Characterization of the Brillouin-loss spectrum of single-mode fibers by use of very short (<10-ns) pulses

Brillouin expanded time-domain analysis based on dual optical frequency combs

Brillouin Optical Time-Domain Analysis (BOTDA) is a widely-used distributed optical fiber sensing technology employing pulse-modulated pump waves for local information retrieval of the Brillouin gain or loss spectra. The spatial resolution of BOTDA systems is intrinsically linked to pulse duration, so high-resolution measurements demand high electronic bandwidths inversely proportional to the resolution. This paper introduces Brillouin Expanded Time-Domain Analysis (BETDA) as a modified BOTDA system, simultaneously achieving high spatial resolution and low detection bandwidth. Utilizing two optical frequency combs (OFCs) with different frequency intervals as pump and probe, local Brillouin gain spectra are recorded by their spectral beating traces in an expanded time domain. A 2-cm-long hotspot located in a 230 m single-mode fiber is successfully measured in the time domain with a detection bandwidth of less than 100 kHz using dual OFCs with tailored spectral phase, line spacing, and bandwidth.

Machine Learning Approaches in Brillouin Distributed Fiber Optic Sensors

This paper presents reported machine learning approaches in the field of Brillouin distributed fiber optic sensors (DFOSs). The increasing popularity of Brillouin DFOSs stems from their capability to continuously monitor temperature and strain along kilometer-long optical fibers, rendering them attractive for industrial applications, such as the structural health monitoring of large civil infrastructures and pipelines. In recent years, machine learning has been integrated into the Brillouin DFOS signal processing, resulting in fast and enhanced temperature, strain, and humidity measurements without increasing the system's cost. Machine learning has also contributed to enhanced spatial resolution in Brillouin optical time domain analysis (BOTDA) systems and shorter measurement times in Brillouin optical frequency domain analysis (BOFDA) systems. This paper provides an overview of the applied machine learning methodologies in Brillouin DFOSs, as well as future perspectives in this area.

Brillouin frequency shift error estimation formula for distributed optical fiber sensing technology based on Brillouin scattering

In this work, the problems in the existing Brillouin frequency shift (BFS) error estimation formulas for distributed optical fiber sensing technology based on Brillouin scattering are discussed. Based on the analysis, a new, to the best of our knowledge, BFS error estimation formula is proposed. To validate the proposed formula, a large number of Brillouin spectra with different frequency sweep spans, signal-to-noise ratios, linewidths, and frequency steps are numerically generated, and at the same time, Brillouin spectra with different values of incident light pulse widths and frequency sweep spans are measured with a Brillouin optical time domain reflectometer. Based on those Brillouin spectra, the errors of the proposed formula and existing formulas are systematically compared. The results reveal that the proposed formula generally has a higher accuracy than the existing typical formulas, especially when the frequency sweep span or incident light pulse width is large. Therefore, it has a much wider application range.

Recent Advances in Sensors for Fire Detection

Fire is indeed one of the major contributing factors to fatalities, property damage, and economic disruption. A large number of fire incidents across the world cause devastation beyond measure and description every year. To minimalize their impacts, the implementation of innovative and effective fire early warning technologies is essential. Despite the fact that research publications on fire detection technology have addressed the issue to some extent, fire detection technology still confronts hurdles in decreasing false alerts, improving sensitivity and dynamic responsibility, and providing protection for costly and complicated installations. In this review, we aim to provide a comprehensive analysis of the current futuristic practices in the context of fire detection and monitoring strategies, with an emphasis on the methods of detecting fire through the continuous monitoring of variables, such as temperature, flame, gaseous content, and smoke, along with their respective benefits and drawbacks, measuring standards, and parameter measurement spans. Current research directions and challenges related to the technology of fire detection and future perspectives on fabricating advanced fire sensors are also provided. We hope such a review can provide inspiration for fire sensor research dedicated to the development of advanced fire detection techniques.

