A RENORMALIZED EQUATION OF TRANSFER FOR RAYLEIGH-SCATTERING

We consider a certain asymptotic limit of the Rayleigh scattering vect or equation of transfer describing the Stokes parameters of light. Thi s limit corresponds to near thermodynamic equilibrium. By introducing appropriate scalings in the vector equation to describe this limit, a renormalized scalar equation of transfer is derived for the total spec ific intensity of radiation. This equation is both the leading order r esult as well as the next higher order result of an asymptotic analysi s. Numerical testing of this renormalized equation for the exponential decay rate in diffuse reflection halfspace problems demonstrates the very good accuracy of this scalar description. This good accuracy is e xtant for conditions even far from the asymptotic limit under consider ation, thus establishing the robustness of this treatment. In particul ar, this equation is more accurate than the scalar equation of transfe r commonly used to describe light transport through a Rayleigh scatter ing medium. This asymptotic analysis also yields simple estimates of t he state of polarization of the light. Carrying the analysis to still one higher order leads to a fundamentally different scalar equation fo r the total intensity. This equation can also be cast into the form of a renormalized equation of transfer, but only formally. (C) 1998 Publ ished by Elsevier Science Ltd. All rights reserved.