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 ${\Phi} _{\textrm {opt}}$Φ_opt can be measured, relating this quantity to ${\Phi}$Φ remains a challenge. Here we derive relationships between the optical porosity, the effective refractive index $n_{\textrm {eff}}$n_eff 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 $\mu _a$μ_a of the material. Hence ${\Phi}$Φ can be derived from combined measurements of $n_{\textrm {eff}}$n_eff and $\mu _a$μ_a. 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$\%$%.