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Major space agencies such as NASA and the ESA have long reported the growing dangers caused by resident space objects orbiting our planet. These objects continue to grow in number as satellites are imploded and space debris impacts each other, causing fragmentation. As a result, significant efforts by both the public and private sectors are geared towards enhancing space domain awareness capabilities to protect future satellites and astronauts from impact by these orbiting debris. Current approaches and standards implement very large radar arrays, telescopes, and laser ranging systems to detect and track such objects. These systems are very expensive, may take significant amounts of time to develop, and are still only sparingly able to efficiently track debris targets less than 10 cm in diameter. This work proposes a theoretical passive-radar-based method using illuminators of opportunity for detecting space debris while estimating motion direction and Doppler. We show that by using a signal processing chain based on the self-mixing technique and digital filters, Doppler information can be extracted and continuously tracked by a uniform linear receiver array. This can be achieved by a passive sensor system, which has the advantage of lower cost without the need to emit signals that constrain the spectrum sharing issues. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Major space agencies such as NASA and the ESA have long reported the growing dangers caused by resident space objects orbiting our planet. These objects continue to grow in number as satellites are imploded and space debris impacts each other, causing fragmentation. As a result, significant efforts by both the public and private sectors are geared towards enhancing space domain awareness capabilities to protect future satellites and astronauts from impact by these orbiting debris. Current approaches and standards implement very large radar arrays, telescopes, and laser ranging systems to detect and track such objects. These systems are very expensive, may take significant amounts of time to develop, and are still only sparingly able to efficiently track debris targets less than 10 cm in diameter. This work proposes a theoretical passive-radar-based method using illuminators of opportunity for detecting space debris while estimating motion direction and Doppler. We show that by using a signal processing chain based on the self-mixing technique and digital filters, Doppler information can be extracted and continuously tracked by a uniform linear receiver array. This can be achieved by a passive sensor system, which has the advantage of lower cost without the need to emit signals that constrain the spectrum sharing issues.

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. [ABSTRACT FROM AUTHOR]

• For the first time, we have achieved a measurement of the rotational Doppler effect in the laser feedback system. • We observed the frequency shift doubling phenomenon of the rotational Doppler effect under the self-mixing detection system. • We can simultaneously measure the object's speed and direction of rotation through a single measurement. • The method reported in this article can greatly improve the sensitivity of signal detection, thereby effectively increasing the detection distance. • It provides us with insight into the production of the RDE in the new regimes. The Doppler effect is a well-known phenomenon which has been widely applied in many areas. Less well-known than the traditional linear Doppler effect, the rotational Doppler effect (RDE) which arises from the transverse motion between the wave source and the object has attracted a lot of attention in recent years. Here, we report on the demonstration of RDE in a laser self-mixing framework and provide high-sensitivity, auto-alignment rotational velocity (magnitude and direction) detection. This novel self-mixing rotational Doppler detection scheme is different from the existing rotational Doppler detection schemes, with its light source also acts as a signal amplifier. Further, in the vortex retarder-based self-mixing interferometry, we find that the feedback light experience twice the rotational Doppler shift compared to traditional RDE detection methods. At the same time, the direction of rotation can be discriminated with the help of the light frequency modulators, i.e., we can realize the detection of velocity vectors. We demonstrate the mode selection properties of the self-mixing detection framework and successfully realized the high signal-to-noise ratio measurement of the rotational speed, which is expected to greatly expand the detection capability of the RDE-based metrology in the long-range and weak signal detection conditions. This demonstration is of significance as it provides us with insight into the production of the RDE in the new regimes. [ABSTRACT FROM AUTHOR]

In this paper, a method is proposed to recover displacements with nanometric precision based on spectral analysis of the feedback phase of self-mixing laser interferometric signal. This method is an enhancement of the previously developed method called Time-domain Frequency-domain Signal Processing (TFSP) which could only recover target vibration(s) with greater than lambda/8 amplitude (where lambda is the laser’s wavelength) so long as at least one of the vibration’s components has an amplitude greater than or equal to lambda/2. Using TFSP reconstruction as a first approximation of the main target displacement combined with parameter (optical feedback factor C and linewidth enhancement factor alpha) estimation, the proposed method can provide a better in-depth analysis of the self-mixing signal spectrum and thus achieve the detection of even lower amplitude vibrations. Studies presented in the paper indicate that the proposed method does not require accurate parameter estimation. Experimental results obtained using a laser diode based self-mixing sensor with lambda = 785 nm show that the adding this method on top of TFSP allows to recover target vibrations with amplitude down to approximately lambda/32 with an average amplitude root-mean-square error of 1.56 nm, which corresponds to a 4 fold improvement over TFSP. [ABSTRACT FROM AUTHOR]

