Equation of Radiative Transfer

In this section it is assumed that all parameters are measured at a single wavelength, λ, which is omitted for brevity. The intensity of a narrow beam of light emanating from a source can be described by its radiance: energy per unit area per unit solid angle (the cone into which the light radiates, or is measured, units of steradian, sr). Units of radiance are therefore W/m² sr, the symbol is L. Imagine this narrow beam being attenuated by absorption and scattering in a medium. It makes sense for the loss of radiance ΔL due to attenuation over short distances D r to be proportional to the distance traveled and radiance itself. We then get that: ΔL = -cL ΔDr, where c is a proportionality constant, called the attenuation coefficient, units of m^-1. Taking the limit, we obtain dL/dr = -cL, so that L(r) = L(0) exp(-cr). This equation is used in beam attenuation meters, such as the WET Labs ac-s, ac-9 or C-Star, which contain highly collimated sources to obtain the attenuation coefficient, c. This coefficient is both a function of wavelength and location; c should thus be properly given by c(λ , ) , where is the position vector (x,y,z).

Continued...(in MS Word) to accomodate equations.