Quantitative spectroscopic analysis of light scattering in rough granular coatings: an optimized Kubelka-Munk...

The quantitative spectroscopic analysis of rough, granular matrices presents significant challenges due to complex non-linear light scattering and variable background absorption. To address the spectral deviations caused by these optical phenomena in agricultural-grade phosphate coatings, this study proposes a physically corrected spectroscopic model based on optimizing the Kubelka-Munk (K-M) theory. A comparative analysis reveals that while empirical mathematical corrections (Quadratic model) improve the mathematical fitting of reflectance spectra, they fail to capture the underlying physical relationship between concentration and absorption, resulting in significant quantification errors (Average Relative Deviation, ARD = 2.80) for complex spectral series. In contrast, the k-corrected model, which explicitly incorporates Saunderson coefficients to account for surface refractive index and internal scattering, demonstrates superior accuracy in predicting the spectral response. Experimental validation confirms that this physically based approach significantly reduces the concentration quantification error (ARD) for the complex green series from 1.17 to 0.85 and minimizes the spectral colorimetric difference (∆E_ab^∗)by approximately 50% (from 2.67 to 1.35). Furthermore, for the Yellow and Coffee-brown target spectra, color differences were consistently reduced to below 1.0. These findings indicate that accounting for physical optical properties-specifically surface and internal scattering-is critical for the accurate spectroscopic modeling of granular coatings, providing a robust framework for predicting the optical behavior of complex dyed systems.