Displacement Sensing for Laser Self-Mixing Interferometry by Amplitude Modulation and Integral Reconstruction.

To robustly and adaptively reconstruct displacement, we propose the amplitude modulation integral reconstruction method (AM-IRM) for displacement sensing in a self-mixing interferometry (SMI) system. By algebraically multiplying the SMI signal with a high-frequency sinusoidal carrier, the frequency spectrum of the signal is shifted to that of the carrier. This operation overcomes the issue of frequency blurring in low-frequency signals associated with continuous wavelet transform (CWT), enabling the precise extraction of the Doppler frequency of the SMI signal. Furthermore, the synchrosqueezing wavelet transform (SSWT) is utilized to enhance the frequency resolution of the Doppler signal. Our experimental results demonstrate that the proposed method achieves a displacement reconstruction accuracy of 21.1 nm (0.89%). Additionally, our simulations demonstrated that this method can accurately reconstruct target displacement under the conditions of time-varying optical feedback intensity or a signal-to-noise ratio (SNR) of 0 dB, with a maximum root mean square (RMS) error of 22.2 nm. These results highlight its applicability in real-world environments. This method eliminates the need to manually determine the window length for time-frequency conversion, calculate the parameters of the SMI system, or add additional optical devices, making it easy to implement.

Self-Mixing Interferometer for Acoustic Measurements through Vibrometric Calibration.

The Self-Mixing Interformeter (SMI) is a self-aligned optical interferometer which has been used for acoustic wave sensing in air through the acousto-optic effect. This paper presents how to use a SMI for the measurement of Sound Pressure Level (SPL) in acoustic waveguides. To achieve this, the SMI is first calibrated in situ as a vibrometer. The optical feedback parameters C and α in the strong feedback regime (C≥4.6) are estimated from the SMI vibrometric signals and by the solving of non-linear equations governing the SMI behaviour. The calibration method is validated on synthetic SMI signals simulated from SMI governing equations for C ranging from 5 to 20 and α ranging from 4 to 10. Knowing C and α, the SMI is then used as an acoustic pressure sensor. The SPLs obtained using the SMI are compared with a reference microphone, and a maximal deviation of 2.2 dB is obtained for plane waves of amplitudes ranging from 20 to 860 Pa and frequencies from 614 to 17,900 Hz. The SPL measurements are carried out for C values ranging from 7.1 to 21.5.

Demonstration of Pressure Wave Observation by Acousto-Optic Sensing Using a Self-Mixing Interferometer.

In this paper, we demonstrate that a compact and inexpensive interferometric sensor based on the self-mixing effect in the laser cavity can be used for the characterization of shock waves. The sensor measures the changes in the refractive index induced by the shock wave. It is based on the self-mixing interferometry scheme. We describe the architecture of the dynamic sensor and the design of the experimental setup used for the characterization that involves a shock tube. Thus, we detail the experimental measurements for shock wave pressure amplitude of 5 bar and address their interpretation with regard to the most admitted models for acousto-optics.

A Novel Method for Detecting Fe2+ at a Micromolar Concentration Based on Multiple Self-Mixing Interference Using a Fiber Laser.

The concentration of an electrolyte is an optical characteristic of drinking water. We propose a method based on the multiple self-mixing interference with absorption for detecting the Fe2+ indicator as the electrolyte sample at a micromolar concentration. The theoretical expressions were derived based on the lasing amplitude condition in the presence of the reflected lights considering the concentration of the Fe2+ indicator via the absorption decay according to Beer's law. The experimental setup was built to observe MSMI waveform using a green laser whose wavelength was located in the extent of the Fe2+ indicator's absorption spectrum. The waveforms of the multiple self-mixing interference were simulated and observed at different concentrations. The simulated and experimental waveforms both contained the main and parasitic fringes whose amplitudes varied at different concentrations with different degrees, as the reflected lights participated in the lasing gain after absorption decay by the Fe2+ indicator. The experimental results and the simulated results showed a nonlinear logarithmic distribution of the amplitude ratio, the defined parameter estimating the waveform variations, versus the concentration of the Fe2+ indicator via numerical fitting.

Feedback Regimes of LFI Sensors: Experimental Investigations.

