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 that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
or
sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
, are forced to deviate from a straight
trajectory
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete traj ...
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
Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface.
The law of reflection states that a reflected ray of light emerges from the reflecting surface at the same angle to the surfa ...
. Reflections of radiation that undergo scattering are often called ''
diffuse reflection
Diffuse reflection is the reflection (physics), reflection of light or other radiation, waves or particles from a surface such that a ray (optics), ray incident on the surface is scattering, scattered at many angles rather than at just one angle ...
s'' and unscattered reflections are called ''
specular
Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface.
The law of reflection states that a reflected ray of light emerges from the reflecting surface at the same angle to the surfa ...
'' (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, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that
William Herschel
Frederick William Herschel (; german: Friedrich Wilhelm Herschel; 15 November 1738 – 25 August 1822) was a German-born British astronomer and composer. He frequently collaborated with his younger sister and fellow astronomer Caroline H ...
could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800.
John Tyndall
John Tyndall FRS (; 2 August 1820 – 4 December 1893) was a prominent 19th-century Irish physicist. His scientific fame arose in the 1850s from his study of diamagnetism. Later he made discoveries in the realms of infrared radiation and the p ...
, 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 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 ele ...
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 physicist who came to be known as the father of nuclear physics.
''Encyclopædia Britannica'' considers him to be the greatest ...
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 can refer to the consequences of
particle-particle collisions between molecules, atoms,
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
s, photons and other particles. Examples include:
cosmic ray
Cosmic rays are high-energy particles or clusters of particles (primarily represented by protons or atomic nuclei) that move through space at nearly the speed of light. They originate from the Sun, from outside of the Solar System in our own ...
scattering in the Earth's upper atmosphere; particle collisions inside
particle accelerator
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 ...
s; electron scattering by gas atoms in fluorescent lamps; and
neutron scattering
Neutron scattering, the irregular dispersal of free neutrons by matter, can refer to either the naturally occurring physical process itself or to the man-made experimental techniques that use the natural process for investigating materials. Th ...
inside
nuclear reactor
A nuclear reactor is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat from nu ...
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 which can be described by several physical property, physical or chemical property, chemical ...
s,
bubble
Bubble, Bubbles or The Bubble may refer to:
Common uses
* Bubble (physics), a globule of one substance in another, usually gas in a liquid
** Soap bubble
* Economic bubble, a situation where asset prices are much higher than underlying fundame ...
s,
droplet
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 drop called a pendant d ...
s,
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
fluctuations in
fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
s,
crystallite
A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains.
Bacillite is a type of crystallite. It is rodlike with parallel longulites.
Stru ...
s in
polycrystal
A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains.
Bacillite is a type of crystallite. It is rodlike with parallel longulites.
Stru ...
line solids, defects in
monocrystal
In materials science, a single crystal (or single-crystal solid or monocrystalline solid) is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries.RIWD. "R ...
line solids,
surface roughness
Surface roughness, often shortened to roughness, is a component of surface finish (surface texture). It is quantified by the deviations in the direction of the normal vector of a real surface from its ideal form. If these deviations are large, ...
,
cell
Cell most often refers to:
* Cell (biology), the functional basic unit of life
Cell may also refer to:
Locations
* Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...
s in organisms, and textile
fiber
Fiber or fibre (from la, fibra, links=no) is a natural or artificial substance that is significantly longer than it is wide. Fibers are often used in the manufacture of other materials. The strongest engineering materials often incorporate ...
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 and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunli ...
.
Some areas where scattering and scattering theory are significant include radar sensing,
medical ultrasound
Medical ultrasound includes diagnostic techniques (mainly imaging techniques) using ultrasound, as well as therapeutic applications of ultrasound. In diagnosis, it is used to create an image of internal body structures such as tendons, muscles ...
,
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 the fabrication of integrated circuits and, in photovoltaics, to manufacture solar cells. The wafer serv ...
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. There are ...
process monitoring, acoustic tiling, free-space communications and
computer-generated imagery
Computer-generated imagery (CGI) is the use of computer graphics to create or contribute to images in art, printed media, video games, simulators, and visual effects in films, television programs, shorts, commercials, and videos. The images may ...
. Particle-particle scattering theory is important in areas such as
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
,
atomic, molecular, and optical physics
Atomic, molecular, and optical physics (AMO) is the study of matter-matter and light-matter interactions; at the scale of one or a few atoms and energy scales around several electron volts. The three areas are closely interrelated. AMO theory in ...
,
nuclear physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter.
Nuclear physics should not be confused with atomic physics, which studies the ...
and
astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...
. In
Particle Physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
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 process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT).
More forma ...
, 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 e ...
and
Werner Heisenberg
Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series ...
.
Scattering is quantified using many different concepts, including
scattering cross section
In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation (e.g. a particle beam, sound wave, light, or an X-ray) intersects a localized phenomenon (e.g. a particle o ...
