  Asymptotic radiative transfer (ART), like diffusion theory, assumes the
angular intensity distribution incident at a boundary is identical with that in
the depth of the scattering medium. However, the asymptotic intensity profile
and accurate attenuation coefficient corresponding to the scattering phase
function are used in preference to the P1 approximations of diffusion theory,
thereby extending the range of asymptotic radiative transfer to the lowest
particle scattering albedoes. Asymptotic calculations for scattering media with
refracting boundaries are compared with diffusion theory and accurate radiative
transfer data to illustrate this. The error involved can be further reduced by
the addition of a suitable boundary transient
