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

The angular dependence of scattering is called the scattering function, p() which has units of [sr^{-1}] and describes the probability of a photon scattering into a unit solid angle oriented at an angle relative to the photons original trajectory. Note that the function depends on only on the deflection angle and not on the azimuthal angle . 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() has historically been also called the scattering phase function.

The scattering can be described in two ways:

- Plotting p() indicates how photons will scatter as a function of 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()2sin indicates how photons will scatter as a function of the deflection angle regardless of the azimuthal angle , in other words integrating over all possible in an azimuthal ring of width d and perimeter 2sin at some given . The p()2sin 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()

corresponding to an experimental goniometric measurement in a single source-scatterer-observer plane,

and p()2sin which integrates over all possible azimuthal angles .

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