Numerical determination of visible/NIR optical constants from laboratory spectra of HED meteorites

Abstract

Radiative transfer models in particulate media (Hapke, 1981, 1993, 2012b; Shkuratov et al., 1999) are the most versatile tool that can be used to retrieve both composition and surface physical properties from observation of asteroids and other atmosphereless bodies of the Solar System. One caveat is that these methods require as input a sufficiently comprehensive set of optical constants of suitable template materials. These optical constants are the real and imaginary parts of the refractive indexes of the material as function of wavelength, and have to be derived from laboratory measurements of samples of minerals and meteorites. Optical constants can be calculated from a variety of types of measurements, and each has its problems and limitations. In particular, a problem with the determination of optical constants from measurement of reflectance is that the measurements need to be themselves interpreted using radiative transfer models. This is an issue because the number of parameters used in the most accurate versions of the radiative transfer models is large, and for most of the samples many of these parameters were not measured independently. As a result, attempts in the literature to retrieve optical constants from reflectance measurements tend to assume values for the unknown parameters, which can lead to uncertainties in the retrieved optical constants that can be difficult to quantify. In this work we propose a numerical method that allows the simultaneous inversion of the optical constant and the model parameters. This model is then applied to a set of reflectance spectra of 5 HED meteorites from the RELAB database that were measured with the same setup for samples with several particle size intervals. Our results indicate that our method is able to retrieve optical constants which are able to reproduce the measured reflectance of the samples over a large range (25–500 µm) of particle diameters. It is also found that the solutions obtained in this way are non-unique, in the sense that many combination of the model parameters can yield different sets of optical constants that fit equally well the reflectance spectra. Thus, in the absence of the independent determination of at least some of the model parameter the method is unable to decide which solution correspond to the physical optical constants of the materials. Even so, the dispersion of the model parameters (in particular effective particle diameter and porosity) for acceptable solutions (defined as the ones that reproduce the measured reflectance spectra at all size range with residues smaller than 10%) is within a radius of around 30% of the value of the best fit solution for each parameter. Given the ability of the optical constants derived with this method to reproduce the sample spectra over a large range of particle sizes, they can be used without other restriction to assess if a given meteorite assemblage is contributing to the observed spectra of asteroids. However, quantitative informations that can also be derived using these optical constants, like particle sizes, porosity and volumetric fractions of each end-member in a mixture should be regarded only as rough estimates.