Review: distributed time-domain sensors based on Brillouin scattering and FWM enhanced SBS for temperature, strain and acoustic wave detection

Distributed time-domain Brillouin scattering fiber sensors have been widely used to measure the changes of the temperature and strain. The linear dependence of the temperature and strain on the Brillouin frequency shift enabled the distributed temperature and strain sensing based on mapping of the Brillouin gain spectrum. In addition, an acoustic wave can be detected by the four wave mixing (FWM) associated SBS process, in which phase matching condition is satisfied via up-down conversion of SBS process through birefringence matching before and after the conversion process. Brillouin scattering can be considered as the scattering of a pump wave from a moving grating (acoustic phonon) which induces a Doppler frequency shift in the resulting Stokes wave. The frequency shift is dependent on many factors including the velocity of sound in the scattering medium as well as the index of refraction. Such a process can be used to monitor the gain of random fiber laser based on SBS, the distributed acoustic wave reflect the distributed SBS gain for random lasing radiation, as well as the relative intensity noise inside the laser gain medium. In this review paper, the distributed time-domain sensing system based on Brillouin scattering including Brillouin optical time-domain reflectometry (BOTDR), Brillouin optical time-domain analysis (BOTDA), and FWM enhanced SBS for acoustic wave detection are introduced for their working principles and recent progress. The distributed Brillouin sensors based on specialty fibers for simultaneous temperature and strain measurement are summarized. Applications for the Brillouin scattering time-domain sensors are briefly discussed.

Optimized cross-correlation method for Brillouin frequency shift estimation in Brillouin scattering-based sensors

The cross-correlation method has a low computational burden and is less sensitive to noise, but the method may have a long spectra measurement time, especially for Brillouin spectra with an asymmetric frequency sweep span. To improve the real-time performance of spectra measurement, the influence of the frequency sweep span, sweep span deviation, and frequency step on the error in the estimated Brillouin frequency shift (BFS) is systematically investigated. Based on the results, the optimal sweep span and its influencing factors are investigated. The results reveal that when the frequency sweep span is not wide enough and there is a sweep span deviation, the BFS error will not decrease with a decreasing frequency step. The error decreases rapidly with an increasing frequency sweep span, and then it tends to a stable value. The linewidth and sweep span deviation have an important effect on the optimal sweep span. An estimation formula for the optimal sweep span is presented, and an improved cross-correlation method is proposed based on it. The proposed method is compared with existing classic cross-correlation methods. The results reveal that the proposed method can ensure high BFS accuracy and decrease measurement time.

Benefits of Spectral Property Engineering in Distributed Brillouin Fiber Sensing

As one of the most consolidated distributed fiber sensors based on stimulated Brillouin scattering, the Brillouin optical time-domain analyzer (BOTDA) has been developed for decades. Despite the commercial availability and outstanding progresses which has been achieved, the intrinsic Lorentzian gain spectrum restricts the sensing performance from possible further enhancements and hence limits the field of validity of the technique. In this paper, the novel method of engineering the gain spectral properties of the Brillouin scattering and its application on static and dynamic BOTDA sensors will be reviewed. Such a spectral property engineering has not only provided improvements to BOTDA, but also might open a new way to enhance the performance of all kinds of distributed Brillouin fiber sensors.

High Resolution Brillouin Sensing of Micro-Scale Structures

Brillouin distributed measurement techniques have been extensively developed for structural health monitoring using fibre optic nerve systems. The recent advancement in the spatial resolution capabilities of correlation-based Brillouin distributed technique have reached the sub-mm regime, making this approach a suitable candidate for monitoring and characterizing integrated photonic devices. The small dimension associated with the short length of these devices—on the order of the cm- and mm-scale—requires high sensitivity detection techniques and sub-mm spatial resolution. In this paper, we provide an overview of the different Brillouin sensing techniques in various micro-scale structures such as photonic crystal fibres, microfibres, and on-chip waveguides. We show how Brillouin sensing is capable of detecting fine transverse geometrical features with the sensitivity of a few nm and also extremely small longitudinal features on the order of a few hundreds of μ m . We focus on the technique of Brillouin optical correlation domain analysis (BOCDA), which enables such high spatial resolution for mapping the opto-acoustic responses of micro-scale waveguides.

