Maximum time-resolved hemispherical reflectance of absorbing and isotropically scattering media

This paper presents a parametric study of the time-resolved hemispherical reflectance of a plane-parallel slab of homogeneous, cold, absorbing, and isotropically scattering medium exposed to a collimated Gaussian pulse. The front surface of the slab is transparent while the back surface is assumed to be cold and black. The 1-D time-dependent radiation transfer equation is solved using the modified method of characteristics. The parameters explored include (1) the optical thickness, (2) the single scattering albedo of the medium, and (3) the incident pulse width. The study pays particular attention to the maximum transient hemispherical reflectance and identifies optically thin and thick regimes. It shows that the maximum reflectance is independent of the optical thickness in the optically thick regime. In the optically thin regime, however, the maximum hemispherical reflectance depends on all three parameters explored. The transition between the optically thick and thin regimes occurs when the optical thickness is approximately equal to the dimensionless pulse width. Finally, correlations relating the maximum of the hemispherical reflectance as a function of the optical thickness, the single scattering albedo of the materials, and the incident pulse width have been developed. These correlations could be used to retrieve radiation characteristics or serve as initial guesses for more complex inversion schemes accounting for anisotropic scattering.