Wedge Artifacts Research Articles

Computational Tools to Improve Visualization by Cryo-Electron Tomography

Cryo-electron tomography (CryoET) can directly visualize frozen, hydrated macromolecules inside cells without staining artifacts or fluorescent tags at nanometer resolution. However, imaging tilted specimens is limited to ±60° tilt, causing a “missing wedge” of data that induces smearing artifacts in tomograms. Furthermore, each image is subject to a defocusing artifact known as the contrast transfer function (CTF) of the electron microscope. Lastly, high noise and low contrast make feature identification difficult and error prone. Although contrast is typically improved by denoising (filtering), the tomographic reconstruction process introduces additional artifacts that can be accentuated when filters are applied to tomograms in 3-D.We developed tools for CTF correction in cryoET tiltseries and to fill in the missing wedge. We implemented them in EMAN2, a widely used software package for cryo elctron microscopy data processing. Using our first too, we applied CTF correction on cryoET tiltseries of viral particles of known structure recorded with a direct electron detector (DE20). Images collected in “movie-mode” were first corrected for drift. We achieve a resolution improvement from ∼25A to ∼13A. Our second tool “fills in” the missing wedge with reprojections of tomographic data from angular directions not accessible experimentally in the electron microscope. Results on viral particle data show decreased missing wedge artifacts (smearing). We also applied pre-reconstruction denoising filters directly to 2-D images in tiltseries, which improved the accuracy of automated particle picking (measured against manual particle picking, considered ground truth).Lastly, we applied pre-reconstruction denoising filters to tiltseries of mammalian cells to minimize artifacts and enhance the reliability of feature identification. For example, in platelets, microtubules and the cell membrane become clearer with pre-filtration, compared to the standard post-reconstruction filtering approach, and mitochondria become more easily distinguishable from granules.

Missing wedge computed tomography by iterative algorithm DIRECTT.

A strategy to mitigate typical reconstruction artefacts in missing wedge computed tomography is presented. These artefacts appear as elongations of reconstructed details along the mean direction (i.e. the symmetry centre of the projections). Although absent in standard computed tomography applications, they are most prominent in advanced electron tomography and also in special topics of X-ray and neutron tomography under restricted geometric boundary conditions. We investigate the performance of the DIRECTT (Direct Iterative Reconstruction of Computed Tomography Trajectories) algorithm to reduce the directional artefacts in standard procedures. In order to be sensitive to the anisotropic nature of missing wedge artefacts, we investigate isotropic substructures of metal foam as well as circular disc models. Comparison is drawn to filtered backprojection and algebraic techniques. Reference is made to reconstructions of complete data sets. For the purpose of assessing the reconstruction quality, Fourier transforms are employed to visualize the missing wedge directly. Deficient reconstructions of disc models are evaluated by a length-weighted kernel density estimation, which yields the probabilities of boundary orientations. The DIRECTT results are assessed at different signal-to-noise ratios by means of local and integral evaluation parameters.

Electron tomography image reconstruction using data-driven adaptive compressed sensing.

Electron tomography (ET) is an increasingly important technique for the study of the three-dimensional morphologies of nanostructures. ET involves the acquisition of a set of two-dimensional projection images, followed by the reconstruction into a volumetric image by solving an inverse problem. However, due to limitations in the acquisition process, this inverse problem is ill-posed (i.e., a unique solution may not exist). Furthermore, reconstruction usually suffers from missing wedge artifacts (e.g., star, fan, blurring, and elongation artifacts). Recently, compressed sensing (CS) has been applied to ET and showed promising results for reducing missing wedge artifacts. This uses image sparsity as a priori knowledge to improve the accuracy of reconstruction, and can require fewer projections than other reconstruction techniques. The performance of CS relies heavily on the degree of sparsity in the selected transform domain and this depends essentially on the choice of sparsifying transform. We propose a new image reconstruction algorithm for ET that learns the sparsifying transform adaptively using a dictionary-based approach. We demonstrate quantitatively using simulations from complex phantoms that this new approach reconstructs the morphology with higher fidelity than either analytically based CS reconstruction algorithms or traditional weighted back projection from the same dataset. SCANNING 38:251-276, 2016. © 2015 Wiley Periodicals, Inc.

