This section should be summarized and a link to Optics provided by using the main template per the guidance in Wikipedia:Summary style.

Geometrical optics, or ray optics, describes light propagation in terms of "rays". The "ray" in geometric optics is an abstraction, or "instrument", which can be used to approximately model how light will propagate. Light rays are defined to propagate in a rectilinear path as far as they travel in a homogeneous medium. Rays bend (and may split in two) at the interface between two dissimilar media, may curve in a medium where the refractive index changes, and may be absorbed and reflected. Geometrical optics provides rules, which may depend on the color (wavelength) of the ray, for propagating these rays through an optical system. This is a significant simplification of optics that fails to account for optical effects such as diffraction and interference. It is an excellent approximation, however, when the wavelength is very small compared with the size of structures with which the light interacts. Geometric optics can be used to describe the geometrical aspects of imaging, including optical aberrations.

Explanation[link]

As light travels through space, it oscillates in amplitude. In this image, each maximum amplitude crest is marked with a plane to illustrate the wavefront. The ray is the arrow perpendicular to these parallel surfaces.

A light ray is a line or curve that is perpendicular to the light's wavefronts (and is therefore collinear with the wave vector).

A slightly more rigorous definition of a light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.^[1]

Geometrical optics is often simplified by making the paraxial approximation, or "small angle approximation." The mathematical behavior then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of Gaussian optics and paraxial ray tracing, which are used to find basic properties of optical systems, such as approximate image and object positions and magnifications.^[2]

Reflection[link]

Diagram of specular reflection

Glossy surfaces such as mirrors reflect light in a simple, predictable way. This allows for production of reflected images that can be associated with an actual (real) or extrapolated (virtual) location in space.

With such surfaces, the direction of the reflected ray is determined by the angle the incident ray makes with the surface normal, a line perpendicular to the surface at the point where the ray hits. The incident and reflected rays lie in a single plane, and the angle between the reflected ray and the surface normal is the same as that between the incident ray and the normal.^[3] This is known as the Law of Reflection.

For flat mirrors, the law of reflection implies that images of objects are upright and the same distance behind the mirror as the objects are in front of the mirror. The image size is the same as the object size. (The magnification of a flat mirror is equal to one.) The law also implies that mirror images are parity inverted, which is perceived as a left-right inversion.

Mirrors with curved surfaces can be modeled by ray tracing and using the law of reflection at each point on the surface. For mirrors with parabolic surfaces, parallel rays incident on the mirror produce reflected rays that converge at a common focus. Other curved surfaces may also focus light, but with aberrations due to the diverging shape causing the focus to be smeared out in space. In particular, spherical mirrors exhibit spherical aberration. Curved mirrors can form images with magnification greater than or less than one, and the image can be upright or inverted. An upright image formed by reflection in a mirror is always virtual, while an inverted image is real and can be projected onto a screen.^[3]

Refraction[link]

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Illustration of Snell's Law

Refraction occurs when light travels through an area of space that has a changing index of refraction. The simplest case of refraction occurs when there is an interface between a uniform medium with index of refraction Failed to parse (Missing texvc executable; please see math/README to configure.): n_1

and another medium with index of refraction Failed to parse (Missing texvc executable; please see math/README to configure.): n_2

. In such situations, Snell's Law describes the resulting deflection of the light ray:

Failed to parse (Missing texvc executable; please see math/README to configure.): n_1\sin\theta_1 = n_2\sin\theta_2\

where Failed to parse (Missing texvc executable; please see math/README to configure.): \theta_1

and Failed to parse (Missing texvc executable; please see math/README to configure.): \theta_2
are the angles between the normal (to the interface) and the incident and refracted waves, respectively. This phenomenon is also associated with a changing speed of light as seen from the definition of index of refraction provided above which implies:

Failed to parse (Missing texvc executable; please see math/README to configure.): v_1\sin\theta_2\ = v_2\sin\theta_1

where Failed to parse (Missing texvc executable; please see math/README to configure.): v_1

and Failed to parse (Missing texvc executable; please see math/README to configure.): v_2
are the wave velocities through the respective media.[3]

Various consequences of Snell's Law include the fact that for light rays traveling from a material with a high index of refraction to a material with a low index of refraction, it is possible for the interaction with the interface to result in zero transmission. This phenomenon is called total internal reflection and allows for fiber optics technology. As light signals travel down a fiber optic cable, it undergoes total internal reflection allowing for essentially no light lost over the length of the cable. It is also possible to produce polarized light rays using a combination of reflection and refraction: When a refracted ray and the reflected ray form a right angle, the reflected ray has the property of "plane polarization". The angle of incidence required for such a scenario is known as Brewster's angle.^[3]

Snell's Law can be used to predict the deflection of light rays as they pass through "linear media" as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. Additionally, since different frequencies of light have slightly different indexes of refraction in most materials, refraction can be used to produce dispersion spectra that appear as rainbows. The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton.^[3]

Some media have an index of refraction which varies gradually with position and, thus, light rays curve through the medium rather than travel in straight lines. This effect is what is responsible for mirages seen on hot days where the changing index of refraction of the air causes the light rays to bend creating the appearance of specular reflections in the distance (as if on the surface of a pool of water). Material that has a varying index of refraction is called a gradient-index (GRIN) material and has many useful properties used in modern optical scanning technologies including photocopiers and scanners. The phenomenon is studied in the field of gradient-index optics.^[4]

A ray tracing diagram for a simple converging lens.

