Physically motivated global alignment method for electron tomography

Abstract

Electron tomography is widely used for nanoscale determination of 3-D structures in many areas of science. Determining the 3-D structure of a sample from electron tomography involves three major steps: acquisition of sequence of 2-D projection images of the sample with the electron microscope, alignment of the images to a common coordinate system, and 3-D reconstruction and segmentation of the sample from the aligned image data. The resolution of the 3-D reconstruction is directly influenced by the accuracy of the alignment, and therefore, it is crucial to have a robust and dependable alignment method. In this paper, we develop a new alignment method which avoids the use of markers and instead traces the computed paths of many identifiable 'local' center-of-mass points as the sample is rotated. Compared with traditional correlation schemes, the alignment method presented here is resistant to cumulative error observed from correlation techniques, has very rigorous mathematical justification, and is very robust since many points and paths are used, all of which inevitably improves the quality of the reconstruction and confidence in the scientific results.

Recovering fine details from under-resolved electron tomography data using higher order total variationℓ1regularization

“…Our interest in this paper is the aforementioned 1 regularization that encourages sparsity of f in some appropriate domain by setting the regularization term to T f 1 , where T is the linear transformation under which the solution is assumed to be sparse. Most commonly in electron tomography is to choose the regularization term as the TV norm [19,25,15,30], which is equivalent to the first order finite difference operator that maps f to the differences between all adjacent pixels.…”

MoS2 Thin Films for Photo-Voltaic Applications

“…The elastic modulus E can be estimated using Eq. (4); having Eeff as effective reduced elastic modulus of the system in array film/substrate, contact area is determinate by A as function of the penetration depth, ν is the Poisson ratio, t represents film thickness, and α is a parameter which depends on the material and the indenter geometry, in our case a pyramidal shape, as described by Domínguez-Rios et al [29] and Hurtado-Macias et al [30]. 4By using CSM method, it is was possible to estimate elastic modulus and hardness values as follows: Three regions of test are observed in the Figures 12 and 13, where region I is hardness values for MoS 2 crystallites with penetration depth of 0-90 nm, having no influence from silicon oxide substrate and a hardness value of H = 6.0 ± 0.1 GPa and elastic modulus of E = 136 ± 2 GPa.…”

Automatic alignment for three-dimensional tomographic reconstruction

“…non-truncated projection data. Hence, they are -strictly speaking -not applicable to region-of-interest tomography, although necessary conditions [11] and heuristic adaptations [33] have been proposed recently. Local consistency conditions can also be defined in some cases, e.g.…”