Monte Carlo simulations of subsurface analysis of painted layers in micro-scale spatially offset Raman spectroscopy

A recently developed micrometer-scale spatially offset Raman spectroscopy (micro-SORS) method provides a new analytical capability for investigating nondestructively the chemical composition of subsurface, micrometer-scale-thick, diffusely scattering layers at depths beyond the reach of conventional confocal Raman microscopy. Here we provide, for the first time, the theoretical foundations for the micro-SORS defocusing concept based on Monte Carlo simulations. Specifically, we investigate a defocusing variant of micro-SORS that we used in our recent proof-of-concept study in conditions involving thin, diffusely scattering layers on top of an extended, diffusely scattering substrate. This configuration is pertinent, for example, for the subsurface analysis of painted layers in cultural heritage studies. The depth of the origin of Raman signal and the relative micro-SORS enhancement of the sublayer signals reached are studied as a function of layer thickness, sample photon transport length, and absorption. The model predicts that sublayer enhancement initially rapidly increases with increasing defocusing, ultimately reaching a plateau. The magnitude of the enhancement was found to be larger for thicker layers. The simulations also indicate that the penetration depths of micro-SORS can be between one and two orders of magnitude larger than those reached using conventional confocal Raman microscopy. The model provides a deeper insight into the underlying Raman photon migration mechanisms permitting the more effective optimization of experimental conditions for specific sample parameters.