A device which produces converging or diverging light rays due to refraction is known as a lens. Thin lenses produce focal points on either side that can be modeled using the lensmaker's equation.^[5] In general, two types of lenses exist: convex lenses, which cause parallel light rays to converge, and concave lenses, which cause parallel light rays to diverge. The detailed prediction of how images are produced by these lenses can be made using ray-tracing similar to curved mirrors. Similarly to curved mirrors, thin lenses follow a simple equation that determines the location of the images given a particular focal length (Failed to parse (Missing texvc executable; please see math/README to configure.): f ) and object distance (Failed to parse (Missing texvc executable; please see math/README to configure.): S_1 ):

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{S_1} + \frac{1}{S_2} = \frac{1}{f}

where Failed to parse (Missing texvc executable; please see math/README to configure.): S_2

is the distance associated with the image and is considered by convention to be negative if on the same side of the lens as the object and positive if on the opposite side of the lens.[5] The focal length f is considered negative for concave lenses.

Incoming parallel rays are focused by a convex lens into an inverted real image one focal length from the lens, on the far side of the lens. Rays from an object at finite distance are focused further from the lens than the focal distance; the closer the object is to the lens, the further the image is from the lens. With concave lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at an upright virtual image one focal length from the lens, on the same side of the lens that the parallel rays are approaching on. Rays from an object at finite distance are associated with a virtual image that is closer to the lens than the focal length, and on the same side of the lens as the object. The closer the object is to the lens, the closer the virtual image is to the lens.

Likewise, the magnification of a lens is given by

Failed to parse (Missing texvc executable; please see math/README to configure.): M = - \frac{S_2}{S_1} = \frac{f}{f - S_1}

where the negative sign is given, by convention, to indicate an upright object for positive values and an inverted object for negative values. Similar to mirrors, upright images produced by single lenses are virtual while inverted images are real.^[3]

Lenses suffer from aberrations that distort images and focal points. These are due to both to geometrical imperfections and due to the changing index of refraction for different wavelengths of light (chromatic aberration).^[3]

Underlying mathematics[link]

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As a mathematical study, geometrical optics emerges as a short-wavelength limit for solutions to hyperbolic partial differential equations. In this short-wavelength limit, it is possible to approximate the solution locally by

Failed to parse (Missing texvc executable; please see math/README to configure.): u(t,x) \approx a(t,x)e^{i(k\cdot x - \omega t)}

where Failed to parse (Missing texvc executable; please see math/README to configure.): k, \omega

satisfy a dispersion relation, and the amplitude Failed to parse (Missing texvc executable; please see math/README to configure.): a(t,x)
varies slowly.  More precisely, the leading order solution takes the form

Failed to parse (Missing texvc executable; please see math/README to configure.): a_0(t,x) e^{i\varphi(t,x)/\varepsilon}.

The phase Failed to parse (Missing texvc executable; please see math/README to configure.): \varphi(t,x)/\varepsilon

can be linearized to recover large wavenumber Failed to parse (Missing texvc executable; please see math/README to configure.): k:= \nabla_x \varphi

, and frequency Failed to parse (Missing texvc executable; please see math/README to configure.): \omega := -\partial_t \varphi . The amplitude Failed to parse (Missing texvc executable; please see math/README to configure.): a_0

satisfies a transport equation.  The small parameter Failed to parse (Missing texvc executable; please see math/README to configure.): \varepsilon\,
enters the scene due to highly oscillatory initial conditions.  Thus, when initial conditions oscillate much faster than the coefficients of the differential equation, solutions will be highly oscillatory, and transported along rays.  Assuming coefficients in the differential equation are smooth, the rays will be too.  In other words, refraction does not take place.  The motivation for this technique comes from studying the typical scenario of light propagation where short wavelength light travels along rays that minimize (more or less) its travel time.  Its full application requires tools from microlocal analysis.

A simple example[link]

Starting with the wave equation for Failed to parse (Missing texvc executable; please see math/README to configure.): (t,x) \in \mathbb{R}\times\mathbb{R}^n

Failed to parse (Missing texvc executable; please see math/README to configure.): L(\partial_t, \nabla_x) u := \left( \frac{\partial^2}{\partial t^2} - c(x)^2 \Delta \right)u(t,x) = 0, \;\; u(0,x) = u_0(x),\;\; u_t(0,x) = 0

assume an asymptotic series solution of the form

Failed to parse (Missing texvc executable; please see math/README to configure.): u(t,x) \sim a_\varepsilon(t,x)e^{i\varphi(t,x)/\varepsilon} = \sum_{j=0}^\infty i^j \varepsilon^j a_j(t,x) e^{i\varphi(t,x)/\varepsilon}.

Check that

Failed to parse (Missing texvc executable; please see math/README to configure.): L(\partial_t,\nabla_x)(e^{i\varphi(t,x)/\varepsilon}) a_\varepsilon(t,x) = e^{i\varphi(t,x)/\varepsilon} \left( \left(\frac{i}{\varepsilon} \right)^2 L(\varphi_t, \nabla_x\varphi)a_\varepsilon + \frac{2i}{\varepsilon} V(\partial_t,\nabla_x)a_\varepsilon + \frac{i}{\varepsilon} (a_\varepsilon L(\partial_t,\nabla_x)\varphi) + L(\partial_t,\nabla_x)a_\varepsilon \right)

with

Failed to parse (Missing texvc executable; please see math/README to configure.): V(\partial_t,\nabla_x) := \frac{\partial \varphi}{\partial t} \frac{\partial}{\partial t} - c^2(x)\sum_j \frac{\partial \varphi}{\partial x_j} \frac{\partial}{\partial x_j}

Plugging the series into this equation, and equating powers of Failed to parse (Missing texvc executable; please see math/README to configure.): \varepsilon , the most singular term Failed to parse (Missing texvc executable; please see math/README to configure.): O(\varepsilon^{-2})

satisfies the eikonal equation (in this case called a dispersion relation),

Failed to parse (Missing texvc executable; please see math/README to configure.): 0 = L(\varphi_t,\nabla_x\varphi) = (\varphi_t)^2 - c(x)^2(\nabla_x \varphi)^2.