In this article, we revisit the concept of optical feedback regimes in diode lasers and explore each regime experimentally from a somewhat unconventional point of view by relating the feedback regimes to the laser bias current and its optical feedback level. The results enable setting the operating conditions of the diode laser in different applications requiring operation in different feedback regimes. We experimentally explored and theoretically supported this relationship from the standard Lang and Kobayashi rate equation model for a laser diode under optical feedback. All five regimes were explored for two major types of laser diodes: inplane lasers and vertical-cavity surface emitting lasers. For both lasers, we mapped the self-mixing strength vs. drive current and feedback level, observed the differences in the shape of the self-mixing fringes between the two laser architectures and a general simulation, and monitored other parameters of the lasers with changing optical feedback.

Fringe Detection and Displacement Sensing for Variable Optical Feedback-Based Self-Mixing Interferometry by Using Deep Neural Networks.

Laser feedback-based self-mixing interferometry (SMI) is a promising technique for displacement sensing. However, commercial deployment of such sensors is being held back due to reduced performance in case of variable optical feedback which invariably happens due to optical speckle encountered when sensing the motion of non-cooperative remote target surfaces. In this work, deep neural networks have been trained under variable optical feedback conditions so that interferometric fringe detection and corresponding displacement measurement can be achieved. We have also proposed a method for automatic labelling of SMI fringes under variable optical feedback to facilitate the generation of a large training dataset. Specifically, we have trained two deep neural network models, namely Yolov5 and EfficientDet, and analysed the performance of these networks on various experimental SMI signals acquired by using different laser-diode-based sensors operating under different noise and speckle conditions. The performance has been quantified in terms of fringe detection accuracy, signal to noise ratio, depth of modulation, and execution time parameters. The impact of network architecture on real-time sensing is also discussed.

Self-Mixing Laser Distance-Sensor Enhanced by Multiple Modulation Waveforms.

Optical rangefinders based on Self-Mixing Interferometry are widely described in literature, but not yet on the market as commercial instruments. The main reason is that it is relatively easy to propose new elaboration techniques and get results in controlled conditions, while it is very difficult to develop a reliable instrument. In this paper, we propose a laser distance sensor with improved reliability, realized through a wavelength modulation at a different frequency, able to decorrelate single measurement errors and obtain improvement by averages. A dedicated software is implemented to automatically calculate the modulation pre-emphasis, needed to linearize the wavelength modulation. Finally, data selection algorithms allow to overcome signal fading problems due to the speckle effect. A prototype demonstrates the approach with about 0.1 mm accuracy up to 2 m of distance at 200 measurements per second.

Combined Feature Extraction and Random Forest for Laser Self-Mixing Vibration Measurement without Determining Feedback Intensity.

To measure the vibration of a target by laser self-mixing interference (SMI), we propose a method that combines feature extraction and random forest (RF) without determining the feedback strength (C). First, the temporal, spectral, and statistical features of the SMI signal are extracted to characterize the original SMI signal. Secondly, these interpretable features are fed into the pretrained RF model to directly predict the amplitude and frequency (A and f) of the vibrating target, recovering the periodic vibration of the target. The results show that the combination of RF and feature extraction yields a fit of more than 0.94 for simple and quick measurement of A and f of unsmooth planar vibrations, regardless of the feedback intensity and the misalignment of the retromirror. Without a complex optical stage, this method can quickly recover arbitrary periodic vibrations from SMI signals without C, which provides a novel method for quickly implementing vibration measurements.

Amplification of optical signals in a bistable vertical-cavity surface-emitting laser by vibrational resonance.

The paper presents the results of the experimental study of an application of the phenomenon of vibrational resonance (VR) for enhancement of the response of a bistable vertical-cavity surface-emitting laser (VCSEL) to the effect of optical modulating signals. Specifically, two different cases were investigated: (a) the control of all-optical switching caused by a modulated orthogonal optical injection from another VCSEL and (b) the amplification of autodyne signals from a vibrating diffusely reflecting surface in the self-mixing optical interferometry. It is experimentally demonstrated that an application of the phenomenon of VR in both cases studied leads to a strong amplification of the input optical signals by a factor from 10 to 200 depending on the experimental conditions with respect to the initial values. The effect of the asymmetry of a bistable potential on the amplification factor was also studied. The results obtained can be used to improve all-optical switchings for application in communication systems and enhancement of autodyne signals in self-mixing optical interferometry. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Toward an Estimation of the Optical Feedback Factor C on the Fly for Displacement Sensing.

