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An Analysis of the Nonlinear Spectral Mixing of Didymium and Soda-Lime Glass Beads Using Hyperspectral Imagery (HSI) Microscopy

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Nonlinear spectral mixing occurs when materials are intimately mixed. Intimate mixing is a common characteristic of granular materials such as soils. A linear spectral unmixing inversion applied to a nonlinear mixture will yield subpixel abundance estimates that do not equal the true values of the mixtures components. These aspects of spectral mixture analysis theory are well documented. Several methods to invert and model nonlinear spectral mixtures have been proposed. Examples include Hapke theory, the extended endmember matrix method, and kernel-based methods. There is however, a relative paucity of real spectral image data sets that contain well characterized intimate mixtures. To address this, special materials were custom fabricated, mechanically mixed to form intimate mixtures, and measured with a hyperspectral imaging HSI microscope. The results of analyses of visiblenear-infrared VNIR 400 nm to 900 nm HSI microscopy image cubes in reflectance of intimate mixtures of the two materials are presented. The materials are spherical beads of didymium glass and soda-lime glass both ranging in particle size from 63 mm to 125 mm. Mixtures are generated by volume and thoroughly mixed mechanically. Three binary mixtures and the two endmembers are constructed and emplaced in the wells of a 96-well sample plate. Analysis methods are linear spectral unmixing LSU, LSU applied to reflectance converted to single-scattering albedo SSA using Hapke theory, and two kernel-based methods. The first kernel method uses a generalized kernel with a gamma parameter that gauges non-linearity, applying the well-known kernel trick to the least squares formulation of the constrained linear model. This method attempts to determine if each pixel in a scene is linear or non-linear, and adapts to compute a mixture model at each pixel accordingly. The second method uses K-hype with a polynomial quadratic kernel.

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  • Ceramics, Refractories and Glass
  • Optics

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