Vibration measurement based on multiple Hilbert transform for self-mixing interferometry

In order to reconstruct the micro-vibration quickly and easily, a novel phase unwrapping algorithm based on multiple Hilbert transform is proposed. Hilbert transform is performed once and three times for self-mixing fringes on different inclined directions, then the unwrapped phase is obtained and the micro-vibration can be reconstructed under weak or even moderate feedback. In this paper, the validity of the proposed algorithm is confirmed by means of simulated signals and demonstrated by several experimental measurements for both harmonic and aleatory target vibration.