Quantitative inversion of the volume concentration of oil emulsions based on a polynomial-trigonometric nonlinear spectral mixing model.

After an oil spill occurs, oil pollutants typically mix with seawater to form oil-in-water (OW) and water-in-oil (WO) emulsions. Quantifying the volume concentration of these oil emulsions is essential for determining the spilled oil volume and designing appropriate treatment strategies. Current oil spill monitoring studies mainly focus on detecting oil pollutants on sea surface without considering their emulsification status. This study establishes a novel polynomial-trigonometric nonlinear mixing model (PTNMM) to interpret the nonlinear spectral responses of oil emulsions. The polynomial component corrects global spectral distortions, while the trigonometric term characterizes the spectral interference fringes. A constrained least-square-based abundance estimation algorithm is designed to estimate the oil volume concentration in oil emulsions based on PTNMM. The proposed model is validated using the reflectance spectra of OW and WO emulsions acquired from outdoor experiments. Results show that nonlinearity exists in the reflectance spectra of both emulsion types. The trigonometric function contributes more significantly to the spectra of WO emulsions than those of OW emulsions. The PTNMM achieves spectral reconstruction and abundance estimation with lower errors than linear spectral mixing models, especially for WO emulsions: the normalized RMSE was reduced by 34% to 59% after incorporating the trigonometric term, demonstrating the advantage of using a trigonometric function as the nonlinear component in spectral mixing models for oil emulsion quantification. This study provides a potential solution for quantifying the volume concentration of oil emulsions using hyperspectral remote sensing technology.