A novel reconstruction method of nanometer micro-displacement of Fabry–Perot (F-P) interference is proposed in this study. Hilbert transforms are performed for F-P interference fringes, and the obtained signal performs tangent operation with the original signal. Finally, the validity of the proposed algorithm and the structure are verified by simulation and several experimental measurements for vibration. Results from the experiments show that the maximum relative error is 4.9%.

To measure the vibration of a target by laser self-mixing interference (SMI), we propose a method that combines feature extraction and random forest (RF) without determining the feedback strength (C). First, the temporal, spectral, and statistical features of the SMI signal are extracted to characterize the original SMI signal. Secondly, these interpretable features are fed into the pretrained RF model to directly predict the amplitude and frequency (A and f) of the vibrating target, recovering the periodic vibration of the target. The results show that the combination of RF and feature extraction yields a fit of more than 0.94 for simple and quick measurement of A and f of unsmooth planar vibrations, regardless of the feedback intensity and the misalignment of the retromirror. Without a complex optical stage, this method can quickly recover arbitrary periodic vibrations from SMI signals without C, which provides a novel method for quickly implementing vibration measurements.

In this study, we propose a new optical fiber interferometer based on differential structure. The phase delay exists in the two output arms of the coupler. When the interference signal passes through the phase delay twice in the transmission, it produces a phase shift of π with the original signal. This feature can be used to differentially reduce noise. The experimental results show that the signal-to-noise ratio increases by 1.29 dB, and the waveform of the reconstructed signal is reduced by 12 nm. Thus, the structure can effectively improve the quality of the measured signal.