In this paper, a unified behavioral model of laser feedback based self-mixing interferometry (SMI) is proposed which is able to accurately model the SMI sensor signals encountered under experimental variable optical feedback conditions. The model provides correct SMI signals whether feedback is varied in a continuous or discrete manner, while spanning all major feedback regimes (such as weak-, moderate-, and strong-feedback regime) used for sensing applications. As a result, the proposed model allows the simulation of SMI signals in the presence of speckle which is of upmost importance to develop future efficient algorithms to reconstruct target displacements. The optical speckle usually occurs when the target of comparable surface roughness to the laser wavelength is moving as it induces variation of the optical feedback factor. The proposed model is shown to be able to address such cases and in particular to be able to reproduce very similar SMI signals to those acquired in the presence of speckle. It is thus anticipated that the proposed model would facilitate the design and testing of novel SMI algorithms and systems dedicated to the processing of variable optical feedback based SMI signals for metric sensing applications. [ABSTRACT FROM AUTHOR]

Using a self-mixing laser interferometric sensor, the aim of this paper is to propose two new and distinct Fourier transform based methods for estimation of optical coupling factor and linewidth enhancement factor, as well as displacement of a target over all feedback regimes by processing the feedback phase. First algorithm deals only with band-limited smooth displacements, while second method deals with rather more general, smooth displacements. Under noiseless simulations over diverse target motion conditions and optical feedback regimes, these algorithms (first and second) have shown picometric displacement sensing precision of 1.1264 pm and 1.0996 pm respectively, for laser wavelength of 785 nm. The performance of proposed methods has also been quantified in case of additive noise. During experimental verification, by using a reference sensor with 2 nm resolution, their precision was measured to be 36.2142 nm and 34.4388 nm respectively, for weak-, moderate-, and strong-optical feedback regime signals. Importantly, for strong feedback regime, these methods have shown better performance than two previously reported methods. [ABSTRACT FROM AUTHOR]

This paper exploits the difference in amplitude spectrum of perturbed and unperturbed phase of self-mixing (SM) laser, to propose a new method for estimation of coupling factor (C), line-width enhancement factor (LEF), as well as displacement of the vibrating target in three major feedback regimes, i.e, weak-, moderate- and strong-feedback regimes. This result thus fills the gap in limitation of previous methods restricted to fewer regimes. The displacement of target is assumed to be bandlimited and sparse in frequency domain. The proposed algorithm showed an average of 1.0168 nm RMS error in displacement estimation corresponding to single- and multi-tone vibrations of amplitudes varying from 3 to 30 times that of laser’s wavelength, with percentage error of 1.15% and 3.31% in C and LEF estimations, from simulated SM laser signals. Using an SM sensor based on a laser diode emitting at 785 nm wavelength, the proposed method has achieved an average RMS error of 21 nm in weak-, moderate- and strong-feedback regimes, corresponding to a vibrating target of 5 micrometer peak-peak amplitude. [ABSTRACT FROM AUTHOR]

This paper introduces a design of the phase demodulation system based on FPGA for the phase-modulated self-mixing interferometer. By the processing that the modulation SIN signal and the doubling frequency modulation COS signal are respectively multiplied by the phase-modulated self-mixing signal(PSMI) and then low-pass filtered and shaped in the electrical domain, two orthogonal square wave signals sensitive to the object's movement direction are obtained for displacement reconstruction. The FPGA signal processing system controls the generation of a highly stable and accurate sinusoidal signal source for the modulation of the electro-optic crystal(EOM). At the same time, the two orthogonal square wave signals obtained after the demodulation processing are subdivided for the high-precision measurement of a uniformly moving object's displacement. The high-frequency amplifier circuit amplifying the self-mixing interference signal, multiplier & frequency doubler circuits based on MLT04 and low-pass filter circuits are designed. FPGA-based counting programs, DAC circuits and programs used for generating sine waves are also designed. In the experiment, comparison tests for displacement measurement are performed using the PI company's two-dimensional precision electronically-controlled translation stage, and high-precision displacement measurement can be achieved. The demodulation system does not rely on a PC and a high-precision acquisition card, and can realize real-time measurement of displacement, greatly improving the practicability of the system. [ABSTRACT FROM AUTHOR]

This paper, while focusing on post-perturbed phase processing of optical feedback based self-mixing laser displacement sensor, rigorously derives a general strategy to achieve the particular task of retrieving displacement from perturbed (feedback based) phase based on a proposition, which has been proved separately. From this, a new algorithm has been derived for estimation of optical feedback coupling factor and corresponding displacement over weak-, moderate-, and strong-optical feedback regimes, by using the concept of deformation. This method can work on all displacements so long as these are sufficiently smooth, i.e, have enough continuous derivatives. The algorithm’s steps are shown to be mathematically consistent. Furthermore, its performance has also been verified, and compared with a previous method, by using simulated and experimental signals for an SM sensor with emission wavelength of 785 nm. Displacement measurement precision has also been quantified by using a commercial transducer with 2 nm resolution showing that the proposed method provides comparable displacement precision even for fringe-loss affected, strong-feedback regime signals. [ABSTRACT FROM AUTHOR]

