Optical constants and diffuse reflectance of opaque minerals: A modeling study using magnetite

Abstract

We use radiative transfer (RT) models, based upon the Hapke (1993) model, to estimate the imaginary refractive index of magnetite from laboratory reflectance measurements. We used a RT program coupled with a least-squares algorithm to fit measured reflectance data using complex refractive indices of magnetite estimated here and literature values. We included differing representations of the grain size distribution for modeling the measured reflectance of the magnetite samples. Best-fitting models were obtained when using the complex indices of refraction estimated from a specific grain size fraction to fit the same grain size of reflectance data. Magnetite complex refractive indices taken from reported literature studies resulted in the poorest fits to the measured reflectance data.We investigated the multiple-scattering behavior of magnetite using Fresnel's equation and complex refractive indices from literature values and our own estimates. For both we found the reflection coefficient is <1% after four reflections suggesting that multiple scattering is minimal. We also calculated the transmission via the Beer-Lambert law using the same sets of refractive indices. For both, the initial interface transmission had a comparable value near 80%. However, as the distance through the material increases the discrepancy between the two refractive indices had substantial influence. For the literature values the transmission was reduced to <1% after a distance of 8 μm at all wavelengths, whereas for the estimated values the transmission remained ≥75% at this distance. Magnetite, when viewed in a petrographic thin section (~30 μm thick), is opaque. This suggests that the optical constants estimated via the Hapke approach are not realistic.We compared the calculated Fresnel reflectance using one literature value to the measured reflectances and found that the overall spectral shape was similar to the magnetite diffuse reflectance measurements. However, the magnetite diffuse reflectance is only 30–40% of the calculated Fresnel reflectance. We speculate this may be due to the granular surfaces scattering light into a non-specular angle.Hapke-like models have been successfully applied for estimating optical constants of transparent materials. However, the present study finds that such models may not be appropriate for determining the optical constants of low-reflectance, opaque materials, as the results are not comparable to values of optical constants reported in the literature.