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Scattering coefficient of light in a medium, customarily denoted by b [length-1], is defined by the following equation:
| dΦ(z) = -bΦ(z) dz | (1) |
where dΦ and Φ [power] are respectively the powers of light scattered and incident, and z [length] is the distance. This equation leads to the Lambert law of scattering of light in a medium, that holds approximately in turbid media as long as single scattering (see Single and multiple scattering) prevails. Note that the scattering coefficient may depend on position in an inhomogeneous scattering medium.
The inverse of the scattering coefficient is referred to as the scattering length, zb:
| zb = 1 / b | (2) |
It is the average distance between consecutive photon scattering events.
Scattering coefficient is the integral scattering function, β(θ, φ), over the full solid angle (4π):
| b = ∫0π ∫02π β(θ, φ) sinθdθdφ | (3) |
where θ is the scattering angle and φ is the azimuth angle, both of which define the direction (θ, φ) in space.
In the optics of turbid media, a reduced (or transport) scattering coefficient is frequently used. This scattering coefficient is defined as follows:
| b' = b (1 - g) | (4) |
where g is the average cosine of the scattering angle that characterizes the asymmetry of the scattering function. The reduced scattering coefficient is an important parameter in determining whether the medium supports single scattering process (see Eqs. 1 and 2 in Single and multiple scattering).
Scattering coefficient of light in a medium is related to the concentration in that medium of the light-scattering agent. Hence, a related concept of the concentration-specific scattering coefficient, also referred to as the mass-specific scattering coefficient which is used especially in the optics of turbid media (for example, Stramska M et al 2008).
The mass-specific scattering coefficient [mass-1 length2] is defined as follows:
| bm = b / Cmv | (5) |
where b is the scattering coefficient defined by Eq 1, and Cmv [mass length-3] is the mass-per-volume concentration of the light-scattering agent. In aquatic sciences, the mass-specific scattering coefficient is frequently denoted by b* (or bp* when related to the particle concentration) and expressed in g m2.
The forward scattering, bf, and backscattering, bb, coefficients are also used, referreing to the powers of light scattered into the forward and backward hemispheres, respectively. These coefficients are defined by the following equations:
| bf = ∫0π/2 ∫02π β(θ, φ) sinθdθdφ | (6a) |
| bb = ∫π/2π ∫02π β(θ, φ) sinθdθdφ | (6b) |
It follows that:
| b = bf + bb | (7) |
because the sum of the forward and backward scattered powers equals the total scattered power.
The ratio, B, of the backscattering coefficient, bb to the scattering coefficient, b, is an important parameter in remote sensing of the optical properties of a dispersion and in the modeling of the light field in the dispersion (for example, Whitmire AL et al 2007).
See also single scattering albedo.
| CITATION: Jonasz M. 2006. Scattering coefficients (www.tpdsci.com/Tpc/ScaCf.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 17-Jan-2006 Modified: 15-Jun-2009 Peer-reviewed: 19-Feb-2007 |
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