Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more paths due to localized non-uniformities 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. Reflections that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections.
Scattering may also refer to particle-particle collisions between molecules, atoms, electrons, photons and other particles. Examples include: cosmic ray scattering in the Earth's upper atmosphere; particle collisions inside particle accelerators; electron scattering by gas atoms in fluorescent lamps; and neutron scattering inside nuclear reactors.
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 particles, bubbles, droplets, density fluctuations in fluids, crystallites in polycrystalline solids, defects in monocrystalline solids, surface roughness, cells in organisms, and textile fibers 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.
Some areas where scattering and scattering theory are significant include radar sensing, medical ultrasound, semiconductor wafer inspection, polymerization process monitoring, acoustic tiling, free-space communications and computer-generated imagery. Particle-particle scattering theory is important in areas such as particle physics, atomic, molecular, and optical physics, nuclear physics and astrophysics.
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.
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 passing through thick fog. Multiple scattering is highly analogous to diffusion, 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, an enhancement of backscattering that occurs when coherent radiation is multiply scattered by a random medium, is usually attributed to weak localization.
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 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.
Scattering theory is a framework for studying and understanding the scattering of waves and particles. Prosaically, wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a rainbow. Scattering also includes the interaction of billiard balls on a table, the Rutherford scattering (or angle change) of alpha particles by gold nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the inelastic scattering of a fission fragment as it traverses a thin foil. More precisely, scattering consists of the study of how solutions of partial differential equations, propagating freely "in the distant past", come together and interact with one another or with a boundary condition, and then propagate away "to the distant future".
Electromagnetic waves 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) 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 and Mie scattering. Inelastic scattering includes Brillouin scattering, Raman scattering, inelastic X-ray scattering and Compton scattering.
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. The apparent blue color of veins 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), the human blue iris, and the feathers of some birds (Prum et al. 1998). However, resonant light scattering in nanoparticles can produce many different highly saturated and vibrant hues, especially when surface plasmon resonance 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 πDp is the circumference of a particle and λ is the wavelength of incident radiation. Based on the value of α, these domains are:
Rayleigh scattering 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, 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 (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/λ4 relation. Along with absorption, such scattering is a major cause of the attenuation of radiation by the atmosphere. 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.
For larger diameters, the problem of electromagnetic scattering by spheres was first solved by Gustav Mie, and scattering by spheres larger than the Rayleigh range is therefore usually known as Mie scattering. 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 and ellipsoids. 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, which can be detected and used to measure the velocity of the scattering center/s in forms of techniques such as lidar and radar. 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 are mostly sufficient to describe the interaction of light with the particle, and at this point, the interaction is not usually described as scattering.
For modeling of scattering in cases where the Rayleigh and Mie models do not apply such as irregularly shaped particles, there are many numerical methods that can be used. The most common are finite-element methods which solve Maxwell's equations 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.
In physics, attenuation or, in some contexts, extinction is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variable attenuation rates.
Hearing protectors help reduce acoustic flux from flowing into the ears. This phenomenon is called acoustic attenuation and is measured in decibels (dBs).
In electrical engineering and telecommunications, attenuation affects the propagation of waves and signals in electrical circuits, in optical fibers, and in air. Electrical attenuators and optical attenuators are commonly manufactured components in this field.Bragg's law
In physics, Bragg's law, or Wulff–Bragg's condition, a special case of Laue diffraction, gives the angles for coherent and incoherent scattering from a crystal lattice. When X-rays are incident on an atom, they make the electronic cloud move, as does any electromagnetic wave. The movement of these charges re-radiates waves with the same frequency, blurred slightly due to a variety of effects; this phenomenon is known as Rayleigh scattering (or elastic scattering). The scattered waves can themselves be scattered but this secondary scattering is assumed to be negligible.