In this paper, a static multi-longitudinal mode laser self-mixing absolute angle measurement system is developed to accurately monitor the deflection angle. The experimental results show that this multi-longitudinal mode laser angle sensor is capable of effectively measuring the deflection angle of the vertical dihedral mirror. The angle-measurement range and resolution of the self-mixing experimental sensing system can be obtained as ±22.0° and 0.008°, respectively. Furthermore, in-depth analysis of the angle-measurement error and related error sources are performed, of which the absolute error is less than 0.37° that demonstrates the good reliability and practicality of the self-mixing angle sensor. • A self-mixing absolute angle sensor is developed to measure the deflection angle. • The method has been realized the static absolute angle-measurement of the system. • The angle-measurement range is as many as ±22° and angular resolution is 0.008°. • This angle-measurement sensor has good stability, practicability, and reliability. [ABSTRACT FROM AUTHOR]

In this article a comprehensive modeling of cold-biased field-effect transistors (FETs) used as terahertz (THz) detectors is developed. The described model is based upon the transistor Enz-Krummenacher-Vittoz (EKV) model in order to provide valid quantities also near and below the transistor threshold by using available technology parameters, without any extra fitting nor calibration. Important aspects such as the antenna coupling and the effect of amplitude modulation of the THz source are considered in a single, handy, analytical model. THz measurements performed on specifically designed FET detectors confirm its validity, providing a powerful tool and giving a clear insight of the role of available variables. The model can anticipate time-consuming numerical simulations or more physically accurate models requiring experimental parameters calibration, that may complement the results for better accuracy. [ABSTRACT FROM AUTHOR]

Self-Mixing interferometry (SMI) signal characteristics are highly dependent on both the operating optical regime and target surface. In this paper, a method is proposed to overcome some identified limitations of the even power scalable algorithm (EPSA), such as the required operating regime to be weak feedback. In addition, by using the up-sampling techniques, the number of stages involved in the even-power scalable algorithm can be drastically increased without any data acquisition bandwidth modification. Here, 10 successive stages have been successfully implemented to achieve a theoretical resolution of ${\lambda } _{\sf 0}/ {\sf 2}^{\sf 13}$. It is further shown that the proposed method can handle and process weak, moderate and strong feedback regime as well as speckle affected SMI signals more efficiently. Lastly, FPGA based hardware emulation of EPSA is also done for later embedded implementation of this high-resolution algorithm. FPGA synthesis results show that the designed system can measure maximum target velocity up to 1.18 m/s while consuming total power of 1.4W. [ABSTRACT FROM AUTHOR]

In this paper, a method based on the inherent event-based sampling capability of the laser optical feedback interferometry (OFI) is proposed to recover sub- $\lambda $ /2 displacement with a nanometric precision. The proposed method operates in open-loop configuration and relies on OFI’s fringe detection, thereby improving its robustness and ease of use. The measured white noise power spectral density is less than 100pm/ $\sqrt {\text {Hz}}$ with a corner noise frequency of approximately 80Hz for a laser diode emitting wavelength $\lambda _{{0}}$ of 785nm placed at 30cm of the target. [ABSTRACT FROM AUTHOR]

Magma recharge into a differentiated reservoir is one of the main triggering mechanisms for explosive eruptions. Here we describe the petrology of the eruptive products of the last explosive eruption of Tutupaca volcano (southern Peru) in order to constrain the pre-eruptive physical conditions (P-T-XH2O) of the Tutupaca dacitic reservoir. We demonstrate that prior to the paroxysm, magma in the Tutupaca dacitic reservoir was at low temperature and high viscosity (735 ± 23 °C), with a mineral assemblage of plagioclase, low-Al amphibole, biotite, titanite, and Fe-Ti oxides, located at 8.8 ± 1.6 km depth (233 ± 43 MPa). The phenocrysts of the Tutupaca dacites show frequent disequilibrium textures such as reverse zonation, resorption zones, and overgrowth rims. These disequilibrium textures suggest a heating process induced by the recharge of a hotter magma into the dacitic reservoir. As a result, high-Al amphibole and relatively high-Ca plagioclase phenocryst rims and microlites were formed and record high temperatures from just before the eruption (840 ± 45 °C). Based on these data, we propose that the recent eruption of Tutupaca was triggered by the recharge of a hotter magma into a highly crystallized dacitic magma reservoir. As a result, the resident dacitic magma was reheated and remobilized by a self-mixing process. These magmatic processes induced an enhanced phase of dome growth that provoked destabilization of the NE flank, producing a debris avalanche and its accompanying pyroclastic density currents. [ABSTRACT FROM AUTHOR]

