Calculation
where is the complex structure factor for image for a pixel at radius . It is possible convert the SSNR into an equivalent FRC using the following formula:
In scientific imaging, the two-dimensional spectral signal-to-noise ratio (SSNR) is a signal-to-noise ratio measure which measures the normalised cross-correlation coefficient between several two-dimensional images over corresponding rings in Fourier space as a function of spatial frequency. [1] It is a multi-particle extension of the Fourier ring correlation (FRC), which is related to the Fourier shell correlation. The SSNR is a popular method for finding the resolution of a class average in cryo-electron microscopy.
where is the complex structure factor for image for a pixel at radius . It is possible convert the SSNR into an equivalent FRC using the following formula:
A scanning tunneling microscope (STM) is a type of scanning probe microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986. STM senses the surface by using an extremely sharp conducting tip that can distinguish features smaller than 0.1 nm with a 0.01 nm (10 pm) depth resolution. This means that individual atoms can routinely be imaged and manipulated. Most scanning tunneling microscopes are built for use in ultra-high vacuum at temperatures approaching absolute zero, but variants exist for studies in air, water and other environments, and for temperatures over 1000 °C.
Electron diffraction is a generic term for phenomena associated with changes in the direction of electron beams due to elastic interactions with atoms. It occurs due to elastic scattering, when there is no change in the energy of the electrons. The negatively charged electrons are scattered due to Coulomb forces when they interact with both the positively charged atomic core and the negatively charged electrons around the atoms. The resulting map of the directions of the electrons far from the sample is called a diffraction pattern, see for instance Figure 1. Beyond patterns showing the directions of electrons, electron diffraction also plays a major role in the contrast of images in electron microscopes.
In signal processing, the output of the matched filter is given by correlating a known delayed signal, or template, with an unknown signal to detect the presence of the template in the unknown signal. This is equivalent to convolving the unknown signal with a conjugated time-reversed version of the template. The matched filter is the optimal linear filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise.
Jellium, also known as the uniform electron gas (UEG) or homogeneous electron gas (HEG), is a quantum mechanical model of interacting electrons in a solid where the positive charges are assumed to be uniformly distributed in space; the electron density is a uniform quantity as well in space. This model allows one to focus on the effects in solids that occur due to the quantum nature of electrons and their mutual repulsive interactions without explicit introduction of the atomic lattice and structure making up a real material. Jellium is often used in solid-state physics as a simple model of delocalized electrons in a metal, where it can qualitatively reproduce features of real metals such as screening, plasmons, Wigner crystallization and Friedel oscillations.
Electron crystallography is a subset of methods in electron diffraction focusing just upon detailed determination of the positions of atoms in solids using a transmission electron microscope (TEM). It can involve the use of high-resolution transmission electron microscopy images, electron diffraction patterns including convergent-beam electron diffraction or combinations of these. It has been successful in determining some bulk structures, and also surface structures. Two related methods are low-energy electron diffraction which has solved the structure of many surfaces, and reflection high-energy electron diffraction which is used to monitor surfaces often during growth.
A scanning transmission electron microscope (STEM) is a type of transmission electron microscope (TEM). Pronunciation is [stɛm] or [ɛsti:i:ɛm]. As with a conventional transmission electron microscope (CTEM), images are formed by electrons passing through a sufficiently thin specimen. However, unlike CTEM, in STEM the electron beam is focused to a fine spot which is then scanned over the sample in a raster illumination system constructed so that the sample is illuminated at each point with the beam parallel to the optical axis. The rastering of the beam across the sample makes STEM suitable for analytical techniques such as Z-contrast annular dark-field imaging, and spectroscopic mapping by energy dispersive X-ray (EDX) spectroscopy, or electron energy loss spectroscopy (EELS). These signals can be obtained simultaneously, allowing direct correlation of images and spectroscopic data.
The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector specifies how different spatial frequencies are captured or transmitted. It is used by optical engineers to describe how the optics project light from the object or scene onto a photographic film, detector array, retina, screen, or simply the next item in the optical transmission chain. A variant, the modulation transfer function (MTF), neglects phase effects, but is equivalent to the OTF in many situations.
High-resolution transmission electron microscopy is an imaging mode of specialized transmission electron microscopes that allows for direct imaging of the atomic structure of samples. It is a powerful tool to study properties of materials on the atomic scale, such as semiconductors, metals, nanoparticles and sp2-bonded carbon. While this term is often also used to refer to high resolution scanning transmission electron microscopy, mostly in high angle annular dark field mode, this article describes mainly the imaging of an object by recording the two-dimensional spatial wave amplitude distribution in the image plane, similar to a "classic" light microscope. For disambiguation, the technique is also often referred to as phase contrast transmission electron microscopy, although this term is less appropriate. At present, the highest point resolution realised in high resolution transmission electron microscopy is around 0.5 ångströms (0.050 nm). At these small scales, individual atoms of a crystal and defects can be resolved. For 3-dimensional crystals, it is necessary to combine several views, taken from different angles, into a 3D map. This technique is called electron tomography.