A similar process occurs upon scattering neutron waves from the nuclei or by a coherent spin interaction with an unpaired electron. These re-emitted wave fields interfere with each other either constructively or destructively (overlapping waves either add up together to produce stronger peaks or are subtracted from each other to some degree), producing a diffraction pattern on a detector or film. The resulting wave interference pattern is the basis of diffraction analysis. This analysis is called Bragg diffraction.C. V. Raman
Sir Chandrashekhara Venkata Raman (; 7 November 1888 – 21 November 1970) was an Indian physicist born in the former Madras Province in India (presently the state of Tamil Nadu), who carried out ground-breaking work in the field of light scattering, which earned him the 1930 Nobel Prize for Physics. He discovered that when light traverses a transparent material, some of the deflected light changes wavelength and amplitude. This phenomenon, subsequently known as Raman scattering, results from the Raman effect. In 1954, the Indian government honoured him with India's highest civilian award, the Bharat Ratna.Compton scattering
Compton scattering, discovered by Arthur Holly Compton, is the scattering of a photon by a charged particle, usually an electron. It results in a decrease in energy (increase in wavelength) of the photon (which may be an X-ray or gamma ray photon), called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron. Inverse Compton scattering occurs when a charged particle transfers part of its energy to a photon.Cosmic microwave background
The cosmic microwave background (CMB, CMBR), in Big Bang cosmology, is electromagnetic radiation as a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space. It is an important source of data on the early universe because it is the oldest electromagnetic radiation in the universe, dating to the epoch of recombination. With a traditional optical telescope, the space between stars and galaxies (the background) is completely dark. However, a sufficiently sensitive radio telescope shows a faint background noise, or glow, almost isotropic, that is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The accidental discovery of the CMB in 1964 by American radio astronomers Arno Penzias and Robert Wilson was the culmination of work initiated in the 1940s, and earned the discoverers the 1978 Nobel Prize in Physics.
CMB is landmark evidence of the Big Bang origin of the universe. When the universe was young, before the formation of stars and planets, it was denser, much hotter, and filled with a uniform glow from a white-hot fog of hydrogen plasma. As the universe expanded, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons combined to form neutral hydrogen atoms. Unlike the uncombined protons and electrons, these newly conceived atoms could not absorb the thermal radiation, and so the universe became transparent instead of being an opaque fog. Cosmologists refer to the time period when neutral atoms first formed as the recombination epoch, and the event shortly afterwards when photons started to travel freely through space rather than constantly being scattered by electrons and protons in plasma is referred to as photon decoupling. The photons that existed at the time of photon decoupling have been propagating ever since, though growing fainter and less energetic, since the expansion of space causes their wavelength to increase over time (and wavelength is inversely proportional to energy according to Planck's relation). This is the source of the alternative term relic radiation. The surface of last scattering refers to the set of points in space at the right distance from us so that we are now receiving photons originally emitted from those points at the time of photon decoupling.
Tiny residual variations in the glow show a very specific pattern, as would be expected of a fairly uniformly distributed hot gas that has expanded to the current size of the universe. In particular, the spectral radiance contains small anisotropies, or irregularities, which vary with the size of the region examined. They have been measured in detail, and match what would be expected if small thermal variations, generated by quantum fluctuations of matter in a very tiny space, had expanded to the size of the observable universe we see today. Although many different processes might produce the general form of a black body spectrum, no model other than the Big Bang has yet explained the fluctuations. As a result, most cosmologists consider the Big Bang model of the universe to be the best explanation for the CMB.Cross section (physics)
When two particles interact, their mutual cross section is the area transverse to their relative motion within which they must meet in order to scatter from each other. If the particles are hard inelastic spheres that interact only upon contact, their scattering cross section is related to their geometric size. If the particles interact through some action-at-a-distance force, such as electromagnetism or gravity, their scattering cross section is generally larger than their geometric size. When a cross section is specified as a function of some final-state variable, such as particle angle or energy, it is called a differential cross section. When a cross section is integrated over all scattering angles (and possibly other variables), it is called a total cross section. Cross sections are typically denoted σ (sigma) and measured in units of area.
Scattering cross sections may be defined in nuclear, atomic, and particle physics for collisions of accelerated beams of one type of particle with targets (either stationary or moving) of a second type of particle. The probability for any given reaction to occur is in proportion to its cross section. Thus, specifying the cross section for a given reaction is a proxy for stating the probability that a given scattering process will occur.
The measured reaction rate of a given process depends strongly on experimental variables such as the density of the target material, the intensity of the beam, the detection efficiency of the apparatus, or the angle setting of the detection apparatus. However, these quantities can be factored away, allowing measurement of the underlying two-particle collisional cross section.
Differential and total scattering cross sections are among the most important measurable quantities in nuclear, atomic, and particle physics.Deep scattering layer
The deep scattering layer, sometimes referred to as the sound scattering layer, is a name given to 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 was thus sometimes mistaken for the seabed. For this reason it is sometimes called the false bottom or phantom bottom. It can be seen to rise and fall each day in keeping with diel vertical migration.