To order Failed to parse (Missing texvc executable; please see math/README to configure.): \varepsilon^{-1} , the leading order amplitude must satisfy a transport equation

Failed to parse (Missing texvc executable; please see math/README to configure.): 2V a_0 + (L\varphi)a_0 = 0

With the definition Failed to parse (Missing texvc executable; please see math/README to configure.): k : = \nabla_x \varphi , Failed to parse (Missing texvc executable; please see math/README to configure.): \omega := -\varphi_t , the eikonal equation is precisely the dispersion relation that results by plugging the plane wave solution Failed to parse (Missing texvc executable; please see math/README to configure.): e^{i(k\cdot x - \omega t)}

into the wave equation.  The value of this more complicated expansion is that plane waves cannot be solutions when the wavespeed Failed to parse (Missing texvc executable; please see math/README to configure.): c
is non-constant.  However, it can be shown that the amplitude Failed to parse (Missing texvc executable; please see math/README to configure.): a_0
and phase Failed to parse (Missing texvc executable; please see math/README to configure.): \varphi
are smooth, so that on a local scale there are plane waves.  

To justify this technique, the remaining terms must be shown to be small in some sense. This can be done using energy estimates, and an assumption of rapidly oscillating initial conditions. It also must be shown that the series converges in some sense.

References[link]

External links[link]

Illustration of an emission of a gamma ray (γ) from an atomic nucleus

Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency and therefore energy. Gamma rays are ionizing radiation and are thus biologically hazardous. Gamma rays are classically produced by the decay from high energy states of atomic nuclei (gamma decay), but also in many other ways. Natural sources of gamma rays on Earth include gamma decay from naturally-occurring radioisotopes such as potassium-40, and also as a secondary radiation from various atmospheric interactions with cosmic ray particles. Some rare terrestrial natural sources that produce gamma rays that are not of a nuclear origin, are lightning strikes and terrestrial gamma-ray flashes, which produce high energy emissions from natural high-energy voltages. Gamma rays are produced by a number of astronomical processes in which very high-energy electrons are produced. Such electrons produce secondary gamma rays by the mechanisms of bremsstrahlung, inverse Compton scattering and synchrotron radiation. A large fraction of such astronomical gamma rays are screened by Earth's atmosphere and must be detected by spacecraft. Notable artificial sources of gamma rays include fission such as occurs in nuclear reactors, and high energy physics experiments, such as neutral pion decay and nuclear fusion.

The first gamma ray source to be discovered historically was the radioactive decay process called gamma decay. In this type of decay, an excited nucleus emits a gamma ray almost immediately upon formation. Isomeric transition, however, can produce inhibited gamma decay with a measurable and much longer half-life. Paul Villard, a French chemist and physicist, discovered gamma radiation in 1900, while studying radiation emitted from radium.^[1][2] Villard's radiation was named "gamma rays" by Ernest Rutherford in 1903.^[3] Gamma rays were named in order of their penetrating power: alpha rays least, followed by beta rays, followed by gamma rays as the most penetrating.

Gamma rays typically have frequencies above 10 exahertz (or >10¹⁹ Hz), and therefore have energies above 100 keV and wavelengths less than 10 picometers (less than the diameter of an atom).^[4] However, this is not a hard and fast definition but rather only a rule-of-thumb description for natural processes. Gamma rays from radioactive decay commonly have energies of a few hundred keV, and almost always less than 10 MeV. On the other side of the decay energy range, there is effectively no lower limit to gamma energy derived from radioactive decay. By contrast, the energies of gamma rays from astronomical sources can be much higher, ranging over 10 TeV, at a level far too large to result from radioactive decay.^[5]

The distinction between X-rays and gamma rays has changed in recent decades. Originally, the electromagnetic radiation emitted by X-ray tubes almost invariably had a longer wavelength than the radiation (gamma rays) emitted by radioactive nuclei.^[6] Older literature distinguished between X- and gamma radiation on the basis of wavelength, with radiation shorter than some arbitrary wavelength, such as 10⁻¹¹ m, defined as gamma rays.^[7] However, with artificial sources now able to duplicate any electromagnetic radiation that originates in the nucleus, as well as far higher energies, the wavelengths characteristic of radioactive gamma ray sources vs. other types, now completely overlaps. Thus, gamma rays are now usually distinguished by their origin: X-rays are emitted by definition by electrons outside the nucleus, while gamma rays are emitted by the nucleus.^{[6][8][9][10]} Exceptions to this convention occur in astronomy, where gamma decay is seen in the afterglow of certain supernovas, but other high energy processes known to involve other than radioactive decay are still classed as sources of gamma radiation. A notable example is extremely powerful bursts of high-energy radiation normally referred to as long duration gamma-ray bursts, which produce gamma rays by a mechanism not compatible with radioactive decay. These bursts of gamma rays, thought to be due to the collapse of stars called hypernovas, are the most powerful events so far discovered in the cosmos.

Naming conventions and overlap in terminology[link]

In the past, the distinction between X-rays and gamma rays was based on energy, with gamma rays being considered a higher-energy version of electromagnetic radiation. However, modern high-energy X-rays produced by linear accelerators for megavoltage treatment in cancer often have higher energy (4 to 25 MeV) than do most classical gamma rays produced by nuclear gamma decay. One of the most common gamma ray emitting isotopes used in diagnostic nuclear medicine, technetium-99m, produces gamma radiation of the same energy (140 keV) as that produced by diagnostic X-ray machines, but of significantly lower energy than therapeutic photons from linear particle accelerators. In the medical community today, the convention that radiation produced by nuclear decay is the only type referred to as "gamma" radiation is still respected.

