Spatial coherence of electron beams from field emitters and its effect on the resolution of imaged objects

SEM Nano: An Electron Wave Optical Simulation for the Scanning Electron Microscope

The simulation program “SEM Nano” is introduced to explain and visualize probe formation in field-emission scanning electron microscopes (SEMs). The program offers an easy and intuitive graphical user interface (GUI) to provide input in terms of understandable SEM parameters and visualization of the output. The simulations are based on wave optics treatment of the electron beam in the SEM column. Based on input parameters provided by the user, the spatial intensity distribution of electrons is calculated at the specimen by incorporating the effects of diffraction, aberrations, coherence, and noise. Given the specimen structure signal (So), the program has the capability to produce an image of the specimen using the electron probe intensity distribution. Finally, a feature is provided to reconstruct the electron probe intensity from the noisy image using a Wiener filter-based deconvolution.

Deep learning in electron microscopy

Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of deep learning in electron microscopy. Following, we discuss hardware and software needed to get started with deep learning and interface with electron microscopes. We then review neural network components, popular architectures, and their optimization. Finally, we discuss future directions of deep learning in electron microscopy.

Holography and Coherent Diffraction Imaging with Low-(30-250 eV) and High-(80-300 keV) Energy Electrons: History, Principles, and Recent Trends

In this paper, we present the theoretical background to electron scattering in an atomic potential and the differences between low- and high-energy electrons interacting with matter. We discuss several interferometric techniques that can be realized with low- and high-energy electrons and which can be applied to the imaging of non-crystalline samples and individual macromolecules, including in-line holography, point projection microscopy, off-axis holography, and coherent diffraction imaging. The advantages of using low- and high-energy electrons for particular experiments are examined, and experimental schemes for holography and coherent diffraction imaging are compared.

Theory of Quantum Path Entanglement and Interference with Multiplane Diffraction of Classical Light Sources

Quantum history states were recently formulated by extending the consistent histories approach of Griffiths to the entangled superposition of evolution paths and were then experimented with Greenberger–Horne–Zeilinger states. Tensor product structure of history-dependent correlations was also recently exploited as a quantum computing resource in simple linear optical setups performing multiplane diffraction (MPD) of fermionic and bosonic particles with remarkable promises. This significantly motivates the definition of quantum histories of MPD as entanglement resources with the inherent capability of generating an exponentially increasing number of Feynman paths through diffraction planes in a scalable manner and experimental low complexity combining the utilization of coherent light sources and photon-counting detection. In this article, quantum temporal correlation and interference among MPD paths are denoted with quantum path entanglement (QPE) and interference (QPI), respectively, as novel quantum resources. Operator theory modeling of QPE and counterintuitive properties of QPI are presented by combining history-based formulations with Feynman’s path integral approach. Leggett–Garg inequality as temporal analog of Bell’s inequality is violated for MPD with all signaling constraints in the ambiguous form recently formulated by Emary. The proposed theory for MPD-based histories is highly promising for exploiting QPE and QPI as important resources for quantum computation and communications in future architectures.

Observing the Quantum Wave Nature of Free Electrons through Spontaneous Emission

We investigate, both experimentally and theoretically, the interpretation of the free-electron wave function using spontaneous emission. We use a transversely wide single-electron wave function to describe the spatial extent of transverse coherence of an electron beam in a standard transmission electron microscope. When the electron beam passes next to a metallic grating, spontaneous Smith-Purcell radiation is emitted. We then examine the effect of the electron wave function transversal size on the emitted radiation. Two interpretations widely used in the literature are considered: (1) radiation by a continuous current density attributed to the quantum probability current, equivalent to the spreading of the electron charge continuously over space; and (2) interpreting the square modulus of the wave function as a probability distribution of finding a point particle at a certain location, wherein the electron charge is always localized in space. We discuss how these two interpretations give contradictory predictions for the radiation pattern in our experiment, comparing the emission from narrow and wide wave functions with respect to the emitted radiation's wavelength. Matching our experiment with a new quantum-electrodynamics derivation, we conclude that the measurements can be explained by the probability distribution approach wherein the electron interacts with the grating as a classical point charge. Our findings clarify the transition between the classical and quantum regimes and shed light on the mechanisms that take part in general light-matter interactions.

A low-energy electron point-source projection microscope not using a sharp metal tip performs well in long-range imaging

A low-energy electron point-source projection microscope that uses a metal/insulator structure as source instead of a sharp metal needle is presented. By combining this source with an electron optical lens and a high spatial resolution image detector, performances comparable to those of a normal electron projection microscope are easily accessible and presented here. The accessible electron energy range extends from 100 eV to 1000 eV. In the example presented here, instead of the usual near-field source-object distance, long-range imaging at a distance of about 600 µm is achieved.

High spatial resolution detection of low-energy electrons using an event-counting method, application to point projection microscopy

An event-counting method using a two-microchannel plate stack in a low-energy electron point projection microscope is implemented. 15 μm detector spatial resolution, i.e., the distance between first-neighbor microchannels, is demonstrated. This leads to a 7 times better microscope resolution. Compared to previous work with neutrons [Tremsin et al., Nucl. Instrum. Methods Phys. Res., Sect. A 592, 374 (2008)], the large number of detection events achieved with electrons shows that the local response of the detector is mainly governed by the angle between the hexagonal structures of the two microchannel plates. Using this method in point projection microscopy offers the prospect of working with a greater source-object distance (350 nm instead of 50 nm), advancing toward atomic resolution.

Development of a SEM-based low-energy in-line electron holography microscope for individual particle imaging

A new SEM-based in-line electron holography microscope has been under development. The microscope utilizes conventional SEM and BF-STEM functionality to allow for rapid searching of the specimen of interest, seamless interchange between SEM, BF-STEM and holographic imaging modes, and makes use of coherent low-energy in-line electron holography to obtain low-dose, high-contrast images of light element materials. We report here an overview of the instrumentation and first experimental results on gold nano-particles and carbon nano-fibers for system performance tests. Reconstructed images obtained from the holographic imaging mode of the new microscope show substantial image contrast and resolution compared to those acquired by SEM and BF-STEM modes, demonstrating the feasibility of high-contrast imaging via low-energy in-line electron holography. The prospect of utilizing the new microscope to image purified biological specimens at the individual particle level is discussed and electron optical issues and challenges to further improve resolution and contrast are considered.

Precise method for measuring spatial coherence in TEM beams using Airy diffraction patterns

We have developed a method to precisely measure spatial coherence in electron beams. The method does not require an electron biprism and can be implemented in existing analytical transmission electron microscopes equipped with a post-column energy filter. By fitting the Airy diffraction pattern of the selector aperture, various parameters such as geometric aberrations of the lens system and the point-spread function of the diffraction blurring are precisely determined. From the measurements of various beam diameters, components that are attributed to the partial spatial coherence are successfully separated from the point-spread functions. A linear relationship between the spatial coherence length and beam diameter is revealed, thus indicating that a wide range of coherence lengths can be determined by our proposed method as long as the coherence length remains >80% of the aperture diameter. A remarkable feature of this method is its ability to simultaneously determine diffraction blurring and lens aberrations. Possible applications of this method are also discussed.