Extinction (astronomy)

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https://en.wikipedia.org/wiki/Extinction_(astronomy)

An extreme example of visible light extinction, caused by a dark nebula

In astronomy, extinction is the absorption and scattering of electromagnetic radiation by dust and gas between an emitting astronomical object and the observer. Interstellar extinction was first documented as such in 1930 by Robert Julius Trumpler. However, its effects had been noted in 1847 by Friedrich Georg Wilhelm von Struve, and its effect on the colors of stars had been observed by a number of individuals who did not connect it with the general presence of galactic dust. For stars that lie near the plane of the Milky Way and are within a few thousand parsecs of the Earth, extinction in the visual band of frequencies (photometric system) is roughly 1.8 magnitudes per kiloparsec.

For Earth-bound observers, extinction arises both from the interstellar medium (ISM) and the Earth's atmosphere; it may also arise from circumstellar dust around an observed object. Strong extinction in earth's atmosphere of some wavelength regions (such as X-ray, ultraviolet, and infrared) is overcome by the use of space-based observatories. Since blue light is much more strongly attenuated than red light, extinction causes objects to appear redder than expected, a phenomenon referred to as interstellar reddening.

Interstellar reddening

In astronomy, interstellar reddening is a phenomenon associated with interstellar extinction where the spectrum of electromagnetic radiation from a radiation source changes characteristics from that which the object originally emitted. Reddening occurs due to the light scattering off dust and other matter in the interstellar medium. Interstellar reddening is a different phenomenon from redshift, which is the proportional frequency shifts of spectra without distortion. Reddening preferentially removes shorter wavelength photons from a radiated spectrum while leaving behind the longer wavelength photons (in the optical, light that is redder), leaving the spectroscopic lines unchanged.

In most photometric systems filters (passbands) are used from which readings of magnitude of light may take account of latitude and humidity among terrestrial factors. Interstellar reddening equates to the "color excess", defined as the difference between an object's observed color index and its intrinsic color index (sometimes referred to as its normal color index). The latter is the theoretical value which it would have if unaffected by extinction. In the first system, the UBV photometric system devised in the 1950s and its most closely related successors, the object's color excess ${\displaystyle E_{B-V}}$ is related to the object's B−V color (calibrated blue minus calibrated visible) by:

${\displaystyle E_{B-V}=(B-V{)}_{\text{observed}}-(B-V{)}_{\text{intrinsic}}}$

For an A0-type main sequence star (these have median wavelength and heat among the main sequence) the color indices are calibrated at 0 based on an intrinsic reading of such a star (± exactly 0.02 depending on which spectral point, i.e. precise passband within the abbreviated color name is in question, see color index). At least two and up to five measured passbands in magnitude are then compared by subtraction: U,B,V,I or R during which the color excess from extinction is calculated and deducted. The name of the four sub-indices (R minus I etc.) and order of the subtraction of recalibrated magnitudes is from right to immediate left within this sequence.

General characteristics

Interstellar reddening occurs because interstellar dust absorbs and scatters blue light waves more than red light waves, making stars appear redder than they are. This is similar to the effect seen when dust particles in the atmosphere of Earth contribute to red sunsets (see: Sunset#Colors).

Broadly speaking, interstellar extinction is strongest at short wavelengths, generally observed by using techniques from spectroscopy. Extinction results in a change in the shape of an observed spectrum. Superimposed on this general shape are absorption features (wavelength bands where the intensity is lowered) that have a variety of origins and can give clues as to the chemical composition of the interstellar material, e.g. dust grains. Known absorption features include the 2175 Å bump, the diffuse interstellar bands, the 3.1 μm water ice feature, and the 10 and 18 μm silicate features.

In the solar neighborhood, the rate of interstellar extinction in the Johnson–Cousins V-band (visual filter) averaged at a wavelength of 540 nm is usually taken to be 0.7–1.0 mag/kpc−simply an average due to the clumpiness of interstellar dust. In general, however, this means that a star will have its brightness reduced by about a factor of 2 in the V-band viewed from a good night sky vantage point on earth for every kiloparsec (3,260 light years) it is farther away from us.

The amount of extinction can be significantly higher than this in specific directions. For example, some regions of the Galactic Center are awash with obvious intervening dark dust from our spiral arm (and perhaps others) and themselves in a bulge of dense matter, causing as much as more than 30 magnitudes of extinction in the optical, meaning that less than 1 optical photon in 10¹² passes through. This results in the so-called zone of avoidance, where our view of the extra-galactic sky is severely hampered, and background galaxies, such as Dwingeloo 1, were only discovered recently through observations in radio and infrared.