Key Parameter Extraction for Fiber Brillouin Distributed Sensors Based on the Exact Model

Errors in the extracted key parameters directly influence the errors in the temperature and strain measured by fiber Brillouin distributed sensors. Existing key parameter extraction algorithms for Brillouin gain spectra are mainly based on simplified models, therefore, the extracted parameters may have significant errors. To ensure high accuracy in the extracted key parameters in different cases, and consequently to measure temperature and strain with high accuracy, a key parameter extraction algorithm based on the exact Voigt profile is proposed. The objective function is proposed using the least-squares method. The Levenberg-Marquardt algorithm is used to minimize the objective function and consequently extract the key parameters. The optimization process is presented in detail, at the same time the initial values obtainment method and the convergence criterion are given. The influences of the number of sample points in Gauss-Hermite quadrature on the accuracy and the computation time of the algorithm are investigated and a suggestion about the selection of the number of sample points is given. The direct algorithm, the random algorithm and the proposed algorithm are implemented in Matlab and are used to extract key parameters for abundant numerically generated and measured Brillouin gain spectral signals. The results reveal that the direct algorithm requires less computation time, but its errors are considerably larger than that of the proposed algorithm. The convergence rate of the random algorithm is about 80~90%. The proposed algorithm can converge in all cases. Even for the convergence cases, the computation time and the fitting error of the random algorithm are 1~2 times larger than those of the proposed algorithm.

Support vector machine assisted BOTDA utilizing combined Brillouin gain and phase information for enhanced sensing accuracy

Benefiting from both Brillouin amplitude and phase spectral responses during Brillouin scattering, a support vector machine (SVM) assisted Brillouin optical time domain analyzer (BOTDA) enabling the improvement of sensing accuracy with only a slight sacrifice of processing speed has been proposed and demonstrated. Only one SVM model, i.e. SVM-(g + p), is required to effectively combine the Brillouin gain and phase information in the training and testing phases, which avoids separate Brillouin gain spectrum (BGS) and Brillouin phase spectrum (BPS) fitting, and hence saves the processing time. Both simulation and experiments using different parameters were conducted to evaluate the improved performance of SVM-(g + p). Compared with the case of using BGS only or BPS only, SVM assisted BOTDA using combined BGS and BPS enhances the accuracy of temperature extraction by about 30% over a wide range of simulation and experiment parameters, only at a slight expense of the processing speed. Although the processing of both gain and phase information takes extra time, SVM-(g + p) assisted BOTDA still has a processing speed 80 times faster than that of using a conventional curve fitting method like Lorentzian curve fitting (LCF). The improved accuracy, together with fast processing speed, is crucial for future high-speed and accurate BOTDA sensors based on both Brillouin gain and phase detection.

Detecting cm-scale hot spot over 24-km-long single-mode fiber by using differential pulse pair BOTDA based on double-peak spectrum

In distributed Brillouin optical fiber sensor when the length of the perturbation to be detected is much smaller than the spatial resolution that is defined by the pulse width, the measured Brillouin gain spectrum (BGS) experiences two or multiple peaks. In this work, we propose and demonstrate a technique using differential pulse pair Brillouin optical time-domain analysis (DPP-BOTDA) based on double-peak BGS to enhance small-scale events detection capability, where two types of single mode fiber (main fiber and secondary fiber) with 116 MHz Brillouin frequency shift (BFS) difference have been used. We have realized detection of a 5-cm hot spot at the far end of 24-km single mode fiber by employing a 50-cm spatial resolution DPP-BOTDA with only 1GS/s sampling rate (corresponding to 10 cm/point). The BFS at the far end of 24-km sensing fiber has been measured with 0.54 MHz standard deviation which corresponds to a 0.5°C temperature accuracy. This technique is simple and cost effective because it is implemented using the similar experimental setup of the standard BOTDA, however, it should be noted that the consecutive small-scale events have to be separated by a minimum length corresponding to the spatial resolution defined by the pulse width difference.

