## Sin 0d0 0 sin 0d0

The variation of b(0) with 0 tells us the absolute amount of scattering at different angles, per unit pathlength in a given medium. If we wish to compare the shape of the angular distribution of scattering in different media separately from the absolute amount of scattering that occurs, then it is convenient to use the normalized volume scattering function, /(0), sometimes called the scattering phase function, which is that function (units sr_1) obtained by dividing the volume scattering function by the total scattering coefficient

The integral of /~(0)over all solid angles is equal to 1. The integral of /~(0)up to any given value of 0 is the proportion of the total scattering that occurs in the angular interval between 0 ° and that value of 0. We can also define normalized forward scattering and backward scattering coefficients, bf and bb, as the proportions of the total scattering in forwards and backwards directions, respectively p

Just as it is useful sometimes to express the angular structure of a light field in terms of a single parameter - its average cosine (p) - so it can also be useful in the case of the scattering phase function to have a single parameter that provides some indication of its shape. Such a parameter is the average cosine of scattering, ps, which can be thought of as the average cosine of the singly scattered light field. It is also sometimes referred to as the asymmetry factor, and given the symbol, g. Its value, for any given volume scattering function, may be calculated712 from ps =

4p or (using eqn 1.44 and the fact that the integral of f3(0) over 4p is 1) from

4p s