Effect of linewidth enhancement factor on displacement reconstruction and immediate estimation of feedback factor for weak feedback

Abstract

Metrology based on self-mixing interferometry (SMI) covers a wide range of metrical application such as measurement of distance displacement, vibration, velocity, flow and size of Brownian particles. In general, two SMI parameters namely, optical feedback factor C and linewidth enhancement factor (LEF) α are significant in the above-mentioned measurements. Particularly, the joint estimation of C and α is the key to real-time displacement self-mixing (SM) sensor with sub-wavelength resolution.The application of the approach to the immediate estimation of C and α proposed by Kim et al. (2018) is limited to the moderate and strong feedback regime. The paper presents an approach to the immediate estimation of C for the weak feedback regime, to which the approach by Kim et al. (2018) is impossible to be applied, thus allowing the immediate joint estimation method to be applied to all the regimes. Because the proposed method is incomparably simpler than the previous ones and very efficient in hardware, it will be of great assistance to developing a low-cost real-time SM displacement sensor with sub-wavelength resolution in which complex computation such as optimization are impossible. In addition, the paper discusses the effect of C and α on the accuracy of displacement reconstruction.