Hapke-based computational method to enable unmixing of hyperspectral data of common salts

Environmental scientists are currently assessing the ability of hyper-spectral remote sensing to detect, identify, and analyze natural components, including minerals, rocks, vegetation and soil. This paper discusses the use of a nonlinear reflectance model to distinguish multicomponent particulate mixtures. Analysis of the data presented in this paper shows that, although the identity of the components can often be found from diagnostic wavelengths of absorption bands, the quantitative abundance determination requires knowledge of the complex refractive indices and average particle scattering albedo, phase function and size. The present study developed a method for spectrally unmixing halite and gypsum combinations. Using the known refractive indexes of the components, and with the assistance of Hapke theory and Legendre polynomials, the authors develop a method to find the component particle sizes and mixing coefficients for blends of halite and gypsum. Material factors in the method include phase function parameters, bidirectional reflectance, imaginary index, grain sizes, and iterative polynomial fitting. The obtained Hapke parameters from the best-fit approach were comparable to those reported in the literature. After the optical constants (n, the so-called real index of refraction and k, the coefficient of the imaginary index of refraction) are derived, and the geometric parameters are determined, single-scattering albedo (or ω) can be calculated and spectral unmixing becomes possible.