In this paper, a method based on the inherent event-based sampling capability of laser optical feedback interferometry (OFI) is proposed to assess the optical feedback factor C when the laser operates in the moderate and strong feedback regimes. Most of the phase unwrapping open-loop OFI algorithms rely on the estimation of C to retrieve the displacement with nanometric precision. Here, the proposed method operates in open-loop configuration and relies only on OFI's fringe detection, thereby improving its robustness and ease of use. The proposed method is able to estimate C with a precision of <5%. The obtained performances are compared to three different approaches previously published and the impacts of phase noise and sampling frequency are reported. We also show that this method can assess C on the fly even when C is varying due to speckle. To the best of the authors' knowledge, these are the first reported results of time-varying C estimation. In addition, through C estimation over time, it could pave the way not only to higher performance phase unwrapping algorithms but also to a better control of the optical feedback level via the use of an adaptive lens and thus to better displacement retrieval performances.

Measurement of micro-harmonic vibration from optical feedback interferometry using wavelet trend analysis.

Self-mixed optical feedback interferometry based laser sensors show promising results in the measurement of the vibration frequency. To date several measurement methods have been developed to extract the vibration information from the self-mixed (SM) signal; however, the complexity and accuracy of the methods still need improvement. The presented work tries to fulfill the gap by realizing a novel method using maximal overlap discrete wavelet transformation (MODWT) and multi-resolution analysis (MRA). The proposed method can reconstruct the micro-harmonic (< 5 µ m ) vibration up to 1 kHz even under weak feedback conditions. The mean squared error and the maximum relative error of the proposed method for this range remained below 1.89 × 1 0 - 3 & 8.79%, respectively. Although, above 1 kHz, the proposed method turns out to be futile to reconstruct the vibration signal but still capable to measure vibration frequency up to 10 kHz with an accuracy of ± 0.0001. The method also found suitable to measure non-sinusoidal vibration frequency with reasonable accuracy even for the moderate feedback conditions. The authors envision that the proposed method will provide a compact, non-contact, and low-cost alternative for the vibration frequency measurement hence useful in early fault detection schemes and lung abnormality diagnosis.

Versatile Multimodality Imaging System Based on Detectorless and Scanless Optical Feedback Interferometry-A Retrospective Overview for A Prospective Vision.

In this retrospective compendium, we attempt to draw a "fil rouge" along fifteen years of our research in the field of optical feedback interferometry aimed at guiding the readers to the verge of new developments in the field. The general reader will be moved at appreciating the versatility and the still largely uncovered potential of the optical feedback interferometry, for both sensing and imaging applications. By discovering the broad range of available wavelengths (0.4-120 µm), the different types of suitable semiconductor lasers (Fabry-Perot, distributed feedback, vertical-cavity, quantum-cascade), and a number of unconventional tenders in multi-axis displacement, ablation front progression, self-referenced measurements, multispectral, structured light feedback imaging and compressive sensing, the specialist also could find inspirational suggestions to expand his field of research.

Laser Self-Mixing Fiber Bragg Grating Sensor for Acoustic Emission Measurement.

Fiber Bragg grating (FBG) is considered a good candidate for acoustic emission (AE) measurement. The sensing and measurement in traditional FBG-based AE systems are based on the variation in laser intensity induced by the Bragg wavelength shift. This paper presents a sensing system by combining self-mixing interference (SMI) in a laser diode and FBG for AE measurement, aiming to form a new compact and cost-effective sensing system. The measurement model of the overall system was derived. The performance of the presented system was investigated from both aspects of theory and experiment. The results show that the proposed system is able to measure AE events with high resolution and over a wide dynamic frequency range.

Measuring Linewidth Enhancement Factor by Relaxation Oscillation Frequency in a Laser with Optical Feedback.

This paper presents a new method for measuring the linewidth enhancement factor (alpha factor) by the relaxation oscillation (RO) frequency of a laser with external optical feedback (EOF). A measurement formula for alpha is derived which shows the alpha can be determined by only using the RO frequencies and no need to know any other parameters related to the internal or external parameters associated to the laser. Unlike the existing EOF based alpha measurement methods which require an external target has a symmetric reciprocate movement. The proposed method only needs to move the target to be in a few different positions along the light beam. Furthermore, this method also suits for the case with alpha less than 1. Both simulation and experiment are performed to verify the proposed method.

