Mie Theory

The solution of Maxwell's equations for the geometry of the aerosol (usually considered to be spherical) in the medium of interest (e.g., air or ocean water) yields the connection between the index of refraction $\idxrfr$ and the single scattering properties $\tauext$, $\ssa$, and $\asmprm$. The complete solution to this important problem was first discovered by the physicist Mie and the subject is called Mie theory in his honor. In depth discussions of Mie theory are presented in , , and .

Mie theory predicts the optical efficiencies $\fshxxx$ of particles of a given size at a given wavelength. Here $\xxx$ stands for a, s, or e which represent the processes of absorption, scattering, and extinction, respectively. The optical efficiency for each of these processes is the optical depth of a single particle due to the process divided by the cross sectional area of the particle. These optical efficiencies are not independent of one another. Two of the efficiency factors, usually the extinction efficiency $\fshext$ and the scattering efficiency $\fshsct$, are predicted directly by Mie theory. The third efficiency factor, the absorption efficiency $\fshabs$, must satisfy the requirement of energy conservation

$$\fshabs(\rds,\wvl) = \fshext(\rds,\wvl) - \fshsct(\rds,\wvl)$$ (98)

This relation states that extinction is the sum of absorption and scattering. Note that the optical efficiencies are dimensionless factors.

The final property provided by Mie is the particle phase function, which describes the angular dependence of the scattering. The phase function $\phzfnc$ measures the probability that photons incoming from the direction $(\plr,\azi)$ will, if scattered, be scattered to outgoing direction $(\plrprm,\aziprm)$. It is usually assumed that $\phzfnc$ depends only on the angle between incident and emergent angles, and not on the absolute angles themselves. The phase function is normalized so that the total probability of scattering is unity

$$\int_\ngl \phzfnc \, d\ngl = 1$$ (99)

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Mie theory predicts the optical efficiencies $\fshxxx$ of particles of a given size at a given wavelength. Here $\xxx$ stands for a, s, or e which represent the processes of absorption, scattering, and extinction, respectively. The optical efficiency for each of these processes is the optical depth of a single particle due to the process divided by the cross sectional area of the particle. These optical efficiencies are not independent of one another. Two of the efficiency factors, usually the extinction efficiency $\fshext$ and the scattering efficiency $\fshsct$, are predicted directly by Mie theory. The third efficiency factor, the absorption efficiency $\fshabs$, must satisfy the requirement of energy conservation

$$\fshabs(\rds,\wvl) = \fshext(\rds,\wvl) - \fshsct(\rds,\wvl)$$ (98)

This relation states that extinction is the sum of absorption and scattering. Note that the optical efficiencies are dimensionless factors.

The final property provided by Mie is the particle phase function, which describes the angular dependence of the scattering. The phase function $\phzfnc$ measures the probability that photons incoming from the direction $(\plr,\azi)$ will, if scattered, be scattered to outgoing direction $(\plrprm,\aziprm)$. It is usually assumed that $\phzfnc$ depends only on the angle between incident and emergent angles, and not on the absolute angles themselves. The phase function is normalized so that the total probability of scattering is unity

$$\int_\ngl \phzfnc \, d\ngl = 1$$ (99)