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Helmholtz Reciprocity
The Helmholtz reciprocity principle describes how a ray of light and its reverse ray encounter matched optical adventures, such as reflections, refractions, and absorptions in a passive medium, or at an interface. It does not apply to moving, non-linear, or magnetic media. For example, incoming and outgoing light can be considered as reversals of each other,Hapke, B. (1993). ''Theory of Reflectance and Emittance Spectroscopy'', Cambridge University Press, Cambridge UK, , Section 10C, pages 263-264. without affecting the bidirectional reflectance distribution function (BRDF) outcome. If light was measured with a sensor and that light reflected on a material with a BRDF that obeys the Helmholtz reciprocity principle one would be able to swap the sensor and light source and the measurement of flux would remain equal. In the computer graphics scheme of global illumination, the Helmholtz reciprocity principle is important if the global illumination algorithm reverses light paths ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ray (optics)
In optics a ray is an idealized geometrical model of light, obtained by choosing a curve that is perpendicular to the ''wavefronts'' of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of '' ray tracing''. This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. ''Ray optics'' or ''geometrical optics'' does not describe phenomena such as diffraction, which require wave optics theory. Some wave phenomena such as interference can be modeled in limited circumstances by adding phase to the ray model. Definition A l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Born Series
The Born series is the expansion of different scattering quantities in quantum scattering theory in the powers of the interaction potential V (more precisely in powers of G_0 V, where G_0 is the free particle Green's operator). It is closely related to Born approximation, which is the first order term of the Born series. The series can formally be understood as power series introducing the coupling constant by substitution V \to \lambda V . The speed of convergence and radius of convergence of the Born series are related to eigenvalues of the operator G_0 V . In general the first few terms of the Born series are good approximation to the expanded quantity for "weak" interaction V and large collision energy. Born series for scattering states The Born series for the scattering states reads : , \psi\rangle = , \phi \rangle + G_0(E) V , \phi\rangle + _0(E) V2 , \phi\rangle + _0(E) V3 , \phi\rangle + \dots It can be derived by iterating the Lippmann–Schwinger equation : , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inelastic Scattering
In chemistry, nuclear physics, and particle physics, inelastic scattering is a fundamental scattering process in which the kinetic energy of an incident particle is not conserved (in contrast to elastic scattering). In an inelastic scattering process, some of the energy of the incident particle is lost or increased. Although the term is historically related to the concept of inelastic collision in dynamics, the two concepts are quite distinct; inelastic collision in dynamics refers to processes in which the total macroscopic kinetic energy is not conserved. In general, scattering due to inelastic collisions will be inelastic, but, since elastic collisions often transfer kinetic energy between particles, scattering due to elastic collisions can also be ''in''elastic, as in Compton scattering meaning the two particles in the collision transfer energy causing a loss of energy in one particle. Electrons When an electron is the incident particle, the probability of inelastic scatterin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elastic Scattering
Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modified (by interaction with other particles and/or potentials) meaning the two particles in the collision do not lose energy.“Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) for materials characterization,” B.J. Inkson, “Materials Characterization Using Nondestructive Evaluation (NDE) Methods,” 2016. https://www.sciencedirect.com/topics/chemistry/elastic-scattering Furthermore, while the particle's kinetic energy in the center-of-mass frame is constant, its energy in the lab frame is not. Generally, elastic scattering describes a process in which the total kinetic energy of the system is conserved. During elastic scattering of high-energy subatomic particles, linear energy transfer (LET) takes place un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dark-field Microscopy
Dark-field microscopy (also called dark-ground microscopy) describes microscopy methods, in both light and electron microscopy, which exclude the unscattered beam from the image. As a result, the field around the specimen (i.e., where there is no specimen to scatter the beam) is generally dark. In optical microscopes a darkfield condenser lens must be used, which directs a cone of light away from the objective lens. To maximize the scattered light-gathering power of the objective lens, oil immersion is used and the numerical aperture (NA) of the objective lens must be less than 1.0. Objective lenses with a higher NA can be used but only if they have an adjustable diaphragm, which reduces the NA. Often these objective lenses have a NA that is variable from 0.7 to 1.25. Light microscopy applications In optical microscopy, dark-field describes an illumination technique used to enhance the contrast in unstained samples. It works by illuminating the sample with light that wil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kikuchi Pattern