In this paper, spectral processing of laser Self-Mixing (SM) interferometric signal phase has been carried out allowing better measurement accuracy for harmonic and arbitrarily shaped vibrations for an optical feedback based SM interferometric Laser Diode (LD) sensor. The resulting algorithm not only improves the measurement accuracy but also reduces the processing time (by a factor 3.45) as compared with a previous time-domain based displacement retrieval technique called the Phase Unwrapping Method (PUM). Fourier series based analysis of laser feedback phase is carried out to determine processing limits. The proposed algorithm has also been found to be robust against variation in optical feedback coupling C as well as additive noise. This use of spectral analysis not only increases the measurement accuracy but also retrieves information about target movement harmonics which can also be used in modal analysis applications of remote mechanical targets. Using an SM vibration sensor based on a LD emitting at 785 nm, this technique has provided an average RMS error of 12.5 nm (while that of PUM is 39 nm RMS) for harmonic target vibrations of $5~\mu \text{m}$ amplitude. For reduced range of $1 < C < 2$ , an average RMS error of ~8 nm ($\sim \lambda $ /100) is obtained. [ABSTRACT FROM AUTHOR]

• The FSR of a multi-longitudinal mode LD cavity to be measured is 78.95 GHz. • The applicable amplitude limitation range of the MLM-LD-SMVS system is 0 < A l ≤ 2. 0 53 × 1 0 - 3 . • The optimum optical feedback regime of the MLM-LD-SMVS system is 0 < C < 4. 6. The free spectral range of the resonant cavity is calculated to be 78.95 GHz based on 1.90 mm of the waveform separation period as a multi-longitudinal mode laser diode is employed as the light source of the self-mixing vibration measurement system. As such, the influence of the vibration amplitude of the loudspeaker to the self-mixing vibration signal waveform is further researched by means of the feasible theoretical analysis and experimental characterization. The primary experimental results demonstrate that the amplitude limitation ratio coefficient A l of this sensing system is required to design below 2.053 × 10−3 corresponding to an entire waveform separation period, of which is to prevent the self-mixing signal waveform from distorting effectively in the context of the integral order of the external cavity mode. Furthermore, the feedback levels of the multi-longitudinal mode laser self-mixing vibration system are studied in detail. It has been shown that the experimental result of the free spectral range fits well with theoretical value when this system is matched to the applicable amplitude limitation range 0 < A l ≤ 2. 0 53 × 1 0 - 3 and the optimum optical feedback regime 0 < C < 4. 6. [ABSTRACT FROM AUTHOR]

We present our experimental observations of self-mixing laser Doppler velocimetry (LDV) with a laser-diode-pumped microchip Nd:YAG laser. Periodic intensity fluctuations were detected by local maximum analysis, and the real-time temporal waveforms were observed using an oscilloscope. A rotary motor with an aluminum foil surface was used in the laserdiode- pumped Nd:YAG system to generate a feedback beam with Doppler shift frequency. Since a low Doppler shift frequency perturbed this laser system, the observed waveforms existed as pulselike oscillation groups, which presented chaotic oscillations. When the Doppler shift frequency gradually increased, the number of peaks in each pulselike oscillation group decreased, and the self-mixing system was gradually manipulated using the Doppler shift frequency. As the Doppler shift frequency gradually increased to 43 kHz, the output signal was dominated by the Doppler shift frequency such that the oscillation behaved similarly to a periodic fluctuation. [ABSTRACT FROM AUTHOR]

The fringes disappearance phenomenon in the self-mixing interferometry occurs whenever the external round-trip phase at free-running state is modulated by either external modulation such as external cavity length changes or internal modulation when the laser injection current is modulated with a high back-scattered light power. This phenomenon has been observed by many authors for harmonic motion or vibration application and more recently in the case of the absolute distance measurement scheme when the laser injection current is modulated in the triangle waveform. However, there are no clear explanations on the fringes disappearance phenomenon and its dependence on the self-mixing regimes. In this paper, a novel approach that depicts the mechanism of interferometric fringes disappearance is proposed that highlight with a new perspective the impact of the coupling strength between the laser and the external cavity on the number of missing fringes. The proposed modeling is validated by a set of measurements using the optical feedback interferometry absolute distance measurement scheme. [ABSTRACT FROM AUTHOR]

A method based on the self-mixing vibration sensing signal of a multi-longitudinal mode laser is found to measure the temperature of the laser cavity. In the experimental system, the temperature variation of the laser cavity can be extracted from tracking the undistorted waveforms of the superimposed multi-longitudinal mode laser self-mixing vibration sensing signal that are highly susceptible to the compensating length of the external cavity. The temperature measurement resolution of the laser cavity temperature monitoring system is 0.253 K, which corresponds to $39.49~ {\mu }\text{m}$ /K of the external cavity sensitivity. It has also been shown that the experimental results are well consistent with the measurement of using the thermal imaging camera. [ABSTRACT FROM AUTHOR]