The general shape of the ultraviolet through near-infrared (0.125 to 3.5 μm) extinction curve (plotting extinction in magnitude against wavelength, often inverted) looking from our vantage point at other objects in the Milky Way, is fairly well characterized by the stand-alone parameter of relative visibility (of such visible light) R(V) (which is different along different lines of sight), but there are known deviations from this characterization. Extending the extinction law into the mid-infrared wavelength range is difficult due to the lack of suitable targets and various contributions by absorption features.

R(V) compares aggregate and particular extinctions. It is A(V)/E(B−V). Restated, it is the total extinction, A(V) divided by the selective total extinction (A(B)−A(V)) of those two wavelengths (bands). A(B) and A(V) are the total extinction at the B and V filter bands. Another measure used in the literature is the absolute extinction A(λ)/A(V) at wavelength λ, comparing the total extinction at that wavelength to that at the V band.

R(V) is known to be correlated with the average size of the dust grains causing the extinction. For our own galaxy, the Milky Way, the typical value for R(V) is 3.1, but is found to vary considerably across different lines of sight. As a result, when computing cosmic distances it can be advantageous to move to star data from the near-infrared (of which the filter or passband Ks is quite standard) where the variations and amount of extinction are significantly less, and similar ratios as to R(Ks): 0.49±0.02 and 0.528±0.015 were found respectively by independent groups. Those two more modern findings differ substantially relative to the commonly referenced historical value ≈0.7.

The relationship between the total extinction, A(V) (measured in magnitudes), and the column density of neutral hydrogen atoms column, N_H (usually measured in cm⁻²), shows how the gas and dust in the interstellar medium are related. From studies using ultraviolet spectroscopy of reddened stars and X-ray scattering halos in the Milky Way, Predehl and Schmitt found the relationship between N_H and A(V) to be approximately:

${\displaystyle \frac{N_H}{A(V)}\approx 1.8\times {10}^{21}\text{atoms}{\text{cm}}^{-2}{\text{mag}}^{-1}}$

Astronomers have determined the three-dimensional distribution of extinction in the "solar circle" (our region of our galaxy), using visible and near-infrared stellar observations and a model of distribution of stars. The dust causing extinction mainly lies along the spiral arms, as observed in other spiral galaxies.

Measuring extinction towards an object

To measure the extinction curve for a star, the star's spectrum is compared to the observed spectrum of a similar star known not to be affected by extinction (unreddened). It is also possible to use a theoretical spectrum instead of the observed spectrum for the comparison, but this is less common. In the case of emission nebulae, it is common to look at the ratio of two emission lines which should not be affected by the temperature and density in the nebula. For example, the ratio of hydrogen alpha to hydrogen beta emission is always around 2.85 under a wide range of conditions prevailing in nebulae. A ratio other than 2.85 must therefore be due to extinction, and the amount of extinction can thus be calculated.

The 2175-angstrom feature

One prominent feature in measured extinction curves of many objects within the Milky Way is a broad 'bump' at about 2175 Å, well into the ultraviolet region of the electromagnetic spectrum. This feature was first observed in the 1960s, but its origin is still not well understood. Several models have been presented to account for this bump which include graphitic grains with a mixture of PAH molecules. Investigations of interstellar grains embedded in interplanetary dust particles (IDP) observed this feature and identified the carrier with organic carbon and amorphous silicates present in the grains.

Extinction curves of other galaxies

Plot showing the average extinction curves for the MW, LMC2, LMC, and SMC Bar. The curves are plotted versus 1/wavelength to emphasize the UV.

The form of the standard extinction curve depends on the composition of the ISM, which varies from galaxy to galaxy. In the Local Group, the best-determined extinction curves are those of the Milky Way, the Small Magellanic Cloud (SMC) and the Large Magellanic Cloud (LMC).

In the LMC, there is significant variation in the characteristics of the ultraviolet extinction with a weaker 2175 Å bump and stronger far-UV extinction in the region associated with the LMC2 supershell (near the 30 Doradus starbursting region) than seen elsewhere in the LMC and in the Milky Way. In the SMC, more extreme variation is seen with no 2175 Å bump and very strong far-UV extinction in the star forming Bar and fairly normal ultraviolet extinction seen in the more quiescent Wing.

