More about the Volume Scattering Function

Scattering can be partitioned with respect to its angular distribution, the volume scattering function (b(q), VSF), units of m^-1sr^-1.  The VSF is defined by
, where d l (q) is the radiant intensity (w/sr) emanating into a small solid angle when a small volume dV is illuminated by an irradiance E. The beam attenuation coefficient and the volume scattering function are the IOPs that appeared in the equation of radiative transfer and so form the connection between the particulate and dissolved materials and the remotely sensed radiances.

If we integrate the light emitted over all directions, we obtain the total scattering coefficient, b, units of m^-1. The VSF divided by the total scattering coefficient is called the phase function. The scattering coefficient is defined as the energy flux (- DF_b) lost due to scattering in an infinitesimally thin layer of a scattering medium, per unit flux (F) of a collimated beam and divided by the thickness of the layer (Dr).  The symbol is “b” and the units are m^-1.

The subscripts t, p, and w represent total, particulate, and water, respectively. The total scattering coefficient can be divided into forward, b_f, and backward, b_b, components:

b = b_b + b_f

The theoretical aspects of light scattering are treated extensively in van de Hulst (1981). The backscattering coefficient is often separated into operationally defined components such as the dissolved and particulate fractions and water:
b_bt = b_bp + b_bw ,

The subscripts t, p, and w represent total, particulate, and water, respectively. The above equation assumes that scattering from dissolved molecules in seawater will be negligible compared to the other terms. For algorithms focusing on the absorption and backscattering by phytoplankton, an additional partitioning of the particulate component is often made:
b_bp = b_bf + b_bd ,  

where the f and d subscripts represent the algal and non-algal components, respectively.  The non-algal component is comprised of non-living particulate organic material, living particles such as bacteria, inorganic minerals, and bubbles.  The relative contributions of these different particle groups to particulate backscattering is poorly known, but recent progress has been made (Stramski et al. submitted). All the IOPs in Eqs. (26)–(33) have wavelength dependencies, examples of which can be found throughout the books by Shifrin (1988), Kirk (1994), and Mobley (1994).

Scattering coefficient • Scattering by pure water • Scattering by particles • Scattering by turbulence