A Fiber-Coupled Self-Mixing Laser Diode for the Measurement of Young's Modulus.

This paper presents the design of a fiber-coupled self-mixing laser diode (SMLD) for non-contact and non-destructive measurement of Young's modulus. By the presented measuring system, the Young's modulus of aluminum 6061 and brass are measured as 70.0 GPa and 116.7 GPa, respectively, showing a good agreement within the standards in the literature and yielding a much smaller deviation and a higher repeatability compared with traditional tensile testing. Its fiber-coupled characteristics make the system quite easy to be installed in many application cases.

All-Fiber Configuration Laser Self-Mixing Doppler Velocimeter Based on Distributed Feedback Fiber Laser.

In this paper, a novel velocimeter based on laser self-mixing Doppler technology has been developed for speed measurement. The laser employed in our experiment is a distributed feedback (DFB) fiber laser, which is an all-fiber structure using only one Fiber Bragg Grating to realize optical feedback and wavelength selection. Self-mixing interference for optical velocity sensing is experimentally investigated in this novel system, and the experimental results show that the Doppler frequency is linearly proportional to the velocity of a moving target, which agrees with the theoretical analysis commendably. In our experimental system, the velocity measurement can be achieved in the range of 3.58 mm/s-2216 mm/s with a relative error under one percent, demonstrating that our novel all-fiber configuration velocimeter can implement wide-range velocity measurements with high accuracy.

Features of a Self-Mixing Laser Diode Operating Near Relaxation Oscillation.

When a fraction of the light reflected by an external cavity re-enters the laser cavity, both the amplitude and the frequency of the lasing field can be modulated. This phenomenon is called the self-mixing effect (SME). A self-mixing laser diode (SM-LD) is a sensor using the SME. Usually, such LDs operate below the stability boundary where no relaxation oscillation happens. The boundary is determined by the operation condition including the injection current, optical feedback strength and external cavity length. This paper discovers the features of an SM-LD where the LD operates beyond the stability boundary, that is, near the relaxation oscillation (RO) status. We call the signals from such a SM-LD as RO-SM signals to differentiate them from the conventional SM signals reported in the literature. Firstly, simulations are made based on the well-known Lang and Kobayashi (L-K) equations. Then the experiments are conducted on different LDs to verify the simulation results. It shows that a RO-SM signal exhibits high frequency oscillation with its amplitude modulated by a slow time varying envelop which corresponds to the movement of the external target. The envelope has same fringe structure (half-wavelength displacement resolution) with the conventional SM signals. However, the amplitudes of the RO-SM signals are much higher compared to conventional SM signals. The results presented reveal that an SM-LD operating near the RO has potential for achieving sensing with improved sensitivity.

Antenna-integrated 0.6 THz FET direct detectors based on CVD graphene.

We present terahertz (THz) detectors based on top-gated graphene field effect transistors (GFETs) with integrated split bow-tie antennas. The GFETs were fabricated using graphene grown by chemical vapor deposition (CVD). The THz detectors are capable of room-temperature rectification of a 0.6 THz signal and achieve a maximum optical responsivity better than 14 V/W and minimum optical noise-equivalent power (NEP) of 515 pW/Hz(0.5). Our results are a significant improvement over previous work on graphene direct detectors and are comparable to other established direct detector technologies. This is the first time room-temperature direct detection has been demonstrated using CVD graphene, which introduces the potential for scalable, wafer-level production of graphene detectors.

Self-mixing thin-slice solid-state laser metrology.

This paper reviews the dynamic effect of thin-slice solid-state lasers subjected to frequency-shifted optical feedback, which led to the discovery of the self-mixing modulation effect, and its applications to quantum-noise-limited versatile laser metrology systems with extreme optical sensitivity.

Laser-self-mixing interferometry for mechatronics applications.

We report on the development of an all-interferometric optomechatronic sensor for the detection of multi-degrees-of-freedom displacements of a remote target. The prototype system exploits the self-mixing technique and consists only of a laser head, equipped with six laser sources, and a suitably designed reflective target. The feasibility of the system was validated experimentally for both single or multi-degrees-of-freedom measurements, thus demonstrating a simple and inexpensive alternative to costly and bulky existing systems.