This gives clues as to the composition of the ISM in the various galaxies. Previously, the different average extinction curves in the Milky Way, LMC, and SMC were thought to be the result of the different metallicities of the three galaxies: the LMC's metallicity is about 40% of that of the Milky Way, while the SMC's is about 10%. Finding extinction curves in both the LMC and SMC which are similar to those found in the Milky Way and finding extinction curves in the Milky Way that look more like those found in the LMC2 supershell of the LMC and in the SMC Bar has given rise to a new interpretation. The variations in the curves seen in the Magellanic Clouds and Milky Way may instead be caused by processing of the dust grains by nearby star formation. This interpretation is supported by work in starburst galaxies (which are undergoing intense star formation episodes) which shows that their dust lacks the 2175 Å bump.

Atmospheric extinction

Atmospheric extinction gives the rising or setting Sun an orange hue and varies with location and altitude. Astronomical observatories generally are able to characterise the local extinction curve very accurately, to allow observations to be corrected for the effect. Nevertheless, the atmosphere is completely opaque to many wavelengths requiring the use of satellites to make observations.

This extinction has three main components: Rayleigh scattering by air molecules, scattering by particulates, and molecular absorption. Molecular absorption is often referred to as telluric absorption, as it is caused by the Earth (telluric is a synonym for terrestrial). The most important sources of telluric absorption are molecular oxygen and ozone, which strongly absorb radiation near ultraviolet, and water, which strongly absorbs infrared.

The amount of such extinction is lowest at the observer's zenith and highest near the horizon. A given star, preferably at solar opposition, reaches its greatest celestial altitude and optimal time for observation when the star is near the local meridian around solar midnight and if the star has a favorable declination (i.e. similar to the observer's latitude); thus, the seasonal time due to axial tilt is key. Extinction is approximated by multiplying the standard atmospheric extinction curve (plotted against each wavelength) by the mean air mass calculated over the duration of the observation. A dry atmosphere reduces infrared extinction significantly.

Scattering

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https://en.wikipedia.org/wiki/Scattering

 

Feynman diagram of scattering between two electrons by emission of a virtual photon

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 or sound, are forced to deviate from a straight trajectory 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. Reflections of radiation that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as Isaac Newton in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800. John Tyndall, 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 rays (electron beams) and X-rays was observed and discussed. With the discovery of subatomic particles (e.g. Ernest Rutherford 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, 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. In Particle Physics the quantum interaction and scattering of fundamental particles is described by the Scattering Matrix or S-Matrix, introduced and developed by John Archibald Wheeler and Werner Heisenberg.

Scattering is quantified using many different concepts, including scattering cross section (σ), attenuation coefficients, the bidirectional scattering distribution function (BSDF), S-matrices, and mean free path.

Single and multiple scattering

Zodiacal light is a faint, diffuse glow visible in the night sky. The phenomenon stems from the scattering of sunlight by interplanetary dust spread throughout the plane of the Solar System.

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.

Theory

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".

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.

Attenuation due to scattering

Equivalent quantities used in the theory of scattering from composite specimens, but with a variety of units.

When the target is a set of many scattering centers whose relative position varies unpredictably, it is customary to think of a range equation whose arguments take different forms in different application areas. In the simplest case consider an interaction that removes particles from the "unscattered beam" at a uniform rate that is proportional to the incident number of particles per unit area per unit time (${\displaystyle I}$), i.e. that

${\displaystyle \frac{dI}{dx}=-QI}$

where Q is an interaction coefficient and x is the distance traveled in the target.

The above ordinary first-order differential equation has solutions of the form:

${\displaystyle I=I_o{e}^{-Q\mathrm{\Delta }x}=I_o{e}^{-\frac{\mathrm{\Delta }x}{\lambda }}=I_o{e}^{-\sigma (\eta \mathrm{\Delta }x)}=I_o{e}^{-\frac{\rho \mathrm{\Delta }x}{\tau }},}$

where I_o is the initial flux, path length Δx ≡ x − x_o, the second equality defines an interaction mean free path λ, the third uses the number of targets per unit volume η to define an area cross-section σ, and the last uses the target mass density ρ to define a density mean free path τ. Hence one converts between these quantities via Q = 1/λ = ησ = ρ/τ, as shown in the figure at left.

