Thierry Bosch

Laser feedback interferometry: a tutorial on the self-mixing effect for coherent sensing

This tutorial presents a guided tour of laser feedback interferometry, from its origin and early development through its implementation to a slew of sensing applications, including displacement, distance, velocity, flow, refractive index, and laser linewidth measurement. Along the way, we provide a step-by-step derivation of the basic rate equations for a laser experiencing optical feedback starting from the standard Lang and Kobayashi model and detail their subsequent reduction in steady state to the excess-phase equation. We construct a simple framework for interferometric sensing applications built around the laser under optical feedback and illustrate how this results in a series of straightforward models for many signals arising in laser feedback interferometry. Finally, we indicate promising directions for future work that harnesses the self-mixing effect for sensing applications.

Adaptive self-mixing vibrometer based on a liquid lens

A self-mixing laser diode vibrometer including an adaptive optical element in the form of a liquid lens (LL) has been implemented and its benefits demonstrated. The LL arrangement is able to control the feedback level of the self-mixing phenomenon, keeping it in the moderate feedback regime, particularly suitable for displacement measurements. This control capability has enabled a remarkable increase in the sensor-to-target distance range where measurements are feasible. Target vibration signal reconstructions present a maximum error of lambda radical16 as compared with a commercial sensor, thus providing an improved working range of 6.5 cm to 265 cm.

GaN laser self-mixing velocimeter for measuring slow flows

The self-mixing (SM) laser sensing technique allows for a simple, self-aligned, and robust system for measuring velocity. Low-cost blue emitting GaN laser diodes have recently become available owing to the high volume requirements for Blu-ray Disc devices such as high-definition video players and gaming consoles. These GaN lasers have a significantly shorter wavelength (around 405 nm) compared with other semiconductor lasers (generally around 800 nm for SM sensors). Therefore, if used in SM flow sensors, they allow measuring of flow rates that would otherwise be too slow to measure. In this Letter we report what we believe to be the worlds first SM flow measurement system based on a blue emitting semiconductor laser, demonstrating the ability to measure flow rates down to 26 microm/s.

Design and Analysis of an Embedded Accelerometer Coupled Self-Mixing Laser Displacement Sensor

This paper presents the operating principle and signal processing needed for the design of a reliable solid-state accelerometer (SSA) coupled self-mixing (SM) interferometric laser displacement sensor for embedded applications. The influence of signal processing methods and accelerometer characteristics on the complete sensing system performance is studied, and four different SSA-SM sensing systems are examined and characterized. Through comparing their performance, the sensing system precision is limited by the noise density of the employed accelerometer as well as the used SM displacement retrieval technique, whereas the system bandwidth is mainly limited by the choice of a given accelerometer. Furthermore, this paper analyzes the phase and gain-matching properties that the SSA-SM should reach to guarantee proper extraneous vibrations correction. Finally, the proof of concept of a real-time SSA-SM sensing system indicating 30-dB correction is presented. This prototype demonstrates the possibility of using such a real-time sensing system for embedded and industrial applications in which the presence of extraneous movements would hinder traditional sensors use.

Robust Method of Stabilization of Optical Feedback Regime by Using Adaptive Optics for a Self-Mixing Micro-Interferometer Laser Displacement Sensor

A self-mixing (SM) micro-interferometer laser displacement sensor coupled with an adaptive liquid lens (ALL) system is proposed and implemented. This has been made possible by a new method of real-time estimation of the optical feedback coupling factor C. It is shown that such an estimation of C combined with an appropriate amplification of the SM signal Gain allows the ALL system to seek and maintain the SM signal in the moderate optical feedback regime in spite of variations in the optical feedback. The ALL system thus enables robust real-time displacement sensing in an unmanned autonomous manner. The implemented system has provided measurement precision better than 90 nm for different target surfaces and distances. The paper also investigates the impact of the weighting attributed to C and Gain on the retrieved displacement precision. As this autofocus is presently only performed once during the sensor initialization, so maximum displacement span after achieving optical feedback regime locking has also been investigated and tabulated. This proof of concept, thus paves the way for the deployment of autonomous SM sensors.

Solving self-mixing equations for arbitrary feedback levels: a concise algorithm

Self-mixing laser sensors show promise for a wide range of sensing applications, including displacement, velocimetry, and fluid flow measurements. Several techniques have been developed to simulate self-mixing signals; however, a complete and succinct process for synthesizing self-mixing signals has so far been absent in the open literature. This article provides a systematic numerical approach for the analysis of self-mixing sensors using the steady-state solution to the Lang and Kobayashi model. Examples are given to show how this method can be used to synthesize self-mixing signals for arbitrary feedback levels and for displacement, distance, and velocity measurement. We examine these applications with a deterministic stimulus and discuss the velocity measurement of a rough surface, which necessitates the inclusion of a random stimulus.

Imaging of acoustic fields using optical feedback interferometry

This study introduces optical feedback interferometry as a simple and effective technique for the two-dimensional visualisation of acoustic fields. We present imaging results for several pressure distributions including those for progressive waves, standing waves, as well as the diffraction and interference patterns of the acoustic waves. The proposed solution has the distinct advantage of extreme optical simplicity and robustness thus opening the way to a low cost acoustic field imaging system based on mass produced laser diodes.

Classification of laser self-mixing interferometric signal under moderate feedback

This paper presents a different approach to classify self-mixing (SM) signals operating in the moderate feedback regime. A total of six distinct classes of SM signals can be defined based on the SM inherent shapes, which depend on both the feedback factor C and the linewidth enhancement factor α. This classification allows clear identification of SM signals for which normalization issues can arise and thus for which displacement precision is inherently reduced due to the very nature of the signal itself. Finally, it is shown that phase unwrapping approaches can theoretically retrieve displacement with subnanometer precision for usual laser diodes in the moderate feedback regime, in the absence of noise, only for α values greater than approximately 4.3.

Real-Time Algorithm for Versatile Displacement Sensors Based on Self-Mixing Interferometry

This paper presents a general displacement reconstruction algorithm for sensors based on self-mixing (SM) interferometry suitable to work at different optical feedback conditions. The approach relies on a robust phase observation through the analytic signals for the fringe detection stage, while the motion of the pointed target is retrieved by a self-adapting filter in a piecewise basis. The implementation for the real-time calculations demonstrates the feasibility of robust SM sensors for different usage conditions without the need of modifying the base device configuration.

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 Ψr(t) and Ψd(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.