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Computer simulations are utilized to show how to use a transmission electron microscope which has an objective lens with an adjustable coefficient of spherical aberration to determine the three spatial coordinates of a single heavy atom embedded in a crystal. This information can be obtained by forming an image with only those electrons that have been scattered through a large angle by the crystal. By using a high-angle annular dark-field aperture the atoms can be considered as independent scatterers, in contrast with imaging with low-angle coherent scattering. In addition, by reducing the aberration coefficients of the lens, the effective outer radius of the aperture can be made large, thereby leading to a small depth of focus. Calculations show that this form of imaging produces detectable contrast with currently available aberration correctors, sources and detectors. [ABSTRACT FROM AUTHOR]

Quantitative phase maps from Au and polystyrene nanospheres were obtained using the transport of intensity equation approach for phase retrieval in the electron microscope. These were compared to surface plasmon maps, as generated by electron energy loss spectroscopy. Large phase excursions were observed in the vacuum regions surrounding the Au nanospheres, yet not near adjacent polystyrene nanospheres. It is proposed that these phase excursions are associated with surface plasmon excitation. These results suggest that phase retrieval offers an alternative means for sensing and interpreting the optical response of nanostructured metals. [ABSTRACT FROM AUTHOR]

The s-state approach is useful for analysing transmission electron microscope images of a thin crystalline foil consisting of well-separated atomic columns. It assumes that the signal collected (e.g., the annular dark-field image, the EELS spectrum) can be attributed to only the lowest-energy bound eigenstate of the two-dimensional projected potential of a single column. When, however, columns are close, the form of the bound states depends on more than one column, which implies that interpretation of the signal may not be so simple. For closely spaced columns we show that the simple s-state approach fails for the case of a sub-Angstrom probe initially centred on one column of a pair, because two bound states are excited. The energy in the probe is almost completely transferred to the neighbouring column after it has propagated some tens of nanometres through the foil and then is transferred back. Signals which relate directly to the local probe intensity (e.g. annular dark-field formed by thermal diffuse scattering, EELS) must be analysed in terms of the two bound states. Accurate calculations of bound states of pairs of columns are more demanding than for a single column but sufficient accuracy can be achieved from knowledge of the 1s-states of isolated columns. We provide formulae for the bound states of a column pair. These can be used to determine if image analysis requires the extension to the s-state approach described in this paper.