ECE532 Biomedical Optics © 1998 Steven L. Jacques, Scott A. Prahl Oregon Graduate Institute |

The angular dependence of scattering is called the scattering
function, p(θ) which has units of [sr^{-1}] and describes
the probability of a photon scattering into a unit solid angle oriented
at an angle θ relative to the photons original trajectory. Note
that the function depends on only on the deflection angle θ and
not on the azimuthal angle ψ. Such azimuthally symmetric scattering
is a special case, but is usually adopted when discussing scattering.
However, it is possible to consider scattering which does not exhibit
azimuthal symmetry. The p(θ) has historically been also called
the scattering phase function.

The scattering can be described in two ways:

- Plotting p(θ) indicates how photons will scatter as a function
of θ in a single plane of observation (source-scatterer-observer
plane). This pattern is similar to the type of goniometric scattering
experiments commonly conducted.

- Plotting p(θ)2πsinθ indicates how photons will scatter as a function of the deflection angle θ regardless of the azimuthal angle ψ, in other words integrating over all possible ψ in an azimuthal ring of width dθ and perimeter 2πsinθ at some given θ. The p(θ)2πsinθ goes to zero at 0° because the azimuthal ring becomes vanishingly small at 0°. This plot is related to the total energy scattered at a given deflection angle and hence is more pertinent to the value of anisotropy.

Figure depicts a typical forward-directed scattering pattern p(θ) corresponding to an experimental goniometric measurement in a single source-scatterer-observer plane, and p(θ)2πsinθ which integrates over all possible azimuthal angles ψ.