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Whether or not the 3-dimensional surface morphologies of a crystal sample can be reconstructed at atomic-scale from a single 2-dimensional image becomes an interesting issue in high-resolution transmission electron microscopy, after the work by Jia et al. [1]. Here we propose an improved and self-validated algorithm to enhance such an electron tomography method and to make it applicable to more general crystal surfaces even with thin amorphous layers. Our study shows that a resolution in the beam (z) direction and a confidence level have to be defined and estimated after performing tomographic reconstruction in order to evaluate the quality and the reliability of its result. Applying the proposed procedure to the Si[110] image to recover the surface morphologies of a silicon crystal with amorphous contamination, the obtained results show that an atomic-resolution of 0.384 nm in the z-direction and a high confidence level of 95% are achieved for imaging the Si-surface structures, quantitatively described by tomographic parameters, i.e., the height (defocus) and the thickness (atom number) of Si-atomic columns., (Copyright © 2019 Elsevier B.V. All rights reserved.)

Exit wavefunction reconstruction is a powerful image processing technique to enhance the resolution and the signal-to-noise ratio for atomic-resolution imaging in both aberration uncorrected and corrected transmission electron microscopes. The present study aims to improve the performance of the iterative wavefunction reconstruction algorithm in comparison not only with its conventional form but also with the popular commercial Trueimage software for exit wavefunction reconstruction. It is shown that by implementing a wave propagation procedure for refining its image alignment, the iterative wavefunction reconstruction algorithm can be greatly improved in accurately retrieving the wavefunctions while keeping its original advantages, which allow the reconstruction be performed with less images and a larger defocus step in the data set of through-focus image series. In addition, calculations of this algorithm can be accelerated drastically by the graphic processing unit (GPU) hardware programming using the popular computer unified device architecture language, whose computing speed can be 25-38 times as fast as a central processing unit (CPU) program., (Copyright © 2018. Published by Elsevier B.V.)

Three different types of multislice algorithms, namely the conventional multislice (CMS) algorithm, the propagator-corrected multislice (PCMS) algorithm and the fully-corrected multislice (FCMS) algorithm, have been evaluated in comparison with respect to the accelerating voltages in transmission electron microscopy. Detailed numerical calculations have been performed to test their validities. The results show that the three algorithms are equivalent for accelerating voltage above 100kV. However, below 100 kV, the CMS algorithm will introduce significant errors, not only for higher-order Laue zone (HOLZ) reflections but also for zero-order Laue zone (ZOLZ) reflections. The differences between the PCMS and FCMS algorithms are negligible and mainly appear in HOLZ reflections. Nonetheless, when the accelerating voltage is further lowered to 20 kV or below, the PCMS algorithm will also yield results deviating from the FCMS results. The present study demonstrates that the propagation of the electron wave from one slice to the next slice is actually cross-correlated with the crystal potential in a complex manner, such that when the accelerating voltage is lowered to 10 kV, the accuracy of the algorithms is dependent of the scattering power of the specimen., (© 2013 Elsevier B.V. All rights reserved.)