Optimized variational mode decomposition for electro-optic modulating self-mixing interferometry

An electro-optic modulating self-mixing interferometry with the optimized variational mode decomposition (VMD) is presented based on the spectrum characteristics of electro-optic modulating self-mixing interference (SMI) and its perfect alignment with the advantages of VMD. A Bayesian optimization of the key hyperparameters of VMD is designed for the demodulation of electro-optic modulating SMI signals. The experimental methods are proposed using one-step VMD and two-step VMD to optimize the demodulation of the electro-optic modulating SMI signal. Experimental results show that the VMD-based demodulation method can accurately extract zero-order, first-order, and second-order harmonics and successfully perform operations such as arctangent and unwrapping. The experimental measurement accuracy aligns with theoretical analysis, reaching the level of a nanometer, which is comparable to existing methods. It makes a potential contribution to optimize and popularize the end-to-end electro-optic modulating self-mixing interferometry in practical engineering applications.