Attenuation coefficient
Encyclopedia
The attenuation coefficient is a quantity
that characterizes how easily a material
or medium
can be penetrated by a beam of light
, sound
, particle
s, or other energy
or matter
. A large attenuation coefficient means that the beam is quickly "attenuated" (weakened) as it passes through the medium, and a small attenuation coefficient means that the medium is relatively transparent
to the beam. Attenuation coefficient is measured using units of reciprocal length
.
The attenuation coefficient is also called linear attenuation coefficient, narrow beam
attenuation coefficient, or absorption coefficient. Although all four terms are often used interchangeably, they can occasionally have a subtle distinction, as explained below.
or sound
.
A small linear attenuation coefficient indicates that the material in question is relatively transparent, while a larger value indicates greater degrees of opacity
. The linear attenuation coefficient is dependent upon the type of material and the energy of the radiation. Generally, for electromagnetic radiation, the higher the energy of the incident photons and the less dense the material in question, the lower the corresponding linear attenuation coefficient will be.
of transmitted through a layer of material with thickness 
is related to the incident intensity 
according to the inverse exponential power law that is usually referred to as Beer–Lambert law:
where
denotes the path length. The attenuation coefficient (or linear attenuation coefficient) is 
.
The Half Value Layer (HVL) signifies the thickness of a material required to reduce the intensity of the emergent radiation to half its incident magnitude. It is from these equations that engineers decide how much protection is needed for "safety" from potentially harmful radiation. The attenuation factor of a material is obtained by the ratio of the emergent and incident radiation intensities
.
The linear attenuation coefficient and mass attenuation coefficient
are related such that the mass attenuation coefficient is simply
, where 
is the density in g/cm3. When this coefficient is used in the Beer-Lambert law, then "mass thickness" (defined as the mass per unit area) replaces the product of length times density.
The linear attenuation coefficient is also inversely related to mean free path
. Moreover, it is very closely related to the absorption cross section
.
When a narrow (collimated
) beam of light passes through a substance, the beam will lose intensity due to two processes: The light can be absorbed by the substance, or the light can be scattered
(i.e., the photon
s can change direction) by the substance. Just looking at the narrow beam itself, the two processes cannot be distinguished. However, if a detector is set up to measure light leaving in different directions, or conversely using a non-narrow beam, one can measure how much of the lost intensity was scattered, and how much was absorbed.
In this context, the "absorption coefficient" measures how quickly the beam would lose intensity due to the absorption alone, while "attenuation coefficient" measures the total loss of narrow-beam intensity, including scattering as well. "Narrow-beam attenuation coefficient" always unambiguously refers to the latter. The attenuation coefficient is always larger than the absorption coefficient, although they are equal in the idealized case of no scattering.
Quantity
Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more" or "less" or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation...
that characterizes how easily a material
Material
Material is anything made of matter, constituted of one or more substances. Wood, cement, hydrogen, air and water are all examples of materials. Sometimes the term "material" is used more narrowly to refer to substances or components with certain physical properties that are used as inputs to...
or medium
Transmission medium
A transmission medium is a material substance that can propagate energy waves...
can be penetrated by a beam of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
, sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
, particle
Particle
A particle is, generally, a small localized object to which can be ascribed physical properties. It may also refer to:In chemistry:* Colloidal particle, part of a one-phase system of two or more components where the particles aren't individually visible.In physics:* Subatomic particle, which may be...
s, or other energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
or matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
. A large attenuation coefficient means that the beam is quickly "attenuated" (weakened) as it passes through the medium, and a small attenuation coefficient means that the medium is relatively transparent
Transparency and translucency
In the field of optics, transparency is the physical property of allowing light to pass through a material; translucency only allows light to pass through diffusely. The opposite property is opacity...
to the beam. Attenuation coefficient is measured using units of reciprocal length
Reciprocal length
Reciprocal length or inverse length is a measurement used in several branches of science and mathematics. As the reciprocal of length, common units used for this measurement include the reciprocal metre or inverse metre , the reciprocal centimetre or inverse centimetre , and, in optics, the...
