Performance of a direct detection camera for off-axis electron holography

Exit wave reconstruction of a focal series of images with structural changes in high-resolution transmission electron microscopy

High-resolution transmission electron microscopy (HRTEM) images can capture the atomic-resolution details of the dynamically changing structure of nanomaterials. Here, we propose a new scheme and an improved reconstruction algorithm to reconstruct the exit wave function for each image in a focal series of HRTEM images to reveal structural changes. In this scheme, the wave reconstructed from the focal series of images is treated as the initial wave in the reconstruction process for each HRTEM image. Additionally, to suppress noise at the frequencies where the signal is weak due to the modulation of the lens transfer function, a weight factor is introduced in the improved reconstruction algorithm. The advantages of the new scheme and algorithms are validated by using the HRTEM images of a natural specimen and a single-layer molybdenum disulphide. This algorithm enables image resolution enhancement and lens aberration removal, while potentially allowing the visualisation of the structural evolution of nanostructures.

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.

Evaluating direct detection detectors for short-range order characterization of amorphous materials by electron scattering

The introduction of direct electron detectors (DEDs) to transmission electron microscopy has set off the 'resolution revolution', especially for cryoTEM low-dose imaging of soft matter. In comparison to traditional indirect electron detectors such as Charged-Coupled Devices (CCD), DEDs show an improved modulation transfer function (MTF) and detective quantum efficiency (DQE) across all spatial frequencies, as well as faster frame rates which enable single electron counting. The benefits of such characteristics for imaging, spectroscopy and electron holography have been demonstrated previously. However, studies are lacking on the application of DEDs for localized characterization of short- to medium- range-order (SRO, MRO) in amorphous materials using electron scattering. Therefore, we evaluate the performance of a Monolithic Active Pixel Sensor DED for the characterization of SRO and MRO in nanoscale volumes of amorphous materials, using SiO₂ and Ta₂O₅ thin films as test cases. The performance of the detector is compared systematically to electron scattering measurements recorded on an indirect detector (CCD) using 200 keV electrons and electron doses starting at approximately 500e^-Ų . In addition, the effects of sample cooling and energy-filtering on the measured SRO of the oxides were investigated. We demonstrate that the performance of the DED resulted in improved SRO characterization in comparison to that obtained from the CCD measurements. The DED enabled to achieve a larger measured maximal scattering vector, ∼16.51Å compared to ∼151Å, for the CCD. Furthermore, an improved signal-to-noise ratio of approximately two-fold was observed across all spatial frequencies for both 200 keV and 80 keV electrons. These improvements are shown to result from the superior DQE of the DED. Consequently, the DED measurements enabled to determine the coordination numbers of atomic bonds more accurately. We expect that further benefits of the DED for S/MRO characterization will be highlighted for ultra- sensitive materials that cannot withstand electron doses above several e^-Ų .

Quantum Limits of Transmission Electron Microscopy

New-generation transmission electron microscopes (TEMs) are equipped with detectors that approach the shot-noise limit. Hence it is pertinent to ask: What are the quantum limits of electron scattering experiments in the TEM? For example, for a given electron dose, what is the ultimate accuracy allowed by quantum mechanics for the atomic structure of a material? We provide quantitative answers based on quantum estimation theory. We also show that, for an arbitrary set of sample parameters, the quantum limit is achievable under conditions of weak scattering, but not strong multiple scattering (this conclusion extends to scattering of other types of radiation). Implications for structure determination of radiation-sensitive materials are discussed.

Highly complex magnetic behavior resulting from hierarchical phase separation in AlCo(Cr)FeNi high-entropy alloys

Magnetic high-entropy alloys (HEAs) are a new category of high-performance magnetic materials, with multicomponent concentrated compositions and complex multi-phase structures. Although there have been numerous reports of their interesting magnetic properties, there is very limited understanding about the interplay between their hierarchical multi-phase structures and the resulting magnetic behavior. We reveal for the first time the influence of a hierarchically decomposed B2 + A2 structure in an AlCo_0.5Cr_0.5FeNi HEA on the formation of magnetic vortex states within individual A2 (disordered BCC) precipitates, which are distributed in an ordered B2 matrix that is weakly ferromagnetic. Non-magnetic or weakly ferromagnetic B2 precipitates in large magnetic domains of the A2 phase, and strongly magnetic Fe-Co-rich interphase A2 regions, are also observed. These results provide important insight into the origin of coercivity in this HEA, which can be attributed to a complex magnetization process that includes the successive reversal of magnetic vortices.

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Al(Co,Cr)FeNi alloys consist of hierarchically decomposed B2 + magnetic A2 phases

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In AlCoFeNi, nanosized phases form magnetic domains with small angle alignment

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In AlCo_0.5Cr_0.5FeNi, B2 region contains A2 magnetic vortices and A2 with B2 inclusions

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The switching behavior of the magnetic microstructure is related to soft magnetism

Interaction-Free Measurement with Electrons

Here, we experimentally demonstrate interaction-free measurements with electrons using a novel electron Mach-Zehnder interferometer. The flexible two-grating electron interferometer is constructed in a conventional transmission electron microscope and achieves high contrast in discrete output detectors, tunable alignment with independently movable beam splitters, and scanning capabilities for imaging. With this path-separated electron interferometer, which closely matches theoretical expectations, we demonstrate electron interaction-free measurements with an efficiency of 14±1%. Implementing this quantum protocol in electron imaging opens a path toward interaction-free electron microscopy.

