Laser Self-mixing Interferometry Research Articles

Laser self-mixing interferometry for dynamic displacement sensing of multiple targets

Laser self-mixing interferometry for dynamic displacement sensing of multiple targets

Laser self-mixing interference displacement signal filtering method based on empirical mode decomposition and wavelet threshold

In laser self-mixing interferometry displacement measurement, noise interference has a significant impact on the measurement results. To improve measurement accuracy, this paper proposes a filtering method that combines empirical mode decomposition (EMD) with wavelet thresholding. First, the signal is decomposed into several intrinsic mode functions (IMFs) using EMD. Then, wavelet thresholding is applied to each IMF. Subsequently, the processed IMFs are reconstructed to achieve signal filtering. Finally, by integrating the principles of interpolation and fringe counting, the reconstructed displacement signal is recovered, realizing accurate displacement measurement. This paper presents comprehensive simulation analyses and experimental validations for the proposed method. The accuracy of the displacement recovery is quantitatively evaluated using the absolute error and standard error, comparing the recovered displacement signal with the actual displacement. The experimental results demonstrate that the laser self-mixing interferometry displacement signal filtering method based on EMD and wavelet thresholding has high accuracy.

All-fiber laser self-mixing interferometry for signal enhancement with phase-shifted fiber Bragg grating

In this paper, phase-shifted fiber Bragg grating (PSFBG) is introduced in an all-fiber laser self-mixing interferometry (SMI) for signal enhancement. PSFBG is used as an optical filter to enhance the signal to noise ratio (SNR) of SMI signal. When the laser wavelength locates at the edge of the filter, the frequency modulation (FM) can be mapped to the easy-to-detect amplitude modulation (AM) to enhance the SMI signal. Simulation and experimental comparison of unenhanced SMI signal, FBG-enhanced SMI signal and PSFBG-enhanced SMI signal are presented. The enhancement effects of different reflectivity surfaces are comparatively analyzed and the maximum spatial test ranges of lower reflectivity surfaces are compared between unenhanced and PSFBG-enhanced. As well as applying the PSFBG-enhanced to the Doppler effect experiment. Due to the extremely narrow linewidth of PSFBG, the PSFBG-based SMI has the better performance in longer detection range and lower backscattering light. PSFBG-enhanced achieves an impressive enhancement of up to 800 times compared to unenhanced signals.

Generalized multi-cavity laser self-mixing interferometry based on scattering theory.

We present a generalized mathematical model and algorithm for the multi-cavity self-mixing phenomenon based on scattering theory. Scattering theory, which is extensively used for travelling wave is exploited to demonstrate that the self-mixing interference from multiple external cavities can be modelled in terms of individual cavity parameters recursively. The detailed investigation shows that the equivalent reflection coefficient of coupled multiple cavities is a function of both attenuation coefficient and the phase constant, hence propagation constant. The added benefit with recursively model is that it is computationally very efficient to model large number of parameters. Finally, with the aid of simulation and mathematical modelling, we demonstrate how the individual cavity parameters such as cavity length, attenuation coefficient, and refractive index of individual cavities can be tuned to get a self-mixing signal with optimal visibility. The proposed model intends to leverage system description for biomedical applications when probing multiple diffusive media with distinct characteristics, but could be equally extended to any setup in general.

Signal extraction method based on spectral processing for a dual-channel SMI vibration sensor

Laser self-mixing interferometry (SMI) is a powerful measurement technique with high sensitivity and subwavelength precision. However, the simultaneous detection of multi-targets with adjacent frequencies for current SMI systems is an enormous challenge because their spectra are overlapped to be distinguished difficulty. Here, a novel method based on the short-time Fourier transform (STFT) and pre-feedback structure is presented for dual-channel laser SMI, which realizes the recovery of two vibrations with adjacent frequencies. The spectrum of the SMI signal is expanded along the time-axis by STFT, in which the pre-feedback mirror is applied to reallocate the energy of each channel. Further, the signal is extracted separately through spectrum suppression and transformation. Simulation results show that the proposed approach is effective in vibration frequencies over a large range of ratio of 1:1- 1:5 in the weak feedback regime. The RMS errors of the experimental results with less than 11.29 nm (0.87%) indicate the reliability of this scheme, which provides an alternative solution for the simultaneous detection of multi-parameters.