Because of this broad overlap in energy ranges, in physics the two types of electromagnetic radiation are now often defined by their origin: X-rays are emitted by electrons (either in orbitals outside of the nucleus, or while being accelerated to produce Bremsstrahlung-type radiation),^[12] while gamma rays are emitted by the nucleus or by means of other particle decays or annihilation events. There is no lower limit to the energy of photons produced by nuclear reactions, and thus ultraviolet or lower energy photons produced by these processes would also be defined as "gamma rays".^[13] The only naming-convention that is still universally respected is the rule that electromagnetic radiation that is known to be of atomic nuclear origin is always referred to as "gamma rays," and never as X-rays. However, in physics and astronomy, the reverse convention that all gamma rays are considered to be of nuclear origin is frequently violated.

In astronomy, higher energy gamma and X-rays are defined by energy, since the processes which produce them may be uncertain and photon energy, not origin, determines the required astronomical detectors needed.^[14] High energy photons occur in nature which are known to be produced by processes other than nuclear decay but are still referred to as gamma radiation. An example is "gamma rays" from lightning discharges at 10 to 20 MeV, and known to be produced by the Bremsstrahlung mechanism.

Another example is gamma ray bursts, now known to be produced from processes too powerful to involve simple collections of atoms undergoing radioactive decay. This has led to the realization that many gamma rays produced in astronomical processes result not from radioactive decay or particle annihilation, but rather in much the same manner as the production of X-rays. Although gamma rays in astronomy are discussed below as non-radioactive events, in fact a few gamma rays are known in astronomy to originate explicitly from gamma decay of nucleus (by their spectra and half-life). A classic example is that of supernova SN 1987A, which emits an "afterglow" of gamma-ray photons from the decay of newly-made radioactive cobalt-56. Most gamma rays in astronomy, however, arise by other mechanisms. Note that, astronomical literature tends to write "gamma-ray" with a hyphen, by analogy to X-rays, rather than in a way analogous to alpha rays and beta rays. This notation tends to subtly stress the non-nuclear source of most astronomical gamma rays.

Units of measure and exposure[link]

The measure of gamma rays' ionizing ability is called the exposure:

• The coulomb per kilogram (C/kg) is the SI unit of ionizing radiation exposure, and is the amount of radiation required to create 1 coulomb of charge of each polarity in 1 kilogram of matter.
• The röntgen (R) is an obsolete traditional unit of exposure, which represented the amount of radiation required to create 1 esu of charge of each polarity in 1 cubic centimeter of dry air. 1 röntgen = 2.58×10⁻⁴ C/kg

However, the effect of gamma and other ionizing radiation on living tissue is more closely related to the amount of energy deposited rather than the charge. This is called the absorbed dose:

• The gray (Gy), which has units of (J/kg), is the SI unit of absorbed dose, and is the amount of radiation required to deposit 1 joule of energy in 1 kilogram of any kind of matter.
• The rad is the (obsolete) corresponding traditional unit, equal to 0.01 J deposited per kg. 100 rad = 1 Gy.

The equivalent dose is the measure of the biological effect of radiation on human tissue. For gamma rays it is equal to the absorbed dose.

• The sievert (Sv) is the SI unit of equivalent dose, which for gamma rays is numerically equal to the gray (Gy).
• The rem is the traditional unit of equivalent dose. For gamma rays it is equal to the rad or 0.01 J of energy deposited per kg. 1 Sv = 100 rem.

Properties[link]

Shielding[link]

Shielding from gamma rays requires large amounts of mass, in contrast to alpha particles which can be blocked by paper or skin, and beta particles which can be shielded by foil. Gamma rays are better absorbed by materials with high atomic numbers and high density, although neither effect is important compared to the total mass per area in the path of the gamma ray. For this reason, a lead shield is only modestly better (20–30% better) as a gamma shield, than an equal mass of another shielding material such as aluminium, concrete, water or soil; lead's major advantage is not in lower weight, but rather its compactness due to its higher density. Protective clothing, goggles and respirators can protect from internal contact with or ingestion of alpha or beta particles, but provide no protection from gamma radiation from external sources.

The higher the energy of the gamma rays, the thicker the shielding required. Materials for shielding gamma rays are typically measured by the thickness required to reduce the intensity of the gamma rays by one half (the half value layer or HVL). For example gamma rays that require 1 cm (0.4″) of lead to reduce their intensity by 50% will also have their intensity reduced in half by 4.1 cm of granite rock, 6 cm (2½″) of concrete, or 9 cm (3½″) of packed soil. However, the mass of this much concrete or soil is only 20–30% greater than that of lead with the same absorption capability. Depleted uranium is used for shielding in portable gamma ray sources, but again the savings in weight over lead is modest, and the main effect is to reduce shielding bulk. In a nuclear power plant, shielding can be provided by steel and concrete in the pressure and particle containment vessel, while water provides a radiation shielding of fuel rods during storage or transport into the reactor core. The loss of water or removal of a "hot" fuel assembly into the air would result in much higher radiation levels than when kept under water.

Matter interaction[link]

The total absorption coefficient of aluminium (atomic number 13) for gamma rays, plotted versus gamma energy, and the contributions by the three effects. As is usual, the photoelectric effect is largest at low energies, Compton scattering dominates at intermediate energies, and pair production dominates at high energies.

The total absorption coefficient of lead (atomic number 82) for gamma rays, plotted versus gamma energy, and the contributions by the three effects. Here, the photoelectric effect dominates at low energy. Above 5 MeV, pair production starts to dominate.

