Secondary envelope extraction based on multiple Hilbert transforms for laser self-mixing micro-vibration measurement

This paper presents a method that can be applied to weak feedback and full-range moderate feedback in the field of self-mixing interference measurement, and the target motion displacement can be obtained by multiple Hilbert transforms of the signal after the secondary envelope extraction. Simulations and experiments of multiple micro-vibration measurements were performed with different optical feedback factors, and the results were consistent with theoretical analysis. This method effectively eliminates the impact of the self-mixing interference signal with fringe shift on micro-vibration reconstruction.