Extraction of vibration parameters from optical feedback interferometry signals using wavelets

Abstract

This paper proposes the use of the wavelet transform as a technique well-suited for fringe detection and analysis of optical feedback interferometry (OFI) signals, 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 domain, enabling a precise detection of signal fringes and thus, the extraction of amplitude features of the vibrating target with an average error in the order of 0.1λ. Furthermore, using a complex Morlet wavelet as analyzing wavelet enables to extract important information from the time envelope of the OFI signal. Such 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 non-periodic events are also presented using this wavelet approach. The paper, thus presents a novel approach to the processing of optical feedback interferometry signals.

All Analog Processing of Speckle Affected Self-Mixing Interferometric Signals

“…1 and Fig. 3) due to its fading as a function of remote target's surface roughness which scatters the incoming laser light resulting in an interference pattern that is granular due to the superposition of random phases of the beams [21]. For small displacements, it does not affect largely but has a significant effect in the case of large displacements [19].…”

“…One approach is to avoid the Date of publication : 15 th of Sptember 2017 occurrence of speckle within SMI either by using cooperative target surface, or by adding electro-mechanical/optical/laser [15][16][17] components to the SMI sensor. The second approach uses additional DSP algorithms for signal recovery such as Hilbert transform [18], envelope extraction [19] and wavelet transform methods [20,21]. The later approach is thus preferable as it maintains the inherent simplicity of SMI sensor design.…”

“…The challenge, in the framework of analog phase unwrapping [23], was as to how speckle affected SMI signal could be processed in an all analog manner. The proposed work shows that the approach of SMI envelope extraction [19], [21] can be implemented in standard analog circuits so that all analog processing of speckle affected SMI signal can be successfully executed. Such an all analog processing of speckle affected SMI signal appears full of potential as it enables displacement extraction from SMI signals through standard analog circuits thereby removing constraints such as the requirement of highperformance analog to digital converter (ADC) and DSP hardware platforms.…”

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

“…4). Similar to [22], [25], an add-on routine should be then used to determine the displacement direction in order to reconstruct the displacement with a precision of λ/2 ( Fig. 4 (a)).…”

“…Consequently, differential and evolutionary algorithms [24] were necessary to detect the fringes, but at a cost of significant computational requirements. More recently, a method based on the Morlet complex wavelet has been proposed [25] to detect the fringes and changes in displacement direction as well as to remove parasitic noise more efficiently. However, this method has been developed for C values lower or close to 1.…”