FIB creates a cross section and subsequently removes thin slices. The SEM takes images using secondary or backscattered electrons, or maps every slice using X-rays and/or electron backscatter diffraction patterns. The objective of this study is to assess the possibilities of combining FIB-SEM tomography with cathodoluminescence (CL) imaging. The intensity of CL emission is related to variations in defect or impurity concentrations. A potential problem with FIB-SEM CL tomography is that ion milling may change the defect state of the material and the CL emission. In addition the conventional tilted sample geometry used in FIB-SEM tomography is not compatible with conventional CL detectors. Here we examine the influence of the FIB on CL emission in natural diamond and the feasibility of FIB-SEM CL tomography. A systematic investigation establishes that the ion beam influences CL emission of diamond, with a dependency on both the ion beam and electron beam acceleration voltage. CL emission in natural diamond is enhanced particularly at low ion beam and electron beam voltages. This enhancement of the CL emission can be partly explained by an increase in surface defects induced by ion milling. CL emission enhancement could be used to improve the CL image quality. To conduct FIB-SEM CL tomography, a recently developed novel specimen geometry is adopted to enable sequential ion milling and CL imaging on an untilted sample. We show that CL imaging can be manually combined with FIB-SEM tomography with a modified protocol for 3D microstructure reconstruction. In principle, automated FIB-SEM CL tomography should be feasible, provided that dedicated CL detectors are developed that allow subsequent milling and CL imaging without manual intervention, as the current CL detector needs to be manually retracted before a slice can be milled. Due to the required high electron beam acceleration voltage for CL emission, the resolution for FIB-SEM CL tomography is currently limited to several hundreds of nm in XY and up to 650 nm in Z for diamonds. Opaque materials are likely to have an improved Z resolution, as CL emission generated deeper in the material is not able to escape from it.     

A novel method for focus assessment in atomic resolution STEM HAADF experiments

Analysis of the Fourier components of through-focal images in scanning transmission electron microscopy with a high angle annular dark field detector is used to assess illumination defocus values. The method is based on a least squares fitting of the peculiar dependence of Fourier components of the high angle annular dark field image on defocus. The validity of the method has been checked against simulations and experiments obtaining a good level of accuracy on the defocus measurement (δf=2 nm) for simulated specimen thickness up to 40 nm. The difference between simulated and experimental Fourier coefficients for large defoci can be used to estimate the specimen thickness at least up to 30 nm but with decreasing precision for larger thickness.     

Imaging a dense nanodot assembly by phase retrieval from TEM images

Phase retrieval is a classical inverse problem in many fields dealing with waves that is becoming of increasing interest in transmission electron microscopy (TEM). A non-interferometric approach is here applied to TEM images. Phase retrieval possibilities given by the transport intensity equation are compared to the ones deriving from the weak phase object approximation. In the limit of small angles, both methods lead to a similar equation between the phase and a set of defocus images. This equation can be solved by an image processing equivalent to using a specific filter in Fourier space. This processing leads to phase images with a spatial resolution here essentially limited by the defocus amount between images. A dense assembly of silicon nanodots is used as a model case to illustrate the interest of this approximate phase retrieval method which can be carried out on standard equipment. The dot heights estimated using the phase images are found to be in good agreement with ones measured by atomic force microscopy. Since image noise and large defocus values may strongly affect the solution given by the approximate method, an iterative phase retrieval method is also used as a test for working conditions.     

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.     

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.     

Calibration method of tilt and azimuth angles for alignment of TEM tomographic tilt series

This paper describes the calibration method of the tilt and azimuth angles of specimen using a digital protractor and a laser autocollimator for alignment of electron tomography. It also suggests an easy method to check whether the specimen is tilted by 180.0°, and whether the azimuth angle is 0.0°; the method involves the use of two images of a rod-shaped specimen collected before and after a 180.0° tilt. The method is based on the assumption that these images are symmetric about the tilt axis when the azimuth angle is 0.0°. In addition, we used an experiment to demonstrate the effect of the incorrect angles on reconstructed images and simulated the image quality against distance away from tilt axis.     