In electromagnetic absorption spectroscopy, for example, interaction coefficient (e.g. Q in cm⁻¹) is variously called opacity, absorption coefficient, and attenuation coefficient. In nuclear physics, area cross-sections (e.g. σ in barns or units of 10⁻²⁴ cm²), density mean free path (e.g. τ in grams/cm²), and its reciprocal the mass attenuation coefficient (e.g. in cm²/gram) or area per nucleon are all popular, while in electron microscopy the inelastic mean free path (e.g. λ in nanometers) is often discussed instead.

Elastic and inelastic scattering

The term "elastic scattering" implies that the internal states of the scattering particles do not change, and hence they emerge unchanged from the scattering process. In inelastic scattering, by contrast, the particles' internal state is changed, which may amount to exciting some of the electrons of a scattering atom, or the complete annihilation of a scattering particle and the creation of entirely new particles.

The example of scattering in quantum chemistry is particularly instructive, as the theory is reasonably complex while still having a good foundation on which to build an intuitive understanding. When two atoms are scattered off one another, one can understand them as being the bound state solutions of some differential equation. Thus, for example, the hydrogen atom corresponds to a solution to the Schrödinger equation with a negative inverse-power (i.e., attractive Coulombic) central potential. The scattering of two hydrogen atoms will disturb the state of each atom, resulting in one or both becoming excited, or even ionized, representing an inelastic scattering process.

The term "deep inelastic scattering" refers to a special kind of scattering experiment in particle physics.

Mathematical framework

In mathematics, scattering theory deals with a more abstract formulation of the same set of concepts. For example, if a differential equation is known to have some simple, localized solutions, and the solutions are a function of a single parameter, that parameter can take the conceptual role of time. One then asks what might happen if two such solutions are set up far away from each other, in the "distant past", and are made to move towards each other, interact (under the constraint of the differential equation) and then move apart in the "future". The scattering matrix then pairs solutions in the "distant past" to those in the "distant future".

Solutions to differential equations are often posed on manifolds. Frequently, the means to the solution requires the study of the spectrum of an operator on the manifold. As a result, the solutions often have a spectrum that can be identified with a Hilbert space, and scattering is described by a certain map, the S matrix, on Hilbert spaces. Spaces with a discrete spectrum correspond to bound states in quantum mechanics, while a continuous spectrum is associated with scattering states. The study of inelastic scattering then asks how discrete and continuous spectra are mixed together.

An important, notable development is the inverse scattering transform, central to the solution of many exactly solvable models.

Theoretical physics

Top: the real part of a plane wave travelling upwards. Bottom: The real part of the field after inserting in the path of the plane wave a small transparent disk of index of refraction higher than the index of the surrounding medium. This object scatters part of the wave field, although at any individual point, the wave's frequency and wavelength remain intact.

In mathematical physics, scattering theory is a framework for studying and understanding the interaction or scattering of solutions to partial differential equations. In acoustics, the differential equation is the wave equation, and scattering studies how its solutions, the sound waves, scatter from solid objects or propagate through non-uniform media (such as sound waves, in sea water, coming from a submarine). In the case of classical electrodynamics, the differential equation is again the wave equation, and the scattering of light or radio waves is studied. In particle physics, the equations are those of Quantum electrodynamics, Quantum chromodynamics and the Standard Model, the solutions of which correspond to fundamental particles.

In regular quantum mechanics, which includes quantum chemistry, the relevant equation is the Schrödinger equation, although equivalent formulations, such as the Lippmann-Schwinger equation and the Faddeev equations, are also largely used. The solutions of interest describe the long-term motion of free atoms, molecules, photons, electrons, and protons. The scenario is that several particles come together from an infinite distance away. These reagents then collide, optionally reacting, getting destroyed or creating new particles. The products and unused reagents then fly away to infinity again. (The atoms and molecules are effectively particles for our purposes. Also, under everyday circumstances, only photons are being created and destroyed.) The solutions reveal which directions the products are most likely to fly off to and how quickly. They also reveal the probability of various reactions, creations, and decays occurring. There are two predominant techniques of finding solutions to scattering problems: partial wave analysis, and the Born approximation.

Electromagnetics

A Feynman diagram of scattering between two electrons by emission of a virtual photon.

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:

$${\displaystyle \alpha =\pi D_{\text{p}}/\lambda ,}$$

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 (small particle compared to wavelength of light);
• α ≈ 1: Mie scattering (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 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. 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 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 involves the migration of macromolecules 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.