(σ),
attenuation coefficient
The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient valu ...
s, the
bidirectional scattering distribution function The 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 de ...
(BSDF),
S-matrices
In physics, the ''S''-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT).
More formal ...
, and
mean free path
In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...
.
Single and multiple scattering
![Zodiacal Glow Lightens Paranal Sky](https://upload.wikimedia.org/wikipedia/commons/5/5d/Zodiacal_Glow_Lightens_Paranal_Sky.jpg)
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 theory Photon transport in biological tissue can be equivalently modeled numerically with Monte Carlo simulations or analytically by the radiative transfer equation (RTE). However, the RTE is difficult to solve without introducing approximations. A common ...
.
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 energy radiating from a light source. Sunlight forms a light beam (a sunbeam) when filtered through media such as clouds, foliage, or windows. To artificially produce a light ...
passing through thick
fog
Fog is a visible aerosol consisting of tiny water droplets or ice crystals suspended in the air at or near the Earth's surface. Reprint from Fog can be considered a type of low-lying cloud usually resembling stratus, and is heavily influ ...
. 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 to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
, and the terms ''multiple scattering'' and ''diffusion'' are interchangeable in many contexts. Optical elements designed to produce multiple scattering are thus known as ''diffusers''.
Coherent backscattering
In physics, coherent backscattering is observed when coherent radiation (such as a laser beam) propagates through a medium which has a large number of scattering centers (such as milk or a thick cloud) of size comparable to the wavelength of the ra ...
, 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, a ...
that occurs when coherent radiation is multiply scattered by a random medium, is usually attributed to
weak localization Weak 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 is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
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
speckles. 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 concepts "particle" or "wave" to fully describe the ...
.
Theory
Scattering theory is a framework for studying and understanding the scattering of
wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
s and
particles
In the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass.
They vary greatly in size or quantity, from su ...
. Prosaically, wave scattering corresponds to the collision and scattering of a wave with some material object, for instance (sunlight) scattered by
rain drop
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 drop called a pendant d ...
s to form a
rainbow
A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Rainbows c ...
. 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, and snooker. The number, type, diameter, color, and pattern of the balls differ depending upon the specific game being played. Various particular ball pr ...
on a table, the
Rutherford scattering
In particle physics, Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model ...
(or angle change) of
alpha particle
Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produce ...
s by
gold
Gold is a chemical element with the symbol Au (from la, aurum) and atomic number 79. This makes it one of the higher atomic number elements that occur naturally. It is a bright, slightly orange-yellow, dense, soft, malleable, and ductile met ...
nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the
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 proces ...
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, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function.
The function is often thought of as an "unknown" to be solved for, similarly to ...
, propagating freely "in the distant past", come together and interact with one another or with a
boundary condition
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to th ...
, and then propagate away "to the distant future".
Electromagnetics
Electromagnetic waves
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) lig ...
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 is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
) 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 19th-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 of the ...
and
Mie scattering
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 f ...
. Inelastic scattering includes
Brillouin scattering Brillouin scattering (also known as Brillouin light scattering or BLS), named after Léon Brillouin, refers to the interaction of light with the material waves in a medium (e.g. electrostriction and magnetostriction). It is mediated by the refractiv ...
,
Raman scattering
Raman scattering or the Raman effect () is the inelastic scattering of photons by matter, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves vibrational energy being gained by a ...
, inelastic
X-ray
An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...
scattering and
Compton scattering
Compton scattering, discovered by Arthur Holly Compton, is the scattering of a high frequency photon after an interaction with a charged particle, usually an electron. If it results in a decrease in energy (increase in wavelength) of the photon ...
.
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
Lustre or Luster may refer to:
Places
* Luster, Norway, a municipality in Vestlandet, Norway
** Luster (village), a village in the municipality of Luster
* Lustre, Montana, an unincorporated community in the United States
Entertainment
* '' ...
or
sheen
Sheen may refer to:
Places
* Sheen or West Sheen, an alternative name for Richmond, London, England
** East Sheen
** North Sheen
** Sheen Priory
* Sheen, Staffordshire, a village and civil parish in the Staffordshire Moorlands, England
* Sheenb ...
) 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 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 modi ...
. The apparent blue color of
veins
Veins are blood vessels in humans and most other animals that carry blood towards the heart. Most veins carry deoxygenated blood from the tissues back to the heart; exceptions are the pulmonary and umbilical veins, both of which carry oxygenated 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 19th-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 of the ...
), the human blue
iris
Iris most often refers to:
*Iris (anatomy), part of the eye
*Iris (mythology), a Greek goddess
* ''Iris'' (plant), a genus of flowering plants
*Iris (color), an ambiguous color term
Iris or IRIS may also refer to:
Arts and media
Fictional enti ...
