Generalized multi-cavity laser self-mixing interferometry based on scattering theory

We present a generalized mathematical model and algorithm for the multi-cavity self-mixing phenomenon based on scattering theory. Scattering theory, which is extensively used for travelling wave is exploited to demonstrate that the self-mixing interference from multiple external cavities can be modelled in terms of individual cavity parameters recursively. The detailed investigation shows that the equivalent reflection coefficient of coupled multiple cavities is a function of both attenuation coefficient and the phase constant, hence propagation constant. The added benefit with recursively model is that it is computationally very efficient to model large number of parameters. Finally, with the aid of simulation and mathematical modelling, we demonstrate how the individual cavity parameters such as cavity length, attenuation coefficient, and refractive index of individual cavities can be tuned to get a self-mixing signal with optimal visibility. The proposed model intends to leverage system description for biomedical applications when probing multiple diffusive media with distinct characteristics, but could be equally extended to any setup in general.