Optical response of strongly absorbing inhomogeneous materials: application to paper degradation

In this paper, we present a new noninvasive and nondestructive approach to recover scattering and absorption coefficients from reflectance measurements of highly absorbing and optically inhomogeneous media. Our approach is based on the Yang and Miklavcic theoretical model of light propagation through turbid media, which is a generalization of the Kubelka-Munk theory, extended to accommodate optically thick samples. We show its applications to paper, a material primarily composed of a web of fibers of cellulose, whose optical properties are strongly governed by light scattering effects. Samples studied were ancient and industrial paper sheets, aged in different conditions and highly absorbing in the ultraviolet region. The recovered experimental absorptions of cellulose fibers have been compared to theoretical ab initio quantum-mechanical computational simulations carried out within time-dependent density functional theory. In this way, for each sample, we evaluate the absolute concentration of different kinds of oxidized groups formed upon aging and acting as chromophores causing paper discoloration. We found that the relative concentration of different chromophores in cellulose fibers depends on the aging temperature endured by samples. This clearly indicates that the oxidation of cellulose follows temperature-dependent reaction pathways. Our approach has a wide range of applications for cellulose-based materials, like paper, textiles, and other manufactured products of great industrial and cultural interest, and can potentially be extended to other strongly absorbing inhomogeneous materials.