• A method based on MML-SMV is presented to measure the FSR of the laser cavity. • The FSR of the He-Ne laser cavity to be measured is 0.633 GHz. • The precision of self-mixing FSR measurement system is 2.67 MHz. • The method is also suitable for a laser diode, which the FSR is 88.24 GHz. A method by tracing the multi-longitudinal mode laser self-mixing vibrator waveform with adjusting of the external cavity length based on the laser self-mixing effect is proposed to measure the free spectral range of the laser cavity. According to the variation period of the external cavity, the free spectral range of the He-Ne laser cavity is calculated to be 0.633 GHz with the resolution of 2.67 MHz. Simultaneously, we further investigate the relationship between the waveform separation degree and the phase delay of two adjacent peaks caused by the superimposed self-mixing vibration signal waveforms of different modes. The experimental results have been demonstrated that this strategy is appropriate for the measurement of the free spectral range of the laser cavity duo to the significant merits of general complexity and cost, and non-contact measurement. [ABSTRACT FROM AUTHOR]

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 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.

In this paper, a novel self-mixing interferometer is proposed with spectral analysis by multiple reflection technique. The relationship between the vibration amplitude, the dominant frequency, and the reflection time is deduced, which indicates that the theoretical minimum measurable vibration amplitude is $0.21\lambda $ /G(N, $\theta$) and the precision is about $0.08\lambda $ /G(N, $\theta$). The displacement sensitivity gain G(N, $\theta$) increases with the reflection time. Theoretical analysis results show that the proposed method for vibration measurement has the advantages of high precision and broad measurement range, especially for the measurement of amplitude much smaller than $\lambda $ /2. The validity of the method is tested by several experiments with different amplitudes and reflection times. An amplitude of 75 nm has been proved to be measurable and the absolute error is 5.43 nm, which is within the theoretical error range. The proposed method plays an important role in high precision and nanoscale measurement. [ABSTRACT FROM AUTHOR]

Abstract A modified small-angle measurement system is proposed to improve the angle measurement resolution by selecting a rotatable pentagonal prism to replace the right-angle prism based on the original small-angle measurement system. In our measurement system, the right-angle side length of pentagonal prism is crucial to the measurement resolution. For the pentagonal prism with 2 cm side length, the resolution can reach 64.68 urad, while the resolution is up to 30.48 urad for the pentagonal prism with 4 cm side length. Therefore, it is possible to obtain higher measurement resolution by choosing the pentagonal prism with a larger side length within a proper range as the key optical element in the modified small-angle measurement system, so as to achieve the purpose of system optimization. In addition, the small-angle measurement system with a rotatable pentagonal prism we have designed can be helpful and referential to the future study of self-mixing interference technology with high-resolution requirements on the basis of different prisms. Highlights • A novel small-angle measurement system based on a rotatable pentagonal prism is proposed. • The laser can return to the laser cavity along the original path by rotating a pentagonal prism. • The right-angle side length of pentagonal prism is crucial to the measurement resolution. • The measurement resolution of the small-angle measurement system can reach 30.48 urad. [ABSTRACT FROM AUTHOR]

Optical feedback interferometer (OFI) lasers, also called self-mixing (SM) lasers, have been widely explored over the last couple of decades due to their low cost, compactness, and self-aligned nature and they provide a very good solution for measurements of displacement, vibration, distance, velocity, etc. The SM effect takes place when a part of the laser beam is fed back to the active laser cavity after reflecting from the target. The reflected beam interferes with the emitted beam and hence the optical and spectral characteristics of the laser get changed. To retrieve the vibration or displacement signal of the target from the SM signal, different postprocessing algorithms have been proposed, such as the phase unwrapping method (PUM). The first step of the PUM leads to the coarse estimation of the laser phase and the final step is an iterative joint estimation of 2 parameters, namely laser coupling coefficient C and linewidth enhancement factor α. To make this algorithm applicable for real-time measurements, parallel joint estimation for a wide range of C and α values needs to be done. In this research, 3 algorithms, namely PUM, direct fringe unwrapping (DFU), and improved DFU (IDFU) were tested for FPGA implementation by using Verilog HDL (hardware description language) so that more precise and real-time vibration and displacement signals of targets could be extracted from the SM sensor in an embedded systems environment. These algorithms were developed using Verilog HDL for implementation on the Xilinx Spartan-3 Xcs400-FG320 development board. Our designed IDFU algorithm performed 0.492 times better than the parallel PUM algorithm in maximum clock frequency and 1.53 and 1.21 times better than the PUM in slice registers and LUT utilization of hardware resources, respectively. The designed DFU algorithm can operate 1.355 times better than IDFU in maximum clock frequency and 25.34 and 14.25 times better than IDFU in slice registers and LUT utilization of hardware resources, respectively. [ABSTRACT FROM AUTHOR]

