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Absorption cross section a particle, customarily denoted by Ca [length2], is defined by the following equation (for example, Bohren and Huffman 1983):
| Ca = Φap / E | (1) |
where Φap [power] is the power absorbed by the particle, and E [power length-2] is the irradiance of a beam of electromagnetic radiation (ER) beam illuminating the particle.
The absorption cross section, Ca, characterizes the ability of a single particle to absorb ER. As the absorption coefficient, a, is a result of interaction of particles in a dispersion with ER, it must be linked to the absorption cross section of the dispersion. Indeed, let us assume for simplicity that we have a dispersion made of particles such that each of them absorbs the same amount of the ER power, Φap, when illuminated by a beam of irradiance, E, and consider a parcel of the dispersion containing N particles.
It is not sufficient to say that the particles are identical: they may be identically nonhomogeneous and/or nonspherical and yet each absorb ER differently because they are differently oriented in relation to the direction of the incident ER. Also note that if the dispersion is made of several types of particles, we simply need to sum over all these types of particles.
For the sake of simplicity, but without limiting generality of the derivation, let the parcel be pillbox shaped, with a face of area A perpendicular to the direction of the incident ER of irradiance E, and depth dz oriented along the direction of that light propagation. If the dispersion is dilute so that vitrually no particle shadows another, the power of ER, Φa, absorbed from the incident beam by the particles of the pillbox parcel equals:
| Φa | = N Φap | |
| = N Ca E | (2) |
On the other hand, from Eq. 1 in Absorption coefficient, we can express Φa as follows (note that we dropped the minus sign which should be used to indicate the loss of power of the ER, because we are interested in the power absorbed and not in a change in the power of ER, dΦ):
| Φa | = a Φ dz | |
| = a E A dz | ||
| = a E dV | (3) |
where dV = A dz is the volume of the parcel. We also used the definition of irradiance, E: Φ = E A, where E is specified at z, the position of the front face of the pillbox.
From equations 2 and 3 it follows that:
| Ca = a / n | (4) |
because n = N / dV, where dV = A dz is the volume of the parcel. This equation provides an operational method of experimental determination of the absorption cross section for a dispersion of particles. From Eq. 4 it follows that the absorption cross section is numerically equal to the absorption coefficient for a dispersion with the unity number concentration of the particles.
Similar considerations can be given for the scattering cross section and the attenuation cross section.
| CITATION: Jonasz M. 2006. Absorption cross section (www.tpdsci.com/Tpc/AbsCs.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 20-Jan-2006 Modified: 07-Sep-2006 Peer-reviewed: 19-Feb-2007 |
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