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Light traversing a medium may be attenuated by absorption (Fig. 1), scattering (Fig. 2, Fig. 3), or both. In a medium, which contains both light absorbing and scattering centers, the interactions of photons with these centers may be of mixed type, i.e. a photon may be scattered one or more times until it is eventually absorbed. The average pathlength between attenuation (absorption/scattering) events, i.e. the mean free pathlength of a photon is the inverse of the attenuation coefficient of the medium.
The simplified picture of the interaction of light with absorption and scattering centers shown in the figures referred to above, is actually used verbatum in the Monte Carlo method of numerical simulation of radiative transfer (for example, Mobley CD 1994, Ch. 6). On the other hand, the "analytical" description of propagation of light in a medium is provided by an integro-differential radiative transfer equation (RTE) which expresses the principle of conservation of the radiative power. This equation has analytical solutions only in a limited number of asymptotic cases, for example, if light scattering is negligible (see also, Kokhanovsky AA 2007a). In most cases, it must be solved numerically.
As monochromatic light traverses a random, attenuating medium where the probability of a photon experiencing an absorption/scattering event is small, the radiant power flux decays exponentially with the product of the path length in the medium and the attenuation coefficient of the medium. This relationship is known as Lambert's law. When the attenuation coefficient is expressed in terms of the concentration of particles and/or light-absorbing dissolved substances, the formula for the exponential decay of radiation power is known as the Beer law.
The Beer-Lambert law is derived from the radiative transfer equation (RTE) under the assumptions that there are no radiation sources in the medium and either there is no scattering of radiation by the medium (i.e. radiation power losses are due to absorption only) or the acceptance solid angle of the detector is small enough that the contribution of the scattered light to the power received by the detector is negligible (see RTE and Lambert's law). Hence, the Beer-Lambert law is often called the law of optical absorption.
If the probability of a photon encountering a scattering center is large, (i.e. in media containing a high concentration of the scattering centers, or at sufficiently large distances in less concentrated media), the decay of the radiation power with distance deviates from that predicted by the Beer-Lambert law (for example, Swanson NL et al 1999, Zaccanti G and Bruscaglioni 1988). In such cases, multiple-scattering (Fig. 3) contributes significantly to the process of interaction of light with the medium.
Note that significant multiple-scattering (Fig. 3) may also increase the effective absorption of light (Butler 1962). Indeed, multiple scattering of light lengthens the effective distance travelled in the medium by photons and hence increases the probability of absorption.
See also: Radiative transfer equation and transmission measurement and Radiative transfer equation and Lambert's law
| CITATION: Swanson N. L., Jonasz M. 2007. Attenuation of light: Contributing processes (www.tpdsci.com/Tpc/AtnCtb.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 21-Nov-2007 Modified: 02-Jan-2008 Peer-reviewed: 22-Dec-2007 |
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