Sensitivity enhancement in laser self-mixing nano-particle sizer with linear current tuning based frequency shifting method

Laser self-mixing interferometry (SMI) has been widely researched and applied to the field of traditional physical quantities (such as displacement, distance, velocity and vibration) detection due to the well-known merits of compact structure, low-cost and high sensitivity, additionally, it has also shown great potential in nano-particle sizing during the last two decades, primarily depending on the incoherent stochastic superposition of laser beam’s interaction with each particle in the illuminating volume, and the particle diameter can be determined from the power spectra of self-mixed signals through Lorentz fitting. SMI particle sensing generally uses constant current driving laser diodes (LD), so the power spectrum peak occurs around zero-frequency and merely exhibits the right-hand half. Some other particle sensors using solid-state lasers (SSL), however, prefer to employ a pair of acousto-optic modulators (AOM) as frequency shifters, which pronouncedly increases the complexity and the cost of the whole system. In this paper, linear modulation current is applied to a LD to achieve laser frequency tuning and conveniently shift the concerned Lorentz peak to any desired spectrum position. Moreover, higher-order harmonics of the shifted Lorentz peak, arising from intrinsically tilted SMI fringes, exhibit wider spectrum broadening than the main peak and can be employed to improve the sensitivity in nano-particle recognition. The technique proposed has been validated by simulation and experimental results, and it is beneficial to developing low-cost, compact and highly sensitive SMI particle sensors or instruments.

Robust Signal Extraction Based on Time-Frequency Joint Analysis and GRNN for a Laser SMI System

In pursuit of vibration recovery, with subwavelength precision based on laser self-mixing interferometry (SMI), the estimation of two key parameters, i.e., the optical feedback parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C$</tex-math></inline-formula> and linewidth enhancement factor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> , is of vital importance. However, the above process is not ideal in terms of accuracy and real-time performance. Aiming to overcome these deficiencies, a time-domain-based frequency-domain processing method (TFPM) has been proposed for the SMI system in this paper, which realizes robust and fast extraction of the vibration signals without the estimation of the parameters and does not require fringe detection. The method achieves the extraction of motion information via a mathematical transformation, namely, short-time Fourier transform (STFT), in which the limitations caused by STFT are alleviated by using generalized regression neural network (GRNN). In processing the SMI signal of the target with non-stationary motion, the TFPM finally achieves an expected root-mean-square (RMS) error of 0.24 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> , which demonstrates the high performance of the proposed method.

High Sensitivity and Full-Circle Optical Rotary Sensor for Non-Cooperatively Tracing Wrist Tremor With Nanoradian Resolution

In this article, a novel optical rotary sensor based on laser self-mixing interferometry is developed for the full-circle rotation measurement. The proposed sensor is convenient to use for it does not need any contact with the target or a cooperative mirror. A prototype is fabricated and tested. The measured results demonstrate good performance compared with other optical rotary sensors, in terms of the 0.1 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> rad resolution, the 2.33 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> linearity, and 2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> rad stability over 1 h. Additionally, the repeatability error is below 14.66 mrad under nine-group full-circle tests, which exhibits the potential to be instrumentalized reliably. Error analysis and limitation discussion have been also carried out. Although the accuracy needs further improvement compared with the best rotary sensor, this method has its unique advantages of high resolution, non-cooperative target sensing, and electromagnetic immunity. Hence, the proposed optical rotary sensor provides a promising alternative in precise rotation measurement, tremor tracing, and nanomotion monitoring.

