Laser self-mixing displacement sensing using entropy-based wavelets

Laser feedback-based self-mixing interferometry (SMI) enables compact, auto-aligned, and cost-effective sensing applications. However, the corresponding sensor signal is complex in nature, and retrieval of displacement information from the signal is non-trivial. In this paper, we demonstrate the utilization of discrete wavelet transform (DWT) in conjunction with entropy to improve the measurement performance of a previously reported SMI processing method, called consecutive samples unwrapping (CSU). This has resulted in improved measurement performance under stationary as well as non-stationary motion conditions. The entropy-based DWT method has also resulted in making the method more robust and self-adaptive while operating over a wider range of optical feedback strength. Using a commercial piezoelectric transducer with 2 nm resolution as the reference, the proposed method has improved relative RMS error and max error by approximately 27%, and 54%, respectively, with respect to CSU, for experimental SMI signals acquired using a laser-diode with a wavelength of 1550 nm under non-stationary target motion.