TheInfoList

Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as
light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nan ...

or
sound In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

, are forced to deviate from a straight
trajectory A trajectory or flight path is the path that an with in follows through as a function of time. In , a trajectory is defined by via ; hence, a complete trajectory is defined by position and momentum, simultaneously. The mass might be a or ...

by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the
law of reflection Image:Tso Kiagar Lake Ladakh.jpg, Reflections on still water are an example of specular reflection. Specular reflection, or regular reflection, is the mirror-like reflection (physics), reflection of waves, such as light, from a surface. The la ...
. Reflections of radiation that undergo scattering are often called ''
diffuse reflection Diffuse reflection is the reflectionReflection or reflexion may refer to: Philosophy * Self-reflection Science * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflec ...

s'' and unscattered reflections are called ''
specular Specular reflection, or regular reflection, is the mirror A mirror is an object that Reflection (physics), reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the l ...

'' (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that
William Herschel Sir Frederick William Herschel (; german: Friedrich Wilhelm Herschel; 15 November 1738 – 25 August 1822) was a German-born British astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a spe ...

could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800.
John Tyndall John Tyndall FRS FRS may also refer to: Government and politics * Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United States * Family Resourc ...

, a pioneer in light scattering research, noted the connection between light scattering and acoustic scattering in the 1870s. Near the end of the 19th century, the scattering of
cathode ray Cathode rays (electron beam or e-beam) are streams of electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle p ...
s (electron beams) and X-rays was observed and discussed. With the discovery of subatomic particles (e.g.
Ernest Rutherford Ernest Rutherford, 1st Baron Rutherford of Nelson, (30 August 1871 – 19 October 1937) was a New Zealand-born British physicist A physicist is a scientist A scientist is a person who conducts scientific research The sci ...
in 1911) and the development of quantum theory in the 20th century, the sense of the term became broader as it was recognized that the same mathematical frameworks used in light scattering could be applied to many other phenomena. Scattering thus refers to particle-particle collisions between molecules, atoms,
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

s, photons and other particles. Examples include:
cosmic ray Cosmic rays are high-energy proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approx ...
scattering in the Earth's upper atmosphere; particle collisions inside
particle accelerator A particle accelerator is a machine that uses electromagnetic fields to propel electric charge, charged particles to very high speeds and energies, and to contain them in well-defined particle beam, beams. Large accelerators are used for funda ...
s; electron scattering by gas atoms in fluorescent lamps; and
neutron scattering Neutron scattering, the irregular dispersal of free neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons ...
inside
nuclear reactor A nuclear reactor, formerly known as an atomic pile, is a device used to initiate and control a fission nuclear chain reaction 300px, A possible nuclear fission chain reaction: 1) A uranium-235 atom absorbs a neutron">uranium-235.html" ;"ti ...

s. The types of non-uniformities which can cause scattering, sometimes known as ''scatterers'' or ''scattering centers'', are too numerous to list, but a small sample includes
particle In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can be ascribed several physical property, physical or chemical property, chemical p ...

s,
bubble Bubble or Bubbles may refer to: Physical bubbles * Bubble (physics), a globule of one substance in another, usually gas in a liquid ** Soap bubble, commonly referred to as a "bubble" People * Bubbles, a contestant on ''Real Chance of Love ( ...
s,
droplet A drop or droplet is a small column of liquid A liquid is a nearly incompressible In fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics Mechanics (Ancient Greek, Greek: ) is the area of ph ...

s,
density The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its per unit . The symbol most often used for density is ''ρ'' (the lower case Greek letter ), although the Latin letter ''D'' can also ...

fluctuations in
fluid In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
s,
crystallite A crystallite is a small or even microscopic crystal A crystal or crystalline solid is a solid Solid is one of the four fundamental states of matter (the others being liquid A liquid is a nearly incompressible fluid In phys ...

s in
polycrystal A crystallite is a small or even microscopic crystal A crystal or crystalline solid is a solid Solid is one of the four fundamental states of matter (the others being liquid A liquid is a nearly incompressible fluid In phys ...
line solids, defects in
monocrystal A single-crystal, or monocrystalline, solid Solid is one of the four fundamental states of matter (the others being liquid, gas and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic e ...
line solids,
surface roughness Surface roughness, often shortened to roughness, is a component of surface texture Surface finish, also known as surface texture or surface topography, is the nature of a interface (matter), surface as defined by the three characteristics of l ...