A multiresolution approach to discrete tomography using DART.

In discrete tomography, a scanned object is assumed to consist of only a few different materials. This prior knowledge can be effectively exploited by a specialized discrete reconstruction algorithm such as the Discrete Algebraic Reconstruction Technique (DART), which is capable of providing more accurate reconstructions from limited data compared to conventional reconstruction algorithms. However, like most iterative reconstruction algorithms, DART suffers from long computation times. To increase the computational efficiency as well as the reconstruction quality of DART, a multiresolution version of DART (MDART) is proposed, in which the reconstruction starts on a coarse grid with big pixel (voxel) size. The resulting reconstruction is then resampled on a finer grid and used as an initial point for a subsequent DART reconstruction. This process continues until the target pixel size is reached. Experiments show that MDART can provide a significant speed-up, reduce missing wedge artefacts and improve feature reconstruction in the object compared with DART within the same time, making its use with large datasets more feasible.

Compressed Sensing Electron tomography using adaptive dictionaries: a simulation study

Electron tomography (ET) is an increasingly important technique for examining the three-dimensional morphologies of nanostructures. ET involves the acquisition of a set of 2D projection images to be reconstructed into a volumetric image by solving an inverse problem. However, due to limitations in the acquisition process this inverse problem is considered ill-posed (i.e., no unique solution exists). Furthermore reconstruction usually suffers from missing wedge artifacts (e.g., star, fan, blurring, and elongation artifacts). Compressed sensing (CS) has recently been applied to ET and showed promising results for reducing missing wedge artifacts caused by limited angle sampling. CS uses a nonlinear reconstruction algorithm that employs image sparsity as a priori knowledge to improve the accuracy of density reconstruction from a relatively small number of projections compared to other reconstruction techniques. However, The performance of CS recovery depends heavily on the degree of sparsity of the reconstructed image in the selected transform domain. Prespecified transformations such as spatial gradients provide sparse image representation, while synthesising the sparsifying transform based on the properties of the particular specimen may give even sparser results and can extend the application of CS to specimens that can not be sparsely represented with other transforms such as Total variation (TV). In this work, we show that CS reconstruction in ET can be significantly improved by tailoring the sparsity representation using a sparse dictionary learning principle.

A simple Fourier filter for suppression of the missing wedge ray artefacts in single-axis electron tomographic reconstructions

The limited specimen tilting range that is typically available in electron tomography gives rise to a region in the Fourier space of the reconstructed object where experimental data are unavailable – the missing wedge. Since this region is sharply delimited from the area of available data, the reconstructed signal is typically hampered by convolution with its impulse response, which gives rise to the well-known missing wedge artefacts in 3D reconstructions. Despite the recent progress in the field of reconstruction and regularization techniques, the missing wedge artefacts remain untreated in most current reconstruction workflows in structural biology. Therefore we have designed a simple Fourier angular filter that effectively suppresses the ray artefacts in the single-axis tilting projection acquisition scheme, making single-axis tomographic reconstructions easier to interpret in particular at low signal-to-noise ratio in acquired projections. The proposed filter can be easily incorporated into current electron tomographic reconstruction schemes.

3D spatial resolution improvement by dual-axis electron tomography: Application to tri-gate transistors

The performance of semiconductor devices can be linked to geometry and variations of the structure. For transistors in particular, the geometry of the gate stack is essential. In this work we investigate the gate stack of a tri-gate transistor using dual-axis electron tomography. This allows the reconstruction of all surfaces of the gate of the transistor with high resolution and measurement of the local thickness of the gate oxide. While previously, dual-axis electron tomography was employed for reducing missing wedge artifacts, our work demonstrates the potential of dual-axis tomography for improving the resolution of a tomographic reconstruction, even for structures not affected by missing wedge artifacts. By simulations and experiments we show the value of dual-axis tomography for characterization of nanoscale devices as an approach that requires no prior information and that can be easily extended even to more than two tilt axes.