.
The attenuation coefficient is also called linear attenuation coefficient, narrow beam
Pencil beam
In optics, a pencil or pencil of rays is a geometric construct used to describe a beam or portion of a beam of electromagnetic radiation or charged particles, typically in the form of a narrow cone or cylinder....
attenuation coefficient, or absorption coefficient. Although all four terms are often used interchangeably, they can occasionally have a subtle distinction, as explained below.
Overview
The attenuation coefficient describes the extent to which the intensity of an energy beam is reduced as it passes through a specific material. This might be a beam of electromagnetic radiationElectromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
or sound
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...
.
- It is used in the context of X-rayX-rayX-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
s or Gamma rayGamma rayGamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...
s, where it is represented using the symbol
, and measured in cm−1. - It is also used for modeling solarVisible spectrumThe visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...
and infraredInfraredInfrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...
radiative transfer in the atmosphereAtmosphereAn atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...
, albeit usually denoted with another symbol (given the standard use of
for slant paths). - In the case of ultrasound attenuation it is usually denoted as
and measured in dB/cm/MHz. - The attenuation coefficient is widely used in acousticsAcousticsAcoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
for characterizing particle size distributionParticle size distributionThe particle-size distribution of a powder, or granular material, or particles dispersed in fluid, is a list of values or a mathematical function that defines the relative amounts of particles present, sorted according to size...
. A common unit in this contexts is inverse metres, and the most common symbol is the Greek letter
. - It is also used in acoustics for quantifying how well a wall in a building absorbs sound. Wallace Sabine was a pioneer of this concept. A unit named in his honor is the sabin: the absorption by a 1 square metres (10.8 sq ft) slab of perfectly-absorptive material (the same amount of sound loss as if there were a 1-square-metre window). Note that the sabin is not a unit of attenuation coefficient; rather, it is the unit of a related quantity.
A small linear attenuation coefficient indicates that the material in question is relatively transparent, while a larger value indicates greater degrees of opacity
Opacity (optics)
Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc...
. The linear attenuation coefficient is dependent upon the type of material and the energy of the radiation. Generally, for electromagnetic radiation, the higher the energy of the incident photons and the less dense the material in question, the lower the corresponding linear attenuation coefficient will be.
Definitions and formulas
The measured intensity of transmitted through a layer of material with thickness is related to the incident intensity according to the inverse exponential power law that is usually referred to as Beer–Lambert law:where
denotes the path length. The attenuation coefficient (or linear attenuation coefficient) is .The Half Value Layer (HVL) signifies the thickness of a material required to reduce the intensity of the emergent radiation to half its incident magnitude. It is from these equations that engineers decide how much protection is needed for "safety" from potentially harmful radiation. The attenuation factor of a material is obtained by the ratio of the emergent and incident radiation intensities
.The linear attenuation coefficient and mass attenuation coefficient
Mass attenuation coefficient
The mass attenuation coefficient is a measurement of how strongly a chemical species or substance absorbs or scatters light at a given wavelength, per unit mass...
are related such that the mass attenuation coefficient is simply
, where is the density in g/cm3. When this coefficient is used in the Beer-Lambert law, then "mass thickness" (defined as the mass per unit area) replaces the product of length times density.The linear attenuation coefficient is also inversely related to mean free path
Mean free path
In physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...
. Moreover, it is very closely related to the absorption cross section
Absorption cross section
Absorption cross section is a measure for the probability of an absorption process. More generally, the term cross section is used in physics to quantify the probability of a certain particle-particle interaction, e.g., scattering, electromagnetic absorption, etc...
.
Attenuation versus absorption
The terms "attenuation coefficient" and "absorption coefficient" are generally used interchangeably. However, in certain situations they are distinguished, as follows.When a narrow (collimated
Collimated light
Collimated light is light whose rays are parallel, and therefore will spread slowly as it propagates. The word is related to "collinear" and implies light that does not disperse with distance , or that will disperse minimally...
