Strain Dynamic Range Research Articles

Interval-locked dual-frequency φ-OFDR with an enhanced strain dynamic range and a long-term stability.

We report on an interval-locked dual-frequency phase-sensitive optical frequency-domain reflectometry relying on a common-reference optical phase-locked loop. With a shared unbalanced interferometry, this design allows for synchronizing the frequency drift of two lasers, leading to a steadily stabilized dual frequency with an arbitrary interval. Equivalently to a longer synthetic wavelength, their phase difference is utilized to demodulate the ambient changes of interest with an enhanced dynamic range and long-term stability. With a stabilized interval of 1 THz, it allows for an enhancement in a strain measurement range of up to 193-fold in theory. Demonstration in terms of distributed strain sensing covering a distance of 500 m with a 10 cm spatial resolution has been verified, showing a significant extension in the achievable strain dynamic range with a preserved sensitivity over 1 h.

Total spectral power-based method for estimating Brillouin frequency shift in optical fibers

A cost-effective method for estimating the Brillouin frequency shift (BFS) of the whole sensing fiber without using an electrical spectrum analyzer is developed. The Brillouin gain spectrum is down-converted and low-pass-filtered, and its total transmitted power is used to estimate the BFS. The strain dynamic range of this method is experimentally shown to be double the value of a conventional slope-assisted method.

Distributed vibration sensor with a high strain dynamic range by harmonics analysis

Distributed vibration sensors (DVSs) have important applications in industrial production. A large strain dynamic range is very important for DVSs, but difficult to achieve as it often requires a complex sensing system or cumbersome data processing. This study shows that the strain dynamic range of the DVS can be improved by analyzing the harmonic numbers in the vibration response spectrum, and the vibration amplitude can be quantitatively measured with a strain resolution of 0.78 με for each additional harmonic. The system and data analysis method can significantly improve the strain dynamic range in comparison with traditional DVS based on the intensity or polarization information.

High sensitive and large dynamic range quasi-distributed sensing system based on slow-light π-phase-shifted fiber Bragg gratings

In this paper, we theoretically analyze the slow-light π-phase-shifted fiber Bragg grating (π-FBG) and its applications for single and multipoint/quasi-distributed sensing. Coupled-mode theory (CMT) and transfer matrix method (TMM) are used to establish the numerical modeling of slow-light π-FBG. The impact of slow-light FBG parameters, such as grating length (L), index change (Δn), and loss coefficient (α) on the spectral properties of π-FBG along with strain and thermal sensitivities are presented. Simulation results show that for the optimum grating parameters L = 50 mm, Δn = 1.5×10−4, and α = 0.10 m-1, the proposed slow-light π-FBG is characterized with a peak transmissivity of 0.424, the maximum delay of 31.95 ns, strain sensitivity of 8.380 με-1, and temperature sensitivity of 91.064 °C-1. The strain and temperature sensitivity of proposed slow-light π-FBG is the highest as compared to the slow-light sensitivity of apodized FBGs reported in the literature. The proposed grating have the overall full-width at half maximum (FWHM) of 0.2245 nm, and the FWHM of the Bragg wavelength peak transmissivity is of 0.0798 pm. The optimized slow-light π-FBG is used for quasi-distributed sensing applications. For the five-stage strain quasi-distributed sensing network, a high strain dynamic range of value 1469 με is obtained for sensors wavelength spacing as small as 2 nm. In the case of temperature of quasi-distributed sensing network, the obtained dynamic range is of 133 °C. For measurement system with a sufficiently wide spectral range, the π-FBGs wavelength grid can be broadened which results in substantial increase of dynamic range of the system.

