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Contrast Transfer Function
The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample.Spence, John C. H. (1988 2nd ed) ''Experimental high-resolution electron microscopy'' (Oxford U. Press, NY) .Ludwig Reimer (1997 4th ed) ''Transmission electron microscopy: Physics of image formation and microanalysis'' (Springer, BerlinpreviewEarl J. Kirkland (1998) ''Advanced computing in electron microscopy'' (Plenum Press, NY). This contrast transfer function (CTF) sets the resolution of high-resolution transmission electron microscopy (HRTEM), also known as phase contrast TEM. By considering the recorded image as a CTF-degraded true object, describing the CTF allows the true object to be reverse-engineered. This is typically denoted CTF-correction, and is vital to obtain high resolution structures in three-dimensional electron microscopy, especially electron cryo-microscopy. Its equivalent in light-based optics is the optical tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contrast Transfer Function
The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample.Spence, John C. H. (1988 2nd ed) ''Experimental high-resolution electron microscopy'' (Oxford U. Press, NY) .Ludwig Reimer (1997 4th ed) ''Transmission electron microscopy: Physics of image formation and microanalysis'' (Springer, BerlinpreviewEarl J. Kirkland (1998) ''Advanced computing in electron microscopy'' (Plenum Press, NY). This contrast transfer function (CTF) sets the resolution of high-resolution transmission electron microscopy (HRTEM), also known as phase contrast TEM. By considering the recorded image as a CTF-degraded true object, describing the CTF allows the true object to be reverse-engineered. This is typically denoted CTF-correction, and is vital to obtain high resolution structures in three-dimensional electron microscopy, especially electron cryo-microscopy. Its equivalent in light-based optics is the optical tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delta Function
In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. The current understanding of the unit impulse is as a linear functional that maps every continuous function (e.g., f(x)) to its value at zero of its domain (f(0)), or as the weak limit of a sequence of bump functions (e.g., \delta(x) = \lim_ \frace^), which are zero over most of the real line, with a tall spike at the origin. Bump functions are thus sometimes called "approximate" or "nascent" delta distributions. The delta function was introduced by physicist Paul Dirac as a tool for the normalization of state vectors. It also has uses in probability theory and signal processing. Its validity was disputed until Laurent Schwartz developed the theory of distributions where it is defined as a linear form acting on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transmission Electron Microscopy
Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a grid. An image is formed from the interaction of the electrons with the sample as the beam is transmitted through the specimen. The image is then magnified and focused onto an imaging device, such as a fluorescent screen, a layer of photographic film, or a sensor such as a scintillator attached to a charge-coupled device. Transmission electron microscopes are capable of imaging at a significantly higher resolution than light microscopes, owing to the smaller de Broglie wavelength of electrons. This enables the instrument to capture fine detail—even as small as a single column of atoms, which is thousands of times smaller than a resolvable object seen in a light microscope. Transmission electron microscopy is a major analytical method i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Transfer Function
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. Either transfer function specifies the response to a periodic sine-wave pattern passing through the lens system, as a function of its spatial frequency or period, and its orientation. Formally, the OTF is defined as the Fourier transform of the point spread function (PSF, that is, the impulse response of the optics, the image of a point source). As a Fourier transform, the OTF is complex-valued; but it will be real-valued in the common case of a PSF that is symmet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Airy Disk
In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best- focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, optics, and astronomy. The diffraction pattern resulting from a uniformly illuminated, circular aperture has a bright central region, known as the Airy disk, which together with the series of concentric rings around is called the Airy pattern. Both are named after George Biddell Airy. The disk and rings phenomenon had been known prior to Airy; John Herschel described the appearance of a bright star seen through a telescope under high magnification for an 1828 article on light for the ''Encyclopedia Metropolitana'': Airy wrote the first full theoretical treatment explaining the phenomenon (his 1835 "On the Diffraction of an Object-glass with Circular Aperture"). Mathematically, the diffraction pattern is characterized by the wavelen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Theory Of Diffraction
The dynamical theory of diffraction describes the interaction of waves with a regular lattice. The wave fields traditionally described are X-rays, neutrons or electrons and the regular lattice are atomic crystal structures or nanometer-scale multi-layers or self-arranged systems. In a wider sense, similar treatment is related to the interaction of light with optical band-gap materials or related wave problems in acoustics. Principle The dynamical theory of diffraction considers the wave field in the periodic potential of the crystal and takes into account all multiple scattering effects. Unlike the kinematic theory of diffraction which describes the approximate position of Bragg or Laue diffraction peaks in reciprocal space, dynamical theory corrects for refraction, shape and width of the peaks, extinction and interference effects. Graphical representations are described in dispersion surfaces around reciprocal lattice points which fulfill the boundary conditions at the crysta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffraction Formalism
Diffraction processes affecting waves are amenable to quantitative description and analysis. Such treatments are applied to a wave passing through one or more slits whose width is specified as a proportion of the wavelength. Numerical approximations may be used, including the Fresnel and Fraunhofer approximations. General diffraction Because diffraction is the result of addition of all waves (of given wavelength) along all unobstructed paths, the usual procedure is to consider the contribution of an infinitesimally small neighborhood around a certain path (this contribution is usually called a wavelet) and then integrate over all paths (= add all wavelets) from the source to the detector (or given point on a screen). Thus in order to determine the pattern produced by diffraction, the phase and the amplitude of each of the wavelets is calculated. That is, at each point in space we must determine the distance to each of the simple sources on the incoming wavefront. If the dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CTF Modified By Spatial And Temporal Envelope Functions
CTF may refer to: Organizations and associations * Cambridge Theological Federation * Canadian Taxpayers Federation * Canadian Teachers' Federation * Child Trust Fund, a UK child savings scheme * Children's Tumor Foundation * Clean Technology Fund * Cyprus Tennis Federation * Chow Tai Fook, Hong Kong based conglomerate Science and technology * Capture the flag (cybersecurity), an educational exercise in computer security * Charge trap flash * Chlorine trifluoride, a highly corrosive chemical * Collaborative Translation Framework, a platform designed by Microsoft to improve machine translation through (possibly crowdsourced) user contributions * Computer to film, an imaging technology used in lithographic printing * Contrast threshold function, in physiological imaging * Contrast transfer function, in general imaging * Controlled thermonuclear fusion * CTF, an undocumented Windows protocol involved with the Microsoft Text Services Framework * Cut-through forwarding, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modulus Squared
In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9. In some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations ''x''^2 (caret) or ''x''**2 may be used in place of ''x''2. The adjective which corresponds to squaring is '' quadratic''. The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial is the quadratic polynomial . One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that (for all nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thin-lens Formula
In optics, a thin lens is a lens with a thickness (distance along the optical axis between the two surfaces of the lens) that is negligible compared to the radii of curvature of the lens surfaces. Lenses whose thickness is not negligible are sometimes called ''thick lenses''. The thin lens approximation ignores optical effects due to the thickness of lenses and simplifies ray tracing calculations. It is often combined with the paraxial approximation in techniques such as ray transfer matrix analysis. Focal length The focal length, ''f'', of a lens in air is given by the lensmaker's equation: :\frac = (n-1) \left \frac - \frac + \frac \right where ''n'' is the index of refraction of the lens material, and ''R''1 and ''R''2 are the radii of curvature of the two surfaces. For a thin lens, ''d'' is much smaller than one of the radii of curvature (either ''R''1 or ''R''2). In these conditions, the last term of the Lensmaker's equation becomes negligible, and the focal length of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
