TPDSci Scattering coefficient

Scattering coefficients

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 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. It is the average distance between photon scattering events.

Scattering coefficient is the integral scattering function, β(θ, φ), over the full solid angle (4π):

b = ∫₀^π ∫₀^2π β(θ, φ)sinθdθdφ

(2)

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)

(3)

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).

The forward scattering, b_f , and backscattering, b_b, coefficients are also used. They are defined by the following equation:

dΦ_x(z) = -b_x Φ(z) dz

(4)

where x is either f - for forward scattering, or b for backscattering, and dΦ_x, denotes accordingly the power of light scattered forward (i.e. into a hemisphere defined by the scattering angle ranging from 0° to 90°) or the power scattered backward (i.e into the backward hemisphere: from 90° to 180°). It follows that:

b = b_f + b_b

(5)

because the sum of the forward and backward scattered powers equals the total scattered power.

The ratio, B, of the backscattering coefficient, b_b 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).

Topics in Particle and Dispersion Science