Temperature extraction in Brillouin optical time-domain analysis sensors using principal component analysis based pattern recognition

We propose and experimentally demonstrate the use of principal component analysis (PCA) based pattern recognition to extract temperature distribution from the measured Brillouin gain spectra (BGSs) along the fiber under test (FUT) obtained by Brillouin optical time domain analysis (BOTDA) system. The proposed scheme employs a reference database consisting of relevant ideal BGSs with known temperature attributes. PCA is then applied to the BGSs in the reference database as well as to the measured BGSs so as to reduce their size by extracting their most significant features. Now, for each feature vector of the measured BGS, we determine its best match in the reference database comprised of numerous reduced-size feature vectors of the ideal BGSs. The known temperature attribute corresponding to the best-matched BGS in the reference database is then taken as the extracted temperature of the measured BGS. We analyzed the performance of PCA-based pattern recognition algorithm in detail and compared it with that of curve fitting method. The experimental results validate that the proposed technique can provide better accuracy, faster processing speed and larger noise tolerance for the measured BGSs. Therefore, the proposed PCA-based pattern recognition algorithm can be considered as an attractive method for extracting temperature distributions along the fiber in BOTDA sensors.

Signal processing using artificial neural network for BOTDA sensor system

We experimentally demonstrate the use of artificial neural network (ANN) to process sensing signals obtained from Brillouin optical time domain analyzer (BOTDA). The distributed temperature information is extracted directly from the local Brillouin gain spectra (BGSs) along the fiber under test without the process of determination of Brillouin frequency shift (BFS) and hence conversion from BFS to temperature. Unlike our previous work for short sensing distance where ANN is trained by measured BGSs, here we employ ideal BGSs with different linewidths to train the ANN in order to take the linewidth variation due to different conditions from the training and testing phases into account, making it feasible for long distance sensing. Moreover, the performance of ANN is compared with other two techniques, Lorentzian curve fitting and cross-correlation method, and our results show that ANN has higher accuracy and larger tolerance to measurement error, especially at large frequency scanning step. We also show that the temperature extraction from BOTDA measurements employing ANN is significantly faster than the other two approaches. Hence ANN can be an excellent alternative tool to process BGSs measured by BOTDA and obtain temperature distribution along the fiber, especially when large frequency scanning step is adopted to significantly reduce the measurement time but without sacrifice of sensing accuracy.

Evaluating and overcoming the impact of second echo in Brillouin echoes distributed sensing

The detrimental impact of the second echo phenomenon that commonly exists in Brillouin echoes distributed sensing (BEDS) methods is thoroughly investigated by further developing the analytical model of the Brillouin gain on the probe wave. The presented analysis not only points out that the most severe impact imposed by the second echo occurs when the length of the heated/stressed fiber section is exactly equal to the spatial resolution, but also quantifies the systematic error on the estimated Brillouin frequency shift, the maximum of which could reach up to 8.5 MHz. A novel parabolic-amplitude four-section pulse is proposed, which can compensate the impact of the second echo optically, without using extra measurement time and post-processing. The key parameters of the proposed pulse are optimized by combining an upgraded mathematical model and the iterative algorithm. The experimental results show a good agreement with the analysis about the behavior of the second echo, and demonstrate that the proposed technique is capable of providing sub-meter spatial resolution and the natural linewidth of Brillouin gain spectrum simultaneously, while completely eliminating the impact of the second echo.

