Fast and highly accurate estimation of feedback coupling factor and linewidth enhancement factor for displacement sensing under different feedback regimes

Abstract

In self-mixing interferometry, the fast and accurate estimation of fundamental feedback parameters, such as optical feedback coupling factor C and linewidth enhancement factor α, is critical for high-resolution real-time displacement sensing using an SMI sensor.In this work, a Marquardt’s algorithm (MA) based fast and highly accurate method is proposed to estimate C and α. The proposed method utilizes the SMI signal phase and applies a simple numerical analysis to estimate C and α. The proposed method can accurately estimate C and α for all three major feedback regimes (i.e., week, moderate and strong). A detailed comparison is also made with previously proposed algorithms to show the superiority of the proposed algorithm in terms of initial conditions, number of iterations, accuracy, and ability to work under all feedback regimes. The results have shown that our method has a negligible average error of around 0.0023 and 0.0006 for C and α estimation, respectively. The proposed method only requires approximately five iterations for accurate estimation. The method’s simplicity, accuracy, and fast nature enable compact and cost-effective SMI sensors with high-resolution real-time displacement sensing.