Rayleigh scattering, as described above, is valid for an ensemble of isotropic spherical particles. However, the molecules which comprise air (principly N2 and O2) 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
Assuming initially unpolarized light, the degree of linear polarization
upon a Rayleigh scattering event is, by equation (2.42),
Raman scattering, the inelastic version of Rayleigh scattering, is discussed briefly in Chapter 6 as it impacts the retrieval of atmospheric trace gases.