, 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 that is between 1 and 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 1 ...
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 in a particle stimulated by incident light. SPR is the basis of many standard tools for measu ...
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:
where ''πD''
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 19th-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 of the ...
(small particle compared to wavelength of light);
* ''α'' ≈ 1:
Mie scattering
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 f ...
(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 19th-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 of the ...
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 an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. Amo ...
, 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, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
(''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 () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A s ...
. 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, 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 deriv ...
.
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.
Life
Mie was born in Rostock, Mecklenburg-Schwerin, Germany in 1868. From 1886 he studied mathematics and physics at the University of ...
, and scattering by spheres larger than the Rayleigh range is therefore usually known as
Mie scattering
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 f ...
. 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 ...
and
ellipsoids
An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.
An ellipsoid is a quadric surface; that is, a surface that may be defined as the ...
. 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 who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who d ...
, 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 or a surface with a laser and measuring the time for the reflected light to return to the receiver. It can also be ...
and
radar
Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
. 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 (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
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, or Maxwell–Heaviside 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 circuits.
...
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 Ancient Greek ἤλεκτρον (ḗlektron, "amber") and φόρησις (phórēsis, "the act of bearing"), is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric fie ...
involves the migration of
macromolecule
A macromolecule is a very large molecule important to biophysical processes, such as a protein or nucleic acid. It is composed of thousands of covalently bonded atoms. Many macromolecules are polymers of smaller molecules called monomers. The ...
s under the influence of an electric field.
Electrophoretic light scattering
Electrophoretic light scattering (also known as laser Doppler electrophoresis and phase analysis light scattering ) is based on dynamic light scattering. The frequency shift or phase shift of an incident laser beam depends on the dispersed particl ...
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
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Attenuation#Light scattering
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Bragg diffraction
In physics and chemistry , Bragg's law, Wulff–Bragg's condition or Laue–Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a crystal lattice. It encompasses the superposition of wave ...
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Brillouin scattering Brillouin scattering (also known as Brillouin light scattering or BLS), named after Léon Brillouin, refers to the interaction of light with the material waves in a medium (e.g. electrostriction and magnetostriction). It is mediated by the refractiv ...
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Characteristic mode analysis Characteristic modes (CM) form a set of functions which, under specific boundary conditions, diagonalizes operator relating field and induced sources. Under certain conditions, the set of the CM is unique and complete (at least theoretically) and th ...
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Compton scattering
Compton scattering, discovered by Arthur Holly Compton, is the scattering of a high frequency photon after an interaction with a charged particle, usually an electron. If it results in a decrease in energy (increase in wavelength) of the photon ...
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Coulomb scattering
In particle physics, Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model ...
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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, as ships found a layer that scattered the sound and w ...
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Doppler effect
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 who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who d ...
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Dynamic Light Scattering
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using t ...
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Electrophoretic light scattering
Electrophoretic light scattering (also known as laser Doppler electrophoresis and phase analysis light scattering ) is based on dynamic light scattering. The frequency shift or phase shift of an incident laser beam depends on the dispersed particl ...
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Kikuchi line
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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 ...
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Mie scattering
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 f ...
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Mott scattering
Mott scattering in physics, also referred to as spin-coupling inelastic Rutherford scattering, Coulomb scattering, is the separation of the two spin states of an electron beam by scattering the beam off the Coulomb field of heavy atoms. It is named ...
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Neutron scattering
Neutron scattering, the irregular dispersal of free neutrons by matter, can refer to either the naturally occurring physical process itself or to the man-made experimental techniques that use the natural process for investigating materials. Th ...
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Phase space measurement with forward modeling Phase space measurement with forward modeling is one approach to address the scattering issue in biomedical imaging.
Scattering is one of the biggest problems in biomedical imaging, given that scattered light is eventually defocused, thus resulting ...
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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 wal ...
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Powder diffraction
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is call ...
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Raman scattering
Raman scattering or the Raman effect () is the inelastic scattering of photons by matter, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves vibrational energy being gained by a ...
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Rayleigh scattering
Rayleigh scattering ( ), named after the 19th-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 of the ...
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Rutherford scattering
In particle physics, Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model ...
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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 sma ...
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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.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 process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT).
More forma ...
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Tyndall effect
The Tyndall effect is light scattering by particles in a colloid or in a very fine suspension. Also known as Tyndall scattering, it is similar to Rayleigh scattering, in that the intensity of the scattered light is inversely proportional to the ...
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Thomson scattering
Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is the low-energy limit of Compton scattering: the particle's kinetic energy and photon frequency ...
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Wolf effect
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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 diffract into many specific directions. By measuring the angles ...
References
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
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Physical phenomena
Atomic physics
Nuclear physics
Particle physics
Radar theory
Scattering, absorption and radiative transfer (optics)