Automatic TEM image alignment by trifocal geometry

Here we propose a novel method for automatic, markerless, feature‐based alignment of TEM images suitable for electron tomography. The proposed method, termed trifocal alignment, is more accurate than the previous markerless methods. The key components developed are: (1) a reliable multi‐resolution algorithm for matching feature points between images; (2) a robust, maximum‐likelihood‐based estimator for determining the geometry of three views – the trifocal constraint – required for validating the correctness of the matches; and (3) a robust, large‐scale optimization framework to compute the alignment parameters from hundreds of thousands of feature point measurements from a few hundred images. The ability to utilize such a large number of measurements successfully compensates for point localization errors. The method was experimentally confirmed with electron tomography tilt series of biological and material sciences samples, consisting of from 40 to 150 images. The results show that, with this feature‐based alignment approach, a level of accuracy comparable with fiducial marker alignment can be achieved.     

CTF determination and correction in electron cryotomography

Electron cryotomography (cryoET) has the potential to elucidate the structure of complex biological specimens at molecular resolution but technical and computational improvements are still needed. This work addresses the determination and correction of the contrast transfer function (CTF) of the electron microscope in cryoET. Our approach to CTF detection and defocus determination depends on strip-based periodogram averaging, extended throughout the tilt series to overcome the low contrast conditions found in cryoET. A method for CTF correction that deals with the defocus gradient in images of tilted specimens is also proposed. These approaches to CTF determination and correction have been applied here to several examples of cryoET of pleomorphic specimens and of single particles. CTF correction is essential for improving the resolution, particularly in those studies that combine cryoET with single particle averaging techniques.     

Automated detection of fluorescent cells in in‐resin fluorescence sections for integrated light and electron microscopy

Integrated array tomography combines fluorescence and electron imaging of ultrathin sections in one microscope, and enables accurate high‐resolution correlation of fluorescent proteins to cell organelles and membranes. Large numbers of serial sections can be imaged sequentially to produce aligned volumes from both imaging modalities, thus producing enormous amounts of data that must be handled and processed using novel techniques. Here, we present a scheme for automated detection of fluorescent cells within thin resin sections, which could then be used to drive automated electron image acquisition from target regions via ‘smart tracking’. The aim of this work is to aid in optimization of the data acquisition process through automation, freeing the operator to work on other tasks and speeding up the process, while reducing data rates by only acquiring images from regions of interest. This new method is shown to be robust against noise and able to deal with regions of low fluorescence.     

Simulation of transmission electron microscope images of biological specimens

We present a new approach to simulate electron cryo‐microscope images of biological specimens. The framework for simulation consists of two parts; the first is a phantom generator that generates a model of a specimen suitable for simulation, the second is a transmission electron microscope simulator. The phantom generator calculates the scattering potential of an atomic structure in aqueous buffer and allows the user to define the distribution of molecules in the simulated image. The simulator includes a well defined electron–specimen interaction model based on the scalar Schrödinger equation, the contrast transfer function for optics, and a noise model that includes shot noise as well as detector noise including detector blurring. To enable optimal performance, the simulation framework also includes a calibration protocol for setting simulation parameters. To test the accuracy of the new framework for simulation, we compare simulated images to experimental images recorded of the Tobacco Mosaic Virus (TMV) in vitreous ice. The simulated and experimental images show good agreement with respect to contrast variations depending on dose and defocus. Furthermore, random fluctuations present in experimental and simulated images exhibit similar statistical properties. The simulator has been designed to provide a platform for development of new instrumentation and image processing procedures in single particle electron microscopy, two‐dimensional crystallography and electron tomography with well documented protocols and an open source code into which new improvements and extensions are easily incorporated.     

Comparing electron tomography and HRTEM slicing methods as tools to measure the thickness of nanoparticles

Nanoparticles’ morphology is a key parameter in the understanding of their thermodynamical, optical, magnetic and catalytic properties. In general, nanoparticles, observed in transmission electron microscopy (TEM), are viewed in projection so that the determination of their thickness (along the projection direction) with respect to their projected lateral size is highly questionable. To date, the widely used methods to measure nanoparticles thickness in a transmission electron microscope are to use cross-section images or focal series in high-resolution transmission electron microscopy imaging (HRTEM “slicing”). In this paper, we compare the focal series method with the electron tomography method to show that both techniques yield similar particle thickness in a range of size from 1 to 5 nm, but the electron tomography method provides better statistics since more particles can be analyzed at one time. For this purpose, we have compared, on the same samples, the nanoparticles thickness measurements obtained from focal series with the ones determined from cross-section profiles of tomograms (tomogram slicing) perpendicular to the plane of the substrate supporting the nanoparticles. The methodology is finally applied to the comparison of CoPt nanoparticles annealed ex situ at two different temperatures to illustrate the accuracy of the techniques in detecting small particle thickness changes.     