Single-particle cryo-EM: alternative schemes to improve dose efficiency

Imaging of biomolecules by ionizing radiation, such as electrons, causes radiation damage which introduces structural and compositional changes of the specimen. The total number of high-energy electrons per surface area that can be used for imaging in cryogenic electron microscopy (cryo-EM) is severely restricted due to radiation damage, resulting in low signal-to-noise ratios (SNR). High resolution details are dampened by the transfer function of the microscope and detector, and are the first to be lost as radiation damage alters the individual molecules which are presumed to be identical during averaging. As a consequence, radiation damage puts a limit on the particle size and sample heterogeneity with which electron microscopy (EM) can deal. Since a transmission EM (TEM) image is formed from the scattering process of the electron by the specimen interaction potential, radiation damage is inevitable. However, we can aim to maximize the information transfer for a given dose and increase the SNR by finding alternatives to the conventional phase-contrast cryo-EM techniques. Here some alternative transmission electron microscopy techniques are reviewed, including phase plate, multi-pass transmission electron microscopy, off-axis holography, ptychography and a quantum sorter. Their prospects for providing more or complementary structural information within the limited lifetime of the sample are discussed.

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 detection limits in off-axis electron holography from pixelated detectors: gain variations, geometric distortion and failure of reference-hologram correction

We investigate the effect that recording off-axis electron holograms on pixelated detectors, such as charge-coupled devices (CCD) and direct-detection devices (DDD), can have on measured amplitudes and phases. Theory will be developed for the case of perfectly uniform interference fringes illuminating an imperfect detector with gain variations and pixel displacements. We will show that both these types of defect produce a systematic noise in the phase images that depends on the position of the holographic fringes with respect to the detector. Subtracting a reference hologram from the object hologram will therefore not remove the phase noise if the initial phases of the two holograms do not coincide exactly. Another finding is that pi-shifted holograms are much less affected by gain variations but show no improvement concerning geometric distortions. The resulting phase errors will be estimated and simulations presented that confirm the theoretical developments.

Magnetic flux density measurements from narrow grain boundaries produced in sintered permanent magnets

This review examines methods of magnetic flux density measurements from the narrow grain boundary (GB) regions, the thickness of which is of the order of nanometers, produced in Nd-Fe-B-based sintered magnets. Despite of the complex crystallographic microstructure and the significant stray magnetic field of the sintered magnet, recent progress in electron holography allowed for the determination of the intrinsic magnetic flux density due to the GB which is embedded in the polycrystalline thin-foil. The methods appear to be useful as well for intensive studies about interface magnetism in a variety of systems.

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.

Accuracy improvement of phase estimation in electron holography using noise reduction methods

We try to improve the limit of the phase estimation of the interference fringe at low electron dose levels in electron holography by a noise reduction method. In this paper, we focus on unsupervised approaches to apply it to electron beam-sensitive and unknown samples and describe an overview of denoising methods used widely in image processing, such as wiener filter, total variation denoising, nonlocal mean filters and wavelet thresholding. We compare the wavelet hidden Markov model (WHMM) denoising that we have studied so far with the other conventional noise reduction methods. We evaluate the denoise performance of each method using the peak signal-to-noise ratio between noise-free and the target holograms (noisy or denoised holograms) and the root mean-square error (RMSE) between the true phase of the fringe and the measured phase by the discrete Fourier transform phase estimator. We show the denoised holograms for simulation and experimental data by using each noise reduction method and then discuss evaluation indexes obtained from these denoised holograms. From experimental results, it can be seen that the WHMM denoising can reduce the RMSE of fringe phase to about 1/4.5 for noisy simulation holograms and it has stable and good performance for noise reduction of observed holograms with various image qualities.

Direct measurement of electrostatic potentials at the atomic scale: A conceptual comparison between electron holography and scanning transmission electron microscopy

Off-axis electron holography and first moment STEM are sensitive to electromagnetic potentials or fields, respectively. In this work, we investigate in what sense the results obtained from both techniques are equivalent and work out the major differences. The analysis is focused on electrostatic (Coulomb) potentials at atomic spatial resolution. It is shown that the probe-forming/objective aperture strongly affects the reconstructed electrostatic potentials and that, as a result of the different illumination setups, dynamical diffraction effects show a specific response with increasing specimen thickness. It is shown that thermal diffuse scattering is negligible for a wide range of specimen thicknesses, when evaluating the first moment of diffraction patterns.