We proposed an all-fiber tunable distributed Bragg reflector (DBR) laser rangefinder, which realized high-accuracy measurement of the absolute distance in the range of 1.88 to 3.33 m based on the self-mixing effect. The theoretical analysis of the all-fiber tunable DBR laser shows that wavelength tuning range and frequency of the laser can influence the measurement range and resolution. In addition, the experimental results indicate that the influence factors of measurement accuracy and sensitivity in absolute distance measurement are modulation response linearity, experimental equipment, and circuit bandwidth, which is in good agreement with theory analysis. Moreover, increasing the linear wavelength tuning range of the tunable DBR laser is an essential method to improve the measurement accuracy and sensitivity of the absolute distance measurement system. [ABSTRACT FROM AUTHOR]

• A transverse dynamical response model of LFSF is proposed considering mode-mismatch. • By decomposing the echo wave to the eigenmodes of the laser, a quantitative calculation method of the effective reflectivity and mode-matching factor is presented. • Accurate calculations of the effective reflectivity and mode-matching factor enable precise description of LFSF response behavior and exploration of optimal coupling strategies. • A simple scheme is proposed to calibrate the effective reflectivity of scattering surfaces by employing an optimal coupling target-cat's eye retroreflector. • This model promises an effective theoretical basis to make full use of the high sensitivity of LFSF and apply it in a wide range. The transverse mode mismatch between the echo wave and optical fields in the laser cavity substantially impacts the responses of the laser frequency-shifted feedback (LFSF) system. This mismatch widely exists in experiments, which limits the detection sensitivity and degrades the signal-to-noise ratio. However, current research on the dynamic response of LFSF has predominantly concentrated on longitudinal modes and intensity modulation, with a lack of quantitative analysis regarding the dynamic response of the transverse modes. In this paper, we establish a transverse dynamical response model of LFSF considering the mode-mismatch. A calculation method of the effective reflectivity (ER) and mode-matching factor (MMF) is presented by decomposing the echo wave to the eigenmodes of the laser. The theoretical model is highly consistent with the experimental data. Finally, with this transverse dynamical response model, we develop a simple scheme to calibrate the effective reflectivity of scattering surfaces by employing a cat's eye retroreflector. Overall, this paper provides a detailed demonstration of the mismatch, which promises an effective theoretical basis to make full use of the high sensitivity of LFSF and apply it over a long distance. [ABSTRACT FROM AUTHOR]

In this paper, we present a method of velocity measurement using of a novel self-mixing velocimeter with orthogonal-beam incident system (OSMV), which enables the velocity measurement without knowing the incident angle information. The fiber ring laser used could provide a stable and narrow-width laser light source, which could enhance the stability and the signal-to-noise ratio of the novel self-mixing fiber ring laser velocimeter. The result indicates a much better linearity of our novel velocimeter than the traditional one in the turntable experiment due to the use of the orthogonal-beam incident system and fiber ring laser source. The relative error rates of our novel velocimeter system are up to 1.258% in contrast with the 13.720% result of the traditional one.

A novel instrument based on Self-mixing interferometry is proposed to simultaneously measure absolute distance and velocity. The measurement method is designed for working directly on each kind of surface, in industrial environment, overcoming also problems due to speckle pattern effect. The laser pump current is modulated at quite high frequency (40 kHz) and the estimation of the induced fringes frequency allows an almost instantaneous measurement (measurement time equal to 25 µs). A real time digital elaboration processes the measurement data and discards unreliable measurements. The simultaneous measurement reaches a relative standard deviation of about 4·10 −4 in absolute distance, and 5·10 −3 in velocity measurement. Three different laser sources are tested and compared. The instrument shows good performances also in harsh environment, for example measuring the movement of an opaque iron tube rotating under a running water flow. [ABSTRACT FROM AUTHOR]

Self-mixing or optical feedback interferometry has been widely used for displacement and velocity measurement applications. For metric information retrieval with $< \lambda /2$ precision, various phase unwrapping methods have been proposed. However, these are computationally heavy and require large number of hardware resources, thereby hindering the development of real-time, embedded solutions for large bandwidth applications. In this regard, a simple and efficient feedback phase retrieval algorithm, called consecutive samples-based unwrapping (CSU) is presented. Detailed analysis of its error performance has been conducted as a function of key optical feedback parameters. A theoretical study has also been conducted to explain as to why such good error performance is obtained for such a simple algorithm by establishing a linear relation between the modulated laser power signal and the laser phase in the absence of optical feedback for specific ranges of key optical feedback parameters. We applied CSU on various simulated and experimentally acquired signals using SMI for the retrieval of harmonic and arbitrary displacements and found out that CSU retrieves target displacement with a precision of about $\lambda /10$ while consuming much less time and hardware resources. The paper also presents FPGA based hardware design results of CSU and compares its performance with a traditional analytical phase unwrapping method in terms of maximum clock frequency, latency, and on-chip hardware resources. This hardware comparison strongly establishes the advantages of such a fast and computationally light algorithm, readily suitable for large bandwidth, embedded, and real-time sensing applications. [ABSTRACT FROM PUBLISHER]

