Interpreting spectral unmixing coefficients: From spectral weights to mass fractions

Here, we present a method to transform the mixing coefficients to mass fractions for arbitrary combinations of extinction coefficients and densities. The required parameters are computed from reflectance measurements of well defined endmember mixtures. Consequently, additional measurements, e.g., the endmember density, are no longer required. We evaluate the method based on laboratory measurements and various results presented in the literature, respectively. It is shown that the procedure transforms the mixing coefficients to mass fractions yielding an accuracy comparable to carefully calibrated laboratory measurements without additional knowledge. For our laboratory measurements, the square root of the mean squared error is less than 4.82  wt%. In addition, the method corrects for systematic effects originating from mixtures of endmembers showing a highly varying albedo, e.g., plagioclase and pyroxene.