Electron tomography using a geometric surface-tangent algorithm: Application to atom probe specimen morphology

Abstract

To adapt electron tomography for the specific study of specimen morphology, a novel reconstruction algorithm is proposed which treats strong intensity gradients in images as arising from the projected edges of surfaces. Images portraying scattering interfaces arising from absorption, elastic, or Fresnel diffraction processes are used to identify edge maps that define the abscissa of projected surface tangents. Differential geometry is used to calculate the shape of these surfaces by considering smooth variations of measured tangent abscissa to infer local tangent intersections. The approach outlined here is not restricted to convex shapes and is designed for cases where morphology is more important than retrieval of the three-dimensional scattering density. The proposed algorithm is tested on simulated data, experimental benchmark specimens of MgO nanoparticles and is then applied to a nanosized atom probe tip, for which the approach here was specifically developed.

Atom probe tomography spatial reconstruction: Status and directions

“…A natural goal would be to re-compute the exact trajectory of each ion based on an atomically-defined specimen inserted within a simulation model, and hence allow overcoming the distortions induced by the simplicity of the projection used in the current paradigm. Haley et al used a finite-element-based electrostatic computation of the distribution of the electric field generated by specimens [101], the shape of which had been extracted, in threedimensions, using electron tomography techniques [102,103]. They discussed the complexity of implementing such methods, which do not account for the detailed atomic structure of the emitting surface (near field).…”

Atom probe trajectory mapping using experimental tip shape measurements

“…The detector to tip mapping may now be performed in a significantly less equivocal manner than before, by utilization of TEM data to augment decision making in the reconstruction process. Although the aluminium system under analysis here is relatively simple in nature, the STOMO method algorithm has been shown to function on more complex specimens, such as TEM data of highly diffracting samples like MgO cubes (Petersen & Ringer, 2009), it is expected that the method should be extensible to arbitrary systems, as it does not rely on the simple evaporation behaviour of aluminium tips.…”

“…All three tilt series were carefully aligned using Fourier transform based phase‐correlation algorithms (Klugin & Hines, 1975) as described elsewhere (Petersen & Ringer, 2009). In this work, we also included corrections for small relative rotations between tilt images using an in‐house script to implement robust correlation‐based (De Castro & Moriandi, 1987) peak finding, which operated on 20 rotations between each image pair in increments of 0.05 ° for the in‐plane angle.…”

“…TEM tomographic methods have been well explored and are regularly utilized in the generation of 3D scalar density fields from 2D images under angle‐independent imaging density assumptions (Frank, 1992; Markoe, 2006). Recently, a surface reconstruction method which utilizes a feature tracking approach to link features between images in a TEM tilt series has been proposed (Petersen & Ringer, 2009), thus estimating their motion vectors and subsequently their position in 3D space. The advantage of this method is that this is more robust under non‐attenuative imaging assumptions (such as the Radon transform) which are critical to back projection methods.…”

“…Recently a local electron tomography algorithm has been developed to measure specimen morphology, referred to as 'STOMO', which is well suited for estimating atom probe tip shapes in three dimensions (Petersen & Ringer, 2009). Hence there exists an opportunity to evaluate the lens action of atom probe specimens using classical electrostatics in three dimensions.…”