Geometric reconstruction methods for electron tomography

Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and non-linear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full 180° tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce and discuss several algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire.

Statistical Comparison of Various Reconstruction Algorithms with respect to Missing Wedge Artifacts in Computed Tomography

ABSTRACTThe presence of elongation, streak and blurring artifacts in tomograms recorded under a missing wedge of rotation angles presents a major challenge for the quantitative analysis of tomographic image data. We show that the missing wedge artifacts of standard reconstruction algorithms may be reduced by the innovative reconstruction technique DIRECTT. For the comparison of missing wedge artifacts we apply techniques from spatial statistics, which have been specifically designed to investigate the shape of phase boundaries in tomograms.

Electron tomography based on a total variation minimization reconstruction technique

The 3D reconstruction of a tilt series for electron tomography is mostly carried out using the weighted backprojection (WBP) algorithm or using one of the iterative algorithms such as the simultaneous iterative reconstruction technique (SIRT). However, it is known that these reconstruction algorithms cannot compensate for the missing wedge. Here, we apply a new reconstruction algorithm for electron tomography, which is based on compressive sensing. This is a field in image processing specialized in finding a sparse solution or a solution with a sparse gradient to a set of ill-posed linear equations. Therefore, it can be applied to electron tomography where the reconstructed objects often have a sparse gradient at the nanoscale. Using a combination of different simulated and experimental datasets, it is shown that missing wedge artefacts are reduced in the final reconstruction. Moreover, it seems that the reconstructed datasets have a higher fidelity and are easier to segment in comparison to reconstructions obtained by more conventional iterative algorithms.

Novel Artifacts Using Simple Geometries for Evaluation of a Gear Measuring Instrument

Evaluating Gear Measuring Instrument (GMI) performance is difficult, even using a master gear, because manufacturing such a gear with the ideal involute form is difficult and accuracy cannot be guaranteed. To evaluate GMI performance, we propose artifacts using simple geometries such as planes, spheres, and cylinders whose form deviates little and that are easier to manufacture than a master gear. We estimated sphere, plane, and cylinder form deviation to be less than 50 nm. For profile evaluation, we developed a Double Ball Artifact (DBA) [1, 2] consisting of a base plate and two spheres. For helix evaluation, we developed a Wedge Artifact (WA) [3, 4] consisting of a plane and sphere. For pitch evaluation, we developed a MultiBall Artifact (MBA) [5, 6] consisting of a plane and multiple spheres. The GMI measures these instead of a gear, and we compared results to mathematical results, with the difference between measured and mathematical results showing GMI measurement capabilities. Evaluation uncertainty is a few hundred nanometers. We present the artifact concept and GMI measurement and evaluation results using these artifacts.

Measuring Porosity at the Nanoscale by Quantitative Electron Tomography

Quantitative electron tomography is proposed to characterize porous materials at a nanoscale. To achieve reliable three-dimensional (3D) quantitative information, the influence of missing wedge artifacts and segmentation methods is investigated. We are presenting the "Discrete Algebraic Reconstruction Algorithm" as the most adequate tomography method to measure porosity at the nanoscale. It provides accurate 3D quantitative information, regardless the presence of a missing wedge. As an example, we applied our approach to nanovoids in La2Zr2O7 thin films.

Artifact Design and Measurement Error Analysis in the Evaluation of Lead Measurement Accuracy of Helical Gear Using Wedge Artifact

The reduction in the vibration and noise of gears is an important issue in mechanical devices such as vehicles and wind turbines. The characteristics of the vibration and noise of gears are markedly affected by deviations of the tooth flank form of micrometer order; therefore, strict quality control of the tooth flank form is required. The accuracy of the lead measurement for a gear-measuring instrument is usually evaluated using a helicoid artifact. However, it is difficult to manufacture it with high accuracy because the helix is a complicated geometrical form. To solve this problem, a method of evaluating a gear-measuring instrument using a wedge artifact, which includes a highly precise plane surface, has been proposed. In this research, to put the wedge artifact into practice, a design method of the wedge artifact is developed. In addition, the effects of the measuring condition and the setting error of the wedge artifact on the measurement result are investigated. The uncertainty for the evaluation method using a wedge artifact is assessed by a measurement experiment and simulation.

