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 <i>in vivo</i> 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.