The Volume Scattering Function, or VSF, notated mathematically as ß ("beta"), is one of the two fundamental IOPs, and characterizes the intensity of scattering as a function of angle.
The VSF is defined in terms of a beam of light incident on an infinitesimal volume. At each angle from 0° (the original angle of the incident light) to 180°, the VSF is the ratio of the intensity of scattered light (in W/sr) to the incident irradiance (in W/m2), per unit volume (in m3). Therefore the VSF's units are (W/sr) / (W/m2 ? m3) = sr-1 m-1.
The total scattering coefficient b is calculated by integrating ß over all angles. The backscattering coefficient bb is similarly derived by integrating over the angles from 90° to 180°.
Discussions of scattering often refer to the Scattering Phase Function, which is equal to ß/b. Because b is the integral of ß with respect to angle, the integral of the phase function with respect to angle is 1.