Throughput and resolution with a next-generation direct electron detector

Direct electron detectors (DEDs) have revolutionized cryo-electron microscopy (cryo-EM) by facilitating the correction of beam-induced motion and radiation damage, and also by providing high-resolution image capture. A new-generation DED, the DE64, has been developed by Direct Electron that has good performance in both integrating and counting modes. The camera has been characterized in both modes in terms of image quality, throughput and resolution of cryo-EM reconstructions. The modulation transfer function, noise power spectrum and detective quantum efficiency (DQE) were determined for both modes, as well as the number of images per unit time. Although the DQE for counting mode was superior to that for integrating mode, the data-collection throughput for this mode was more than ten times slower. Since throughput and resolution are related in single-particle cryo-EM, data for apoferritin were collected and reconstructed using integrating mode, integrating mode in conjunction with a Volta phase plate (VPP) and counting mode. Only the counting-mode data resulted in a better than 3 Å resolution reconstruction with similar numbers of particles, and this increased performance could not be compensated for by the increased throughput of integrating mode or by the increased low-frequency contrast of integrating mode with the VPP. These data show that the superior image quality provided by counting mode is more important for high-resolution cryo-EM reconstructions than the superior throughput of integrating mode.

Phase sensitivity of off-axis digital holography

In off-axis digital holography, the Fourier transform-based algorithm is commonly used for signal processing. Here, we derive the theoretical phase sensitivity of this algorithm, which can be calculated from a single 2D hologram. This algorithm sensitivity represents the best achievable sensitivity of a system using this algorithm. Our derivation treats the signal in its most general form, considering non-uniform illumination and the effect of sideband filtering. As a result, phase sensitivity varies spatially, determined by local signal-to-noise ratio. Sensitivity expressions for both shot noise and uniform noise models are given. These results are validated with simulations and experiments. Significantly, this theoretical sensitivity can serve as a baseline metric for assessing performance of a phase-imaging system, such as experimental sensitivity and hardware stability, which are critical for high-sensitivity quantitative phase imaging. In addition, the results are equally applicable to other interferometric techniques with similar interferogram patterns and signal processing algorithms.

Experimental observation of chiral magnetic bobbers in B20-type FeGe

Chiral magnetic skyrmions^1,2 are nanoscale vortex-like spin textures that form in the presence of an applied magnetic field in ferromagnets that support the Dzyaloshinskii-Moriya interaction (DMI) because of strong spin-orbit coupling and broken inversion symmetry of the crystal^3,4. In sharp contrast to other systems^5,6 that allow for the formation of a variety of two-dimensional (2D) skyrmions, in chiral magnets the presence of the DMI commonly prevents the stability and coexistence of topological excitations of different types ⁷ . Recently, a new type of localized particle-like object-the chiral bobber (ChB)-was predicted theoretically in such materials ⁸ . However, its existence has not yet been verified experimentally. Here, we report the direct observation of ChBs in thin films of B20-type FeGe by means of quantitative off-axis electron holography (EH). We identify the part of the temperature-magnetic field phase diagram in which ChBs exist and distinguish two mechanisms for their nucleation. Furthermore, we show that ChBs are able to coexist with skyrmions over a wide range of parameters, which suggests their possible practical applications in novel magnetic solid-state memory devices, in which a stream of binary data bits can be encoded by a sequence of skyrmions and bobbers.

Fine electron biprism on a Si-on-insulator chip for off-axis electron holography

Off-axis electron holography allows both the amplitude and the phase shift of an electron wavefield propagating through a specimen in a transmission electron microscope to be recovered. The technique requires the use of an electron biprism to deflect an object wave and a reference wave to form an interference pattern. Here, we introduce an approach based on semiconductor processing technology to fabricate fine electron biprisms with rectangular cross-sections. By performing electrostatic calculations and preliminary experiments, we demonstrate that such biprisms promise improved performance for electron holography experiments.

Ultrafast electron microscopy integrated with a direct electron detection camera

In the past decade, we have witnessed the rapid growth of the field of ultrafast electron microscopy (UEM), which provides intuitive means to watch atomic and molecular motions of matter. Yet, because of the limited current of the pulsed electron beam resulting from space-charge effects, observations have been mainly made to periodic motions of the crystalline structure of hundreds of nanometers or higher by stroboscopic imaging at high repetition rates. Here, we develop an advanced UEM with robust capabilities for circumventing the present limitations by integrating a direct electron detection camera for the first time which allows for imaging at low repetition rates. This approach is expected to promote UEM to a more powerful platform to visualize molecular and collective motions and dissect fundamental physical, chemical, and materials phenomena in space and time.

Direct observation of the thermal demagnetization of magnetic vortex structures in nonideal magnetite recorders

The thermal demagnetization of pseudo-single-domain (PSD) magnetite (Fe₃O₄) particles, which govern the magnetic signal in many igneous rocks, is examined using off-axis electron holography. Visualization of a vortex structure held by an individual Fe₃O₄ particle (~250 nm in diameter) during in situ heating is achieved through the construction and examination of magnetic-induction maps. Stepwise demagnetization of the remanence-induced Fe₃O₄ particle upon heating to above the Curie temperature, performed in a similar fashion to bulk thermal demagnetization measurements, revealed that its vortex state remains stable under heating close to its unblocking temperature and is recovered upon cooling with the same or reversed vorticity. Hence, the PSD Fe₃O₄ particle exhibits thermomagnetic behavior comparable to a single-domain carrier, and thus, vortex states are considered reliable magnetic recorders for paleomagnetic investigations.