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Tomography for HAADF-STEM


the recording scheme. The impact of the CTFS can further be understood by considering the Fourier transform of a reconstructed tomogram. In the case of the tilt series ( Figure 5a ), sharp streaks are present corresponding to the tilt directions. T e missing wedge eff ect is also clearly visible, and the sequential algebraic reconstruction technique (SART) algorithm used to compute the tomogram can reconstruct almost no information in the missing wedge region. In the case of the CTFS method ( Figure 5b ), the streaks corresponding to the tilt directions are less pronounced and spread over an angular region equal to the beam-opening angle, so additional information is present between the tilt directions. T e missing wedge is still present in the CTFS recording, but in the central vertical region low spatial frequency signal components are now present (orange arrow).


Discussion


Alternative approaches exist to reduce axial elongation for situations with a very limited tilt range using prior knowledge reconstructions. Making the assumption that the gradient of the reconstruction volume is sparse, one can formulate reconstruction algorithms that generate only a fi nite number of diff erent gray values, for example discrete algebraic reconstruction technique (DART) [ 23 ] or compressed sensing approaches [ 24 ]. These approaches are independent of the CTFS recording scheme. We expect that new algorithms using a sparse gradient assumption for the reconstruction of CTFS data will be developed in the future.


Conclusion


For the imaging of thick samples of 0.5 µm or more, the HAADF-STEM mode is a powerful alternative to conventional TEM. Because aberration-corrected STEM images have a very limited DOF, tilt-series STEM tomography can be supple- mented by depth sectioning. T is approach helps to gather 3D information, particularly in situations where the accessible tilt range is very limited, as it is typically the case for very thick specimens. T e recording scheme is called CTFS and consists of a tilt series, where for each tilt direction an entire focal series is recorded. Reconstructions from CTFS data were reconstructed using an iterative reconstruction algorithm that considered the convergent nature of the electron beam in the forward model. T e CTFS led to a signifi cant reduction of the axial elongation, a signifi cant reduction of the missing wedge eff ect, and a better representation of the 3D shape of objects in the sample.


Acknowledgements T is research was partially funded by the European Research Project NOTOX (FP7-267038) and the DFG grant IMCL (AOBJ: 600875). T e authors thank Eduard Arzt for his support through INM and the DFKI GmbH for additional funding. T e authors acknowledge the electron microscopy supported by the Materials Sciences and Engineering Division, Basic Energy Sciences, Offi ce of Science, U.S. Department of Energy (ARL), using instru- mentation at the Oak Ridge National Laboratory’s Center for Nanophase Materials Sciences (CNMS), which is sponsored by the Scientifi c User Facilities Division, Offi ce of Basic Energy Sciences, U.S. Department of Energy, as well as the electron microscopy support provided by the Karlsruhe Nano Micro Facility (KNMF), a Helmholtz large-scale user facility operated at the Karlsruhe Institute of Technology (KIT).


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