Transparency and translucency

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Dichroic filters are created using optically transparent materials.

In the field of optics, transparency (also called pellucidity or diaphaneity) is the physical property of allowing light to pass through the material without appreciable scattering of light. On a macroscopic scale (one in which the dimensions are much larger than the wavelengths of the photons in question), the photons can be said to follow Snell's law. Translucency (also called translucence or translucidity) 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 material is made up of components with different indices of refraction. A transparent material is made up of components with a uniform index of refraction. 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.

Comparisons of 1. opacity, 2. translucency, and 3. transparency; behind each panel (from top to bottom: grey, red, white) is a star.

Etymology

• late Middle English: from Old French, from medieval Latin transparent- ‘shining through’, from Latin transparere, from trans- ‘through’ + parere ‘be visible’.
• late 16th century (in the Latin sense): from Latin translucent- ‘shining through’, from the verb translucere, from trans- ‘through’ + lucere ‘to shine’.
• late Middle English opake, from Latin opacus ‘darkened’. The current spelling (rare before the 19th century) has been influenced by the French form.

Introduction

With regard to the absorption of light, primary material considerations include:

• At the electronic level, absorption in the ultraviolet and visible (UV-Vis) portions of the spectrum depends on whether the electron orbitals are spaced (or "quantized") such that they can absorb a quantum of light (or photon) of a specific frequency, and does not violate selection rules. For example, in most glasses, electrons have no available energy levels above them in range of that associated with visible light, or if they do, they violate selection rules, meaning there is no appreciable absorption in pure (undoped) glasses, making them ideal transparent materials for windows in buildings.
• At the atomic or molecular level, physical absorption in the infrared portion of the spectrum depends on the frequencies of atomic or molecular vibrations or chemical bonds, and on selection rules. Nitrogen and oxygen are not greenhouse gases because there is no molecular dipole moment.

With regard to the scattering of light, the most critical factor is the length scale of any or all of these structural features relative to the wavelength of the light being scattered. Primary material considerations include:

• Crystalline structure: whether the atoms or molecules exhibit the 'long-range order' evidenced in crystalline solids.
• Glassy structure: scattering centers include fluctuations in density or composition.
• Microstructure: scattering centers include internal surfaces such as grain boundaries, crystallographic defects and microscopic pores.
• Organic materials: scattering centers include fiber and cell structures and boundaries.

Main article: Light scattering

 

General mechanism of diffuse reflection

Diffuse reflection - Generally, when light strikes the surface of a (non-metallic and non-glassy) solid material, it bounces off in all directions due to multiple reflections by the microscopic irregularities inside the material (e.g., the grain boundaries of a polycrystalline material, or the cell or fiber boundaries of an organic material), and by its surface, if it is rough. Diffuse reflection is typically characterized by omni-directional reflection angles. Most of the objects visible to the naked eye are identified via diffuse reflection. Another term commonly used for this type of reflection is "light scattering". Light scattering from the surfaces of objects is our primary mechanism of physical observation.

Light scattering in liquids and solids depends on the wavelength of the light being scattered. Limits to spatial scales of visibility (using white light) therefore arise, depending on the frequency of the light wave and the physical dimension (or spatial scale) of the scattering center. Visible light has a wavelength scale on the order of a half a micrometer. Scattering centers (or particles) as small as one micrometer have been observed directly in the light microscope (e.g., Brownian motion).

Transparent ceramics

Optical transparency in polycrystalline materials is limited by the amount of light which is scattered by their microstructural features. Light scattering depends on the wavelength of the light. Limits to spatial scales of visibility (using white light) therefore arise, depending on the frequency of the light wave and the physical dimension of the scattering center. For example, since visible light has a wavelength scale on the order of a micrometer, scattering centers will have dimensions on a similar spatial scale. Primary scattering centers in polycrystalline materials include microstructural defects such as pores and grain boundaries. In addition to pores, most of the interfaces in a typical metal or ceramic object are in the form of grain boundaries which separate tiny regions of crystalline order. When the size of the scattering center (or grain boundary) is reduced below the size of the wavelength of the light being scattered, the scattering no longer occurs to any significant extent.

In the formation of polycrystalline materials (metals and ceramics) the size of the crystalline grains is determined largely by the size of the crystalline particles present in the raw material during formation (or pressing) of the object. Moreover, the size of the grain boundaries scales directly with particle size. Thus a reduction of the original particle size well below the wavelength of visible light (about 1/15 of the light wavelength or roughly 600/15 = 40 nanometers) eliminates much of light scattering, resulting in a translucent or even transparent material.

