Biological application of Compressed Sensing Tomography in the Scanning Electron Microscope

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.

Advances in Focused Ion Beam Tomography for Three-Dimensional Characterization in Materials Science

Over the years, FIB-SEM tomography has become an extremely important technique for the three-dimensional reconstruction of microscopic structures with nanometric resolution. This paper describes in detail the steps required to perform this analysis, from the experimental setup to the data analysis and final reconstruction. To demonstrate the versatility of the technique, a comprehensive list of applications is also summarized, ranging from batteries to shale rocks and even some types of soft materials. Moreover, the continuous technological development, such as the introduction of the latest models of plasma and cryo-FIB, can open the way towards the analysis with this technique of a large class of soft materials, while the introduction of new machine learning and deep learning systems will not only improve the resolution and the quality of the final data, but also expand the degree of automation and efficiency in the dataset handling. These future developments, combined with a technique that is already reliable and widely used in various fields of research, are certain to become a routine tool in electron microscopy and material characterization.

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.

Powder Nano-Beam Diffraction in Scanning Electron Microscope: Fast and Simple Method for Analysis of Nanoparticle Crystal Structure

We introduce a novel scanning electron microscopy (SEM) method which yields powder electron diffraction patterns. The only requirement is that the SEM microscope must be equipped with a pixelated detector of transmitted electrons. The pixelated detectors for SEM have been commercialized recently. They can be used routinely to collect a high number of electron diffraction patterns from individual nanocrystals and/or locations (this is called four-dimensional scanning transmission electron microscopy (4D-STEM), as we obtain two-dimensional (2D) information for each pixel of the 2D scanning array). Nevertheless, the individual 4D-STEM diffractograms are difficult to analyze due to the random orientation of nanocrystalline material. In our method, all individual diffractograms (showing randomly oriented diffraction spots from a few nanocrystals) are combined into one composite diffraction pattern (showing diffraction rings typical of polycrystalline/powder materials). The final powder diffraction pattern can be analyzed by means of standard programs for TEM/SAED (Selected-Area Electron Diffraction). We called our new method 4D-STEM/PNBD (Powder NanoBeam Diffraction) and applied it to three different systems: Au nano-islands (well diffracting nanocrystals with size ~20 nm), small TbF3 nanocrystals (size < 5 nm), and large NaYF4 nanocrystals (size > 100 nm). In all three cases, the STEM/PNBD results were comparable to those obtained from TEM/SAED. Therefore, the 4D-STEM/PNBD method enables fast and simple analysis of nanocrystalline materials, which opens quite new possibilities in the field of SEM.

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

We broaden the applicability of sparse coding, a machine learning method, to low-dose electron holography by using simulated holograms for learning and validation processes. The holograms, with shot noise, are prepared to generate a model, or a dictionary, that includes basic features representing interference fringes. The dictionary is applied to sparse representations of other simulated holograms with various signal-to-noise ratios (SNRs). Results demonstrate that this approach successfully removes noise for holograms with an extremely small SNR of 0.10, and that the denoised holograms provide the accurate phase distribution. Furthermore, this study demonstrates that the dictionary learned from the simulated holograms can be applied to denoising of experimental holograms of a p-n junction specimen recorded with different exposure times. The results indicate that the simulation-trained sparse coding is suitable for use over a wide range of imaging conditions, in particular for observing electron beam-sensitive materials.

Tomographic Collection of Block-Based Sparse STEM Images: Practical Implementation and Impact on the Quality of the 3D Reconstructed Volume

The reduction of the electron dose in electron tomography of biological samples is of high significance to diminish radiation damages. Simulations have shown that sparse data collection can perform efficient electron dose reduction. Frameworks based on compressive-sensing or inpainting algorithms have been proposed to accurately reconstruct missing information in sparse data. The present work proposes a practical implementation to perform tomographic collection of block-based sparse images in scanning transmission electron microscopy. The method has been applied on sections of chemically-fixed and resin-embedded Trypanosoma brucei cells. There are 3D reconstructions obtained from various amounts of downsampling, which are compared and eventually the limits of electron dose reduction using this method are explored.