Analysis and Implementation of a Direct Phase Unwrapping Method for Displacement Measurement Using Self-Mixing Interferometry

Abstract

Self-mixing or optical feedback interferometry has been widely used for displacement and velocity measurement applications. For metric information retrieval with $ precision, various phase unwrapping methods have been proposed. However, these are computationally heavy and require large number of hardware resources, thereby hindering the development of real-time, embedded solutions for large bandwidth applications. In this regard, a simple and efficient feedback phase retrieval algorithm, called consecutive samples-based unwrapping (CSU) is presented. Detailed analysis of its error performance has been conducted as a function of key optical feedback parameters. A theoretical study has also been conducted to explain as to why such good error performance is obtained for such a simple algorithm by establishing a linear relation between the modulated laser power signal and the laser phase in the absence of optical feedback for specific ranges of key optical feedback parameters. We applied CSU on various simulated and experimentally acquired signals using SMI for the retrieval of harmonic and arbitrary displacements and found out that CSU retrieves target displacement with a precision of about $\lambda /10$ while consuming much less time and hardware resources. The paper also presents FPGA based hardware design results of CSU and compares its performance with a traditional analytical phase unwrapping method in terms of maximum clock frequency, latency, and on-chip hardware resources. This hardware comparison strongly establishes the advantages of such a fast and computationally light algorithm, readily suitable for large bandwidth, embedded, and real-time sensing applications.