Radiative transfer in two dimensions through fog.

The 3-D time-independent unpolarized radiative transfer equation is developed into a form amenable to numerical solution by expansion of the total intensity in orders of scattering. A 2-D numerical algorithm is formulated using an eight-direction quadrature approximation to the source function and an optimized path-by-path intensity integration scheme. Computer code generated from the algorithm is used to examine the multiple scattering effects at 1.06 microm, 3.0 microm, and 10.6 microm in Deirmendjian C3 fog on a finite uniform intensity profile beam and an infinite Gaussian intensity profile beam. Transmission and backscatter for both beams are examined as well as contrast degradation of the uniform beam and spread of the Gaussian beam.