, cells in organisms, and textile
fiber Fiber or fibre (from la, fibra, links=no) is a natural Nature, in the broadest sense, is the natural, physical, material world or universe The universe ( la, universus) is all of space and time and their contents, including ...

s in clothing. The effects of such features on the path of almost any type of propagating wave or moving particle can be described in the framework of
scattering theory In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and t ...
. Some areas where scattering and scattering theory are significant include radar sensing,
medical ultrasound Medical ultrasound includes diagnostic Diagnosis is the identification of the nature and cause of a certain phenomenon. Diagnosis is used in many different disciplines, with variations in the use of logic Logic is an interdisciplinary ...

,
semiconductor wafer In electronics, a wafer (also called a slice or substrate) is a thin slice of semiconductor, such as a crystalline silicon (c-Si), used for Semiconductor device fabrication, the fabrication of integrated circuits and, in photovoltaics, to manufact ...
inspection,
polymerization In polymer chemistry, polymerization (American English), or polymerisation (British English), is a process of reacting monomer, monomer molecules together in a chemical reaction to form polymer chains or three-dimensional networks.Clayden, J ...
process monitoring, acoustic tiling, free-space communications and
computer-generated imagery Computer-generated imagery (CGI) is the application of computer graphics Computer graphics deals with generating images with the aid of computers A computer is a machine that can be programmed to Execution (computing), carry out seque ...
. Particle-particle scattering theory is important in areas such as
particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which rel ...
,
atomic, molecular, and optical physics Atomic, molecular, and optical physics (AMO) is the study of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately ...
,
nuclear physics Nuclear physics is the field of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in ot ...
and
astrophysics Astrophysics is a science that employs the methods and principles of physics in the study of astronomical objects and phenomena. Among the subjects studied are the Sun, other stars, galaxy, galaxies, extrasolar planets, the interstellar medium and ...
. In
Particle Physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which rel ...
the quantum interaction and scattering of fundamental particles is described by the Scattering Matrix or
S-Matrix In physics, the ''S''-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering, scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). ...
, introduced and developed by
John Archibald Wheeler John Archibald Wheeler (July 9, 1911April 13, 2008) was an American theoretical physicist. He was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in ex ...
and
Werner Heisenberg Werner Karl Heisenberg (; ; 5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the key pioneers of quantum mechanics Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstr ...
. Scattering is quantified using many different concepts, including scattering cross section (σ),
attenuation coefficient:''For "attenuation coefficient" as it applies to electromagnetic theory and telecommunications see Attenuation constant The propagation constant of a sinusoidal electromagnetic wave Electromagnetism is a branch of physics involving the study o ...
s, the
bidirectional scattering distribution functionThe definition of the BSDF (bidirectional scattering distribution function) is not well standardized. The term was probably introduced in 1980 by Bartell, Dereniak, and Wolfe. Most often it is used to name the general mathematical function which des ...

(BSDF), S-matrices, and
mean free path In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...

.

# Single and multiple scattering

When radiation is only scattered by one localized scattering center, this is called ''single scattering''. It is very common that scattering centers are grouped together; in such cases, radiation may scatter many times, in what is known as ''multiple scattering''. The main difference between the effects of single and multiple scattering is that single scattering can usually be treated as a random phenomenon, whereas multiple scattering, somewhat counterintuitively, can be modeled as a more deterministic process because the combined results of a large number of scattering events tend to average out. Multiple scattering can thus often be modeled well with
diffusion theoryPhoton transport in biological tissue can be equivalently modeled numerically with Monte Carlo simulations or analytically by the radiative transfer Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radi ...
. Because the location of a single scattering center is not usually well known relative to the path of the radiation, the outcome, which tends to depend strongly on the exact incoming trajectory, appears random to an observer. This type of scattering would be exemplified by an electron being fired at an atomic nucleus. In this case, the atom's exact position relative to the path of the electron is unknown and would be unmeasurable, so the exact trajectory of the electron after the collision cannot be predicted. Single scattering is therefore often described by probability distributions. With multiple scattering, the randomness of the interaction tends to be averaged out by a large number of scattering events, so that the final path of the radiation appears to be a deterministic distribution of intensity. This is exemplified by a
light beam A light beam or beam of light is a directional projection of light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible lig ...
passing through thick
fog Fog is a visible aerosol An aerosol (abbreviation of "aero-solution") is a suspension Suspension or suspended may refer to: Science and engineering * Suspension (topology), in mathematics * Suspension (dynamical systems), in mathematic ...

