Fast and highly accurate phase unwrapping algorithm for displacement retrieval using self-mixing interferometry sensor

Abstract

Self-Mixing interferometry (SMI) has been widely used for displacement, vibration and velocity measurement applications. Many phase unwrapping methods are proposed for high precision measurement. However, most of these methods are compute-intensive and non-real-time in nature due to time-consuming iterative processing, which hinders the development of real-time SMI based sensor for sensing applications. On the other hand, available computationally lighter real-time methods have a very low measurement precision, limiting them to applications not demanding high accuracy measurement. Thus, in this work, a much simpler and highly accurate modified phase unwrapping method (MPUM) is proposed. MPUM is based on two steps processing. The first step of the algorithm is rough phase retrieval, where the wrapped rough phase of the normalized SMI signal is directly unwrapped using a simple threshold-based approach. In second step, this rough unwrapped phase is cleaned to extract desired target displacement by applying a simple phase localization technique. The proposed method is not only simpler and computationally lighter compared to previously proposed methods, but also improves measurement resolution. Furthermore, the proposed method can work for all three (Weak, moderate and strong) feedback regime signals. MPUM was tested for a variety of simulated and experimental SMI signals, and results were compared with already proposed conventional phase unwrapping methods. MPUM has a measurement precision of around 10.7 nm (λ0/73), compared to conventional phase unwrapping methods having precision ranging from λ0/10 to λ0/40. MPUM is 66.8% faster than PUM and improved displacement measurement by 67.2% compared to PUM. Such a high precision and computationally much simpler method will be a critical step for the development of an embedded real-time system for autonomous measurements using an SMI sensor.