Sonar operators, using the newly developed sonar technology during World War II, were puzzled by what appeared to be a false sea floor 300–500 metres deep at day, and less deep at night. Initially this mysterious phenomenon was called the ECR layer using the initials of its discoverers. It turned out to be due to millions of marine organisms, most particularly small mesopelagic fish, with swimbladders that reflected the sonar. These organisms migrate up into shallower water at dusk to feed on plankton. The layer is deeper when the moon is out, and can become shallower when clouds pass over the moon. Lanternfish account for much of the biomass responsible for the deep scattering layer of the world's oceans. Sonar reflects off the millions of lanternfish swim bladders, giving the appearance of a false bottom.Dune (franchise)
Dune is a science fiction media franchise that originated with the 1965 novel Dune by Frank Herbert. Dune is frequently cited as the best-selling science fiction novel in history. It won the 1966 Hugo Award and the inaugural Nebula Award for Best Novel, and was later adapted into a 1984 film and a 2000 television miniseries. Herbert wrote five sequels, and the first two were presented as a miniseries in 2003. The Dune universe has also inspired some traditional games and a series of video games. Since 2009, the names of planets from the Dune novels have been adopted for the real-world nomenclature of plains and other features on Saturn's moon Titan.Frank Herbert died in 1986. Beginning in 1999, his son Brian Herbert and science fiction author Kevin J. Anderson published a number of prequel novels, as well as two which complete the original Dune series (Hunters of Dune in 2006 and Sandworms of Dune in 2007), partially based on Frank Herbert's notes discovered a decade after his death.The political, scientific, and social fictional setting of Herbert's novels and derivative works is known as the Dune universe, or Duniverse. Set tens of thousands of years in the future, the saga chronicles a civilization which has banned all forms of computers, or "thinking machines", but has also developed advanced technology and mental and physical abilities. Vital to this empire is the harsh desert planet Arrakis, only known source of the spice melange, the most valuable substance in the universe.
Due to the similarities between some of Herbert's terms and ideas and actual words and concepts in the Arabic language—as well as the series' "Islamic undertones" and themes—a Middle Eastern influence on Herbert's works has been noted repeatedly.Geometric albedo
In astronomy, the geometric albedo of a celestial body is the ratio of its actual brightness as seen from the light source (i.e. at zero phase angle) to that of an idealized flat, fully reflecting, diffusively scattering (Lambertian) disk with the same cross-section. (This phase angle refers to the direction of the light paths and is not a phase angle in its normal meaning in optics or electronics.)
Diffuse scattering implies that radiation is reflected isotropically with no memory of the location of the incident light source. Zero phase angle corresponds to looking along the direction of illumination. For Earth-bound observers this occurs when the body in question is at opposition and on the ecliptic.
The visual geometric albedo refers to the geometric albedo quantity when accounting for only electromagnetic radiation in the visible spectrum.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 form of an infinite series of spherical multipole partial waves. It is named after 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 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, "Mie scattering" suggests situations where the size of the scattering particles is comparable to the wavelength of the light, rather than much smaller or much larger.
Mie scattering (sometimes referred to as a non-molecular or aerosol particle scattering) takes place in the lower 4.5 km of the atmosphere, where there may be many essentially spherical particles present with diameters approximately equal to the size of the wavelength of the incident energy. Mie scattering theory has no upper size limitation, and converges to the limit of geometric optics for large particles.Molecular mass
Relative molecular mass or molecular weight is the mass of a molecule. It is calculated as the sum of the relative atomic masses of each constituent element multiplied by the number of atoms of that element in the molecular formula. The molecular mass of small to medium size molecules, measured by mass spectrometry, determines stoichiometry. For large molecules such as proteins, methods based on viscosity and light-scattering can be used to determine molecular mass when crystallographic data are not available.Opacity (optics)
Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc. An opaque object is neither transparent (allowing all light to pass through) nor translucent (allowing some light to pass through). When light strikes an interface between two substances, in general some may be reflected, some absorbed, some scattered, and the rest transmitted (also see refraction). Reflection can be diffuse, for example light reflecting off a white wall, or specular, for example light reflecting off a mirror. An opaque substance transmits no light, and therefore reflects, scatters, or absorbs all of it. Both mirrors and carbon black are opaque. Opacity depends on the frequency of the light being considered. For instance, some kinds of glass, while transparent in the visual range, are largely opaque to ultraviolet light. More extreme frequency-dependence is visible in the absorption lines of cold gases. Opacity can be quantified in many ways; for example, see the article mathematical descriptions of opacity.
Different processes can lead to opacity including absorption, reflection, and scattering.Raman scattering
Raman scattering or the Raman effect is the inelastic scattering of a photon by molecules which are excited to higher energy levels. The effect was discovered in 1928 by C. V. Raman and his student K. S. Krishnan in liquids, and independently by Grigory Landsberg and Leonid Mandelstam in crystals.
