On Two Fourier Transform Based Methods For Estimation of Displacement and Parameters of Self-Mixing Interferometry Over Major Optical Feedback Regimes

Using a self-mixing laser interferometric sensor, the aim of this paper is to propose two new and distinct Fourier transform based methods for estimation of optical coupling factor and linewidth enhancement factor, as well as displacement of a target over all feedback regimes by processing the feedback phase. First algorithm deals only with band-limited smooth displacements, while second method deals with rather more general, smooth displacements. Under noiseless simulations over diverse target motion conditions and optical feedback regimes, these algorithms (first and second) have shown picometric displacement sensing precision of 1.1264 pm and 1.0996 pm respectively, for laser wavelength of 785 nm. The performance of proposed methods has also been quantified in case of additive noise. During experimental verification, by using a reference sensor with 2 nm resolution, their precision was measured to be 36.2142 nm and 34.4388 nm respectively, for weak-, moderate-, and strong-optical feedback regime signals. Importantly, for strong feedback regime, these methods have shown better performance than two previously reported methods.