Determining System Parameters and Target Movement Directions in a Laser Self-Mixing Interferometry Sensor

Self-mixing interferometry (SMI) is a promising sensing technology. As well as its compact structure, self-alignment and low implementation cost, it has an important advantage that conventional two-beam interferometry does not have, i.e., SMI signal fringe evolves into asymmetrical shape with increasing optical feedback level, which leads to discrimination of target movement directions for unambiguous displacement measurement possible by a single-channel interferometric signal. It is usually achieved by using SMI signals in moderate feedback regime, where the signals exhibit hysteresis and discontinuity. However, in some applications, e.g., in biomedical sensing where the target has a low reflectivity, it is hard for the SMI system to operate in a moderate feedback regime. In this work, we present comprehensive analyses on SMI signal waveforms for determining system parameters and movement directions by a single-channel weak feedback SMI signal. We first investigated the influence of two system parameters, i.e., linewidth enhancement factor and optical feedback factor, on the symmetry of SMI signals. Based on the analyses on signal waveform, we then proposed a method of estimating the system parameters and displacement directions. The method was finally verified by experiments. The results are helpful for developing sensing applications based on weak feedback SMI systems.

Measuring parameters of laser self-mixing interferometry sensor based on back propagation neural network.

Self-mixing interferometry (SMI) is a well-known non-destructive sensing technique that has been widely applied in both laboratory and engineering applications. In a laser SMI sensing system, there are two vital parameters, i.e., optical feedback factor C and line-width enhancement factor α, which influence the operation characteristics of the laser as well as the sensing performance. Therefore, many efforts have been made to determine them. Most of the existing methods of estimating these two parameters can often be operated in a certain feedback regime, e.g., weak or moderate feedback regime. In this paper, we propose a new method to estimate C and α based on back-propagation neural network for all feedback regimes. A parameter predicting model was trained and built. The performance of the proposed predicting model was tested using simulation and experiment data. The results show that the proposed method can estimate C and α with an average error of 2.76% and 2.99%, respectively. Additionally, the proposed method is noise-proof. The method and results are useful for extending the utilization of SMI technology in practical engineering fields.

Frequency-shifted nano-particle sizing using laser self-mixing interferometry under linear current tuning

In addition to the traditional physical quantities (such as displacement, distance, velocity and vibration) detection that has been widely researched and reported, laser self-mixing interferometry (SMI) has shown great potential in nano-particle sizing during the last two decades, primarily depending on the incoherent stochastic superposition of the laser beam’s interaction with each particle in the illuminating volume. Particle diameter can be determined from the power spectra of self-mixed signals through Lorentz fitting. SMI particle sensing using laser diodes (LDs) always adopts direct current (DC) driving, so the spectrum peak occurs around zero-frequency and merely exhibits the right-hand half. Some other particle sensors using solid-state lasers (SSLs), however, prefer to employ a pair of acousto-optic modulators (AOMs) as frequency shifters, which pronouncedly increase the complexity and the cost of the whole measurement system. In this letter, linearly injected current is applied to a LD to achieve laser frequency tuning and conveniently shift the concerned Lorentz peak to any specified spectrum position, which simplifies the measurement setup and greatly avoids the influence of DC or low-frequency disturbance. The technique proposed is beneficial to developing low-cost, compact and precise SMI particle sensors or instruments.

Precision improvement in laser self-mixing nanoparticle sizing with all phase FFT amplitude correction

As a well-known noncontact optical sensing technique, laser self-mixing interferometry (SMI) exhibits outstanding merits of low-cost, self-alignment, compactness, and high sensitivity, and it has been applied to typical geometrical quantity measurements, tomography, object imaging, as well as nanoparticle sizing. In SMI nanoparticle detection, as a result of Brownian motion, laser beam stochastically interacts with each particle in the illuminating volume, producing self-mixed signals with Lorentz shape power spectra, whose spectral broadening width is directly related with particle sizes. In general, FFT is always the first choice to obtain signals’ power spectra, but due to the influence of spectrum leakage, the heights of spectral lines may rise or fall and then change original Lorentz shapes and further increase sizing errors. Here, an all phase FFT (apFFT) method has been proposed to greatly suppress spectrum leakage, correct spectral line heights and further improve nanoparticle sizing errors for Rayleigh scattering cases. The apFFT method proposed is advantageous to developing precise SMI particle sensors or instruments, which may be applicable to chemical or medical applications.