When a gamma ray passes through matter, the probability for absorption is proportional to the thickness of the layer, the density of the material, and the absorption cross section of the material. The total absorption shows an exponential decrease of intensity with distance from the incident surface:

Failed to parse (Missing texvc executable; please see math/README to configure.): I(x) = I_0 \cdot e ^{-\mu x}

where x is the distance from the incident surface, μ = nσ is the absorption coefficient, measured in cm⁻¹, n the number of atoms per cm³ of the material (atomic density), σ the absorption cross section in cm² and x the distance from the incident surface of the gamma rays in cm.

As it passes through matter, gamma radiation ionizes via three processes: the photoelectric effect, Compton scattering, and pair production.

• Photoelectric effect: This describes the case in which a gamma photon interacts with and transfers its energy to an atomic electron, causing the ejection of that electron from the atom. The kinetic energy of the resulting photoelectron is equal to the energy of the incident gamma photon minus the energy that originally bound the electron to the atom (binding energy). The photoelectric effect is the dominant energy transfer mechanism for X-ray and gamma ray photons with energies below 50 keV (thousand electron volts), but it is much less important at higher energies.
• Compton scattering: This is an interaction in which an incident gamma photon loses enough energy to an atomic electron to cause its ejection, with the remainder of the original photon's energy emitted as a new, lower energy gamma photon whose emission direction is different from that of the incident gamma photon, hence the term "scattering". The probability of Compton scattering decreases with increasing photon energy. Compton scattering is thought to be the principal absorption mechanism for gamma rays in the intermediate energy range 100 keV to 10 MeV. Compton scattering is relatively independent of the atomic number of the absorbing material, which is why very dense materials like lead are only modestly better shields, on a per weight basis, than are less dense materials.
• Pair production: This becomes possible with gamma energies exceeding 1.02 MeV, and becomes important as an absorption mechanism at energies over 5 MeV (see illustration at right, for lead). By interaction with the electric field of a nucleus, the energy of the incident photon is converted into the mass of an electron-positron pair. Any gamma energy in excess of the equivalent rest mass of the two particles (totaling at least 1.02 MeV) appears as the kinetic energy of the pair and in the recoil of the emitting nucleus. At the end of the positron's range, it combines with a free electron, and the two annihilate, and the entire mass of these two is then converted into two gamma photons of at least 0.51 MeV energy each (or higher according to the kinetic energy of the annihilated particles).

The secondary electrons (and/or positrons) produced in any of these three processes frequently have enough energy to produce much ionization themselves.

Light interaction[link]

High-energy (from 80 to 500 GeV) gamma rays arriving from far-distant quasars are used to estimate the extragalactic background light in the universe: The highest-energy rays interact more readily with the background light photons and thus the density of the background light may be estimated by analyzing the incoming gamma ray spectrums.^[15]

Gamma ray production[link]

Gamma rays can be produced by a wide range of phenomena.

Radioactive decay (gamma decay)[link]

Gamma rays from radioactive gamma decay are produced alongside other forms of radiation such as alpha or beta, and are produced after the other types of decay occur. The mechanism is that when a nucleus emits an α or β particle, the daughter nucleus is usually left in an excited state. It can then move to a lower energy state by emitting a gamma ray, in much the same way that an atomic electron can jump to a lower energy state by emitting a photon. Emission of a gamma ray from an excited nuclear state typically requires only 10⁻¹² seconds, and is thus nearly instantaneous. Gamma decay from excited states may also follow nuclear reactions such as neutron capture, nuclear fission, or nuclear fusion.

In certain cases, the excited nuclear state following the emission of a beta particle may be more stable than average, and is termed a metastable excited state, if its decay is 100 to 1000 times longer than the average 10⁻¹² seconds. Such nuclei have half-lives that are easily measurable, and are termed nuclear isomers. Some nuclear isomers are able to stay in their excited state for minutes, hours, days, or occasionally far longer, before emitting a gamma ray. Isomeric transition is the name given to a gamma decay from such a state. The process of isomeric transition is therefore similar to any gamma emission, but differs in that it involves the intermediate metastable excited states of the nuclei.

An emitted gamma ray from any type of excited state may transfer its energy directly to one of the most tightly bound electrons causing it to be ejected from the atom, a process termed the photoelectric effect (it should not be confused with the internal conversion process, in which no real gamma ray photon is produced as an intermediate particle).

Decay scheme of 60
Co

Gamma rays, X-rays, visible light, and radio waves are all forms of electromagnetic radiation. The only difference is the frequency and hence the energy of those photons. Gamma rays are generally the most energetic of these, although broad overlap with X-ray energies occurs. An example of gamma ray production follows:

First 60
Co decays to excited 60
Ni by beta decay by emission of a electron of 0.31 MeV. Then the excited 60
Ni drops down to the ground state (see nuclear shell model) by emitting two gamma rays in succession (1.17 MeV then 1.33 MeV). This path is followed 99.88% of the time:

60 27Co	→	60 28Ni*	+	e−	+	ν e	+	γ	+	1.17 MeV
60 28Ni*	→	60 28Ni					+	γ	+	1.33 MeV

Another example is the alpha decay of 241
Am to form 237
Np; this alpha decay is accompanied by gamma emission. In some cases, the gamma emission spectrum for a nucleus (daughter nucleus) is quite simple, (e.g. 60
Co/60
Ni) while in other cases, such as with (241
Am/237
Np and 192
Ir/192
Pt), the gamma emission spectrum is complex, revealing that a series of nuclear energy levels can exist. The fact that an alpha spectrum can have a series of different peaks with different energies reinforces the idea that several nuclear energy levels are possible.

Because a beta decay is accompanied by the emission of a neutrino which also carries energy away, the beta spectrum does not have sharp lines, but instead has a broad peak. Hence from beta decay alone it is not possible to probe the different energy levels found in the nucleus.

