Comments over homogenisation scales for interfacial emission and scattering by a divided medium: Beerian and non Beerian behaviours

•Characterisation of radiative properties by extinction and scattering pdfs.•Exact phase functions depending on incidence and scattering directions.•Validity conditions of ray shoots from random isotropic volume source points.•Cases of Beerian and non Beerian homogenised phases.•Cases of diffuse and general reflection laws.•Influence of homogenisation scale compared to medium optical thickness.•Strong correlation between emission, transmission (non Beerian case).•Correlated emission accounted for by the reciprocity theorem. In statistical methods of characterisation of porous media radiative properties, interfacial extinction cumulative distribution functions, scattering or absorption cumulative probabilities and general phase functions are generally determined from shots issued from random volume points instead of random interfacial points. Indeed, the first method is numerically much simpler and accurate than the second one. The validity of this approach is discussed and its limitations enlightened for both Beerian and non Beerian homogenised phases, and in the case of a diffuse reflection law or a general one. The explanation of the identity or difference between the results of the two previous types of extinction cumulative distribution functions comes from the comparison between the spatial scale at which these functions are determined and the own scales of the divided medium. The conditions for which a medium follows the Beer’s law are then defined in terms of spatial scales. Moreover, the modeling of interfacial emission for a non Beerian homogenised phase is in principle based on the reciprocity theorem and an integral formulation of the Generalised Radiative Transfer Equation. The validity of a simpler approach based on an effective absorption coefficient is also discussed, from the previous analysis. The validity of results of recent works published in IJHMT are finally discussed.