Nanometric Vibration Sensing Using Spectral Processing of Laser Self-Mixing Feedback Phase

In this paper, a method is proposed to recover displacements with nanometric precision based on spectral analysis of the feedback phase of self-mixing laser interferometric signal. This method is an enhancement of the previously developed method called Time-domain Frequency-domain Signal Processing (TFSP) which could only recover target vibration(s) with greater than lambda/8 amplitude (where lambda is the laser's wavelength) so long as at least one of the vibration's components has an amplitude greater than or equal to lambda/2. Using TFSP reconstruction as a first approximation of the main target displacement combined with parameter (optical feedback factor C and linewidth enhancement factor alpha) estimation, the proposed method can provide a better in-depth analysis of the self-mixing signal spectrum and thus achieve the detection of even lower amplitude vibrations. Studies presented in the paper indicate that the proposed method does not require accurate parameter estimation. Experimental results obtained using a laser diode based self-mixing sensor with lambda = 785 nm show that the adding this method on top of TFSP allows to recover target vibrations with amplitude down to approximately lambda/32 with an average amplitude root-mean-square error of 1.56 nm, which corresponds to a 4 fold improvement over TFSP.