Analyses of spectral data often assume a linear mixing hypothesis, which states that the spectrum of a mixed substance is approximately the mixture of the individual spectra of its constituent parts. We evaluate this hypothesis in the context of dissolved organic matter (DOM) fluorescence spectroscopy for endmember abundance recovery from mixtures of three different DOM endmembers. We quantify two key sources of experimental variation, and statistically evaluate the linear mixing hypotheses in the context of this variation. We find that there is not strong statistical evidence against this hypothesis for high-fluorescence readings, and that true abundances of high-fluorescence endmembers are accurately recovered from the excitation-emission fluorescence spectra of mixed samples using linear methods. However, abundances of a low-fluorescence endmember are less well-estimated, in that the abundance coefficient estimates exhibit a high degree of variability across replicate experiments.

翻译：光谱数据分析通常基于线性混合假设，即混合物质的光谱近似等于其各组分光谱的线性组合。本研究在溶解性有机质（DOM）荧光光谱学背景下，通过三种不同DOM端元组分的混合实验，评估该假设对端元丰度反演的适用性。我们量化了两个关键实验变异来源，并在此变异框架下对线性混合假设进行统计检验。研究发现：对于高荧光强度读数，不存在强有力的统计证据否定该假设；利用线性方法可从混合样品的激发-发射荧光光谱中准确反演高荧光端元的真实丰度。然而，低荧光端元的丰度估计效果较差，其丰度系数估计值在重复实验中表现出高度变异性。