Unraveling the optical shape of snow.

The reflection of sunlight off the snow is a major driver of the Earth's climate. This reflection is governed by the shape and arrangement of ice crystals at the micrometer scale, called snow microstructure. However, snow optical models overlook the complexity of this microstructure by using simple shapes, and mainly spheres. The use of these various shapes leads to large uncertainties in climate modeling, which could reach 1.2 K in global air temperature. Here, we accurately simulate light propagation in three-dimensional images of natural snow at the micrometer scale, revealing the optical shape of snow. This optical shape is neither spherical nor close to the other idealized shapes commonly used in models. Instead, it more closely approximates a collection of convex particles without symmetry. Besides providing a more realistic representation of snow in the visible and near-infrared spectral region (400 to 1400 nm), this breakthrough can be directly used in climate models, reducing by 3 the uncertainties in global air temperature related to the optical shape of snow.

Photon path distributions in optically thin slabs.

The probability distribution function of photon path length in a scattering medium contains valuable information on that medium. While strongly scattering optically thick media have been extensively studied, in particular, with resort to the diffusion approximation, optically thin media have received much less attention. Here, we derive the probability distribution functions for the lengths of singly- and twice-scattered photon paths in an isotropically scattering slab of optical thickness τ, for both reflected and transmitted photons. We show that, in the case of an optically thin slab, these photons dominate the overall response of the medium. We confirm that the second moment of the distribution deviates from the ballistic limit in the case of collimated illumination. Interestingly, we show that under diffuse illumination, the second moment of the distribution is dominated by unscattered transmitted photons, hence is proportional to lnτ, and independent of the phase function. Higher moments of order n (≥3) scale as Hnτn-2. When only reflected or transmitted photons are considered, the second moment scales as H2τ-1, whatever the illumination and viewing conditions. This provides direct access to τ. These theoretical results are extensively supported by Monte Carlo ray-tracing simulations. Extension to anisotropic scattering using these same simulations shows that the results hold, given a scaling factor for collimated illumination, and without any dependence on the phase function for diffuse illumination. These results overall demonstrate that the optical thickness of an optically thin slab can be estimated from the second moment of the distribution. Along with the fact that under diffuse illumination the geometrical thickness can be derived from the first moment of the distribution, this proves that the extinction coefficient of the medium can be estimated from the combination of both moments. This study thus opens new perspectives for non-invasive characterization of optically thin media either in the laboratory or by remote sensing.

Optical porosimetry of weakly absorbing porous materials.

The physical porosity ${\Phi}$Φ of a porous material determines most of its properties. Although the optical porosity ${\Phi} _{\textrm {opt}}$Φopt can be measured, relating this quantity to ${\Phi}$Φ remains a challenge. Here we derive relationships between the optical porosity, the effective refractive index $n_{\textrm {eff}}$neff and the physical porosity of weakly absorbing porous media. It introduces the absorption enhancement parameter ${B}$B, which quantifies the asymmetry of photon path lengths between the solid material and the pores and can be derived from the absorption coefficient $\mu _a$µa of the material. Hence ${\Phi}$Φ can be derived from combined measurements of $n_{\textrm {eff}}$neff and $\mu _a$µa. The theory is validated against laboratory measurements and numerical experiments, thus solving a long-standing issue in optical porosimetry. This suggests that optical measurements can be used to estimate physical porosity with an accuracy better than 10$\%$%.