In optical spectroscopy, it is well known that an entity which emits light can also absorb light at the same wavelength (photon energy). For instance, a sodium flame can emit yellow light as well as absorb the yellow light from another sodium vapor lamp. In the case of gamma rays, this can be seen in Mössbauer spectroscopy. Here, a correction for the Doppler shift due to recoil of the nucleus usually is not required, since the emitting and absorbing atoms are locked into a crystal, which absorbs their momentum (see Mössbauer effect). In this way, the exact conditions for gamma ray absorption through resonance can be attained.

This is similar to the Franck Condon effects seen in optical spectroscopy.

Gamma rays from sources other than radioactive decay[link]

A few gamma rays in astronomy are known to arise from gamma decay (see discussion of SN1987A) but most do not.

Gamma radiation, like X-radiation, can be produced by a variety of phenomena. When high-energy gamma rays, electrons, or protons bombard materials, the excited atoms within emit characteristic "secondary" gamma rays, which are products of the temporary creation of excited nuclear states in the bombarded atoms (such transitions form a topic in nuclear spectroscopy). Such gamma rays are produced by the nucleus, but not as a result of nuclear excitement from radioactive decay.

Energy in the gamma radiation range, often explicitly called gamma-radiation when it comes from astrophysical sources, is also produced by sub-atomic particle and particle-photon interactions. These include electron-positron annihilation, neutral pion decay, bremsstrahlung, inverse Compton scattering and synchrotron radiation. In a terrestrial gamma-ray flash a brief pulse of gamma radiation can occur high in the Earth's atmosphere, above thunderstorms. These gamma rays are thought to be produced by high intensity static electric fields accelerating electrons, which then produce gamma rays by bremsstrahlung as they collide with and slowed by atoms in the atmosphere.

High energy gamma rays in astronomy include the gamma ray background produced when cosmic rays (either high speed electrons or protons) interact with ordinary matter, producing pair-production gamma rays at 511 keV. Alternatively bremsstrahlung at energies of tens of MeV or more are produced when cosmic ray electrons interact with nuclei of sufficiently high atomic number (see gamma ray image of the Moon at the beginning of this article, for illustration).

Image of entire sky in 100 MeV or greater gamma rays as seen by the EGRET instrument aboard the CGRO spacecraft. Bright spots within the galactic plane are pulsars while those above and below the plane are thought to be quasars.

• Pulsars and magnetars. The gamma ray sky (see illustration at right) is dominated by the more common and longer-term production of gamma rays in beams that emanate from pulsars within the Milky Way. Sources from the rest of the sky are mostly quasars. Pulsars are thought to be neutron stars with magnetic fields that produce focused beams of radiation, and are far less energetic, more common, and much nearer (typically seen only in our own galaxy) than are quasars or the rarer sources of gamma ray bursts. In a pulsar, which produces gamma rays for much longer than a burst, the relatively long-lived magnetic field of the pulsar produces focused beams of relativistic speed charged particles, which produce gamma rays (bremsstrahlung) when these charged particles strike gas or dust in the nearby medium, and are decelerated. This is a similar mechanism to the production of high energy photons in megavoltage radiation therapy machines (see bremsstrahlung). The "inverse Compton effect," in which charged particles (usually electrons) scatter from low-energy photons to convert them to higher energy photons is another possible mechanism of gamma ray production from relativistic charged particle beams. Neutron stars with a very high magnetic field (magnetars) are thought to produce astronomical soft gamma repeaters, which are another relatively long-lived star-powered source of gamma radiation.

• Quasars and active galaxies. More powerful gamma rays from more distant quasars and active nearby galaxies probably have a roughly similar linear particle accelerator-like method of gamma ray production. High energy electrons produced by the quasar, followed again by inverse Compton scattering, synchrotron radiation, or bremsstrahlung, likely produce the gamma rays. As the black hole at the center of such galaxies intermittantly destroys stars and focuses charged particles derived from them into beams, these beams interact with gas, dust, and lower energy photons to produce X-ray and gamma ray radiation. These sources are known to fluctuate with durations of a few weeks, indicating their relatively small size (less than a few light-weeks across). The particle beams emerge from the rotatational poles of the supermassive black hole at a galactic center, which is thought to form the power source of the quasar. Such sources of gamma and X-rays are the most commonly-visible high intensity sources outside our own galaxy, since they shine not as bursts (see illustration), but instead relatively continuously when viewed with gamma ray telescopes. The power of a typical quasar is about 10⁴⁰ watts, of which only a small fraction is emitted as gamma radiation, and much of the rest is emitted as electromagnetic waves at all frequencies, including radio waves.

A hypernova. Artist's illustration showing the life of a massive star as nuclear fusion converts lighter elements into heavier ones. When fusion no longer generates enough pressure to counteract gravity, the star rapidly collapses to form a black hole. Theoretically, energy may be released during the collapse along the axis of rotation to form a long duration gamma-ray burst.

• Gamma-ray bursts. The most intense sources of gamma rays known, are also the most intense sources of any type of electromagnetic radiation presently known. They are rare compared with the sources discussed above. These intense sources are the "long duration burst" sources of gamma rays in astronomy ("long" in this context, meaning a few tens of seconds). By contrast, "short" gamma ray bursts, which are not associated with supernovae, are thought to produce gamma rays during the collision of pairs of neutron stars, or a neutron star and black hole after they spiral toward each other by emission of gravitational waves; such bursts last two seconds or less, and are of far lower energy than the "long" bursts (they are often seen only in our own galaxy for this reason).^[16]

The so-called long duration gamma ray bursts produce events in which energies of ~ 10⁴⁴ joules (as much energy as our Sun will produce in its entire life-time) but over a period of only 20 to 40 seconds, accompanied by high-efficiency conversion to gamma rays (on the order of 50% total energy conversion). The leading hypotheses for the mechanism of production of these highest-known intensity beams of radiation, are inverse Compton scattering and synchrotron radiation production of gamma rays from high-energy charged particles. These processes occur as relativistic charged particles leaving the region near the event horizon of the newly-formed black hole during the supernova explosion, and focused for a few tens of seconds into a relativistic beam by the magnetic field of the exploding hypernova. The fusion explosion of the hypernova drives the energetics of the process. If the narrowly directed beam happens to be pointed toward the Earth, it shines with high gamma ray power even at distances of up to 10 billion light years—close to the edge of the visible universe.

