Rayleigh scattering, as described above, is valid for an ensemble of isotropic spherical particles. However, the molecules which comprise air (principly N_{2} and O_{2}) are diatomic and hence slightly anisotropic. The polarizability of a molecule will depend on its orientation relative to the direction of the incident light and, in general, is a tensor of rank 2. For diatomic molecules, the polarizability reduces to parallel and perpendicular components.
In practice, molecular anisotropy can be accounted for by considering molecular scattering to be a combination of true Rayleigh and isotropic scattering (Chandrasekhar, 1959) through the use of a depolarization factor. Assuming incident unpolarized radiation, the depolarization factor has a value equal to the ratio of the perpendicular and parallel scattered intensities at right angles, . The depolarization factor is slightly wavelength-dependent and is different for different molecules. The value for air is 0.031 (Hansen and Travis, 1974).
After accounting for depolarization, the Rayleigh scattering matrix takes the
form,
(3.56) |
(3.57) |
(3.58) |
Assuming initially unpolarized light, the degree of linear polarization
upon a Rayleigh scattering event is, by equation (2.42),
(3.59) |
Raman scattering, the inelastic version of Rayleigh scattering, is discussed briefly in Chapter 6 as it impacts the retrieval of atmospheric trace gases.