Synthetic spectrum approach for Brillouin optical time-domain reflectometry

We propose a novel method to improve the spatial resolution of Brillouin optical time-domain reflectometry (BOTDR), referred to as synthetic BOTDR (S-BOTDR), and experimentally verify the resolution improvements. Due to the uncertainty relation between position and frequency, the spatial resolution of a conventional BOTDR system has been limited to about one meter. In S-BOTDR, a synthetic spectrum is obtained by combining four Brillouin spectrums measured with different composite pump lights and different composite low-pass filters. We mathematically show that the resolution limit, in principle, for conventional BOTDR can be surpassed by S-BOTDR and experimentally prove that S-BOTDR attained a 10-cm spatial resolution. To the best of our knowledge, this has never been achieved or reported.

Stokes and anti-Stokes differential pulse pair based distributed Brillouin fiber sensor with double-sideband probe wave

We propose and demonstrate a distributed Brillouin fiber sensor using Stokes and anti-Stokes differential pulse pair based on double- sideband probe wave, in which the two sidebands of probe wave are used to balance the power of two pump pulses. The spatial resolution is determined by the slightly width difference of the two balanced pulses, without Brillouin gain spectrum broadening. The pulses perform gain-loss process in optical field before the probe signal being detected, without any post-processing or extra measurement time. The proposed technique can achieve high spatial resolution, natural Brillouin gain spectrum linewidth, normal measurement time and long sensing range simultaneously.

Modeling and evaluating the performance of Brillouin distributed optical fiber sensors

A thorough analysis of the key factors impacting on the performance of Brillouin distributed optical fiber sensors is presented. An analytical expression is derived to estimate the error on the determination of the Brillouin peak gain frequency, based for the first time on real experimental conditions. This expression is experimentally validated, and describes how this frequency uncertainty depends on measurement parameters, such as Brillouin gain linewidth, frequency scanning step and signal-to-noise ratio. Based on the model leading to this expression and considering the limitations imposed by nonlinear effects and pump depletion, a figure-of-merit is proposed to fairly compare the performance of Brillouin distributed sensing systems. This figure-of-merit offers to the research community and to potential users the possibility to evaluate with an objective metric the real performance gain resulting from any proposed configuration.

Characterized Brillouin scattering in silica optical fiber tapers based on Brillouin optical correlation domain analysis

This paper demonstrates stimulated Brillouin scattering (SBS) characterization in silica optical fiber tapers drawn from commercial single mode optical fibers by hydrogen flame. They have different waist diameters downscaled from 5 μm to 42 μm. The fully-distributed SBS measurement along the fiber tapers is implemented by Brillouin optical correlation domain analysis technique with millimeter spatial resolution. It is found that the Brillouin frequency shift (BFS) in the waist of all fiber tapers is approximately the same (i.e., ~11.17 GHz at 1550 nm). However, the BFS is gradually reduced and the Brillouin gain decreases from the waist to the untapered zone in each fiber taper.

2 cm spatial-resolution and 2 km range Brillouin optical fiber sensor using a transient differential pulse pair

We report a high-spatial-resolution and long-range distributed temperature sensor through optimizing differential pulse-width pair Brillouin optical time-domain analysis (DPP-BOTDA). In DPP-BOTDA, the differential signal suffers from a signal-to-noise ratio (SNR) reduction with respect to the original signals, and for a fixed pulse-width difference the SNR reduction increases with the pulse width. Through reducing the pulse width to a transient regime (near to or less than the phonon lifetime) to decrease the SNR reduction after the differential process, the optimized 8/8.2 ns pulse pair is applied to realize a 2 cm spatial resolution, where a pulse generator with a 150 ps fall-time is used to ensure the effective resolution of DPP-BOTDA. In the experiment, a 2 cm spatial-resolution hot-spot detection with a 2 °C temperature accuracy is demonstrated over a 2 km sensing fiber.

