Quantitative determination of the mineral phases on planetary surfaces places critical constraints on our ability to model planetary surface geology. However, many of the relevant remote sensing instruments used to analyze planetary surfaces (Casini VIMS, MRO CRISM, and AVIRIS) cover the visible and near-infrared (VNIR; 0.35-2.5 µm) wavelength range, where spectral response is not a linear function of composition. Therefore, direct extraction of quantitative abundances through linear unmixing is not possible. For these data sets, the interaction of light with particulate matter must be explicitly modeled in order to perform quantitative spectral deconvolution. For planetary surfaces where the grain size is much greater than the wavelength of light used for the observation, and the surface can be considered an intimate mixture of phases, radiative transfer (RT) theory can be used to extract quantitative mineral abundances if the optical constants (the real and imaginary indices or refraction, n and k) for all minerals in the mixture are known.
Spectral unmixing using RT theory requires a broad library of robust optical constants from well characterized samples so that end member optical constants for each possible mineral in a mixture are represented. Optical constant determination is performed using laboratory spectra coupled with the appropriate theory. Where large, single crystals are available, Lorentz-Lorentz dispersion analysis can be performed on polarized spectra of oriented crystal faces. However, classical dispersion theory breaks down when k is small, as in the VNIR, which leaves determining k from transmission spectra of thin sections and using the Fresnel reflectance equation to determine n. For samples that only form as fine-grained powders, RT theory can be used to determine k from reflectance spectra of powders with grain size >> λ. The Kramers-Kronig relation can then be used to determine n from k in an iterative fashion. Each method for optical constant determination presents both analytical and computational challenges, thus optical constant libraries are limited. Here we begin to address this deficiency through the determination of optical constants of two feldspars, bytownite and labradorite, whose compositions are common in the crusts of terrestrial planets and asteroids.
Bulk feldspars were acquired, crushed, hand-picked for purity, ground in a shatterbox, and wet-sieved into 10 grain sizes. Samples of 4 grain sizes were then analyzed at Brown University using the NASA/Keck Reflectance Experiment Laboratory (RELAB) facility using their bidirectional spectrometer to obtain data from 0.32 to 2.55 µm, referenced to Spectralon. Each grain size was analyzed at i=20, 30, 40, 50, 60, and 70, and e=0. The spectra were then used to determine optical constants through an in-house MATLAB minimization routine. This is the beginning of a project that aims to determine optical constants for a variety of common planetary materials through multiple techniques in order to build a robust library of optical constants while investigating the limitations of this technique.