The effect had been predicted theoretically by Adolf Smekal in 1923.When photons are scattered by a material, most of them are elastically scattered (Rayleigh scattering), such that the scattered photons have the same energy (frequency and wavelength) as the incident photons but different direction. However, a small fraction of the scattered photons (approximately 1 in 10 million) are scattered inelastically, with the scattered photons having an energy different from, and usually lower than, those of the incident photons—these are Raman scattered photons. Because of conservation of energy, the material either gains or loses energy in the process. Typically this is vibrational energy and the incident photons are of visible light, although rotational energy (if gas samples are used) and electronic energy levels (if an X-ray source is used) may also be probed. The Raman effect forms the basis for Raman spectroscopy which is used by chemists and physicists to gain information about materials.Raman spectroscopy
Raman spectroscopy (); named after Indian physicist Sir C. V. Raman) is a spectroscopic technique used to observe vibrational, rotational, and other low-frequency modes in a system. Raman spectroscopy is commonly used in chemistry to provide a structural fingerprint by which molecules can be identified.
It relies on inelastic scattering, or Raman scattering, of monochromatic light, usually from a laser in the visible, near infrared, or near ultraviolet range. The laser light interacts with molecular vibrations, phonons or other excitations in the system, resulting in the energy of the laser photons being shifted up or down. The shift in energy gives information about the vibrational modes in the system. Infrared spectroscopy yields similar, but complementary, information.
Typically, a sample is illuminated with a laser beam. Electromagnetic radiation from the illuminated spot is collected with a lens and sent through a monochromator. Elastic scattered radiation at the wavelength corresponding to the laser line (Rayleigh scattering) is filtered out by either a notch filter, edge pass filter, or a band pass filter, while the rest of the collected light is dispersed onto a detector.
Spontaneous Raman scattering is typically very weak, and as a result the main difficulty of Raman spectroscopy is separating the weak inelastically scattered light from the intense Rayleigh scattered laser light. Historically, Raman spectrometers used holographic gratings and multiple dispersion stages to achieve a high degree of laser rejection. In the past, photomultipliers were the detectors of choice for dispersive Raman setups, which resulted in long acquisition times. However, modern instrumentation almost universally employs notch or edge filters for laser rejection and spectrographs either axial transmissive (AT), Czerny–Turner (CT) monochromator, or FT (Fourier transform spectroscopy based), and CCD detectors.
The advanced types of Raman spectroscopy include surface-enhanced Raman, resonance Raman, tip-enhanced Raman, polarized Raman, stimulated Raman (analogous to stimulated emission), transmission Raman, spatially offset Raman, and hyper Raman.Rayleigh scattering
Rayleigh scattering (pronounced RAY-lee), named after the 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 radiation. Rayleigh scattering does not change the state of material and is, hence, a parametric process. The particles may be individual atoms or molecules. It can occur when light travels through transparent solids and liquids, and is most prominently seen in gases. Rayleigh scattering results from the electric polarizability of the particles. The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency. The particle therefore becomes a small radiating dipole whose radiation we see as scattered light. This radiation is an integral part of the photon and no excitation or deexcitation occurs.
Rayleigh scattering of sunlight in Earth's atmosphere causes diffuse sky radiation, which is the reason for the blue color of the daytime and twilight sky, as well as the yellowish to reddish hue of the low Sun.
For wave frequencies well below the resonance frequency of the scattering particle (normal dispersion regime), the amount of scattering is inversely proportional to the fourth power of the wavelength.
Rayleigh scattering of molecular nitrogen and oxygen in the atmosphere includes elastic scattering as well as the inelastic contribution from rotational Raman scattering in air, since the changes in wavenumber of the scattered photon are typically smaller than 50 cm−1. This can lead to changes in the rotational state of the molecules. Furthermore, the inelastic contribution has the same wavelengths dependency as the elastic part.
Scattering by particles similar to, or larger than, the wavelength of light is typically treated by the Mie theory, the discrete dipole approximation and other computational techniques. Rayleigh scattering applies to particles that are small with respect to wavelengths of light, and that are optically "soft" (i.e., with a refractive index close to 1). On the other hand, anomalous diffraction theory applies to optically soft but larger particles.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 sunlight scattered by rain drops to form a rainbow. Scattering also includes the interaction of billiard balls on a table, the Rutherford scattering (or angle change) of alpha particles by gold nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the inelastic scattering of a fission fragment as it traverses a thin foil. More precisely, scattering consists of the study of how solutions of partial differential equations, propagating freely "in the distant past", come together and interact with one another or with a boundary condition, and then propagate away "to the distant future". The direct scattering problem is the problem of determining the distribution of scattered radiation/particle flux basing on the characteristics of the scatterer. The inverse scattering problem is the problem of determining the characteristics of an object (e.g., its shape, internal constitution) from measurement data of radiation or particles scattered from the object.