Health effects[link]

All ionizing radiation causes similar damage at a cellular level, but because rays of alpha particles and beta particles are relatively non-penetrating, external exposure to them causes only localized damage, e.g. radiation burns to the skin. Gamma rays and neutrons are more penetrating, causing diffuse damage throughout the body (e.g. radiation sickness, cell's DNA damage, cell death due to damaged DNA, increasing incidence of cancer) rather than burns. External radiation exposure should also be distinguished from internal exposure, due to ingested or inhaled radioactive substances, which, depending on the substance's chemical nature, can produce both diffuse and localized internal damage. The most biological damaging forms of gamma radiation occur in the gamma ray window, between 3 and 10 MeV. See cobalt-60.

Uses[link]

Gamma-ray image of a truck with two stowaways taken with a VACIS (vehicle and container imaging system)

Gamma rays travel to Earth across vast distances of the universe, only to be absorbed by Earth's atmosphere. Different wavelengths of light penetrate Earth's atmosphere to different depths. Instruments aboard high-altitude balloons and such satellites as the Compton Observatory provide our only view of the gamma spectrum sky.

Gamma-induced molecular changes can also be used to alter the properties of semi-precious stones, and is often used to change white topaz into blue topaz.

Non-contact industrial sensors used in the Refining, Mining, Chemical, Food, Soaps and Detergents, and Pulp and Paper industries, in applications measuring levels, density, and thicknesses commonly use sources of gamma. Typically these use Co-60 or Cs-137 isotopes as the radiation source.

In the US, gamma ray detectors are beginning to be used as part of the Container Security Initiative (CSI). These US$5 million machines are advertised to scan 30 containers per hour. The objective of this technique is to screen merchant ship containers before they enter US ports.

Gamma radiation is often used to kill living organisms, in a process called irradiation. Applications of this include sterilizing medical equipment (as an alternative to autoclaves or chemical means), removing decay-causing bacteria from many foods or preventing fruit and vegetables from sprouting to maintain freshness and flavor.

Despite their cancer-causing properties, gamma rays are also used to treat some types of cancer, since the rays kill cancer cells also. In the procedure called gamma-knife surgery, multiple concentrated beams of gamma rays are directed on the growth in order to kill the cancerous cells. The beams are aimed from different angles to concentrate the radiation on the growth while minimizing damage to surrounding tissues.

Gamma rays are also used for diagnostic purposes in nuclear medicine in imaging techniques. A number of different gamma-emitting radioisotopes are used. For example, in a PET scan a radiolabled sugar called fludeoxyglucose emits positrons that are converted to pairs of gamma rays that localize cancer (which often takes up more sugar than other surrounding tissues). The most common gamma emitter used in medical applications is the nuclear isomer technetium-99m which emits gamma rays in the same energy range as diagnostic X-rays. When this radionuclide tracer is administered to a patient, a gamma camera can be used to form an image of the radioisotope's distribution by detecting the gamma radiation emitted (see also SPECT). Depending on what molecule has been labeled with the tracer, such techniques can be employed to diagnose a wide range of conditions (for example, the spread of cancer to the bones in a bone scan).

Body response[link]

When gamma radiation breaks DNA molecules, a cell may be able to repair the damaged genetic material, within limits. However, a study of Rothkamm and Lobrich has shown that this repair process works well after high-dose exposure but is much slower in the case of a low-dose exposure.^[17]

Risk assessment[link]

The natural outdoor exposure in Great Britain ranges from 2 to 4 nSv/h (nanosieverts per hour).^[18] Natural exposure to gamma rays is about 1 to 2 mSv per year, and the average total amount of radiation received in one year per inhabitant in the USA is 3.6 mSv.^[19] There is a small increase in the dose, due to naturally occurring gamma radiation, around small particles of high atomic number materials in the human body caused by the photoelectric effect.^[20]

By comparison, the radiation dose from chest radiography (about 0.06 mSv) is a fraction of the annual naturally occurring background radiation dose,.^[21] A chest CT delivers 5 to 8 mSv. A whole-body PET/CT scan can deliver 14 to 32 mSv depending on the protocol.^[22] The dose from fluoroscopy of the stomach is much higher, approximately 50 mSv (14 times the annual yearly background).

An acute full-body equivalent single exposure dose of 1 Sv (1000 mSv) causes slight blood changes, but 2.0–3.5 Sv (2.0–3.5 Gy) causes very severe syndrome of nausea, hair loss, and hemorrhaging, and will cause death in a sizable number of cases—-about 10% to 35% without medical treatment. A dose of 5 Sv^[23] (5 Gy) is considered approximately the LD₅₀ (lethal dose for 50% of exposed population) for an acute exposure to radiation even with standard medical treatment. A dose higher than 5 Sv (5 Gy) brings an increasing chance of death above 50%. Above 7.5–10 Sv (7.5–10 Gy) to the entire body, even extraordinary treatment, such as bone-marrow transplants, will not prevent the death of the individual exposed (see Radiation poisoning).^{[citation needed]}. (Doses much larger than this may, however, be delivered to selected parts of the body in the course of radiation therapy.)