Suppression of undamped relaxation oscillation in a laser self-mixing interferometry sensing system.

Undamped relaxation oscillation (RO) in a laser self-mixing interferometry (SMI) system may occur in some common application conditions, which may impact the stable operation of the system and degrade its sensing performance. In this work, we proposed to suppress the undamped RO by controlling the system operation parameters in a laser SMI sensing system. By numerically solving the famous Lang Kobayashi equations, the stability of a laser SMI system in a 3-parameter space of external cavity length, injection current and optical feedback factor were investigated. Based on the stability analyses, we determined the system operation conditions required for suppressing the undamped RO and derived an analytical expression for describing the relationship between the operation parameters. An experimental SMI system based on a laser diode (Sanyo, DL4140-001s) was implemented and verified the suppressing method. The experimental results showed that the SMI system in a moderate feedback regime can operate in steady state without undamped RO by setting proper operation parameters. This work provides useful guidance to design a stable SMI sensing system for practical applications.

Implementation of hilbert transform based high-resolution phase unwrapping method for displacement retrieval using laser self mixing interferometry sensor

Laser self-mixing interferometry (SMI) is an attractive sensing scheme due to its compact, self-align, and cost-effective nature. In this work, an SMI based compute-intensive phase unwrapping method was implemented on FPGA. Before implementation, the algorithm was segmented into different processing stages. A limitation in PUM was also identified, and its signal processing-based solution was proposed. Lastly, the implementation of PUM was done on the targeted FPGA board. Results have shown 170 K times speed improvement compared to software-based implementation on a personal computer. Furthermore, the proposed implementation can process maximum target velocity up to 2.88 m/s. The proposed implementation consumes 0.7 W of dynamic power. From the results, the proposed implementation is suitable for low power and high bandwidth applications.

Improved displacement sensing by spectral processing of laser self-mixing interferometry signal phase

In Laser self-mixing interferometry (SMI), phase unwrapping methods are widely utilized for high-resolution displacement measurements. In this work, a Time-frequency signal processing (TFSP) method for SMI based displacement retrieval is analyzed. Its limitations are identified, and an improved and more robust version of TFSP is proposed for enhanced resolution and better sensing in a non-ideal situation. By rectifying the phase inversion errors present in TFSP, the proposed work can process the laser phase more efficiently than TFSP. Furthermore, the proposed work can also accommodate significant amplitude fading of laser feedback signal by applying the Hilbert transform based signal processing technique, making it robust than TFSP.The proposed work demonstrates that the Hilbert processing technique and improved phase estimation shows approximately 90% improvement over the TFSP method for simulated SMI signals from different feedback regimes and amplitude variations. Additionally, experimental results for various C values indicate an average improvement of around 29% compared to TFSP.Lastly, FPGA based emulation of ITFSP is performed for embedded sensing applications. While operating at 180 MHz, the ITFSP can measure a maximum target velocity of 4.5 m/s.The development of such a robust and high-resolution method is a critical step towards a compact laser-based sensor for high-resolution applications, even for non-cooperative targets and rough environments causing laser light fading.

All-phase FFT based distance measurement in laser self-mixing interferometry

As is widely known in the field of laser self-mixing interferometry (SMI), a commercial laser diode (LD) under linear injection current modulation can serve as a low-cost laser rangefinder, whose self-mixed signal exhibits a beat frequency proportional to the distance to be measured. So exact frequency extraction becomes a significant issue in this measurement scheme. In order to obtain better frequency and then better distance estimation performance, a new frequency extraction technique based on all-phase FFT (apFFT) is proposed to deal with SMI signals to suppress the influence of spectrum leakage and signal noise. Related mathematical derivation shows the advantages of the apFFT, then the simulation analysis indicates that the relative frequency errors can be evaluated to be lower than 10−3 even under the signal-to-noise ratio (SNR) of 5 dB. While in the experiments, the corresponding distance resolution is about 30 µm in the range examined. Additionally, the discussions of several influencing factors are included. The method proposed is effective in detecting target distance and can provide an interesting and attractive technical route for SMI distance measurement.

