Study of Laser Feedback Phase Under Self-Mixing Leading to Improved Phase Unwrapping for Vibration Sensing

In this paper, the inherent error as well as the robustness of a previously published displacement retrieval technique called the phase unwrapping method (PUM) is analyzed. This analysis, based on a detailed study of laser feedback phase behavior, results in a new algorithm that removes the PUM inherent error while maintaining its robustness. The said algorithm has been successfully tested on simulated and experimental self-mixing (SM) interferometric signals. Simulations in weak and moderate feedback regimes demonstrate that the said algorithm can reach a subnanometric precision compared with approximately 25 nm for PUM. For experimental SM signals affected by noise, the measured rms displacement error and the maximum absolute error are 14 and 37 nm, respectively, for the proposed algorithm and 34 and 123 nm for the PUM, which indicates a threefold displacement precision improvement over the PUM. Finally, it is explained that the precision can be further improved by a reduction of the noise level of experimental SM signals.