) beam of light passes through a substance, the beam will lose intensity due to two processes: The light can be absorbed by the substance, or the light can be scattered
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
(i.e., the photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s can change direction) by the substance. Just looking at the narrow beam itself, the two processes cannot be distinguished. However, if a detector is set up to measure light leaving in different directions, or conversely using a non-narrow beam, one can measure how much of the lost intensity was scattered, and how much was absorbed.
In this context, the "absorption coefficient" measures how quickly the beam would lose intensity due to the absorption alone, while "attenuation coefficient" measures the total loss of narrow-beam intensity, including scattering as well. "Narrow-beam attenuation coefficient" always unambiguously refers to the latter. The attenuation coefficient is always larger than the absorption coefficient, although they are equal in the idealized case of no scattering.
See also
- Scattering theoryScattering theoryIn mathematics and physics, 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...
- Mean free pathMean free pathIn physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...
- Scattering cross-sectionScattering cross-sectionThe scattering cross-section, σscat, is a hypothetical area which describes the likelihood of light being scattered by a particle. In general, the scattering cross-section is different from the geometrical cross-section of a particle, and it depends upon the wavelength of light and the...
- Absorption (electromagnetic radiation)Absorption (electromagnetic radiation)In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...
- Absorption cross sectionAbsorption cross sectionAbsorption cross section is a measure for the probability of an absorption process. More generally, the term cross section is used in physics to quantify the probability of a certain particle-particle interaction, e.g., scattering, electromagnetic absorption, etc...
- Absorption spectrum
- Beer–Lambert law
- Compton edgeCompton edgeIn spectrophotometry, the Compton edge is a feature of the spectrograph that results from the Compton scattering in the scintillator or detector. When a gamma-ray scatters off the scintillator but escapes, only a fraction of its energy is registered by the detector. This leads to a spectrum of...
- Compton scatteringCompton scatteringIn physics, Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an X-ray or gamma ray photon, called the Compton effect...
- Propagation constantPropagation constantThe propagation constant of an electromagnetic wave is a measure of the change undergone by the amplitude of the wave as it propagates in a given direction. The quantity being measured can be the voltage or current in a circuit or a field vector such as electric field strength or flux density...
- TransmittanceTransmittanceIn optics and spectroscopy, transmittance is the fraction of incident light at a specified wavelength that passes through a sample. A related term is absorptance, or absorption factor, which is the fraction of radiation absorbed by a sample at a specified wavelength...
- AttenuationAttenuationIn physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, X-rays are attenuated by lead, and light and sound are attenuated by water.In electrical engineering and telecommunications, attenuation affects the...
- Attenuation lengthAttenuation lengthIn physics, the attenuation length or absorption length is the distance \lambda into a material when the probability has dropped to 1/e that a particle has not been absorbed...
- Radiation lengthRadiation lengthIn physics, the radiation length is a characteristic of a material, related to the energy loss of high energy, electromagnetic-interacting particles with it.-Definition:High-energy electrons predominantly lose energy in matter...
- High energy X-raysHigh energy X-raysHigh energy X-rays or HEX-rays are very hard X-rays, with typical energies of 80 keV - 1000 keV , about one order of magnitude higher than conventional X-rays . They are produced at modern synchrotron radiation sources such as the beamline ID15 at the European Synchrotron Radiation Facility...
- Cargo scanningCargo scanningCargo scanning or non-intrusive inspection refers to non-destructive methods of inspecting and identifying goods in transportation systems. It is often used for scanning of intermodal freight shipping containers...
- Grey AtmosphereGrey atmosphereGrey atmosphere is a useful set of approximations made for radiative transfer applications. The application of the grey atmosphere approximation is the primary method astronomers use to determine the temperature and basic radiative properties of astronomical objects including the sun, planets with...
External links
- Absorption Coefficients α of Building Materials and Finishes
- Sound Absorption Coefficients for Some Common Materials
- Computations for Radio Wave PropagationComputation of radiowave attenuation in the atmosphereOne of the causes of attenuation of radio propagation is the absorption by the atmosphere. There are many well known facts on the phenomenon and qualitative treatments in textbooks. A document published by the International Telecommunication Union...
- Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest