Quantitative analysis of pigment mixtures on paper using fiber-optic reflectance spectroscopy and advanced optical modeling

Non-invasive methods are essential for studying materials in cultural heritage artworks. Among them, Fiber Optic Reflectance Spectroscopy (FORS) is widely employed for in situ analysis due to its portability and direct relationship with the optical properties governing color. However, FORS remains largely qualitative, as reflectance spectra of pigment mixtures show nonlinear behavior caused by complex absorption and scattering processes, especially on strongly scattering substrates such as paper. This work introduces the first quantitative application of the Yang–Miklavcic model to heritage pigments on paper. This model, an extension of the Kubelka–Munk theory, retrieves intrinsic absorption and scattering coefficients in inhomogeneous, highly scattering layers by accounting for the scattering-induced path variation of photons. Experimental tests were performed on mock-ups prepared on paper with single and binary mixtures of five pigments: ultramarine blue, chromium oxide green, burnt sienna, titanium white, and Naples yellow. Reflectance spectra were acquired with an integrating-sphere setup to measure diffuse reflectance. By using intrinsically derived optical coefficients, the method enables the separation of pigment scattering from that of the paper substrate, allowing accurate identification and quantitative estimation of the components in binary pigment mixtures on paper. The results demonstrate that FORS, when coupled with advanced optical modelling, provides reliable, non-invasive, and cost-effective quantitative compositional data for painted surfaces.