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Absorption coefficient of light in a medium, also referred to as absorbance, and customarily denoted by a [length-1], is defined by the following equation:
| dΦ(z) = -aΦ(z) dz | (1) |
where Φ [power] is the power of light in a collimated beam, z [length] is the distance. Notation "[power]" means the "unit of power", for example, Watt. This equation leads to the Lambert law of absorption of light and applies to a medium in which the scattering of light is negligible. Propagation of light in scattering media is described by the radiative transfer equation. Note that the absorption coefficient may depend on position in the medium.
The inverse of the absorption coefficient is referred to as the absorption length. It is the average distance a photon can travel in a medium before being absorbed (see Problem: Absorption length)
The absorption coefficient is generally expressed by solving Eq. 1 using the natural logarithm, i.e. a = - (1 / z) ln[Φ(z) / Φ(0)]. However, the decimal logarithm is sometimes used instead. This latter approach leads to the decadic absorption coefficient (for example, Litjens RAJ et al 1999, Quickenden TI et al 1980). The decadic absorption coefficient, a10, is related to the absorption coefficient, a, as follows (see Problem: Decadic absorption coefficient):
| a10 = a / ln10 | (2) |
Thus, it is important to understand which definition of the absorption coefficient is used in a publication, because each leads to a different numerical value although the units (for example, m-1) may be the same.
The absorption coefficient can be defined for homogeneous media as well as for dispersions. However, as discussed by Duysens (1956), the absorption coefficient spectrum of a dispersion of pigmented particles may differ from the absorption coefficient spectrum of the pigment solution. This pigment packaging (for example, Finlay and Foster 2004 - red blood cells, and Morel and Bricaud 1981 - phytoplankton) causes a flattening of the absorption spectrum of the dispersion as compared to that of the pigment solution (see also Pigment packaging and absorption spectra of dispersions).
For a homogeneous material, the absorption coefficient is related to the imaginary part of the complex refractive refractive index of the material by Eq. 3 of Refractive index. The preceeding discussion implies that this relationship does not apply to a dispersion.
See also topics on the measurement of absorption of light in turbid media: Optoacoustic measurement methods and Photothermal deflection spectroscopy (PDS).
See also: single scattering albedo, Absorption of light by various materials.
| CITATION: Jonasz M. 2006. Absorption coefficient (www.tpdsci.com/Tpc/AbsCf.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 13-Jan-2006 Modified: 05-Mar-2008 Peer-reviewed: 19-Feb-2007 |
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