Influence of linewidth enhancement factor $$\alpha $$ on self-mixing interferometry in solid-state lasers

Up to now, laser self-mixing interferometry (SMI) has been widely applied to numerous scientific and industry fields. A easily negligible parameter, linewidth enhancement factor $$\alpha $$ , influences the inclination of SMI signals, and larger $$\alpha $$ generally indicates more inclined fringes. It is demonstrated in the paper that solid-state lasers (SSL) have smaller linewidth enhancement factors compared with semiconductor ones, which interrupt the movement reconstruction of external targets. For Nd:YAG SSLs, $$\alpha $$ is experimentally analyzed to be around one, resulting in less tilted SMI fringes, and the direction discrimination property of SMI becomes less obvious even when a smooth target supplies more amount of feedback light. In the Nd:YAG SSL scheme and for harmonic vibrations, a simple and effective method is also proposed to obtain the frequency and amplitude information of external targets. Simulations and experiments show that the method can achieve the frequency accuracy within 1% and the amplitude accuracy better than 3%.

Real-time human blood pressure measurement based on laser self-mixing interferometry with extreme learning machine

In this paper, we present a method based on self-mixing interferometry combing extreme learning machine for real-time human blood pressure measurement. A signal processing method based on wavelet transform is applied to extract reversion point in the self-mixing interference signal, thus the pulse wave profile is successfully reconstructed. Considering the blood pressure values are intrinsically related to characteristic parameters of the pulse wave, 80 samples from the MIMIC-II database are used to train the extreme learning machine blood pressure model. In the experiment, 15 measured samples of pulse wave signal are used as the prediction sets. The results show that the errors of systolic and diastolic blood pressure are both within 5 mmHg compared with that by the Coriolis method.

Fringe slope discrimination in laser self-mixing interferometry using artificial neural network

Due to high sensitivity, self-aligned configuration and laser type independence, Laser Self-Mixing Interferometry (SMI) has always been an interesting and attractive technique in the field of laser interferometry, with displacement and vibration measurements being the most frequently encountered applications. Fringe slope is the most distinctive merit which traditional two-beam interferometry does not have, and it is always utilized to indicate the moving direction of external targets. Due to the existence of noise and even speckle effect, the slope of SMI fringes may be difficult to determine and therefore attracts much more research attention. In order to bring about a robust and easy-to-use method in fringe detection, an Artificial Neural Network (ANN) model established by a well-known Machine Learning (ML) framework named pytorch is proposed to recognize SMI fringes, and through elaborate training, it can distinguish left or right tilted unseen fringes at the accuracy of about 100% in the simulations under good Signal-to-Noise Ratio (SNR) and 96% during the experiments without any noise filtering. Relatively satisfactory results can still be obtained with the feedback strength parameter C lowed to about 0.4 and the SNR reduced to 5 dB. The manuscript explores the application of ML in the field of SMI, with a focus on the accurate and effective SMI fringe recognition, while the subsequent displacement or vibration measurement is not in our research scope.

Multiple self-mixing interferometry based on lock-in amplifier analysis for vibration measurement

In this paper, a novel phase demodulation method for multiple self-mixing interferometry (MSMI) is proposed, which can improve the resolution and accuracy of vibration measurement in laser self-mixing interferometry (SMI). The sinusoidal phase modulation of the beam is obtained by an electro-optic modulator (EOM), and phase demodulation is performed by a lock-in amplifier analysis method. The phase equation of MSMI was derived and the theory of the lock-in amplification technique was analyzed in detail. The validity of the proposed method is confirmed by means of simulated signals and then demonstrated by several experimental measurements. The experimental results indicated a good correspondence between theory and experiment.