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Scherzer's Theorem
Scherzer's theorem is a theorem in the field of electron microscopy. It states that there is a limit of resolution for electronic lenses because of unavoidable aberrations. German physicist Otto Scherzer found in 1936 that the electromagnetic lenses, which are used in electron microscopes to focus the electron beam, entail unavoidable imaging errors. These aberrations are of spherical and chromatic nature, that is, the spherical aberration coefficient ''Cs'' and the chromatic aberration In optics, chromatic aberration (CA), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the w ... coefficient ''Cc'' are always positive. Scherzer solved the system of Laplace equations for electromagnetic potentials assuming the following conditions: # electromagnetic fields are rotationally symmetric, # electromagnetic fields are stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Microscopy
An electron microscope is a microscope that uses a beam of accelerated electrons as a source of illumination. As the wavelength of an electron can be up to 100,000 times shorter than that of visible light photons, electron microscopes have a higher resolving power than light microscopes and can reveal the structure of smaller objects. A scanning transmission electron microscope has achieved better than 50 pm resolution in annular dark-field imaging mode and magnifications of up to about 10,000,000× whereas most light microscopes are limited by diffraction to about 200 nm resolution and useful magnifications below 2000×. Electron microscopes use shaped magnetic fields to form electron optical lens systems that are analogous to the glass lenses of an optical light microscope. Electron microscopes are used to investigate the ultrastructure of a wide range of biological and inorganic specimens including microorganisms, cells, large molecules, biopsy samples, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Aberration
In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics. In an imaging system, it occurs when light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements. An image-forming optical system with aberration will produce an image which is not sharp. Makers of optical instruments need to correct optical systems to compensate for aberration. Aberration can be anal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Otto Scherzer
Otto Scherzer (9 March 1909 – 15 November 1982) was a German theoretical physicist who made contributions to electron microscopy. Education Scherzer studied physics at the Munich Technical University and the Ludwig Maximilians University of Munich (LMU) from 1927 to 1931. At LMU his thesis advisor was Arnold Sommerfeld, and he was granted his doctorate in 1931. His thesis was on the quantum theory of Bremsstrahlung. From 1932 to 1933, Scherzer was an assistant to Carl Ramsauer at the ''Allgemeine Elektrizitäts-Gesellschaft'', an electric combine with headquarters in Berlin and Frankfurt-on-Main. There, he did research on electron optics. He completed his Habilitation in 1934, and he then became a Privatdozent at LMU and an assistant to Sommerfeld. Career In 1935, Scherzer moved to the '' Technische Hochschule Darmstadt'' In 1936, he became an extraordinarius professor and director of the theoretical physics department.Hentschel, 1966, Appendix F, p. XLV. In a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Lens
thumb thumb A subtype of a magnetic lens ( quadrupole magnet) in the Maier-Leibnitz laboratory, Munich A magnetic lens is a device for the focusing or deflection of moving charged particles, such as electrons or ions, by use of the magnetic Lorentz force. Its strength can often be varied by usage of electromagnets. Magnetic lenses are used in diverse applications, from cathode ray tubes over electron microscopy to particle accelerators. Design A magnetic lens typically consists of several electromagnets arranged in a quadrupole (see quadrupole magnet), sextupole, or higher format; the electromagnetic coils are placed at the vertices of a square or another regular polygon. From this configuration a customized magnetic field can be formed to manipulate the particle beam. The passing particle is subjected to two vector forces H_Z (parallel to the core), and H_R (parallel to the radius of the lens). H_R causes the particle to spiral through the lens, and this spiraling expose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Beam
Cathode rays or electron beam (e-beam) are streams of electrons observed in discharge tubes. If an evacuated glass tube is equipped with two electrodes and a voltage is applied, glass behind the positive electrode is observed to glow, due to electrons emitted from the cathode (the electrode connected to the negative terminal of the voltage supply). They were first observed in 1859 by German physicist Julius Plücker and Johann Wilhelm Hittorf, and were named in 1876 by Eugen Goldstein ''Kathodenstrahlen'', or cathode rays. In 1897, British physicist J. J. Thomson showed that cathode rays were composed of a previously unknown negatively charged particle, which was later named the ''electron''. Cathode-ray tubes (CRTs) use a focused beam of electrons deflected by electric or magnetic fields to render an image on a screen. Description Cathode rays are so named because they are emitted by the negative electrode, or cathode, in a vacuum tube. To release electrons into the tube, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Aberration
In optics, spherical aberration (SA) is a type of optical aberration, aberration found in optical systems that have elements with spherical surfaces. Lens (optics), Lenses and curved mirrors are prime examples, because this shape is easier to manufacture. Light rays that strike a spherical surface off-centre are refraction, refracted or reflection (physics), reflected more or less than those that strike close to the centre. This deviation reduces the quality of images produced by optical systems. Overview A spherical lens has an Optical aberration#Aberration of elements, i.e. smallest objects at right angles to the axis, aplanatic point (i.e., no spherical aberration) only at a radius that equals the radius of the sphere divided by the index of refraction of the lens material. A typical value of refractive index for crown glass is 1.5 (see List of refractive indices, list), which indicates that only about 43% of the area (67% of diameter) of a spherical lens is useful. It is o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chromatic Aberration
In optics, chromatic aberration (CA), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the wavelength of light. The refractive index of most transparent materials decreases with increasing wavelength. Since the focal length of a lens depends on the refractive index, this variation in refractive index affects focusing. Chromatic aberration manifests itself as "fringes" of color along boundaries that separate dark and bright parts of the image. Types There are two types of chromatic aberration: ''axial'' (''longitudinal''), and ''transverse'' (''lateral''). Axial aberration occurs when different wavelengths of light are focused at different distances from the lens (focus ''shift''). Longitudinal aberration is typical at long focal lengths. Transverse aberration occurs when different wavelengths are focused at different positions i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace's Equation
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as \nabla^2\! f = 0 or \Delta f = 0, where \Delta = \nabla \cdot \nabla = \nabla^2 is the Laplace operator,The delta symbol, Δ, is also commonly used to represent a finite change in some quantity, for example, \Delta x = x_1 - x_2. Its use to represent the Laplacian should not be confused with this use. \nabla \cdot is the divergence operator (also symbolized "div"), \nabla is the gradient operator (also symbolized "grad"), and f (x, y, z) is a twice-differentiable real-valued function. The Laplace operator therefore maps a scalar function to another scalar function. If the right-hand side is specified as a given function, h(x, y, z), we have \Delta f = h. This is called Poisson's equation, a generalization of Laplace's equation. Laplace's equation and Poisson's equation are the simplest exa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Accelerators
A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle physics. The largest accelerator currently active is the Large Hadron Collider (LHC) near Geneva, Switzerland, operated by the CERN. It is a collider accelerator, which can accelerate two beams of protons to an energy of 6.5 TeV and cause them to collide head-on, creating center-of-mass energies of 13 TeV. Other powerful accelerators are, RHIC at Brookhaven National Laboratory in New York and, formerly, the Tevatron at Fermilab, Batavia, Illinois. Accelerators are also used as synchrotron light sources for the study of condensed matter physics. Smaller particle accelerators are used in a wide variety of applications, including particle therapy for oncological purposes, radioisotope production for medical diagnostics, ion imp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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