mixedspectrum

Mixed spectrum is a spectrum that results from the combination of spectral contributions from two or more sources, materials, or processes. It is commonly encountered in analytical chemistry, remote sensing, astronomy, and materials science. In such cases the observed signal cannot be attributed to a single pure substance or source, and the spectrum shows overlapping features from its constituents.

Causes include spatial mixing, such as a pixel that covers multiple materials; chemical mixing, such as a solution containing several species; and optical or instrumental effects, including atmospheric interference and instrument response. In astronomy, the spectrum of an object can be a mix of stellar continua, nebular emission, and absorption features along the line of sight.

Mathematically, a mixed spectrum is often modeled by a linear mixing model: M(λ) ≈ Σ_i a_i S_i(λ) + ε(λ), where S_i(λ) are endmember or component spectra, a_i are nonnegative abundances, and ε(λ) is noise. Nonlinear mixing may occur in cases with intimate mixing or multiple scattering, complicating unmixing.

Spectral unmixing is the set of methods used to estimate the components and abundances from M. Techniques include constrained least squares, nonnegative matrix factorization, independent component analysis, and model-based fitting. Endmember extraction, calibration, and atmospheric correction are important practical steps.

Applications abound: in remote sensing to map surface materials; in analytical chemistry to deconvolve mixtures; in astronomy to separate continuum, emission lines, and absorption features; and in forensics to separate overlapping signals.

Related concepts include spectral unmixing and the linear mixing model.