Computer modeling of light transmission through translucent ceramic alumina has shown that microscopic pores trapped near grain boundaries act as primary scattering centers. The volume fraction of porosity had to be reduced below 1% for high-quality optical transmission (99.99 percent of theoretical density). This goal has been readily accomplished and amply demonstrated in laboratories and research facilities worldwide using the emerging chemical processing methods encompassed by the methods of sol-gel chemistry and nanotechnology.

Translucency of a material being used to highlight the structure of a mushroom

Transparent ceramics have created interest in their applications for high energy lasers, transparent armor windows, nose cones for heat seeking missiles, radiation detectors for non-destructive testing, high energy physics, space exploration, security and medical imaging applications. Large laser elements made from transparent ceramics can be produced at a relatively low cost. These components are free of internal stress or intrinsic birefringence, and allow relatively large doping levels or optimized custom-designed doping profiles. This makes ceramic laser elements particularly important for high-energy lasers.

The development of transparent panel products will have other potential advanced applications including high strength, impact-resistant materials that can be used for domestic windows and skylights. Perhaps more important is that walls and other applications will have improved overall strength, especially for high-shear conditions found in high seismic and wind exposures. If the expected improvements in mechanical properties bear out, the traditional limits seen on glazing areas in today's building codes could quickly become outdated if the window area actually contributes to the shear resistance of the wall.

Currently available infrared transparent materials typically exhibit a trade-off between optical performance, mechanical strength and price. For example, sapphire (crystalline alumina) is very strong, but it is expensive and lacks full transparency throughout the 3–5 micrometer mid-infrared range. Yttria is fully transparent from 3–5 micrometers, but lacks sufficient strength, hardness, and thermal shock resistance for high-performance aerospace applications. Not surprisingly, a combination of these two materials in the form of the yttrium aluminium garnet (YAG) is one of the top performers in the field.

Absorption of light in solids

When light strikes an object, it usually has not just a single frequency (or wavelength) but many. Objects have a tendency to selectively absorb, reflect or transmit light of certain frequencies. That is, one object might reflect green light while absorbing all other frequencies of visible light. Another object might selectively transmit blue light while absorbing all other frequencies of visible light. The manner in which visible light interacts with an object is dependent upon the frequency of the light, the nature of the atoms in the object, and often the nature of the electrons in the atoms of the object.

Some materials allow much of the light that falls on them to be transmitted through the material without being reflected. Materials that allow the transmission of light waves through them are called optically transparent. Chemically pure (undoped) window glass and clean river or spring water are prime examples of this.

Materials which do not allow the transmission of any light wave frequencies are called opaque. Such substances may have a chemical composition which includes what are referred to as absorption centers. Most materials are composed of materials which are selective in their absorption of light frequencies. Thus they absorb only certain portions of the visible spectrum. The frequencies of the spectrum which are not absorbed are either reflected back or transmitted for our physical observation. In the visible portion of the spectrum, this is what gives rise to color.

Absorption centers are largely responsible for the appearance of specific wavelengths of visible light all around us. Moving from longer (0.7 micrometer) to shorter (0.4 micrometer) wavelengths: red, orange, yellow, green and blue (ROYGB) can all be identified by our senses in the appearance of color by the selective absorption of specific light wave frequencies (or wavelengths). Mechanisms of selective light wave absorption include:

• Electronic: Transitions in electron energy levels within the atom (e.g., pigments). These transitions are typically in the ultraviolet (UV) and/or visible portions of the spectrum.
• Vibrational: Resonance in atomic/molecular vibrational modes. These transitions are typically in the infrared portion of the spectrum.

UV-Vis: Electronic transitions

In electronic absorption, the frequency of the incoming light wave is at or near the energy levels of the electrons within the atoms which compose the substance. In this case, the electrons will absorb the energy of the light wave and increase their energy state, often moving outward from the nucleus of the atom into an outer shell or orbital.

The atoms that bind together to make the molecules of any particular substance contain a number of electrons (given by the atomic number Z in the periodic table). Recall that all light waves are electromagnetic in origin. Thus they are affected strongly when coming into contact with negatively charged electrons in matter. When photons (individual packets of light energy) come in contact with the valence electrons of atom, one of several things can and will occur:

• A molecule absorbs the photon, some of the energy may be lost via luminescence, fluorescence and phosphorescence.
• A molecule absorbs the photon which results in reflection or scattering.
• A molecule cannot absorb the energy of the photon and the photon continues on its path. This results in transmission (provided no other absorption mechanisms are active).

