Sparsity Promoting Frequency Sampling Method for Estimation of Displacement and Self-Mixing Interferometry Parameters

Abstract

This paper exploits the difference in amplitude spectrum of perturbed and unperturbed phase of self-mixing (SM) laser, to propose a new method for estimation of coupling factor (C), line-width enhancement factor (LEF), as well as displacement of the vibrating target in three major feedback regimes, i.e, weak-, moderate- and strong-feedback regimes. This result thus fills the gap in limitation of previous methods restricted to fewer regimes. The displacement of target is assumed to be bandlimited and sparse in frequency domain. The proposed algorithm showed an average of 1.0168 nm RMS error in displacement estimation corresponding to single- and multi-tone vibrations of amplitudes varying from 3 to 30 times that of laser's wavelength, with percentage error of 1.15% and 3.31% in C and LEF estimations, from simulated SM laser signals. Using an SM sensor based on a laser diode emitting at 785 nm wavelength, the proposed method has achieved an average RMS error of 21 nm in weak-, moderate- and strong-feedback regimes, corresponding to a vibrating target of 5 micrometer peak-peak amplitude.