Trade-off relation between strain dynamic range and spatial resolution in slope-assisted Brillouin optical correlation-domain reflectometry

Slope-assisted Brillouin optical correlation-domain reflectometry (SA-BOCDR) is one of the high-speed distributed strain sensing techniques, but its strain dynamic range has been limited to approximately 0.15%, which is far from being sufficient for some practical applications. In this paper, we clarify that, unlike widely used time-domain techniques, SA-BOCDR has a trade-off relation between the strain dynamic range and the spatial resolution. This trade-off originates from the unique bell-shaped noise floor inherently involved in the Brillouin gain spectrum observed with correlation-domain techniques. We experimentally show that, at the cost of three times lowered spatial resolution, the strain dynamic range of >0.6% can be achieved.

Realization of Sub-Nano-Strain Static Resolution With Injection-Locking Between Two Fiber Laser Sensors

Fiber Bragg grating (FBG) based sensors have achieved great performance in dynamic strain sensing, while static strain measurement is still very challenging because it requires extra reference for temperature compensation. In this paper, a high-resolution FBG laser sensor system is presented, which is capable of both static and dynamic strain measurements. In the proposed sensor, a distributed feedback fiber laser (DFB-FL) works as the strain sensing element, and a distributed Bragg reflector fiber laser (DBR-FL) works as the reference. The DFB-FL is injection-locked to the DBR-FL with closed loop control using Pound–Drever–Hall (PDH) technique and an acousto-optic frequency shifter. No independent narrow-linewidth probe laser source is required. In experiments, a frequency fluctuation range of 31.6 kHz in 1000 s between the DFB-FL and the DBR-FL is obtained, corresponding to a static strain resolution of 248 pico-strain. Meanwhile, a dynamic resolution of 580 femto-strain at l kHz is achieved. The limitation on strain resolution and dynamic range of the sensor is also discussed. Due to the high strain resolution and moderate cost, the proposed sensor system provides a powerful tool for various applications of strain measurement.

Brillouin Optical Correlation-Domain Technologies Based on Synthesis of Optical Coherence Function as Fiber Optic Nerve Systems for Structural Health Monitoring

Brillouin optical correlation-domain technologies are reviewed as “fiber optic nerve systems” for the health monitoring of large structures such as buildings, bridges, and aircraft bodies. The Brillouin scattering property is used as a sensing mechanism for strain and/or temperature. Continuous lightwaves are used in the technologies, and their optical coherence properties are synthesized to realize position-selective measurement. This coherence manipulation technology is called the “synthesis of optical coherence function (SOCF)”. By utilizing SOCF technologies, stimulated Brillouin scattering is generated position-selectively along the fiber, which is named “Brillouin optical correlation domain analysis (BOCDA)”. Spontaneous Brillouin scattering, which takes place at any portion along the fiber, can also be measured position-selectively by the SOCF technology. This is called “Brillouin optical correlation domain reflectometry (BOCDR)”. When we use pulsed lightwaves that have the position information, sensing performances, such as the spatial resolution, are inherently restricted due to the Brillouin scattering nature. However, in the correlation-domain technologies, such difficulties can be reduced. Superior performances have been demonstrated as distribution-sensing mechanisms, such as a 1.6-mm high spatial resolution, a fast measurement speed of 5000 points/s, and a 7000-με strain dynamic range, individually. The total performance of the technologies is also discussed in this paper. A significant feature of the technologies is their random accessibility to discrete multiple points that are selected arbitrarily along the fiber, which is not realized by the time domain pulsed-lightwave technologies. Discriminative and distributed strain/temperature measurements have also been realized using both the BOCDA technology and Brillouin dynamic grating (BDG) phenomenon, which are associated with the stimulated Brillouin scattering process. In this paper, the principles, functions, and applications of the SOCF, BOCDA, BOCDR, and BDG-BOCDA systems are reviewed, and their historical aspects are also discussed.

Enhancing strain dynamic range of slope-assisted BOTDA by manipulating Brillouin gain spectrum shape.