Since its early statement for radiolocation, the problem has found vast number of applications, such as echolocation, geophysical survey, nondestructive testing, medical imaging and quantum field theory, to name just a few.Statistical dispersion
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range.
Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.Transparency and translucency
In the field of optics, transparency (also called pellucidity or diaphaneity) is the physical property of allowing light to pass through the material without being scattered. On a macroscopic scale (one where the dimensions investigated are much larger than the wavelength of the photons in question), the photons can be said to follow Snell's Law. Translucency (also called translucence or translucidity) is a superset of transparency: it allows light to pass through, but does not necessarily (again, on the macroscopic scale) follow Snell's law; the photons can be scattered at either of the two interfaces, or internally, where there is a change in index of refraction. In other words, a translucent medium allows the transport of light while a transparent medium not only allows the transport of light but allows for image formation. Transparent materials appear clear, with the overall appearance of one color, or any combination leading up to a brilliant spectrum of every color. The opposite property of translucency is opacity.
When light encounters a material, it can interact with it in several different ways. These interactions depend on the wavelength of the light and the nature of the material. Photons interact with an object by some combination of reflection, absorption and transmission.
Some materials, such as plate glass and clean water, transmit much of the light that falls on them and reflect little of it; such materials are called optically transparent. Many liquids and aqueous solutions are highly transparent. Absence of structural defects (voids, cracks, etc.) and molecular structure of most liquids are mostly responsible for excellent optical transmission.
Materials which do not transmit light are called opaque. Many such substances have a chemical composition which includes what are referred to as absorption centers. Many substances are selective in their absorption of white light frequencies. They absorb certain portions of the visible spectrum while reflecting others. The frequencies of the spectrum which are not absorbed are either reflected or transmitted for our physical observation. This is what gives rise to color. The attenuation of light of all frequencies and wavelengths is due to the combined mechanisms of absorption and scattering.Transparency can provide almost perfect camouflage for animals able to achieve it. This is easier in dimly-lit or turbid seawater than in good illumination. Many marine animals such as jellyfish are highly transparent.X-ray crystallography
X-ray crystallography (XRC) is a technique used for 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 and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder, and various other information.
Since many materials can form crystals—such as salts, metals, minerals, semiconductors, as well as various inorganic, organic, and biological molecules—X-ray crystallography has been fundamental in the development of many scientific fields. In its first decades of use, this method determined the size of atoms, the lengths and types of chemical bonds, and the atomic-scale differences among various materials, especially minerals and alloys. The method also revealed the structure and function of many biological molecules, including vitamins, drugs, proteins and nucleic acids such as DNA. X-ray crystallography is still the primary method for characterizing the atomic structure of new materials and in discerning materials that appear similar by other experiments. X-ray crystal structures can also account for unusual electronic or elastic properties of a material, shed light on chemical interactions and processes, or serve as the basis for designing pharmaceuticals against diseases.
In a single-crystal X-ray diffraction measurement, a crystal is mounted on a goniometer. The goniometer is used to position the crystal at selected orientations. The crystal is illuminated with a finely focused monochromatic beam of X-rays, producing a diffraction pattern of regularly spaced spots known as reflections. The two-dimensional images taken at different orientations are converted into a three-dimensional model of the density of electrons within the crystal using the mathematical method of Fourier transforms, combined with chemical data known for the sample. Poor resolution (fuzziness) or even errors may result if the crystals are too small, or not uniform enough in their internal makeup.
X-ray crystallography is related to several other methods for determining atomic structures. Similar diffraction patterns can be produced by scattering electrons or neutrons, which are likewise interpreted by Fourier transformation. If single crystals of sufficient size cannot be obtained, various other X-ray methods can be applied to obtain less detailed information; such methods include fiber diffraction, powder diffraction and (if the sample is not crystallized) small-angle X-ray scattering (SAXS).
If the material under investigation is only available in the form of nanocrystalline powders or suffers from poor crystallinity, the methods of electron crystallography can be applied for determining the atomic structure.
For all above mentioned X-ray diffraction methods, the scattering is elastic; the scattered X-rays have the same wavelength as the incoming X-ray. By contrast, inelastic X-ray scattering methods are useful in studying excitations of the sample such as plasmons, crystal-field and orbital excitations, magnons, and phonons, rather than the distribution of its atoms.