Most of the time, it is a combination of the above that happens to the light that hits an object. The states in different materials vary in the range of energy that they can absorb. Most glasses, for example, block ultraviolet (UV) light. What happens is the electrons in the glass absorb the energy of the photons in the UV range while ignoring the weaker energy of photons in the visible light spectrum. But there are also existing special glass types, like special types of borosilicate glass or quartz that are UV-permeable and thus allow a high transmission of ultra violet light.

Thus, when a material is illuminated, individual photons of light can make the valence electrons of an atom transition to a higher electronic energy level. The photon is destroyed in the process and the absorbed radiant energy is transformed to electric potential energy. Several things can happen then to the absorbed energy: it may be re-emitted by the electron as radiant energy (in this case the overall effect is in fact a scattering of light), dissipated to the rest of the material (i.e. transformed into heat), or the electron can be freed from the atom (as in the photoelectric effects and Compton effects).

Infrared: Bond stretching

Normal modes of vibration in a crystalline solid

The primary physical mechanism for storing mechanical energy of motion in condensed matter is through heat, or thermal energy. Thermal energy manifests itself as energy of motion. Thus, heat is motion at the atomic and molecular levels. The primary mode of motion in crystalline substances is vibration. Any given atom will vibrate around some mean or average position within a crystalline structure, surrounded by its nearest neighbors. This vibration in two dimensions is equivalent to the oscillation of a clock's pendulum. It swings back and forth symmetrically about some mean or average (vertical) position. Atomic and molecular vibrational frequencies may average on the order of 10¹² cycles per second (Terahertz radiation).

When a light wave of a given frequency strikes a material with particles having the same or (resonant) vibrational frequencies, then those particles will absorb the energy of the light wave and transform it into thermal energy of vibrational motion. Since different atoms and molecules have different natural frequencies of vibration, they will selectively absorb different frequencies (or portions of the spectrum) of infrared light. Reflection and transmission of light waves occur because the frequencies of the light waves do not match the natural resonant frequencies of vibration of the objects. When infrared light of these frequencies strikes an object, the energy is reflected or transmitted.

If the object is transparent, then the light waves are passed on to neighboring atoms through the bulk of the material and re-emitted on the opposite side of the object. Such frequencies of light waves are said to be transmitted.

Transparency in insulators

An object may be not transparent either because it reflects the incoming light or because it absorbs the incoming light. Almost all solids reflect a part and absorb a part of the incoming light.

When light falls onto a block of metal, it encounters atoms that are tightly packed in a regular lattice and a "sea of electrons" moving randomly between the atoms. In metals, most of these are non-bonding electrons (or free electrons) as opposed to the bonding electrons typically found in covalently bonded or ionically bonded non-metallic (insulating) solids. In a metallic bond, any potential bonding electrons can easily be lost by the atoms in a crystalline structure. The effect of this delocalization is simply to exaggerate the effect of the "sea of electrons". As a result of these electrons, most of the incoming light in metals is reflected back, which is why we see a shiny metal surface.

Most insulators (or dielectric materials) are held together by ionic bonds. Thus, these materials do not have free conduction electrons, and the bonding electrons reflect only a small fraction of the incident wave. The remaining frequencies (or wavelengths) are free to propagate (or be transmitted). This class of materials includes all ceramics and glasses.

If a dielectric material does not include light-absorbent additive molecules (pigments, dyes, colorants), it is usually transparent to the spectrum of visible light. Color centers (or dye molecules, or "dopants") in a dielectric absorb a portion of the incoming light. The remaining frequencies (or wavelengths) are free to be reflected or transmitted. This is how colored glass is produced.

Most liquids and aqueous solutions are highly transparent. For example, water, cooking oil, rubbing alcohol, air, and natural gas are all clear. Absence of structural defects (voids, cracks, etc.) and molecular structure of most liquids are chiefly responsible for their excellent optical transmission. The ability of liquids to "heal" internal defects via viscous flow is one of the reasons why some fibrous materials (e.g., paper or fabric) increase their apparent transparency when wetted. The liquid fills up numerous voids making the material more structurally homogeneous.