Self-mixing (SM) or optical feedback interferometry has been extensively used for high precision displacement and vibration sensing. However, presence of speckle can significantly degrade the SM interferometric signal and cause changes in signal amplitude as well as in the operating optical feedback regime, resulting in reduction in measurement precision. Previously, different advanced digital signal processing techniques have been proposed to undo the effects caused by speckle. However, their complex and computationally heavy nature inhibits their use for real-time, high bandwidth sensing applications. In this regard, an all analog signal processing algorithm has been presented in this paper, which allows real-time processing of speckle affected SM signal while using standard analog circuits. Various simulations indicated that it is able to correctly process speckle affected SM signals having amplitude variation of at least one order and optical feedback parameter $C$ reduction until 0.5. This proposed algorithm has been tested on experimentally acquired speckle affected SM signals and found capable of dealing with variations in optical feedback regime and amplitude modulation of SM signals, in accordance with simulation results. The developed hardware prototype circuit measures a maximum displacement amplitude of 0.4 mm at a maximum target velocity of 8 mm/s for an SM sensor with a laser wavelength of 785 nm as long as $C >0.5$ . The proposed all analog processing could be a significant step toward a robust, low-cost, integrated, real-time SM displacement sensor. [ABSTRACT FROM PUBLISHER]

Graphene field-effect transistors (G-FETs) are being developed with ever increasing sensitivity as terahertz direct detectors at room temperature. The noise-equivalent power is being reduced towards the order of 1 pW / Hz with frequency about 650 GHz. G-FET-based frequency multipliers and subharmonic mixers are becoming new active components for both millimeter and terahertz wave technologies. We report a 650-GHz G-FET coupled with terahertz antennas and a quasi-optical silicon lens for heterodyne/subharmonic detection. Heterodyne detection at 216 and 648 GHz, second-subharmonic detection at 432 GHz, and third-subharmonic detection at 648 GHz were demonstrated and characterized. Self-mixing/homodyne detection was used as a calibration tool for the power levels of the local pump source and the source to be detected. The conversion losses of heterodyne mixing at 216 GHz (off-resonant) and 648 GHz (resonant) were 38.4 dB and 57.9 dB with 12.8 dBm and −14 dBm of local pump power, respectively. The conversion loss of the second-harmonic mixing at 432 GHz is about 8 dB higher than that of the heterodyne mixing at 216 GHz. Calculations based on our quasi-static mixing model agree well with the measured conversion losses. To improve the conversion loss, more details on the G-FET noise, the optimal pump power, and the antenna should be examined. [ABSTRACT FROM AUTHOR]

Determining the mechanisms involved in generating large-volume eruptions (>100 km) of silicic magma with crystallinities approaching rheological lock-up (~50 vol% crystals) remains a challenge for volcanologists. The Cenozoic Southern Rocky Mountain volcanic field, in Colorado and northernmost New Mexico, USA, produced ten such crystal-rich ignimbrites within 3 m.y. This work focuses on the 28.7 Ma Masonic Park Tuff, a dacitic (~62-65 wt% SiO) ignimbrite with an estimated erupted volume of ~500 km and an average of ~45 vol% crystals. Near-absence of quartz, titanite, and sanidine, pronounced An-rich spikes near the rims of plagioclase, and reverse zoning in clinopyroxene record the reheating (from ~750 to >800 °C) of an upper crustal mush in response to hotter recharge from below. Zircon U-Pb ages suggest prolonged magmatic residence, while Yb/Dy vs temperature trends indicate co-crystallization with titanite which was later resorbed. High Sr, Ba, and Ti concentrations in plagioclase microlites and phenocryst rims require in-situ feldspar melting and concurrent, but limited, mass addition provided by the recharge, likely in the form of a melt-gas mixture. The larger Fish Canyon Tuff, which erupted from the same location ~0.7 m.y. later, also underwent pre-eruptive reheating and partial melting of quartz, titanite, and feldspars in a long-lived upper crustal mush following the underplating of hotter magma. The Fish Canyon Tuff, however, records cooler pre-eruptive temperatures (~710-760 °C) and a mineral assemblage indicative of higher magmatic water contents (abundant resorbed sanidine and quartz, euhedral amphibole and titanite, and absence of pyroxene). These similar pre-eruptive mush-reactivation histories, despite differing mineral assemblages and pre-eruptive temperatures, indicate that thermal rejuvenation is a key step in the eruption of crystal-rich silicic volcanics over a wide range of conditions. [ABSTRACT FROM AUTHOR]