Dynamic focussing for recording images from tilted samples in small-spot scanning with a transmission electron microscope

For three-dimensional electron microscopical structure research the specimen must be imaged in a tilted position. Specimen tilt is also often needed to achieve an optimal molecular packing orientation. The tilt with respect to the optical axis causes a defocus gradient alongside the imaged area and thus entails the following complications: (1) The phase-contrast transfer function fades for strong defocus; (2) the Fourier coefficients are split; and (3) the signal-to-noise ratio cannot be enhanced by simple averaging. An image procedure with small-spot scanning and simultaneous defocus compensation is proposed which helps to reduce these problems.     

Essential experimental parameters for quantitative structure analysis using spherical aberration-corrected HAADF-STEM

The accuracy of quantitative analysis for Z-contrast images with a spherical aberration (C_s) corrected high-angle annular dark-field (HAADF) scanning transmission electron microscope (STEM) using SrTiO₃(0 0 1) was systematically investigated. Atomic column and background intensities were measured accurately from the experimental HAADF-STEM images obtained under exact experimental condition. We examined atomic intensity ratio dependence on experimental conditions such as defocus, convergent semi-angles, specimen thicknesses and digitalized STEM image acquisition system: brightness and contrast. In order to carry out quantitative analysis of C_s-corrected HAADF-STEM, it is essential to determine defocus, to measure specimen thickness and to fix setting of brightness, contrast and probe current. To confirm the validity and accuracy of the experimental results, we compared experimental and HAADF-STEM calculations based on the Bloch wave method.     

A robust focusing and astigmatism correction method for the scanning electron microscope

This paper discusses a new approach to focusing and astigmatism correction based on the fast fourier transforms (FFTs) of scanning electron microscopy (SEM) images. From the FFTs, it is possible to obtain information on the severity of the defocus and astigmatism. This information is then processed by an algorithm to perform real-time focusing and astigmatism correction on the SEM. The algorithm has been tested on defocused and astigmatic images of different samples, including those with highly directional features. Experiments show that the images obtained after running the algorithm can be as good as those that an experienced SEM operator can achieve.     

Improved Zernike‐type phase contrast for transmission electron microscopy

Zernike phase contrast has been recognized as a means of recording high‐resolution images with high contrast using a transmission electron microscope. This imaging mode can be used to image typical phase objects such as unstained biological molecules or cryosections of biological tissue. According to the original proposal discussed in Danev and Nagayama (2001) and references therein, the Zernike phase plate applies a phase shift of π/2 to all scattered electron beams outside a given scattering angle and an image is recorded at Gaussian focus or slight underfocus (below Scherzer defocus). Alternatively, a phase shift of ‐π/2 is applied to the central beam using the Boersch phase plate. The resulting image will have an almost perfect contrast transfer function (close to 1) from a given lowest spatial frequency up to a maximum resolution determined by the wave length, the amount of defocus and the spherical aberration of the microscope. In this paper, I present theory and simulations showing that this maximum spatial frequency can be increased considerably without loss of contrast by using a Zernike or Boersch phase plate that leads to a phase shift between scattered and unscattered electrons of only π /4, and recording images at Scherzer defocus. The maximum resolution can be improved even more by imaging at extended Scherzer defocus, though at the cost of contrast loss at lower spatial frequencies.     

A new method for the determination of the wave aberration function for high-resolution TEM.; 2. Measurement of the antisymmetric aberrations

A new method is presented for the determination of the antisymmetric coefficients of the wave aberration function from a tableau of tilted illumination images. The approach is based on measurements of the apparent defocus and two-fold astigmatism using a phase correlation function and phase contrast index calculated from a short focus series acquired at each tilt. This method is shown to be suitable for a wide range of specimens and is sufficiently accurate for exit plane wave restoration at 0.1 nm resolution. Experimental examples of this approach are provided and the method is compared to results obtained from measurements of conventional power spectra.