Simulation-Trained Sparse Coding for High-Precision Phase Imaging in Low-Dose Electron Holography

Noise reduction of electron holography observations for a thin-foiled Nd-Fe-B specimen using the wavelet hidden Markov model

In this study, we investigate the effectiveness of noise reduction in electron holography, based on the wavelet hidden Markov model (WHMM), which allows the reasonable separation of weak signals from noise. Electron holography observations from a Nd2Fe14B thin foil showed that the noise reduction method suppressed artificial phase discontinuities generated by phase retrieval. From the peak signal-to-noise ratio, it was seen that the impact of denoising was significant for observations with a narrow spacing of interference fringes, which is a key parameter for the spatial resolution of electron holography. These results provide essential information for improving the precision of electron holography studies.

Enhancing performance of electron holography with mathematical and machine learning-based denoising techniques

Electron holography is a useful tool for analyzing functional properties, such as electromagnetic fields and strains of materials and devices. The performance of electron holography is limited by the 'shot noise' inherent in electron micrographs (holograms), which are composed of a finite number of electrons. A promising approach for addressing this issue is to use mathematical and machine learning-based image-processing techniques for hologram denoising. With the advancement of information science, denoising methods have become capable of extracting signals that are completely buried in noise, and they are being applied to electron microscopy, including electron holography. However, these advanced denoising methods are complex and have many parameters to be tuned; therefore, it is necessary to understand their principles in depth and use them carefully. Herein, we present an overview of the principles and usage of sparse coding, the wavelet hidden Markov model and tensor decomposition, which have been applied to electron holography. We also present evaluation results for the denoising performance of these methods obtained through their application to simulated and experimentally recorded holograms. Our analysis, review and comparison of the methods clarify the impact of denoising on electron holography research.

Machine learning in electron microscopy for advanced nanocharacterization: current developments, available tools and future outlook

In the last few years, electron microscopy has experienced a new methodological paradigm aimed to fix the bottlenecks and overcome the challenges of its analytical workflow. Machine learning and artificial intelligence are answering this call providing powerful resources towards automation, exploration, and development. In this review, we evaluate the state-of-the-art of machine learning applied to electron microscopy (and obliquely, to materials and nano-sciences). We start from the traditional imaging techniques to reach the newest higher-dimensionality ones, also covering the recent advances in spectroscopy and tomography. Additionally, the present review provides a practical guide for microscopists, and in general for material scientists, but not necessarily advanced machine learning practitioners, to straightforwardly apply the offered set of tools to their own research. To conclude, we explore the state-of-the-art of other disciplines with a broader experience in applying artificial intelligence methods to their research (e.g., high-energy physics, astronomy, Earth sciences, and even robotics, videogames, or marketing and finances), in order to narrow down the incoming future of electron microscopy, its challenges and outlook.

Computational Evaluation of Sparse Coding on off-axis Electron Holograms: Comparison Between Charge-Coupled Device and Direct-Detection Device Cameras

The effectiveness of sparse coding for image inpainting and denoising of off-axis electron holograms was examined computationally based on hologram simulations according to considerations of two types of electron detectors, namely, charge-coupled device (CCD) and direct-detection device (DDD) cameras. In this simulation, we used a simple-phase object with a phase step such as a semiconductor p-n junction and assumed that the holograms recorded by the CCD camera include shot noise, dark-current, and read-out noise, while those recorded by the DDD camera include only shot noise. Simulated holograms with various electron doses were sparsely coded. Even though interference fringes cannot be recognized in the simulated CCD and DDD holograms when subjected to electron doses (per pixel) equal to 1 and 0.01, respectively, both the corresponding sparse-coded holograms exhibit meaningful interference fringes. We demonstrate that a combination of the DDD camera and sparse coding reduces the requisite dose used to obtain holograms to values less than one-thousandth compared with the CCD camera without image postprocessing. This combination is expected to generate lower-dose and/or higher-speed electron holography.

Phase-shifting electron holography for accurate measurement of potential distributions in organic and inorganic semiconductors

Phase-shifting electron holography (PS-EH) is an interference transmission electron microscopy technique that accurately visualizes potential distributions in functional materials, such as semiconductors. In this paper, we briefly introduce the features of the PS-EH that overcome some of the issues facing the conventional EH based on Fourier transformation. Then, we present a high-precision PS-EH technique with multiple electron biprisms and a sample preparation technique using a cryo-focused-ion-beam, which are important techniques for the accurate phase measurement of semiconductors. We present several applications of PS-EH to demonstrate the potential in organic and inorganic semiconductors and then discuss the differences by comparing them with previous reports on the conventional EH. We show that in situ biasing PS-EH was able to observe not only electric potential distribution but also electric field and charge density at a GaAs p-n junction and clarify how local band structures, depletion layer widths and space charges changed depending on the biasing conditions. Moreover, the PS-EH clearly visualized the local potential distributions of two-dimensional electron gas layers formed at AlGaN/GaN interfaces with different Al compositions. We also report the results of our PS-EH application for organic electroluminescence multilayers and point out the significant potential changes in the layers. The proposed PS-EH enables more precise phase measurement compared to the conventional EH, and our findings introduced in this paper will contribute to the future research and development of high-performance semiconductor materials and devices.

Denoising of series electron holograms using tensor decomposition

In this study, a noise-reduction technique for series low-dose electron holograms using tensor decomposition is demonstrated through simulation. We treated an entire dataset of the series holograms with Poisson noise as a third-order tensor, which is a stack of 2D holograms. The third-order tensor, which is decomposed into a core tensor and three factor matrices, is approximated as a lower-rank tensor using only noise-free principal components. This technique is applied to simulated holograms by assuming a p-n junction in a semiconductor sample. The peak signal-to-noise ratios of the holograms and the reconstructed phase maps have been improved significantly using tensor decomposition. Moreover, the proposed method was applied to a more practical situation of time-resolved in situ electron holography by considering a nonuniform fringe contrast and fringe drift relative to the sample. The accuracy and precision of the reconstructed phase maps were quantitatively evaluated to demonstrate its effectiveness for in situ experiments and low-dose experiments on beam-sensitive materials.