Geometric reconstruction methods for electron tomography

Alpers, Andreas; Gardner, Richard J.; König, Stefan; Pennington, Robert S.; Boothroyd, Chris; Houben, Lothar; Dunin-Borkowski, Rafal E.; Batenburg, Kees Joost

doi:10.1016/j.ultramic.2013.01.002

Cited by 29 publications

(31 citation statements)

References 51 publications

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“…2,3,40 In the present study, limitations in the available specimen tilt range to 645 would be likely to result in pronounced artefacts in such a reconstruction. 41 Here, on the assumption of cylindrical symmetry (see Sec. III), we inferred the three-dimensional distributions of electrostatic potential and electric field around the needle from the three charge density distributions indicated in Fig.…”

Section: Resultsmentioning

confidence: 99%

Model-independent measurement of the charge density distribution along an Fe atom probe needle using off-axis electron holography without mean inner potential effects

Migunov

London

Farle

et al. 2015

Journal of Applied Physics

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Towards quantitative off-axis electron holographic mapping of the electric field around the tip of a sharp biased metallic needle J. Appl. Phys. 116, 024305 (2014) Model-independent measurement of the charge density distribution along an Fe atom probe needle using off-axis electron holography without mean inner potential effects The one-dimensional charge density distribution along an electrically biased Fe atom probe needle is measured using a model-independent approach based on off-axis electron holography in the transmission electron microscope. Both the mean inner potential and the magnetic contribution to the phase shift are subtracted by taking differences between electron-optical phase images recorded with different voltages applied to the needle. The measured one-dimensional charge density distribution along the needle is compared with a similar result obtained using model-based fitting of the phase shift surrounding the needle. On the assumption of cylindrical symmetry, it is then used to infer the three-dimensional electric field and electrostatic potential around the needle with $10 nm spatial resolution, without needing to consider either the influence of the perturbed reference wave or the extension of the projected potential outside the field of view of the electron hologram. The present study illustrates how a model-independent approach can be used to measure local variations in charge density in a material using electron holography in the presence of additional contributions to the phase, such as those arising from changes in mean inner potential and specimen thickness.

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Section: Resultsmentioning

confidence: 99%

Model-independent measurement of the charge density distribution along an Fe atom probe needle using off-axis electron holography without mean inner potential effects

Migunov

London

Farle

et al. 2015

Journal of Applied Physics

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“…To remedy this problem, the fix probability can be decreased such that noise is also spread over a large random subset of pixels. While this improves the accuracy of DART with noisy projection data to some extent, it does introduce heavy salt and pepper noise, as was also observed in [13].…”

Section: Algorithm Detailsmentioning

confidence: 72%

“…The middle pixel of the kernel is weighted by a smoothing factor b, the other pixels in the kernel are weighted by (1 − b)/8. Although the smoothing is not used in every implementation of DART [13], it is used in the original paper [8]. The process repeats from step 2.…”

Section: Algorithm Detailsmentioning

confidence: 99%

SDART: An algorithm for discrete tomography from noisy projections

Bleichrodt

Tabak

Batenburg

2014

Computer Vision and Image Understanding

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Computed tomography is a noninvasive technique for reconstructing an object from projection data. If the object consists of only a few materials, discrete tomography allows us to use prior knowledge of the gray values corresponding to these materials to improve the accuracy of the reconstruction. The Discrete Algebraic Reconstruction Technique (DART) is a reconstruction algorithm for discrete tomography. DART can result in accurate reconstructions, computed by iteratively refining the boundary of the object. However, this boundary update is not robust against noise and DART does not work well when confronted with high noise levels.In this paper we propose a modified DART algorithm, which imposes a set of soft constraints on the pixel values. The soft constraints allow noise to be spread across the whole image domain, proportional to these constraints, rather than across boundaries. The results of our numerical experiments show that SDART yields more accurate reconstructions, compared to DART, if the signal-to-noise ratio is low.

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“…it is not partially differentiable). In a very recent paper [1] an implementation of this algorithm in Matlab is compared with other geometric reconstruction techniques.…”

Section: Theoremmentioning

confidence: 99%

Reconstruction of hv-Convex Sets by Their Coordinate X-Ray Functions

Nagy

Vincze

2014

J Math Imaging Vis

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R. J. Gardner and M. Kiderlen [17] presented an algorithm for reconstructing convex bodies from noisy X-ray measurements with a full proof of convergence in 2007. We would like to present some new steps into the direction of reconstructing not necessarily convex bodies by the help of the continuity properties of so-called generalized conic functions. Such a function measures the average taxicab distance of the points from a given compact set K ⊂ R N by integration. The basic result [28] is that the generalized conic function associated to a compact planar set determines the coordinate X-rays and vice versa. Cs. Vincze andÁ Nagy [29] proved continuity properties of the mapping which sends connected compact hv-convex sets having the same axis parallel bounding box to the associated generalized conic functions. We use these results to present an algorithm for the reconstruction of compact connected hv-convex planar bodies given by their coordinate X-rays. The basic method is varied with the quota system scheme. Greedy and anti-greedy versions are also presented with examples.

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Geometric reconstruction methods for electron tomography

Cited by 29 publications

References 51 publications

Model-independent measurement of the charge density distribution along an Fe atom probe needle using off-axis electron holography without mean inner potential effects

Model-independent measurement of the charge density distribution along an Fe atom probe needle using off-axis electron holography without mean inner potential effects

SDART: An algorithm for discrete tomography from noisy projections

Reconstruction of hv-Convex Sets by Their Coordinate X-Ray Functions

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