Accurate estimation of Brillouin frequency shift in Brillouin optical time domain analysis sensors using cross correlation

Current methods of estimating the Brillouin frequency shift in Brillouin optical time domain analysis sensors are based on curve-fitting techniques. These techniques apply the same weight to all portions of the curve and dutifully fit into the peak and noisy ends of the curve. This makes them very sensitive to noise, initialization of fitting parameters, symmetry, and start and stop frequencies. We introduce a method based on the cross-correlation technique to estimate the central frequency of noisy Lorentzian curves, which is more robust to noise and free from initial settings of fitting parameters.

Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile

We present a novel method, based on stimulated Brillouin scattering (SBS), for the simultaneous distributed measurement of fast strain variations along the entire length of the sensing fiber. A specially synthesized and adaptable probe wave is used to place the Brillouin interaction always on the slope of the local Brillouin gain spectrum, allowing a single pump pulse to sample fast strain variations along the full length of a fiber with an arbitrary distribution of the Brillouin frequency shift. In this early demonstration of the method, strain vibrations of a few hundred Hz are demonstrated, simultaneously measured on two different sections of an 85 m long fiber, having different static Brillouin shifts and with a spatial resolution of 1.5 m.

Distributed Brillouin sensing with sub-meter spatial resolution: modeling and processing

A general analytic solution for Brillouin distributed sensing in optical fibers with sub-meter spatial resolution is obtained by solving the acoustical-optical coupled wave equations by a perturbation method. The Brillouin interaction of a triad of square pump pulses with a continuous signal is described, covering a wide range of pumping schemes. The model predicts how the acoustic wave, the signal amplitude and the optical gain spectral profile depend upon the pumping scheme. Sub-meter spatial resolution is demonstrated for bright-, dark- and π-shifted interrogating pump pulses, together with disturbing echo effects, and the results compare favorably with experimental data. This analytic solution is an excellent tool not only for optimizing the pumping scheme but also for post-processing the measured data to remove resolution degrading features.

Recent progress in Brillouin scattering based fiber sensors

Brillouin scattering in optical fiber describes the interaction of an electro-magnetic field (photon) with a characteristic density variation of the fiber. When the electric field amplitude of an optical beam (so-called pump wave), and another wave is introduced at the downshifted Brillouin frequency (namely Stokes wave), the beating between the pump and Stokes waves creates a modified density change via the electrostriction effect, resulting in so-called the stimulated Brillouin scattering. The density variation is associated with a mechanical acoustic wave; and it may be affected by local temperature, strain, and vibration which induce changes in the fiber effective refractive index and sound velocity. Through the measurement of the static or dynamic changes in Brillouin frequency along the fiber one can realize a distributed fiber sensor for local temperature, strain and vibration over tens or hundreds of kilometers. This paper reviews the progress on improving sensing performance parameters like spatial resolution, sensing length limitation and simultaneous temperature and strain measurement. These kinds of sensors can be used in civil structural monitoring of pipelines, bridges, dams, and railroads for disaster prevention. Analogous to the static Bragg grating, one can write a moving Brillouin grating in fibers, with the lifetime of the acoustic wave. The length of the Brillouin grating can be controlled by the writing pulses at any position in fibers. Such gratings can be used to measure changes in birefringence, which is an important parameter in fiber communications. Applications for this kind of sensor can be found in aerospace, material processing and fine structures.

Analysis of pulse modulation format in coded BOTDA sensors

A theoretical and experimental analysis of the impact of pulse modulation format on Brillouin optical time-domain analysis (BOTDA) sensors using pulse coding techniques has been carried out. Pulse coding with conventional non-return-to-zero (NRZ) modulation format is shown to induce significant distortions in the measured Brillouin gain spectrum (BGS), especially in proximity of abrupt changes in the fiber gain spectra. Such an effect, as confirmed by the theoretical analysis, is due to acoustic wave pre-excitation and non-uniform gain which depends on the bit patterns defined by the different codewords. A successful use of pulse coding techniques then requires to suitably optimize the employed modulation format in order to avoid spurious oscillations causing severe penalties in the attained accuracy. Coding technique with return-to-zero (RZ) modulation format is analyzed under different duty-cycle conditions for a 25 km-long sensing scheme, showing that low duty-cycle values are able to effectively suppress the induced distortions in the BGS and allow for spatially-accurate, high-resolution strain and temperature measurements being able to fully exploit the provided coding gain (approximately 7.2 dB along 25 km distance) with unaltered spatial resolution (1 meter). Although Simplex coding is used in our analysis, the validity of the results is general and can be directly applied to any intensity-modulation coding scheme.

