Generation depth modeling in time domain diffuse Raman spectroscopy: the homogeneous case

We present a rigorous analytical model, based on the diffusion equation, to calculate the average generation depth of Raman photons in a semi-infinite, diffusive, homogeneous medium, taking into account variations in optical properties between the wavelength of the excitation photons and that of the Raman-scattered photons. The model quantifies how the generation depth depends on photon time-of-flight for time domain diffuse Raman spectroscopy (TD-DIRS) or source-detector distance for spatially offset Raman spectroscopy (SORS). Monte Carlo simulations demonstrate the model’s reliability. We applied this model to simulate representative cases of in vivo scenarios for which the probed depth is evaluated by the proposed theoretical model. This model provides the basic knowledge to significantly improve the interpretation of SORS and TD-DIRS measurements.