Digital image correlation and tracking is an optical method that employs tracking and image registration techniques for accurate 2D and 3D measurements of changes in images. This method is often used to measure full-field displacement and strains, and it is widely applied in many areas of science and engineering. Compared to strain gauges and extensometers, digital image correlation methods provide finer details about deformation, due to the ability to provide both local and average data.
Resolution in the context of structural biology is the ability to distinguish the presence or absence of atoms or groups of atoms in a biomolecular structure. Usually, the structure originates from methods such as X-ray crystallography, electron crystallography, or cryo-electron microscopy. The resolution is measured of the "map" of the structure produced from experiment, where an atomic model would then be fit into. Due to their different natures and interactions with matter, in X-ray methods the map produced is of the electron density of the system, whereas in electron methods the map is of the electrostatic potential of the system. In both cases, atomic positions are assumed similarly.
Ptychography is a computational method of microscopic imaging. It generates images by processing many coherent interference patterns that have been scattered from an object of interest. Its defining characteristic is translational invariance, which means that the interference patterns are generated by one constant function moving laterally by a known amount with respect to another constant function. The interference patterns occur some distance away from these two components, so that the scattered waves spread out and "fold" into one another as shown in the figure.
In structural biology, as well as in virtually all sciences that produce three-dimensional data, the Fourier shell correlation (FSC) measures the normalised cross-correlation coefficient between two 3-dimensional volumes over corresponding shells in Fourier space (i.e., as a function of spatial frequency). The FSC is the three-dimensional extension of the two-dimensional Fourier ring correlation (FRC); also known as: spatial frequency correlation function.
The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample. This contrast transfer function (CTF) sets the resolution of high-resolution transmission electron microscopy (HRTEM), also known as phase contrast TEM.
Crystallographic image processing (CIP) is traditionally understood as being a set of key steps in the determination of the atomic structure of crystalline matter from high-resolution electron microscopy (HREM) images obtained in a transmission electron microscope (TEM) that is run in the parallel illumination mode. The term was created in the research group of Sven Hovmöller at Stockholm University during the early 1980s and became rapidly a label for the "3D crystal structure from 2D transmission/projection images" approach. Since the late 1990s, analogous and complementary image processing techniques that are directed towards the achieving of goals with are either complementary or entirely beyond the scope of the original inception of CIP have been developed independently by members of the computational symmetry/geometry, scanning transmission electron microscopy, scanning probe microscopy communities, and applied crystallography communities.
Precession electron diffraction (PED) is a specialized method to collect electron diffraction patterns in a transmission electron microscope (TEM). By rotating (precessing) a tilted incident electron beam around the central axis of the microscope, a PED pattern is formed by integration over a collection of diffraction conditions. This produces a quasi-kinematical diffraction pattern that is more suitable as input into direct methods algorithms to determine the crystal structure of the sample.
Lightfieldmicroscopy (LFM) is a scanning-free 3-dimensional (3D) microscopic imaging method based on the theory of light field. This technique allows sub-second (~10 Hz) large volumetric imaging with ~1 μm spatial resolution in the condition of weak scattering and semi-transparence, which has never been achieved by other methods. Just as in traditional light field rendering, there are two steps for LFM imaging: light field capture and processing. In most setups, a microlens array is used to capture the light field. As for processing, it can be based on two kinds of representations of light propagation: the ray optics picture and the wave optics picture. The Stanford University Computer Graphics Laboratory published their first prototype LFM in 2006 and has been working on the cutting edge since then.
John Marius Rodenburg is emeritus professor in the Department of Electronic and Electrical Engineering at the University of Sheffield. He was elected a Fellow of the Royal Society (FRS) in 2019 for "internationally recognised... work on revolutionising the imaging capability of light, X-ray and electron transmission microscopes".
A hemispherical electron energy analyzer or hemispherical deflection analyzer is a type of electron energy spectrometer generally used for applications where high energy resolution is needed—different varieties of electron spectroscopy such as angle-resolved photoemission spectroscopy (ARPES), X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) or in imaging applications such as photoemission electron microscopy (PEEM) and low-energy electron microscopy (LEEM).
There are a variety of technologies available for detecting and recording the images, diffraction patterns, and electron energy loss spectra produced using transmission electron microscopy (TEM).
4D scanning transmission electron microscopy is a subset of scanning transmission electron microscopy (STEM) which utilizes a pixelated electron detector to capture a convergent beam electron diffraction (CBED) pattern at each scan location. This technique captures a 2 dimensional reciprocal space image associated with each scan point as the beam rasters across a 2 dimensional region in real space, hence the name 4D STEM. Its development was enabled by evolution in STEM detectors and improvements computational power. The technique has applications in visual diffraction imaging, phase orientation and strain mapping, phase contrast analysis, among others.
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