. Multiple scattering is highly analogous to
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration In chemistry Chemistry is the study of the properties and behavior of . It is a that covers ...

, and the terms ''multiple scattering'' and ''diffusion'' are interchangeable in many contexts. Optical elements designed to produce multiple scattering are thus known as ''diffusers''. , an enhancement of
backscattering In physics, backscatter (or backscattering) is the reflection of waves, particles, or signals back to the direction from which they came. It is usually a diffuse reflection due to scattering, as opposed to specular reflection as from a mirror, ...
that occurs when coherent radiation is multiply scattered by a random medium, is usually attributed to
weak localizationWeak localization is a physical effect which occurs in disordered electronic systems at very low temperatures. The effect manifests itself as a ''positive'' correction to the resistivity of a metal or semiconductor. The name emphasizes the fact that ...
. Not all single scattering is random, however. A well-controlled laser beam can be exactly positioned to scatter off a microscopic particle with a deterministic outcome, for instance. Such situations are encountered in
radar Radar (radio detection and ranging) is a detection system that uses radio waves to determine the distance (''ranging''), angle, or velocity of objects. It can be used to detect aircraft, Marine radar, ships, spacecraft, guided missiles, motor ...

scattering as well, where the targets tend to be macroscopic objects such as people or aircraft. Similarly, multiple scattering can sometimes have somewhat random outcomes, particularly with coherent radiation. The random fluctuations in the multiply scattered intensity of coherent radiation are called s. Speckle also occurs if multiple parts of a coherent wave scatter from different centers. In certain rare circumstances, multiple scattering may only involve a small number of interactions such that the randomness is not completely averaged out. These systems are considered to be some of the most difficult to model accurately. The description of scattering and the distinction between single and multiple scattering are tightly related to
wave–particle duality Wave–particle duality is the concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave. It expresses the inability of the classical physics, classical concepts "particle" or "wave" to ful ...
.

# Theory

Scattering theory is a framework for studying and understanding the scattering of
wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

s and
particles In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can be ascribed several physical property, physical or chemical , chemical properties ...
. Prosaically, wave scattering corresponds to the collision and scattering of a wave with some material object, for instance (sunlight) scattered by
rain drop Raindrops in a plant. A drop or droplet is a small column of liquid, bounded completely or almost completely by free surfaces. A drop may form when liquid accumulates at the lower end of a tube or other surface boundary, producing a hanging dr ...

s to form a
rainbow A rainbow is a meteorological Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting Weather forecasting is the application of sc ...

. Scattering also includes the interaction of
billiard balls A billiard ball is a small, hard ball used in cue sports, such as carom billiards, Pool (cue sports), pool, and snooker. The number, type, diameter, color, and pattern of the balls differ depending upon the specific game being played. Various pa ...
on a table, the
Rutherford scatteringRutherford scattering is the elastic scattering of Electric charge, charged particles by the Coulomb interaction. It is a physics, physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford mod ...
(or angle change) of
alpha particle Alpha particles, also called alpha rays or alpha radiation, consist of two proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Proto ...

s by
gold Gold is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical elemen ...

nuclei ''Nucleus'' (plural nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA ...
, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the
inelastic scattering In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in the ...
of a fission fragment as it traverses a thin foil. More precisely, scattering consists of the study of how solutions of
partial differential equations In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...
, propagating freely "in the distant past", come together and interact with one another or with a
boundary condition Boundary or Boundaries may refer to: * Border, in political geography Entertainment * ''Boundaries'' (2016 film), a 2016 Canadian film * ''Boundaries'' (2018 film), a 2018 American-Canadian road trip film Mathematics and physics * Boundary (top ...
, and then propagate away "to the distant future".