Distributed fiber sensor based on modulated pulse base reflection and Brillouin gain spectrum analysis

In recent years, several distributed sensor systems based on stimulated Brillouin scattering in optical fibers have been proposed [J. Intell. Mater. Syst. Struct.10, 340 (1999); Proc. SPIE5855, 555 (2005)]. We propose a simpler scheme based on fiber-end reflection and Brillouin gain spectrum analysis. In this setup, only one optical source is necessary to provide both the pump and the probe wave; the latter is provided by the modulated pulse base. First, the physical mechanisms for two different Brillouin scattering processes in our sensor system are analyzed and an approximate theory model is proposed. In addition, it is demonstrated that the simple system configuration allows simultaneous acquisition of the time-domain and the frequency-domain information. It is experimentally demonstrated that this configuration is effective for strain measurements and could as well be applied to temperature monitoring.

Influence of transient phonon relaxation on the Brillouin loss spectrum of nanosecond pulses

For pump-probe stimulated Brillouin scattering with a probe pulse of a few nanoseconds duration and with a finite DC level, the acoustic wave relaxation time varies with the pump power and the DC level. For a pump power of 1-6 mW, the acoustic wave relaxation changes from approximately 9 to 90 ns for polarization-maintaining fiber at a temperature of -40 degrees C for a 2 ns pulse width. When the pulse DC ratio of the probe varies from 10 to 20 dB, the acoustic relaxation time changes from 24 to 45 ns for single-mode fiber at 25 degrees C. This induces a power-increment spectral feature in the detected AC pump signal in the Brillouin loss spectrum of two temperature or strain sections, where both spectral components appeared at positions far from those related to the natural phonon relaxation time (approximately 10 ns) equivalent length. The theoretical calculations confirm the prolonged phonon relaxation.

Simple approach to determining the minimum measurable stress length and stress measurement accuracy in distributed Brillouin sensing

A simple approach is proposed for quantifying the errors in measuring the Brillouin frequency shifts associated with stresses whose lengths are shorter than the pulse length. The smallest detectable Brillouin frequency shift is thus determined with respect to the size of the stressed sections and the frequency resolution. The lowest detectable frequency shift is found to be approximately 42% of the Brillouin gain natural linewidth. A worst-case iso-error curve that associates the minimum frequency shift to the length of the stressed region is derived. A minimum resolvable frequency shift and minimum detectable stress length are defined with an approach based on a Rayleigh equivalent criterion.

Effect of optical phase on a distributed Brillouin sensor at centimeter spatial resolution

Because of the power imbalance between the two arms of an interferometer in an electro-optic modulator (EOM), the output of the EOM is combined amplitude modulation (AM) and phase modulation (PM) for the probe signal consisting of the pulse and the dc component. Because of this PM, the Brillouin gain-loss spectrum becomes asymmetric. The central Brillouin frequency is shifted from that of an AM pulse. The maximum extinction ratio of the EOM is limited to approximately 29 dB for a power-splitting ratio of 51% to 49%. The asymmetric property induced by PM is not pulse shape dependent; for both Gaussian- and super-Gaussian-shaped pulses the Brillouin loss spectrum is symmetric for AM and asymmetric for combined AM and PM (power imbalance).

