The simplest practical method for improving the resolution attainable in TEMs is to take a set of conventional images (as few as 3 or as many as about 50) at different defocus levels (called defocus series) [1 - 4]. These differently aberrated images provide independent information. Based on the recent instrumental [5 - 10] and theoretical [2 - 4, 11 - 14] developments, this method has overcome the difficulties so that the non-linear components of the image intensity (increasing with specimen thickness) can be interpreted, the intensity arising from inelastically scattered electrons can also be interpreted, and at high resolutions the limits of the spatial and temporal coherence due to the range of directions and energies in the illuminating beam in CTEM with LaB6 and W (tungsten) guns has been overcome by introducing FEG-TEM.
Similar to other indirect methods such as tilt azimuth restorations [11 - 12] and holography [15 - 17], focal series restoration has also the advantage of offering both the phase and modulus of the specimen exit plane wave function, free from artifacts, rather than the aberrated image intensity existing in the conventional image.
Recording atomic-resolved images of small clusters is not an easy task, and the 3-D (three-dimensional) determination of atomic structure of nanoclusters is even more challenging. The intrinsic instability of the clusters limits the duration of the TEM observation and the electron beam dosage that can be used. To obtain 3-D information, one needs to take focal series of TEM images in combination with exit wave image reconstructions. [18,19] This method still requires that the nanoclusters stay on the support more than tens of seconds during observation, but this is not applicable for most of small clusters under normal imaging conditions. Electron tomography is capable for 3-D information but again requires a series of images to be taken in different specimen orientations. [20,21]
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