# Electromagnetics

Electromagnetic waves In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through ...

are one of the best known and most commonly encountered forms of radiation that undergo scattering. Scattering of light and radio waves (especially in
radar Radar (radio detection and ranging) is a detection system that uses radio waves to determine the distance (''ranging''), angle, or velocity of objects. It can be used to detect aircraft, Marine radar, ships, spacecraft, guided missiles, motor ...

) is particularly important. Several different aspects of electromagnetic scattering are distinct enough to have conventional names. Major forms of elastic light scattering (involving negligible energy transfer) are
Rayleigh scattering Rayleigh scattering ( ), named after the nineteenth-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength o ...

and
Mie scattering The Mie solution to Maxwell's equations Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric cir ...
. Inelastic scattering includes
Brillouin scatteringBrillouin scattering (also known as Brillouin light scattering or BLS), named after Léon Brillouin, refers to the interaction of light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that ...

,
Raman scattering#REDIRECT Raman scattering Raman scattering or the Raman effect () is the inelastic scattering of photon The photon (Greek: φῶς, phōs, light) is a type of elementary particle. It is the quantum of the electromagnetic field including ele ...

, inelastic
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Moti ...

scattering and
Compton scattering Compton scattering, discovered by Arthur Holly Compton Arthur Holly Compton (September 10, 1892 – March 15, 1962) was an American physicist who won the Nobel Prize in Physics in 1927 for his 1923 discovery of the Compton effect, whic ...

. Light scattering is one of the two major physical processes that contribute to the visible appearance of most objects, the other being absorption. Surfaces described as ''white'' owe their appearance to multiple scattering of light by internal or surface inhomogeneities in the object, for example by the boundaries of transparent microscopic crystals that make up a stone or by the microscopic fibers in a sheet of paper. More generally, the gloss (or lustre or sheen) of the surface is determined by scattering. Highly scattering surfaces are described as being dull or having a matte finish, while the absence of surface scattering leads to a glossy appearance, as with polished metal or stone. Spectral absorption, the selective absorption of certain colors, determines the color of most objects with some modification by
elastic scattering Elastic scattering is a form of particle scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light Light or visible light is electromagne ...
. The apparent blue color of
veins Veins are blood vessels The blood vessels are the components of the circulatory system The circulatory system, also called the cardiovascular system or the vascular system, is an organ system An organ system is a biological system A b ...

in skin is a common example where both spectral absorption and scattering play important and complex roles in the coloration. Light scattering can also create color without absorption, often shades of blue, as with the sky (
Rayleigh scattering Rayleigh scattering ( ), named after the nineteenth-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength o ...

), the human blue iris, and the feathers of some birds (Prum et al. 1998). However, resonant light scattering in
nanoparticles A nanoparticle or ultrafine particle is usually defined as a particle of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched ...

can produce many different highly saturated and vibrant hues, especially when
surface plasmon resonance Surface plasmon resonance (SPR) is the resonant oscillation of conduction electrons at the interface between negative and positive permittivity material stimulated by incident light. SPR is the basis of many standard tools for measuring adsorption ...
is involved (Roqué et al. 2006). Models of light scattering can be divided into three domains based on a dimensionless size parameter, ''α'' which is defined as: :$\alpha = \pi D_\text / \lambda,$ where π''D''p is the circumference of a particle and ''λ'' is the wavelength of incident radiation in the medium. Based on the value of ''α'', these domains are: : ''α'' ≪ 1:
Rayleigh scattering Rayleigh scattering ( ), named after the nineteenth-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength o ...

(small particle compared to wavelength of light); : ''α'' ≈ 1:
Mie scattering The Mie solution to Maxwell's equations Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric cir ...

(particle about the same size as wavelength of light, valid only for spheres); : ''α'' ≫ 1: geometric scattering (particle much larger than wavelength of light).
Rayleigh scattering Rayleigh scattering ( ), named after the nineteenth-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength o ...

is a process in which electromagnetic radiation (including light) is scattered by a small spherical volume of variant refractive indexes, such as a particle, bubble, droplet, or even a density fluctuation. This effect was first modeled successfully by
Lord Rayleigh John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was a British scientist who made extensive contributions to both theoretical A theory is a rational type of abstract thinking about a phenomenon A phenome ...