Brillouin spectral deconvolution method for centimeter spatial resolution and high-accuracy strain measurement in Brillouin sensors

Combining a dc and a short pulse (approximately 1 ns) as the probe beam in the pump-probe configuration of Brillouin-based distributed sensors allows us to represent the Brillouin spectrum as a top Lorentzian-like portion and a bottom Gaussian-like portion. Because of the interaction of these two parts, the Lorentzian-like portion carries spatial information that can be extracted within centimeter spatial resolution. Using this information, we develop a spectrum deconvolution method, which considers the location correlation of the strain distribution, to find the number of Brillouin peaks and their frequencies in the top Lorentzian-like portion and hence achieve accurate strain information. An optimum level of dc to pulse power for the best signal and position detection capability is discussed.

Stimulated Brillouin scattering frequency-domain analysis in a single-mode optical fiber for distributed sensing

A numerical and experimental analysis of the stimulated Brillouin scattering in a single-mode optical fiber for distributed sensing applications is carried out in the frequency domain. The theoretical model describing the Brillouin interaction is solved by taking into account the temporal dynamics of the acoustic wave that is involved. The simulations and the experimental results reveal the role played by the ac component of the acoustic wave, which is responsible for significant changes of the small-signal stimulated Brillouin scattering transfer function that occur when the modulation frequency rises above the natural Brillouin gain spectrum linewidth. One should take these effects into account to perform accurate signal processing of frequency-domain signals in high-resolution distributed sensing applications.

Dependence of the Brillouin gain spectrum on linear strain distribution for optical time-domain reflectometer-type strain sensors

We theoretically derive the shape of the Brillouin gain spectrum, that is, the Briilouin backscattered-light power spectrum produced in an optical fiber under conditions of a strain distribution that changes linearly with a constant slope. The modeled measurement system is an optical time-domain reflectometer-type strain sensor system. The linear strain distribution is one of the fundamental distributions and is produced in, for example, a beam to which a concentrated load is applied. By analyzing a function that expresses the shape of the derived Brillouin gain spectrum, we show that the strain calculated from the frequency at which the spectrum has a peek value coincide. with that at the center of the effective pulsed light. In addition, the peak value and the full width at half maximum of the Brillouin gain spectrum are both influenced by the strain difference between the two ends of the effective pulse. We investigate this influence in detail and obtain the relationship between strain difference and strain measurement error.

Strain measurement in a concrete beam by use of the Brillouin-scattering-based distributed fiber sensor with single-mode fibers embedded in glass fiber reinforced polymer rods and bonded to steel reinforcing bars

The strain measurement of a 1.65-m reinforced concrete beam by use of a distributed fiber strain sensor with a 50-cm spatial resolution and 5-cm readout resolution is reported. The strain-measurement accuracy is +/-15 microepsilon (microm/m) according to the system calibration in the laboratory environment with non-uniform-distributed strain and +/-5 microepsilon with uniform strain distribution. The strain distribution has been measured for one-point and two-point loading patterns for optical fibers embedded in pultruded glass fiber reinforced polymer (GFRP) rods and those bonded to steel reinforcing bars. In the one-point loading case, the strain deviations are +/-7 and +/-15 microepsilon for fibers embedded in the GFRP rods and fibers bonded to steel reinforcing bars, respectively, whereas the strain deviation is +/-20 microepsilon for the two-point loading case.

Transient response in high-resolution Brillouin-based distributed sensing using probe pulses shorter than the acoustic relaxation time

We perform numerical simulations on a model describing a Brillouin-based temperature and strain sensor, testing its response when it is probed with relatively short pulses. Experimental results were recently published [e.g., Opt. Lett. 24, 510 (1999)] that showed a broadening of the Brillouin loss curve when the probe pulse duration is reduced, followed by a sudden and rather surprising reduction of the linewidth when the pulse duration gets shorter than the acoustic relaxation time. Our study reveals the processes responsible for this behavior. We give a clear physical insight into the problem, allowing us to define the best experimental conditions required for one to take the advantage of this effect.