Robust Detection of Non-Regular Interferometric Fringes From a Self-Mixing Displacement Sensor Using Bi-Wavelet Transform

An innovative signal processing method based on custom-made wavelet transform (WT) is presented for robust detection of fringes contained in the interferometric signal of self-mixing (SM) laser diode sensors. It enables the measurement of arbitrarily-shaped vibrations even in the corruptive presence of speckle. Our algorithm is based on the pattern recognition capability of bespoke WTs for detecting SM fringes. Once the fringes have been correctly detected, phase unwrapping methods can be applied to retrieve the complete instantaneous phase of the SM signals. Here, the novelty consists in using two distinct mother wavelets $\Psi _{r}$ ( ${t}$ ) and $\Psi _{d}$ ( ${t}$ ) specifically designed to distinguish SM patterns as well as the displacement direction. The peaks, i.e. the maxima modulus of WT, then allow the detection of the fringes.