Quantitative Abundance Estimates From Bidirectional Reflectance Measurements

A simplified approach to the problem of determining the relative proportion of minerals in a mixture from a reflectance spectrum of the mixture is presented. Fundamental to this approach is a priori information concerning reflectance spectra of the minerals in the mixture and some estimate of the particle sizes of the mixture components. Reflectance spectra of intimate mixtures are a systematic but nonlinear combination of the spectra of the minerals in the mixtures. Equations for bidirectional reflectance are used to linearize the systematics of spectral mixing for intimate mixtures. The equations are simplified by assuming that particulate media scatter light isotropically at phase angles between 15 ø and 40 ø. This method for linearizing the mixing systematics is used to determine mineral relative geometric cross sections (proportional to mass fraction/density x particle diameter) from reflectance spectra of mixtures of igneous rock-forming minerals (oilvine, magnetite, enstatite, and anorthite) and to determine endmember relative geometric cross sections from reflectance spectra of mixtures of terrestrial desert soils. Since particle diameters are known, the mass fractions of the mixture components are also calculated. For materials without strongly absorbing components, the accuracy of abundance determinations is better than 5%. The results indicate that the method presented can be used to accurately determine the relative proportions of components (minerals or complex endmembers) in a mixture from a reflectance spectrum of the mixture given information of the endmembers in the mixture, reflectance spectra of the endmembers, and an estimate of particle sizes of the respective mixture components.