Photon Migration in Raman Spectroscopy

Abstract

Monte Carlo simulation has been applied to study time-resolved Raman and Tyndall photon migration in opaque samples under isotropic and forward scattering conditions. For isotropic scattering, Raman and Tyndall intensities are predicted to decay according to t^(1–n) and t⁻ⁿ, respectively, where the value of n depends on the ratio of the optical collection aperture to the mean scattering length. The simulation correctly reproduced the analytical results of n = 3/2 and n = 5/2 for a point source in infinite and semi-infinite media, respectively. In addition the model can be used to relate the time at which a Raman photon exits the sample to the mean depth at which it was generated. This could provide a useful tool for depth profiling the chemical composition of turbid systems, and hence be a useful addition to the established array of photon-migration techniques. The model was applied to analyze experimentally observed Raman and Tyndall decay profiles from powdered trans-stilbene. The transport mean free path (l_t) was calculated to be ∼400 μm, which was significantly larger than the particle sizes present in the sample (∼10–100 μm). This implies that the particles were highly forward scattering, as would be expected for this size range. When highly anisotropic scattering was introduced into the model a much more reasonable scattering length (l_s ∼ 40 μm) was obtained. Finally, a simple analytical model was developed that gives the correct relationship between the Raman and Tyndall decay exponents for isotropic scattering. To the best of our knowledge this work represents the first detailed study of Raman photon migration under time-resolved conditions.