The extinction cross-section per particle, aext, computed by Mie theory needs some care. The extinction (scattering plus absorption) of an EM wave by an infinitesimal layer, dz, of a medium is given, according to Mie theory (see van de Hulst), by the reduction in the magnitude of the electric-field components
where the fraction removed is
with N the number density of the scatterers, all assumed to be of the same radius and refractive index. We have taken the real part of the complex scattering functions, as we are dealing with amplitudes, setting 0 = 0 as we are concerned with extinction of the incident wave, and S(0) = S1(0) = S2(0). Thus, the energy of the incident wave that has been attenuated by forward scattering and absorption within the infinitesimal layer is
However, since 3 is small, we can neglect the 3eLt term and write
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