Abstract: This paper discusses the possibility of retrieving the electron distribution (with highlighted valence electron distribution information) of materials from recorded HREM images. This process can be achieved by solving two inverse problems: reconstruction of the exit wave and reconstruction of the electron distribution from exit waves. The first inverse problem can be solved using a focal series reconstruction method. We show that the second inverse problem can be solved by combining a series of exit waves recorded at different thickness conditions. This process is designed based on an improved understanding of the dynamical scattering process. It also explains the fundamental difficulty of obtaining the valence electron distribution information and the basis of our solution.

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: In thispaperweinvestigatewhichprobesizemaximizesthethroughputwhenmeasuringtheradiusof nanoparticlesinhighangleannulardarkfieldscanningtransmissionelectronmicroscopy(HAADFSTEM). The sizeandthecorrespondingcurrentoftheelectronprobedeterminetheprecisionoftheestimateofa particlesradius.Maximizingthroughputmeansthatamaximumnumberofparticlesshouldbeimaged withinagiventimeframe,sothataprespecifiedprecisionisattained.WeshowthatBayesianstatistical experimentaldesignisaveryusefulapproachtodeterminetheoptimalprobesizeusingacertainamount of priorknowledgeaboutthesample.Thedependenceoftheoptimalprobesizeonthedetectorgeometry and thediameter,variabilityandatomicnumberoftheparticlesisinvestigated.Anexpressionforthe optimalprobesizeintheabsenceofanykindofpriorknowledgeaboutthespecimenisderivedaswell.

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: In order to interpret the amplitude and phase of the exit wave in terms of mass and position of the atoms, one has to invert the dynamic scattering of the electrons in the object so as to obtain a starting structure which can then be used as a seed for further quantitative structure refinement. This is especially challenging in case of a zone axis condition when the interaction of the electrons with the atom column is very strong. Based on the channelling theory we will show that the channelling map not only yields a circle on the Argand plot but also a circular defocus curve for every column. The former gives the number of atoms in each column, while the latter provides the defocus value for each column, which reveals the surface roughness at the exit plane with single atom sensitivity.

Abstract: A model-based method is proposed to relatively quantify the chemical composition of atomic columns using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images. The method is based on a quantification of the total intensity of the scattered electrons for the individual atomic columns using statistical parameter estimation theory. In order to apply this theory, a model is required describing the image contrast of the HAADF STEM images. Therefore, a simple, effective incoherent model has been assumed which takes the probe intensity profile into account. The scattered intensities can then be estimated by fitting this model to an experimental HAADF STEM image. These estimates are used as a performance measure to distinguish between different atomic column types and to identify the nature of unknown columns with good accuracy and precision using statistical hypothesis testing. The reliability of the method is supported by means of simulated HAADF STEM images as well as a combination of experimental images and electron energy-loss spectra. It is experimentally shown that statistically meaningful information on the composition of individual columns can be obtained even if the difference in averaged atomic number Z is only 3. Using this method, quantitative mapping at atomic resolution using HAADF STEM images only has become possible without the need of simultaneously recorded electron energy loss spectra.

Abstract: A non-destructive method for measuring the thickness of thin amorphous films composed of light elements has been developed. The method employs the statistics of the phase of the electron exit wave function. The accuracy of this method has been checked numerically by the multislice method and compared with that based on the mean inner potential.

Abstract: Using a combination of electron holography and energy filtering, interference fringes produced after inelastic interaction of electrons with hydrogen molecules are examined. Surprisingly, the coherence of inelastic scattering increases when moving from the surface of a hydrogen-containing bubble to the vacuum. This phenomenon can be understood in terms of the Feynman two-slit thought experiment with a variable ambiguity of the which-way registration. (C) 2006 Elsevier B.V. All rights reserved.

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: A theoretical framework is described to understand the results of plasmon holography experiments leading to insight in the meaning of the experimental results and pointing out directions for future experiments. The framework is based on the formalism of mutual intensity to describe how coherence is transferred through an optical system. For the inelastic interaction with the object, an expression for the volume. plasmon excitations in a free electron gas is used as a model for the behaviour of aluminium. The formalism leads to a clear graphical intuitive tool for under-standing the experiments. It becomes evident that the measured coherence is solely related to the angular distribution of the plasmon scattering in the case of bulk plasmons. After describing the framework, the special case of coherence outside a spherical particle is treated and the seemingly controversial idea of a plasmon with a limited coherence length obtained front experiments is clarified. (C) 2004 Elsevier B.V. All rights reserved.