For low dose exposure, for example among nuclear workers, who receive an average yearly radiation dose of 19 mSv,^{[clarification needed]} the risk of dying from cancer (excluding leukemia) increases by 2 percent. For a dose of 100 mSv, that risk increase is at 10 percent. By comparison, risk of dying from cancer was increased by 32 percent for the survivors of the atomic bombing of Hiroshima and Nagasaki.^[24]

See also[link]

• Alpha particle
• Beta particle
• Annihilation
• Gamma camera
• Gamma-ray astronomy
• Gamma-ray burst
• Gamma spectroscopy
• Mössbauer effect
• Nuclear fission and fusion
• Radioactive decay

References[link]

External links[link]

• Basic reference on several types of radiation
• Radiation Q & A
• GCSE information
• Radiation information
• Gamma ray bursts
• The Lund/LBNL Nuclear Data Search – Contains information on gamma-ray energies from isotopes.
• Mapping soils with airborne detectors
• The LIVEChart of Nuclides – IAEA with filter on gamma-ray energy
• Health Physics Society Public Education Website

This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (December 2010)

The field of view (also field of vision, abbreviated FOV) is the extent of the observable world that is seen at any given moment.

Different animals have different fields of view, depending on the placement of the eyes. Humans have an almost 180-degree forward-facing horizontal field of view, while some birds have a complete or nearly complete 360-degree field of view. In addition, the vertical range of the field of view in humans is typically around 100 degrees.

The range of visual abilities is not uniform across a field of view, and varies from animal to animal. For example, binocular vision, which is important for depth perception, only covers 120 degrees (horizontally) of the field of vision in humans^{[citation needed]}; the remaining peripheral 60 degrees have no binocular vision (because of the lack of overlap in the images from either eye for those parts of the field of view). Some birds have a scant 10 or 20 degrees of binocular vision.

Similarly, color vision and the ability to perceive shape and motion vary across the field of view; in humans the former is concentrated in the center of the visual field, while the latter tends to be much stronger in the periphery. This is due to the much higher concentration of color-sensitive cone cells in the fovea, the central region of the retina, in comparison to the higher concentration of motion-sensitive rod cells in the periphery. Since cone cells require considerably brighter light sources to be activated, the result of this distribution is that peripheral vision is much stronger at night relative to binocular vision.

Conversions[link]

Many optical instruments, particularly binoculars or spotting scopes, are advertised with their field of view specified in one of two ways: angular field of view, and linear field of view. Angular field of view is typically specified in degrees, while linear field of view is a ratio of lengths. For example, binoculars with a 5.8 degree (angular) field of view might be advertised as having a (linear) field of view of 305 ft per 1000 yd or 102 mm per meter. As long as the FOV is less than about 10 degrees or so, the following approximation formulas allow one to convert between linear and angular field of view. Let Failed to parse (Missing texvc executable; please see math/README to configure.): A

be the angular field of view in degrees.  Let Failed to parse (Missing texvc executable; please see math/README to configure.): L
be the linear field of view in feet per 1000 yd.  Let Failed to parse (Missing texvc executable; please see math/README to configure.): M
be the linear field of view in millimeters per meter.  Then, using the small-angle approximation:

Failed to parse (Missing texvc executable; please see math/README to configure.): A \approx {360^{\circ}\over 2 \pi} \cdot {L\over 3000 } \approx 0.0191 \times L

Failed to parse (Missing texvc executable; please see math/README to configure.): A \approx {360^{\circ}\over 2 \pi} \cdot {M\over 1000 } \approx 0.0573 \times M

Failed to parse (Missing texvc executable; please see math/README to configure.): L \approx {2 \pi \cdot 3000 \over 360^{\circ}} \cdot A \approx 52.36 \times A

Failed to parse (Missing texvc executable; please see math/README to configure.): M \approx {2 \pi \cdot 1000 \over 360^{\circ}} \cdot A \approx 17.45 \times A

Machine vision[link]

In machine vision the lens focal length sets up the fixed relationship between the field of view and the working distance. Field of view is the area of the inspection captured on the camera’s imager. The size of the field of view and the size of the camera’s imager directly affect the image resolution (one determining factor in accuracy). Working distance is the distance between the back of the lens and the target object.

Astronomy[link]

In astronomy the field of view is usually expressed as an angular area viewed by the instrument, in square degrees, or for higher magnification instruments, in square arc-minutes. For reference the Wide Field Channel on the Advanced Camera for Surveys on the Hubble Space Telescope has a field of view of 10 sq. arc-minutes, and the High Resolution Channel of the same instrument has a field of view of 0.15 sq. arc-minutes. Ground based survey telescopes have much wider fields of view. The photographic plates used by the UK Schmidt Telescope had a field of view of 30 sq. degrees. The 1.8 m (71 in) Pan-STARRS telescope, with the most advanced digital camera to date has a field of view of 7 sq. degrees. In the near infra-red WFCAM on UKIRT has a field of view of 0.2 sq. degrees and the forthcoming VISTA telescope will have a field of view of 0.6 sq. degrees. Until recently digital cameras could only cover a small field of view compared to photographic plates, although they beat photographic plates in quantum efficiency, linearity and dynamic range, as well as being much easier to process.

Photography[link]

In photography, the field of view is that part of the world that is visible through the camera at a particular position and orientation in space; objects outside the FOV when the picture is taken are not recorded in the photograph. It is most often expressed as the angular size of the view cone, as an angle of view.

Video games[link]

The field of view in video games refers to the part you see of a game world, which is dependent on the scaling method used.

See also[link]

• Perimetry
• Peripheral vision
• Visual perception
• Useful field of view

References[link]