Displacement Sensing for Laser Self-Mixing Interferometry by Amplitude Modulation and Integral Reconstruction.

To robustly and adaptively reconstruct displacement, we propose the amplitude modulation integral reconstruction method (AM-IRM) for displacement sensing in a self-mixing interferometry (SMI) system. By algebraically multiplying the SMI signal with a high-frequency sinusoidal carrier, the frequency spectrum of the signal is shifted to that of the carrier. This operation overcomes the issue of frequency blurring in low-frequency signals associated with continuous wavelet transform (CWT), enabling the precise extraction of the Doppler frequency of the SMI signal. Furthermore, the synchrosqueezing wavelet transform (SSWT) is utilized to enhance the frequency resolution of the Doppler signal. Our experimental results demonstrate that the proposed method achieves a displacement reconstruction accuracy of 21.1 nm (0.89%). Additionally, our simulations demonstrated that this method can accurately reconstruct target displacement under the conditions of time-varying optical feedback intensity or a signal-to-noise ratio (SNR) of 0 dB, with a maximum root mean square (RMS) error of 22.2 nm. These results highlight its applicability in real-world environments. This method eliminates the need to manually determine the window length for time-frequency conversion, calculate the parameters of the SMI system, or add additional optical devices, making it easy to implement.