Gc. Pomraning, A RENORMALIZED EQUATION OF TRANSFER FOR RAYLEIGH-SCATTERING, Journal of quantitative spectroscopy & radiative transfer, 60(2), 1998, pp. 181-197
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.