For "attenuation coefficient" as it applies to electromagnetic theory and telecommunications
see propagation constant.
For the "mass attenuation coefficient", see the article mass attenuation coefficient.
The attenuation coefficient is a quantity that characterizes how easily a material or
medium can be penetrated by a beam of light, sound, particles, or other energy or matter.
A large attenuation coefficient means that the beam is quickly "attenuated" 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.
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 radiation or sound.
It is used in the context of X-rays or Gamma rays, where it is represented using the symbol
, and measured in cm−1.
It is used in the context of neutrons and nuclear reactors, where it called macroscopic
cross section being represented using the symbol , and measured in m−1.
It is also used for modeling solar and infrared radiative transfer in the atmosphere, albeit
usually denoted with another symbol.
In the case of ultrasound attenuation it is usually denoted as and measured in dBMHz.
The attenuation coefficient is widely used in acoustics for characterizing particle size
distribution.
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-metre slab of perfectly
absorptive material.
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.
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 formulae 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 is . If it is uniform, the situation is referred to as linear
attenuation and the law simplifies:
The Half Value Layer 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" 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.
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 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
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 theory
Mean free path Scattering cross-section
Absorption Absorption cross section
Absorption spectrum Acoustic attenuation
Beer–Lambert law Compton edge
Compton scattering Propagation constant
Transmittance Attenuation
Attenuation length Radiation length
High energy X-rays Cargo scanning
Grey Atmosphere References
External links Absorption Coefficients α of Building Materials
and Finishes Sound Absorption Coefficients for Some Common
Materials Computations for Radio Wave Propagation
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