, from whom it gets its name. In order for Rayleigh's model to apply, the sphere must be much smaller in diameter than the
wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

(''λ'') of the scattered wave; typically the upper limit is taken to be about 1/10 the wavelength. In this size regime, the exact shape of the scattering center is usually not very significant and can often be treated as a sphere of equivalent volume. The inherent scattering that radiation undergoes passing through a pure gas is due to microscopic density fluctuations as the gas molecules move around, which are normally small enough in scale for Rayleigh's model to apply. This scattering mechanism is the primary cause of the blue color of the Earth's sky on a clear day, as the shorter blue wavelengths of sunlight passing overhead are more strongly scattered than the longer red wavelengths according to Rayleigh's famous 1/''λ''4 relation. Along with absorption, such scattering is a major cause of the attenuation of radiation by the
atmosphere An atmosphere (from the greek words ἀτμός ''(atmos)'', meaning 'vapour', and σφαῖρα ''(sphaira)'', meaning 'ball' or 'sphere') is a layer or a set of layers of gases surrounding a planet or other material body, that is held in ...

. The degree of scattering varies as a function of the ratio of the particle diameter to the wavelength of the radiation, along with many other factors including
polarization Polarization or polarisation may refer to: In the physical sciences *Polarization (waves), the ability of waves to oscillate in more than one direction, in particular polarization of light, responsible for example for the glare-reducing effect of ...
, angle, and
coherence Coherence, coherency, or coherent may refer to the following: Physics * Coherence (physics), an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference * Coherence (units of measurement), a derive ...
. For larger diameters, the problem of electromagnetic scattering by spheres was first solved by
Gustav Mie Gustav Adolf Feodor Wilhelm Ludwig Mie (; 29 September 1868 – 13 February 1957) was a German physicist A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical ...
, and scattering by spheres larger than the Rayleigh range is therefore usually known as
Mie scattering The Mie solution to Maxwell's equations Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric cir ...
. In the Mie regime, the shape of the scattering center becomes much more significant and the theory only applies well to spheres and, with some modification,
spheroids 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 t ...

and
ellipsoids An ellipsoid is a surface that may be obtained from a sphere of a sphere A sphere (from Greek language, Greek —, "globe, ball") is a Geometry, geometrical object in solid geometry, three-dimensional space that is the surface of a Ball (mathe ...
. Closed-form solutions for scattering by certain other simple shapes exist, but no general closed-form solution is known for arbitrary shapes. Both Mie and Rayleigh scattering are considered elastic scattering processes, in which the energy (and thus wavelength and frequency) of the light is not substantially changed. However, electromagnetic radiation scattered by moving scattering centers does undergo a
Doppler shift The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer (physics), observer who is moving relative to the wave source. It is named after the Austrian physicist ...

, which can be detected and used to measure the velocity of the scattering center/s in forms of techniques such as
lidar Lidar (, also LIDAR, or LiDAR; sometimes LADAR) is a method for determining ranges (variable distance) by targeting an object with a laser A laser is a device that emits light Light or visible light is electromagnetic radiati ...
and
radar Radar (radio detection and ranging) is a detection system that uses radio waves to determine the distance (''ranging''), angle, or velocity of objects. It can be used to detect aircraft, Marine radar, ships, spacecraft, guided missiles, motor ...

. This shift involves a slight change in energy. At values of the ratio of particle diameter to wavelength more than about 10, the laws of
geometric optics Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that are related ...
are mostly sufficient to describe the interaction of light with the particle. Mie theory can still be used for these larger spheres, but the solution often becomes numerically unwieldy. For modeling of scattering in cases where the Rayleigh and Mie models do not apply such as larger, irregularly shaped particles, there are many numerical methods that can be used. The most common are finite-element methods which solve
Maxwell's equations Maxwell's equations are a set of coupled partial differential equation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), ...
to find the distribution of the scattered electromagnetic field. Sophisticated software packages exist which allow the user to specify the refractive index or indices of the scattering feature in space, creating a 2- or sometimes 3-dimensional model of the structure. For relatively large and complex structures, these models usually require substantial execution times on a computer.
Electrophoresis Electrophoresis (from the Greek "ηλεκτροφόρηση" meaning "to bear electrons") is the motion of Interface and colloid science, dispersed particles relative to a fluid under the influence of a spatially uniform electric field. Electr ...

involves the migration of
macromolecule A macromolecule is a very large molecule A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in ...
s under the influence of an electric field. Electrophoretic light scattering involves passing an electric field through a liquid which makes particles move. The bigger the charge is on the particles, the faster they are able to move.

# See also

*
Bragg diffractionBragg may refer to: Places * Bragg City, Missouri, United States * Bragg, Texas, a ghost town, United States * Bragg, West Virginia, an unincorporated community, United States *Electoral district of Bragg, a state electoral district in South Austral ...

*
Brillouin scatteringBrillouin scattering (also known as Brillouin light scattering or BLS), named after Léon Brillouin, refers to the interaction of light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that ...

* Characteristic mode analysis *
Compton scattering Compton scattering, discovered by Arthur Holly Compton Arthur Holly Compton (September 10, 1892 – March 15, 1962) was an American physicist who won the Nobel Prize in Physics in 1927 for his 1923 discovery of the Compton effect, whic ...

*
Deep scattering layer The deep scattering layer, sometimes referred to as the sound scattering layer, is a layer in the ocean consisting of a variety of marine animals. It was discovered through the use of sonar Sonar (''so''und ''na''vigation and ''r''anging) is ...
*
Doppler effect The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the ...

*
Dynamic Light Scattering Dynamic light scattering (DLS) is a technique in physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Mo ...
* Electrophoretic light scattering * Espresso crema effect * Kikuchi line *
Light scattering by particlesLight scattering by particles is the process by which small particles (e.g. ice crystals, dust, atmospheric particulates, cosmic dust, and blood cells) scatter light causing optical phenomena such as the blue color of the sky, and halos Ha ...
*
Mie scattering The Mie solution to Maxwell's equations Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric cir ...

* *
Neutron scattering Neutron scattering, the irregular dispersal of free neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons ...
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Photon diffusion Photon diffusion is a situation where photons travel through a material without being absorbed, but rather undergoing repeated scattering events which change the direction of their path. The path of any given photon is then effectively a random walk ...
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Powder diffraction upright=2, X-ray powder diffraction of Y2Cu2O5 and yttrium_oxide.html"_;"title="Rietveld_refinement_with_two_phases,_showing_1%_of_yttrium_oxide">Rietveld_refinement_with_two_phases,_showing_1%_of_yttrium_oxide_impurity_(red_tickers). Powder_diff ...
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Raman scattering#REDIRECT Raman scattering Raman scattering or the Raman effect () is the inelastic scattering of photon The photon (Greek: φῶς, phōs, light) is a type of elementary particle. It is the quantum of the electromagnetic field including ele ...

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Rayleigh scattering Rayleigh scattering ( ), named after the nineteenth-century British physicist Lord Rayleigh (John William Strutt), is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength o ...

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Rutherford scatteringRutherford scattering is the elastic scattering of Electric charge, charged particles by the Coulomb interaction. It is a physics, physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford mod ...
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Small-angle scattering Small-angle scattering (SAS) is a scattering technique based on deflection of collimated radiation away from the straight trajectory after it interacts with structures that are much larger than the wavelength of the radiation. The deflection is smal ...
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Scattering amplitude In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. The latter is described by the wavefunction : \psi(\mathbf) = ...
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S-Matrix In physics, the ''S''-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering, scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). ...
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Tyndall effect The Tyndall effect is light scattering by particlesLight scattering by particles is the process by which small particles (e.g. ice crystals, dust, atmospheric particulates, cosmic dust, and blood cells) scatter light causing optical phenomen ...

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Thomson scattering Thomson scattering is the elastic scattering of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural sc ...
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X-ray crystallography X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to Diffraction, diffract into many specific directions. By measurin ...

# External links

Research group on light scattering and diffusion in complex systemsMultiple light scattering from a photonic science point of viewNeutron Scattering WebWorld directory of neutron scattering instruments
{{Authority control Physical phenomena Atomic physics Nuclear physics Particle physics Radar theory Scattering, absorption and radiative transfer (optics)