Evaluation of instruments for helix measurement using wedge artifact

The degree to which the helix measurement accuracy of a gear measuring instrument (GMI) can be calibrated on the sub-micrometer order is limited when using a gear artifact. We propose a new method conducting GMI accuracy evaluation using a wedge artifact (WA) whose plane is treated as the tooth flank. This paper reports (i) a method of measuring the WA with a GMI, (ii) theoretical equation for calculating geometric deviation between a helicoid generated around a reference cylinder by the GMI and the plane of the WA, (iii) useful equations for designing the WA obtained from an analysis of the theoretical equations, (iv) a method of evaluating the helix measurement accuracy with respect to the obtained result, (v) the effect of the setting accuracy of the WA on the GMI, and (vi) evaluation result of a GMI helix measurement accuracy using a WA which we fabricated. Finally, sub-micrometer evaluation was found to be possible.

Three-Dimensional Analysis of Carbon Nanotube Networks in Interconnects by Electron Tomography without Missing Wedge Artifacts

The three-dimensional (3D) distribution of carbon nanotubes (CNTs) grown inside semiconductor contact holes is studied by electron tomography. The use of a specialized tomography holder results in an angular tilt range of +/-90 degrees , which means that the so-called "missing wedge" is absent. The transmission electron microscopy (TEM) sample for this purpose consists of a micropillar that is prepared by a dedicated procedure using the focused ion beam (FIB) but keeping the CNTs intact. The 3D results are combined with energy dispersive X-ray spectroscopy (EDS) to study the relation between the CNTs and the catalyst particles used during their growth. The reconstruction, based on the full range of tilt angles, is compared with a reconstruction where a missing wedge is present. This clearly illustates that the missing wedge will lead to an unreliable interpretation and will limit quantitative studies.

Three-dimensional electron microscopy of individual nanoparticles

The characterization of nanomaterials with complex three-dimensional (3D) geometries is required to further research and enable the continuing development of nanotechnology. In this manuscript, we report a protocol which combines focused ion beam (FIB) milling, thin film deposition and solution chemistry to optimize a rotation holder for 3D structural and chemical analysis of nanoparticles. This protocol is used to customize the geometry, surface and chemistry of a scanning transmission electron microscope (STEM) or transmission electron microscope (TEM) rotation holder for the nanoparticle system of interest. To illustrate this concept, rotation holder stubs were optimized to facilitate the 3D STEM imaging and analysis of core-shell nanoparticles used for DNA detection. Using this approach, it was possible to characterize the morphology, optoelectronic properties and chemical composition of individual core-shell nanoparticles in 3D. STEM images were captured at regular angular intervals over a complete 360 degrees rotation to eliminate missing wedge artifacts. Electron energy-loss spectroscopy (EELS) spectrum images were acquired intermittently for comparative chemical analysis. This approach allows the 3D STEM/TEM analysis to be performed with the nanoparticle of interest cantilevered over vacuum to minimize substrate effects. Standard tomography techniques were used to reconstruct the 3D structure of the individual nanoparticles from the STEM HAADF rotation series. EELS spectrum imaging was used to determine the local material properties such as composition, band-gap and plasmon energy. The nanoparticle analysis protocol reported here can easily be adapted to facilitate 3D TEM/STEM analysis of other nanomaterial systems.

3136 ウェッジアーティファクトを用いたギヤチェッカー検査法(S34-4 伝動装置の基礎と応用(4) 歯車の形状解析,ラック&ピニオン,その他,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

3136 ウェッジアーティファクトを用いたギヤチェッカー検査法(S34-4 伝動装置の基礎と応用(4) 歯車の形状解析,ラック&ピニオン,その他,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)