Mastering Spectroscopy of Inhomogeneous Materials: Advanced Sampling Strategies to Solve the Heterogeneity Problem

Sample heterogeneity represents a fundamental obstacle in quantitative and qualitative spectroscopic analysis. Chemical and physical inhomogeneities—such as varying particle sizes, packing densities, surface textures, and spatial concentration gradients—can introduce significant variation in measured spectra. This tutorial explores the core challenges and modeling strategies used to understand and mitigate these effects. We present matrix-based formulations of spectral mixture models and correction strategies using data fusion, spatial averaging, and spectral preprocessing. Applications in imaging spectroscopy and localized sampling design are discussed in the context of recent research findings. The tutorial concludes with a discussion on future research directions, including adaptive sampling and uncertainty quantification.