Extraction of vibration parameters from optical feedback interferometry signals using wavelets

This paper proposes the use of the wavelet transform as a technique that is suited for fringe detection and analysis of optical feedback interferometry (OFI) signals, thus allowing the retrieval of extremely small physical motion phenomena. A novel algorithm based on wavelet transform is used to process the OFI signal simultaneously in the time and frequency domains, enabling precise detection of signal fringes and, thus, the extraction of amplitude features of the vibrating target with error in the order of 0.1λ. Furthermore, using a complex Morlet wavelet as an analyzing wavelet enables us to extract important information from the time envelope of the OFI signal. Such an envelope can be useful in detecting fringes even in the presence of speckle reducing the error in a displacement reconstruction. Examples of OFI applications, including nanometric displacement sensing without direction ambiguity as well as the measurement of the frequency and velocity of vibrating targets and the detection in time of no periodic events, are also presented using this wavelet approach.