Sample-probe interactions in spectroscopy: Sampling microscopic property gradients

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Abstract
An analytical model is presented to describe the influence of sample-probe interactions on the shape of spectroscopic lines. By considering the discrete sampling of spatial property variations using a focused probe, the model predicts gradient-induced line broadening, as well as probe channeling near free surfaces. The magnitude of sample-probe interactions is governed by two system parameters: the probe size and the spatial property gradient. Furthermore, certain spatial heterogeneities are found to contribute appreciably to the signal and its associated line shape over distances several times the probe size. Experimental observations in fluorescence spectroscopy are used to evaluate the line-shape model. Spectra measured along an embedded ruby fiber under a residual stress gradient are in good agreement with those calculated using the model.