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Light Scattering By Particles
Light scattering by particles is the process by which small particles (e.g. ice crystals, dust, atmospheric particulates, cosmic dust, and blood cells) light scattering, scatter light causing optical phenomena such as the Rayleigh scattering, blue color of the sky, and halo (optical phenomenon), halos. Maxwell's equations are the basis of theoretical and computational methods describing light scattering, but since exact solutions to Maxwell's equations are only known for selected particle geometries (such as spherical), light scattering by particles is a branch of computational electromagnetics dealing with electromagnetic radiation scattering and absorption by particles. In case of shape, geometries for which analytical solutions are known (such as spheres, cluster of spheres, infinite cylinder (geometry), cylinders), the solutions are typically calculated in terms of series (mathematics)#Infinite series, infinite series. In case of more complex geometries and for inhomogeneous p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ice Crystals
Ice crystals are solid water (known as ice) in crystal structure, symmetrical shapes including hexagonal crystal family, hexagonal columns, hexagonal plates, and dendrite (crystal), dendritic crystals. Ice crystals are responsible for various atmospheric optics, atmospheric optical displays and cirrus cloud, cloud formations. Formation At ambient temperature and pressure, Properties of water, water molecules have a V shape. The two hydrogen atoms bond to the oxygen atom at a 105° angle. Ice crystals have a hexagonal Crystal structure, crystal lattice, meaning the water molecules arrange themselves into layered Hexagon, hexagons upon freezing. Slower crystal growth from colder and drier atmospheres produces more hexagonal symmetry. Depending on environmental temperature and humidity, ice crystals can develop from the initial hexagonal prism into many symmetric shapes. Possible shapes for ice crystals are columns, Needle ice, needles, plates and Dendrite (crystal), dendrites ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discretization
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification). Discretization is also related to discrete mathematics, and is an important component of granular computing. In this context, ''discretization'' may also refer to modification of variable or category ''granularity'', as when multiple discrete variables are aggregated or multiple discrete categories fused. Whenever continuous data is discretized, there is always some amount of discretization error. The goal is to reduce the amount to a level ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Optics
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a '' geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, a problem that was stated in terms of elementary arithmetic, and remained unsolved for several centuries. Duri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refraction, refracted, when entering a material. This is described by Snell's law of refraction, , where and are the angle of incidence (optics), angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices and . The refractive indices also determine the amount of light that is reflectivity, reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity (Fresnel equations) and Brewster's angle. The refractive index, n, can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is , and similarly the wavelength in that me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Dipole Approximation Codes
Discrete dipole approximation (DDA), also known as coupled dipole approximation, is a method for computing scattering of radiation by particles of arbitrary shape and by periodic structures. Given a target of arbitrary geometry, one seeks to calculate its scattering and absorption properties by an approximation of the continuum target by a finite array of small polarizable dipoles. This technique is used in a variety of applications including nanophotonics, radar scattering, aerosol physics and astrophysics. Basic concepts The basic idea of the DDA was introduced in 1964 by DeVoe who applied it to study the optical properties of molecular aggregates; retardation effects were not included, so DeVoe's treatment was limited to aggregates that were small compared with the wavelength. The DDA, including retardation effects, was proposed in 1973 by Purcell and Pennypacker who used it to study interstellar dust grains. Simply stated, the DDA is an approximation of the continuum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Codes For Electromagnetic Scattering By Cylinders
Codes for electromagnetic scattering by cylinders – this article list codes for electromagnetic scattering by a cylinder. Majority of existing codes for calculation of electromagnetic scattering by a single cylinder are based on Mie theory, which is an analytical solution of Maxwell's equations in terms of infinite series.Bohren, Craig F. and Donald R. Huffman, Title Absorption and scattering of light by small particles, New York : Wiley, 1998, 530 p., , (second edition). Classification The compilation contains information about the electromagnetic scattering by cylindrical particles, relevant links, and applications.T. Wreidt, Light scattering theories and computer codes, Journal of Quantitative Spectroscopy and Radiative Transfer, 110, 833–843, 2009. Codes for electromagnetic scattering by a single homogeneous cylinder Relevant scattering codes * Discrete dipole approximation codes Discrete dipole approximation (DDA), also known as coupled dipole approximation, is a me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Codes For Electromagnetic Scattering By Spheres
Codes for electromagnetic scattering by spheres - this article list codes for electromagnetic scattering by a homogeneous sphere, layered sphere, and cluster of spheres. Solution techniques Majority of existing codes for calculation of electromagnetic scattering by a single sphere is based on Mie theory which is an analytical solution of Maxwell's equations in terms of infinite series. Other approximations to scattering by a single sphere include: Debye series, ray tracing ( geometrical optics), ray tracing including the effects of interference between rays, Airy theory, Rayleigh scattering, diffraction approximation. There are many phenomena related to light scattering by spherical particles such as resonances, surface waves, plasmons, near-field scattering. Even though Mie theory offers convenient and fast way of solving light scattering problem by homogeneous spherical particles, there are other techniques, such as discrete dipole approximation, FDTD, T-matrix, which can also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface (mathematics), surface obtained by Surface of revolution, rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The ball (gridiron football), American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M's, M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation of the Earth, rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattening, flattened in the direction of its axis of rotation. For that reason, in cartography and geode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mie Theory
In electromagnetism, the Mie solution to Maxwell's equations (also known as the Lorenz–Mie solution, the Lorenz–Mie–Debye solution or Mie scattering) describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the form of an infinite series of Vector spherical harmonics, spherical multipole partial waves. It is named after German physicist Gustav Mie. The term ''Mie solution'' is also used for solutions of Maxwell's equations for scattering by stratified spheres or by infinite cylinders, or other geometries where one can write separation of variables, separate equations for the radial and angular dependence of solutions. The term ''Mie theory'' is sometimes used for this collection of solutions and methods; it does not refer to an independent physical theory or law. More broadly, the "Mie scattering" formulas are most useful in situations where the size of the scattering particles is comparable to the wavelength of the light, rather ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves), phase'' on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The multiplicative inverse, inverse of the wavelength is called the ''spatial frequency''. Wavelength is commonly designated by the Greek letter lambda (''λ''). For a modulated wave, ''wavelength'' may refer to the carrier wavelength of the signal. The term ''wavelength'' may also apply to the repeating envelope (mathematics), envelope of modulated waves or waves formed by Interference (wave propagation), interference of several sinusoids. Assuming a sinusoidal wave moving at a fixed phase velocity, wave speed, wavelength is inversely proportion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
