Uncertainties in Unmixing of Multi-phase Hyperspectral Data in Reflective Region: Effects of Texture and Fabric

Abstract

The Linear Mixing Model (LMM), based on the assumption of single scattering of light is the most preferred approach to unmix (interpret) hyperspectral data due to its simplicity in implementation. However, in most of the natural situations, the reflection process involves multiple scattering and hence, LMM is not very effective. Therefore, nonlinear spectral unmixing model based on Radiative Transfer Equation (RTE) is necessary to understand the influencing factors and effects associated with shadowing or multiple scattering. The reflected spectrum of two juxtaposed materials is the linear sum of the two individual absorption spectra. However, light reflected off an intimate mixture of particles exhibits a spectra that is a nonlinear combination of the two individual spectra. In this work, we have studied the influence of texture (grain size) and fabric (patterns) on reflectance spectra using RTE based nonlinear unmixing model. For this purpose, three types of geological materials namely basalt, anorthosite, and quartzite representing high, moderate and low albedos were used. Multi-phase reflectance spectra of these rocks were acquired in varying combinations of grain size (2-4 mm, 1-2 mm, and <1mm) and patterns. The complexity of fabric was progressively increased from a three-boundary case to intimate mixture. Bi-directional reflectance spectra for different phase angles were collected using a spectroradiometer mounted on a goniometer setup. Subsequently, salient parameters addressing nonlinearity in Hapke model such as phase function, opposition effect, type of scattering for each combination of texture and fabric were estimated from the iteratively modeled spectra. The condition adopted to evaluate the modeling efficacy is the root mean square error (RMSE) between the measured and modeled spectra. When the desired RMSE (<0.01) is achieved, the iteration process is stopped and Hapke parameters corresponding to the best-fit model were retrieved. Analyses of results indicate that grain size, shape, and the fabric cumulatively influence the Hapke parameters such as Bo, b, and c. This clearly indicates that texture and fabric influence the basic physical properties of light scattering namely opposition effect, phase function, and forward/backward scattering property.