Optimal tilt magnitude determination for aberration-corrected super resolution exit wave function reconstruction

An improved iterative wave function reconstruction algorithm in high-resolution transmission electron microscopy

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.

A quantitative method for measuring small residual beam tilts in high-resolution transmission electron microscopy

In a transmission electron microscope, electron illumination beam tilt, or the degree of deviation of electron beam from its optical axis, is an important parameter that has a significant impact on image contrast and image interpretation. Although a large beam tilt can easily be noticed and corrected by the standard alignment procedure, a small residual beam tilt is difficult to measure and, therefore, difficult to account for quantitatively. Here we report a quantitative method for measuring small residual beam tilts, including its theoretical schemes, numerical simulation testing and experimental verification. Being independent of specimen thickness and taking specimen drifts into account in measurement, the proposed method is supplementary to the existing "rotation center" and "coma-free" alignment procedures. It is shown that this method can achieve a rather good accuracy of 94% in measuring small residual beam tilts of about 0.1° or less.

Atomic resolved phase map of monolayer MoS2 retrieved by spherical aberration-corrected transport of intensity equation

An atomic resolution phase map, which enables us to observe charge distribution or magnetic properties at an atomic scale, has been pointed out to be retrieved by transport of intensity equation (TIE) when taking two atomic-resolved transmission electron microscope (TEM) images of small defocus difference. In this work, we firstly obtained the atomic-resolved phase maps of an exfoliated molybdenum disulfide sheet using spherical aberration-corrected transmission electron microscope. We successfully observed 60° grain boundary of mechanically exfoliated monolayer molybdenum disulfide sheet. The relative phase shift of a single molybdenum atomic column to the column consisting of two sulfur atoms was obtained to be about 0.01 rad on average, which was about half lower than the simulated TIE phase map, indicating that the individual atomic sites can be distinguished qualitatively. The appropriate condition for retrieving atomic-resolved TIE phase maps was briefly discussed.

Advanced electron crystallography through model-based imaging

The increasing need for precise determination of the atomic arrangement of non-periodic structures in materials design and the control of nanostructures explains the growing interest in quantitative transmission electron microscopy. The aim is to extract precise and accurate numbers for unknown structure parameters including atomic positions, chemical concentrations and atomic numbers. For this purpose, statistical parameter estimation theory has been shown to provide reliable results. In this theory, observations are considered purely as data planes, from which structure parameters have to be determined using a parametric model describing the images. As such, the positions of atom columns can be measured with a precision of the order of a few picometres, even though the resolution of the electron microscope is still one or two orders of magnitude larger. Moreover, small differences in average atomic number, which cannot be distinguished visually, can be quantified using high-angle annular dark-field scanning transmission electron microscopy images. In addition, this theory allows one to measure compositional changes at interfaces, to count atoms with single-atom sensitivity, and to reconstruct atomic structures in three dimensions. This feature article brings the reader up to date, summarizing the underlying theory and highlighting some of the recent applications of quantitative model-based transmisson electron microscopy.

Hybridization approach to in-line and off-axis (electron) holography for superior resolution and phase sensitivity

Holography--originally developed for correcting spherical aberration in transmission electron microscopes--is now used in a wide range of disciplines that involve the propagation of waves, including light optics, electron microscopy, acoustics and seismology. In electron microscopy, the two primary modes of holography are Gabor's original in-line setup and an off-axis approach that was developed subsequently. These two techniques are highly complementary, offering superior phase sensitivity at high and low spatial resolution, respectively. All previous investigations have focused on improving each method individually. Here, we show how the two approaches can be combined in a synergetic fashion to provide phase information with excellent sensitivity across all spatial frequencies, low noise and an efficient use of electron dose. The principle is also expected to be widely to applications of holography in light optics, X-ray optics, acoustics, ultra-sound, terahertz imaging, etc.

Determination of aberration center of Ronchigram for automated aberration correctors in scanning transmission electron microscopy

A generic method to determine the aberration center is established, which can be utilized for aberration calculation and axis alignment for aberration corrected electron microscopes. In this method, decentering induced secondary aberrations from inherent primary aberrations are minimized to find the appropriate axis center. The fitness function to find the optimal decentering vector for the axis was defined as a sum of decentering induced secondary aberrations with properly distributed weight values according to the aberration order. Since the appropriate decentering vector is determined from the aberration values calculated at an arbitrary center axis, only one aberration measurement is in principle required to find the center, resulting in /very fast center search. This approach was tested for the Ronchigram based aberration calculation method for aberration corrected scanning transmission electron microscopy. Both in simulation and in experiments, the center search was confirmed to work well although the convergence to find the best axis becomes slower with larger primary aberrations. Such aberration center determination is expected to fully automatize the aberration correction procedures, which used to require pre-alignment of experienced users. This approach is also applicable to automated aperture positioning.

Exceeding conventional resolution limits in high-resolution transmission electron microscopy using tilted illumination and exit-wave restoration

Tilted illumination exit-wave restoration is compared for two aberration-corrected instruments at different accelerating voltages. The experimental progress of this technique is also reviewed and the significance of off-axial aberrations examined. Finally, the importance of higher order aberration compensation combined with careful correction of the lower order aberrations is highlighted.