How much is enough? The convergence of finite sample scattering properties to those of infinite media

A Cross-Check of the Reflectance Models to Be Used in Interpretation of Observations of Regolith-Like Surfaces

“…At the same time, as has been noted above, there is a pressing need for models that correctly describe the light scattering characteristics of densely packed media. Because of this, attempts are being made to develop such models on the base of the well-elaborated theory of light scattering by sparse media [see (Mishchenko, 1994;Barrowes et al, 2000;Tishkovets and Mishchenko, 2004;Mishchenko et al, 2006;Mishchenko et al, 2013;Muinonen et al, 2017;Ito et al, 2018;Muinonen et al, 2018;Tishkovets and Petrova, 2020;Penttilä et al, 2021) and references therein].…”

“…For sparse media, it is assumed that the waves propagating between scatterers in the medium are spherical, which essentially simplifies the theoretical analysis. Moreover, in this case, it is relatively easy to obtain the ensemble-averaged reflection matrix analytically for a plane-parallel medium (Tishkovets and Mishchenko, 2004;Mishchenko et al, 2006;Tishkovets et al, 2011;Doicu and Mishchenko, 2019b;Doicu and Mishchenko, 2019c;Tishkovets and Petrova, 2020) or numerically with the Monte-Carlo technique for a spherical volume (Muinonen et al, 2017;Muinonen et al, 2018;Penttilä et al, 2021). To adapt these models to the problems of light scattering by densely packed media, the scattering characteristics of "a volume element" are modified.…”

“…To adapt these models to the problems of light scattering by densely packed media, the scattering characteristics of "a volume element" are modified. Specifically, it is suggested that the mean (coherent) field should be excluded [see (Barrowes et al, 2000;Muinonen et al, 2017;Muinonen et al, 2018;Penttilä et al, 2021) and the references therein], or the static structure factor correction should be made (Mishchenko, 1994;Mishchenko et al, 2013;Ito et al, 2018), or the scattering characteristics of randomly oriented clusters of particles should be considered as those of a volume element Ito et al, 2018).…”

“…Given the laboratory data limitation, the quality of the model may be estimated with the methods that allow the scattering characteristics to be rigorously calculated for some cases. Such an attempt was recently made by Penttilä et al (2021). They considered clusters composed of 10 3 to 10 5 spherical particles and compared their light-scattering characteristics obtained with the rigorous numerical method and with the model, according to which the mean field contribution was excluded (Muinonen et al, 2017;Muinonen et al, 2018;Penttilä et al, 2021).…”

“…Such an attempt was recently made by Penttilä et al (2021). They considered clusters composed of 10 3 to 10 5 spherical particles and compared their light-scattering characteristics obtained with the rigorous numerical method and with the model, according to which the mean field contribution was excluded (Muinonen et al, 2017;Muinonen et al, 2018;Penttilä et al, 2021). The calculations were performed for the backscattering domain, where the weak-localization effect reveals itself.…”