Abstract: 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.

Abstract: Thermal diffuse scattered electrons significantly contribute to high-resolution transmission electron microscopy images. Their intensity adds to the background and is peaked at positions of atomic columns. In this paper we suggest an approximation to simulate intensity of thermal diffuse scattered electrons in plane-wave illumination transmission electron microscopy using an emission-potential multislice algorithm which is computationally less intensive than the frozen lattice approximation or the mutual intensity approach. Intensity patterns are computed for Au and InSb for different crystal orientations. These results are compared with intensities from the frozen lattice approximation based on uncorrelated vibration of atoms as well as with the frozen phonon approximation for Au. The frozen phonon method uses a detailed phonon model based on force constants we computed by a density functional theory approach. The comparison shows that our suggested emission-potential method is in close agreement with both the frozen lattice and the frozen phonon approximations.

Abstract: Using the combination of an electron biprism and an energy filter, the coherence distribution in an inelastically scattered wave-field is measured. It is found that the degree of coherence decreases rapidly with increasing distance between two superimposed points in the object, and with increasing energy-loss. In a Si sample, coherence of plasmon scattering increases in vacuum with the distance from the edge of the sample. (c) 2006 Published by Elsevier B.V.

Abstract: In this paper, it has been investigated how to measure atom column positions as accurately and precisely as possible using a focal series of images. In theory, it is expected that the precision would considerably improve using a maximum likelihood estimator based on the full series of focal images. As such, the theoretical lower bound on the variances of the unknown atom column positions can be attained. However, this approach is numerically demanding. Therefore, maximum likelihood estimation has been compared with the results obtained by fitting a model to a reconstructed exit wave rather than to the full series of focal images. Hence, a real space model-based exit wave reconstruction technique based on the channelling theory is introduced. Simulations show that the reconstructed complex exit wave contains the same amount of information concerning the atom column positions as the full series of focal images. Only for thin samples, which act as weak phase objects, this information can be retrieved from the phase of the reconstructed complex exit wave.

Abstract: Source size broadening is an important resolution limiting effect in modern STEM experiments. Here, we propose an alternative method to measure the source size broadening making use of a holographic biprism to create interference patterns in an empty Ronchigram. This allows us to measure the exact shape of the source size broadening with a much better sampling than previously possible. We find that the shape of the demagnified source deviates considerably from a Gaussian profile that is often assumed. We fit the profile with a linear combination of a Gaussian and a bivariate Cauchy distribution showing that even though the full width at half maximum is similar to previously reported measurements, the tails of the profile are considerable wider. This is of fundamental importance for quantitative comparison of STEM simulations with experiments as these tails make the image contrast dependent on the interatomic distance, an effect that cannot be reproduced by a single Gaussian profile of fixed width alone.

Abstract: Inelastic image simulation software is presented, implementing the double channeling approximation which takes into account the combination of multiple elastic and single inelastic scattering in a crystal. The approach is described with a density matrix formalism. Two applications in high resolution energy filtered (EFTEM) transmission electron microscopy (TEM) images are presented: thickness-defocus maps for SrTiO3 and exit plane intensities for an (LaAlO3)3(SrTiO3)3 multilayer system. Both systems show a severe breakdown in direct interpretability which becomes worse for higher acceleration voltages, thicker samples and lower excitation edge energies. Since this effect already occurs in the exit plane intensity, it is a fundamental limit and image simulations in EFTEM are indispensable just as they are indispensable for elastic high resolution TEM images.

Abstract: A straightforward application of the theoretical framework presented by Verbeeck et al. [Ultramicroscopy 102 (2005) 239] is presented to explain the energy-filtered electron-diffracted beam holography experiments published by Herring [Ultramicroscopy 104 (2005) 261]. It is shown that the theory is in agreement with all experimental findings, which leads to the interpretation that the experiments are mainly measuring the angular coherence of the source image rather than exposing details on the coherence properties of inelastic scattering. A change in experimental parameters is proposed, which could result in interesting information about the coherence in all inelastic scattering process. (c) 2006 Elsevier B.V. All rights reserved.

Abstract: A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has different effects on the transfer of the linear and non-linear terms, such that the non-linear imaging contributions are damped less than the linear imaging contributions at high spatial frequencies. This will be important when coherent aberrations such as spherical aberration and defocus are reduced.

Abstract: Reconstructed exit waves are useful to quantify unknown structure parameters such as the position and composition of the atom columns at atomic scale. Existing techniques provide a complex wave in a flat plane which is close to the plane where the electrons leave the atom columns. However, due to local deviation in the flatness of the exit surface, there will be an offset between the plane of reconstruction and the actual exit of a specific atom column. Using the channelling theory, it has been shown that this defocus offset can in principle be determined atom column-by-atom column. As such, the surface roughness could be quantified at atomic scale. However, the outcome strongly depends on the initial plane of reconstruction especially in a crystalline structure. If this plane is further away from the true exit, the waves of the atom columns become delocalized and interfere mutually which strongly complicates the interpretation of the exit wave in terms of the local structure. In this paper, we will study the delocalization with defocus using the channelling theory in a more systematic way.