Light scattering in an ideal defect-free crystalline (non-metallic) solid which provides no scattering centers for incoming light will be due primarily to any effects of anharmonicity within the ordered lattice. Light transmission will be highly directional due to the typical anisotropy of crystalline substances, which includes their symmetry group and Bravais lattice. For example, the seven different crystalline forms of quartz silica (silicon dioxide, SiO₂) are all clear, transparent materials.

Optical waveguides

Propagation of light through a multi-mode optical fiber

 

A laser beam bouncing down an acrylic rod, illustrating the total internal reflection of light in a multimode optical fiber

Optically transparent materials focus on the response of a material to incoming light waves of a range of wavelengths. Guided light wave transmission via frequency selective waveguides involves the emerging field of fiber optics and the ability of certain glassy compositions to act as a transmission medium for a range of frequencies simultaneously (multi-mode optical fiber) with little or no interference between competing wavelengths or frequencies. This resonant mode of energy and data transmission via electromagnetic (light) wave propagation is relatively lossless.

An optical fiber is a cylindrical dielectric waveguide that transmits light along its axis by the process of total internal reflection. The fiber consists of a core surrounded by a cladding layer. To confine the optical signal in the core, the refractive index of the core must be greater than that of the cladding. The refractive index is the parameter reflecting the speed of light in a material. (Refractive index is the ratio of the speed of light in vacuum to the speed of light in a given medium. The refractive index of vacuum is therefore 1.) The larger the refractive index, the more slowly light travels in that medium. Typical values for core and cladding of an optical fiber are 1.48 and 1.46, respectively.

When light traveling in a dense medium hits a boundary at a steep angle, the light will be completely reflected. This effect, called total internal reflection, is used in optical fibers to confine light in the core. Light travels along the fiber bouncing back and forth off of the boundary. Because the light must strike the boundary with an angle greater than the critical angle, only light that enters the fiber within a certain range of angles will be propagated. This range of angles is called the acceptance cone of the fiber. The size of this acceptance cone is a function of the refractive index difference between the fiber's core and cladding. Optical waveguides are used as components in integrated optical circuits (e.g. combined with lasers or light-emitting diodes, LEDs) or as the transmission medium in local and long haul optical communication systems.

Mechanisms of attenuation

See also: Light scattering

 

Light attenuation by ZBLAN and silica fibers

Attenuation in fiber optics, also known as transmission loss, is the reduction in intensity of the light beam (or signal) with respect to distance traveled through a transmission medium. Attenuation coefficients in fiber optics usually use units of dB/km through the medium due to the very high quality of transparency of modern optical transmission media. The medium is usually a fiber of silica glass that confines the incident light beam to the inside. Attenuation is an important factor limiting the transmission of a signal across large distances. In optical fibers the main attenuation source is scattering from molecular level irregularities (Rayleigh scattering) due to structural disorder and compositional fluctuations of the glass structure. This same phenomenon is seen as one of the limiting factors in the transparency of infrared missile domes. Further attenuation is caused by light absorbed by residual materials, such as metals or water ions, within the fiber core and inner cladding. Light leakage due to bending, splices, connectors, or other outside forces are other factors resulting in attenuation.

As camouflage

Many animals of the open sea, like this Aurelia labiata jellyfish, are largely transparent

 

Further information: List of camouflage methods

Many marine animals that float near the surface are highly transparent, giving them almost perfect camouflage. However, transparency is difficult for bodies made of materials that have different refractive indices from seawater. Some marine animals such as jellyfish have gelatinous bodies, composed mainly of water; their thick mesogloea is acellular and highly transparent. This conveniently makes them buoyant, but it also makes them large for their muscle mass, so they cannot swim fast, making this form of camouflage a costly trade-off with mobility. Gelatinous planktonic animals are between 50 and 90 percent transparent. A transparency of 50 percent is enough to make an animal invisible to a predator such as cod at a depth of 650 metres (2,130 ft); better transparency is required for invisibility in shallower water, where the light is brighter and predators can see better. For example, a cod can see prey that are 98 percent transparent in optimal lighting in shallow water. Therefore, sufficient transparency for camouflage is more easily achieved in deeper waters. For the same reason, transparency in air is even harder to achieve, but a partial example is found in the glass frogs of the South American rain forest, which have translucent skin and pale greenish limbs. Several Central American species of clearwing (ithomiine) butterflies and many dragonflies and allied insects also have wings which are mostly transparent, a form of crypsis that provides some protection from predators.