Determination of Volumetric Abundance of Intimate Mixture Using Bayesian MCMC

The quantitative estimation of volumetric abundance of powder mixture is the basis of quantitative remote sensing analysis. Here, we propose to analyze a unique laboratory measurements set, with precise composition, grain size, and volumetric abundance. We first propose a method to estimate the optical constant of materials, knowing the pure endmember spectra and their grain size. Then, we propose a method to transfer the measurement uncertainties to the volumetric abundance, based on the Bayesian approach and the full Hapke radiative transfer model. Using this approach, we are able to estimate grain size, volumetric abundance, and surface roughness. The results show that this approach is able to well estimate the correct volumetric abundance with an uncertainty of 23% and grain size with a ratio uncertainty of 3.0, i.e., uncertainties in log10 (grain size) = 0.48. The numerical cost of the MCMC is quite large (a few minutes per spectra) but still reasonable to treat a hyperspectral image with the gain of robust handling of nonlinearities and propagating uncertainty.