Contribution of multiple scattering to light transmittance by a collimated beam

A method to study the multiple scattering contribution in a scattering and/or absorbing enclosure traversed by a narrow radiation beam is presented. Based on the isotropic scattering assumption, we derive a set of simplified radiative transfer equations, which are solved numerically using a finite-element method. Results from an example calculation are given in terms of transmittance emerging at the top of the cylindrical model assumed. It is shown that Bouguer's law is valid for low single scattering albedo values (<0.4), but the validity limit shifts toward small optical depths as the albedo value increases. For high albedo values and thick optical depths, the multiple scattering effect dominates the emerging transmittance.