Kikuchi lines are patterns of electrons formed by scattering. They pair up to form bands in electron diffraction from single crystal specimens, there to serve as "roads in orientation-space" for microscopists uncertain of what they are looking at. In transmission electron microscopes, they are easily seen in diffraction from regions of the specimen thick enough for multiple scattering. Unlike diffraction spots, which blink on and off as one tilts the crystal, Kikuchi bands mark orientation space with well-defined intersections (called zones or poles) as well as paths connecting one intersection to the next. Experimental and theoretical maps of Kikuchi band geometry, as well as their direct-space analogs e.g. bend contours, electron channeling patterns, and fringe visibility maps are increasingly useful tools in electron microscopy of crystalline and nanocrystalline materials. Because each Kikuchi line is associated with Bragg diffraction from one side of a single set of lattice pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Diffraction
Electron diffraction refers to the bending of electron beams around atomic structures. This behaviour, typical for waves, is applicable to electrons due to the wave–particle duality stating that electrons behave as both particles and waves. Since the diffracted beams interfere, they generate diffraction patterns widely used for analysis of the objects which caused the diffraction. Therefore, electron diffraction can also refer to derived experimental techniques used for material characterization. This technique is similar to X-ray and neutron diffraction. Electron diffraction is most frequently used in solid state physics and chemistry to study crystalline, quasi-crystalline and amorphous materials using electron microscopes. In these instruments, electrons are accelerated by an electrostatic potential in order to gain energy and shorten their wavelength. With the wavelength sufficiently short, the atomic structure acts as a diffraction grating generating diffraction patte ... [...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] |
Born Approximation
Generally in scattering theory and in particular in quantum mechanics, the Born approximation consists of taking the incident field in place of the total field as the driving field at each point in the scatterer. The Born approximation is named after Max Born who proposed this approximation in early days of quantum theory development. It is the perturbation method applied to scattering by an extended body. It is accurate if the scattered field is small compared to the incident field on the scatterer. For example, the scattering of radio waves by a light styrofoam column can be approximated by assuming that each part of the plastic is polarized by the same electric field that would be present at that point without the column, and then calculating the scattering as a radiation integral over that polarization distribution. Born approximation to the Lippmann–Schwinger equation The Lippmann–Schwinger equation for the scattering state \vert\rangle with a momentum p and out-going ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Green's Function
In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if \operatorname is the linear differential operator, then * the Green's function G is the solution of the equation \operatorname G = \delta, where \delta is Dirac's delta function; * the solution of the initial-value problem \operatorname y = f is the convolution (G \ast f). Through the superposition principle, given a linear ordinary differential equation (ODE), \operatorname y = f, one can first solve \operatorname G = \delta_s, for each , and realizing that, since the source is a sum of delta functions, the solution is a sum of Green's functions as well, by linearity of . Green's functions are named after the British mathematician George Green, who first developed the concept in the 1820s. In the modern study of linear partial differential equations, Green's functions are s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger Equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system. The equation can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated by t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T-symmetry
T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal, : T: t \mapsto -t. Since the second law of thermodynamics states that entropy increases as time flows toward the future, in general, the macroscopic universe does not show symmetry under time reversal. In other words, time is said to be non-symmetric, or asymmetric, except for special equilibrium states when the second law of thermodynamics predicts the time symmetry to hold. However, quantum noninvasive measurements are predicted to violate time symmetry even in equilibrium, contrary to their classical counterparts, although this has not yet been experimentally confirmed. Time ''asymmetries'' generally are caused by one of three categories: # intrinsic to the dynamic physical law (e.g., for the weak force) # due to the initial conditions of the universe (e.g., for the second law of thermodynamics) # due to measurements (e.g., for the noninvasive measur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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