Topics in Particle and Dispersion Science

Lambert's law: Scattering corrections

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During a light transmission measurement some light scattered is received by the detector in a transmissometer due to the finite acceptance angle of such a detector. The amount of scattered light depends on the optical properties of the medium but also on the optical thickness of the medium involved in the transmission measurement. Reception of the scattered light may cause deviations from the Lambert law (see also Radiative transfer equation and transmission measurement).

A number of so-called forward-scattering corrections that quantify this effect have been proposed (for example, Wind and Szymanski 2002, Zardecki 1983). These corrections depend on the optical properties of the medium, most notably the scattering function, as well as on the thickness of the layer of the medium. As shown above, the correction needs to be evaluated by solving the RTE because multiple scattering (see Single and multiple scattering) has to be properly accounted for. Wind and Szymanski (2002) give an estimate of the magnitude of the contribution of multiply scattered light to the light power intercepted by the detector of a transmissometer as a function of the detector acceptance angle and the optical thickness of the medium.

Berrocal E et al (2007) evaluated, by using a Monte Carlo technique, contributions of light scattering orders to the deviation from the Lambert law in nonodisperse turbid medium which negligibly absorbs light. They propose that such a deviation be simply expressed as follows:

Φ(z) = Φ(0) e-cz + f(cz, θ)

(1)

where Φ(z) [power] is the power of light at z [length] in the turbid medium, c [1/length] is the attenuation coefficient, θ [rad] is the acceptance angle of the detector of light in a transmissometer, and

f(cz, θ) = A(cz)B

(2)

where A and B are functions of the optical thickness, cz, the acceptance angle, θ, of the detector, and the diameter of the particles of the medium.

Recently, an analytical solution of the RTE in the small-angle scattering approximation has been developed (Kokhanovsky 2007f; see also Radiative transfer equation (RTE) in the small-angle approximation: Turbid medium illuminated at normal incidence). This solution enables simple calculation of the scattering correction if the optical properties and the optical thickness of the medium are known.

CITATION: Jonasz M. 2006. Lambert's law: Scattering corrections (www.tpdsci.com/Tpc/LmbLwScaCrt.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 14-Feb-2007 Modified: 19-Oct-2007 Peer-reviewed: 12-Feb-2007

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