The progress on laser feedback interferometry technology is reviewed. Laser feedback interferometry is a demonstration of interferometry technology applying a laser reflected from an external surface, which has features including simple structure, easy alignment, and high sensitivity. Theoretical analysis including the Lang– Kobayashi model and three-mirror model are conducted to explain the modulation of the laser output properties under the feedback effect. In particular, the effect of frequency and polarization shift feedback effects are analyzed and discussed. Various applications on various types of lasers are introduced. The application fields range from metrology, to physical quantities, to laser parameters and other applications. The typical applications of laser feedback technology in industrial and research fields are discussed. Laser feedback interferometry has great potential to be further exploited and applied [ABSTRACT FROM AUTHOR]

Multiple mode gain competition in self-mixing laser diode has been investigated assisted by output optical spectrum. Experimental results show that multi-peaks appear in self-mixing signals depending on the length of the external cavity. The numbers of self-mixing peak signals are the same as that of the output optical spectrum. Laser multi-mode gain competition model has been established to analyze the multiple mode competition in self-mixing laser diode. Numerical analysis demonstrates that the sub-peak in self-mixing signals is attributed to mode gain competition between different longitudinal laser modes. [ABSTRACT FROM AUTHOR]

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.

• Dual-target motion monitoring with one single laser. • Spectral processing based on short-time Fourier transform. • Energy reallocation of each channel based on pre-feedback structure. • Two vibrations extraction of adjacent frequencies. 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. [ABSTRACT FROM AUTHOR]

• A new method is presented to measure slow flow velocity based on self-mixing effect. • Flow velocity is obtained by the frequency difference from asymmetric power spectrum. • This scheme can be applied for direction determination of the flow velocity. • The maximum achievable Doppler shift within the pipe is measured as low as 15.37 Hz. In this study, an all-fiber structure self-mixing sensor using a distributed feedback Bragg (DFB) fiber laser as the light source is proposed to measure flow velocity. In pursuit of slower flow velocity, the external cavity frequency-shifting optical technique is introduced into the optical sensing system to effectively avoid complex noises existing in the low-frequency region. Furthermore, the additional bonus is that the identification of the velocity direction can be obtained by the asymmetric shape near the feedback frequency shift on the spectrum. At the same time, a suitable solution is developed for extraction of the characteristic feature parameters from the asymmetrical spectrum of the flow velocity signal. It was demonstrated the actual conformity of the measurement results by means of this new approach of data processing. According to the practical experimental measurements, the maximum measurable Doppler shift concerning the slow fluid can be obtained as low as 15.37 Hz. This indicates that the designed all-fiber laser self-mixing flow velocity meter can be prospectively extended to slow fluid measurement associated with the related sensing and medical applications. [ABSTRACT FROM AUTHOR]

Increasing the measurable distance and the displacement measurement limit of a self-mixing displacement sensor poses one of the most important problems to improve the sensor's performance. In order to solve the problem, there has to be found the estimation method of the optical feedback factor for a strong feedback regime. The hardship of the estimation in this regime is brought about by a strong speckle noise and the restriction of normalization methods presented hitherto. In the paper we have found an approach to improving the accuracy of the self-mixing sensor, which can work even for long range and large displacement, by deciding the region of the optical feedback factor based on the ratio of fringe height and using it and fringe counting method. • To present a new method of displacement reconstruction for long range and large displacement. • To present a new parameter estimation method in a self-mixing interferometer. • To verify the method proposed experimentally. [ABSTRACT FROM AUTHOR]

Using the self-mixing technique, or optical feedback interferometry, fluid velocity measurements of water seeded with titanium dioxide have been performed using a laser diode to measure the effect of the seeding particle concentration and also the pump speed of the flow. The velocimeter utilises commercially available laser diodes with a built-in photodiode for detection of the self-mixing effect. The device has demonstrated an accuracy better than 10% for liquid flow velocities up to 1.5 m/s with a concentration of scattering particles in the range of 0.8–0.03%. This is an improvement of one order of magnitude compared to previous experiments. The proposed velocimeter is to be developed further for application in gas-jet measurements. [ABSTRACT FROM AUTHOR]

A novel hybrid-channel attenuation measurement system has been built for the measurement of $V$ - and $W$ -band waveguide attenuators from 50 to 110 GHz. The measurement system combines two single channels of the $V$ and $W$ bands together into one system. The $V$ -band channel is used as the measurement channel and the $W$ -band channel is used as the synchronization channel when the $V$ -band attenuator is measured and vice versa. The measurement system is free of cross talk between the two channels and removes the need for isolators between the local oscillator and the mixer since the RF signal frequencies in the two channels are different. In addition, a compensation module was designed to cancel the self-mixing produced by the $W$ -band mixer at frequencies above 102 GHz. The expanded uncertainty of the system is evaluated to be 0.004–0.08 dB at frequencies $\le 102$ GHz and 0.005–0.11 dB at frequencies $>102$ GHz for an attenuation range from 0 to 80 dB. [ABSTRACT FROM AUTHOR]