Deconvolution of spectra for intimate mixtures

Visible to near infrared reflectance spectra of macroscopic mixtures have been shown to be linear combinations of the reflections of the pure mineral components in the mixture. However, for microscopic mixtures the mixing systematics are in general nonlinear. The systematics may be linearized by conversion of reflectance to single scattering albedo (w), where the equations which relate reflectance to w depend on the method of data collection. Several proposed mixing models may be used to estimate mineral abundances from the reflectance spectra of intimate mixtures. These models are summarized and a revised model is presented. A noniterative (linear) least squares approach was used for curve fitting and the data, measured as bi-directional reflectance with incidence and emergence angles of 30 and 0 deg were converted to w by a simplified version of Hapke's equation for bi-directional reflectance. This model was tested with two mixture series composed of 45 to 75 micron particles: an anorthite-enstatite series and an olivine-magnetite series. The data indicate that the simplified Hapke's equation may be used to convolve reflectance spectra into mineral abundances if appropriate endmembers are known or derived from other techniques. For surfaces that contain a significant component of very low albedo material, a somewhat modified version of this technique will need to be developed. Since the abundances are calculated using a noniterative approach, the application of this method is especially efficient for large spectral data sets, such as those produced by mapping spectrometers.