A novel technique for improving the dynamic range of slope-assisted Brillouin optical time domain analysis (SA-BOTDA) is proposed. By modulating the pump pulse with a specially designed signal generated using an arbitrary waveform generator, we may manipulate the shape of Brillouin gain spectrum (BGS) to obtain an enlarged strain dynamic range without increasing significant cost on system complexity. In simulation, we realize a 4.8-times improvement by using a 2-tone signal for pump pulse modulation. In experiment, we modulate a 25-ns-width pump pulse with a 2-tone signal whose frequencies are 43 MHz and 86 MHz respectively and achieve a 100-MHz linear slope span, which is about 4.35 times of that in conventional SA-BOTDA technique. Besides, the BGS manipulation technique realizes an efficient utilization of pump power and only introduces a pump power penalty of 3.53 dB, which allows a promising dynamic strain measurement. In the experiment, we successfully measured a sinusoidal strain signal exerted on a 3-m fiber, with a range from -75 με to 875 με and a frequency of 80 Hz. The measured result shows that the suppression ratio of 2nd-order harmonic is 39.35 dB, and the strain measurement accuracy is 5.26 με. The results indicate that the proposed technique has a desirable performance on dynamic strain measurement.

Dynamic strain response of a π-phase-shifted FBG sensor with phase-sensitive detection

Fiber optic sensors realized with passive π–phase-shifted fiber Bragg gratings (πFBG) offer an enhanced detection limit leading to the measurement of weak strain perturbations as compared to a regular FBG sensor. This superior detection limit is due to the extremely narrow reflection notch or transmission peak of a passive πFBG that allows high resolution measurement of spectral separation. We have recently demonstrated an innovative and simple concept based on phase-sensitive detection for the efficient measurement of the wavelength-shift of the transmission peak. This phase-sensitive detection is implemented using a fiber based Mach-Zehnder interferometer (F-MZI). The Bragg wavelength-shift of the narrow transmission peak under the influence of dynamic strain due to acoustic signals is measured at the output of a designed and fabricated F-MZI. Since the bandwidth of this transmission peak is significantly smaller as compared to a regular FBG sensor of similar length, this gives the leverage of a longer optical path difference (OPD) between the two arms of an F-MZI. This new concept was initially demonstrated in our previous article through simulation and very preliminary experimental studies. Here, we present elaborate experimental studies carried out to fully demonstrate the potential of the proposed idea for low-amplitude dynamic strain sensing. We further elucidate the strain sensitivity and dynamic range of the proposed concept. In the current experimental configuration, the minimum detectable dynamic strain is estimated to be 17 pϵ over 1 Hz measurement bandwidth.

Brillouin characterization of slimmed polymer optical fibers for strain sensing with extremely wide dynamic range.

To date, most distributed Brillouin sensors for structural health monitoring have employed glass optical fibers as sensing fibers, but they are inherently fragile and cannot withstand strains of >3%. This means that the maximal detectable strain of glass-fiber-based Brillouin sensors was ~3%, which is far from being sufficient for monitoring the possible distortion caused by big earthquakes. To extend this strain dynamic range, polymer optical fibers (POFs) have been used as sensing fibers. As POFs can generally withstand even ~100% strain, at first, Brillouin scattering in POFs was expected to be useful in measuring such large strain. However, the maximal detectable strain using Brillouin scattering in POFs was found to be merely ~5%, because of a Brillouin-frequency-shift hopping phenomenon accompanied by a slimming effect peculiar to polymer materials. This conventional record of the strain dynamic range (5%) was still far from being sufficient. Here, we have thought of an idea that the strain dynamic range can be further extended by employing a POF with its whole length slimmed in advance and by avoiding the Brillouin-frequency-shift hopping. The experimental results reveal that, by applying 3.0% strain to a slimmed POF beforehand, we can achieve a >25% strain dynamic range, which is >5 times the conventional value and will greatly extend the application fields of fiber-optic Brillouin sensing.

Phase-detected Brillouin optical correlation-domain reflectometry

Optical fiber sensing techniques based on Brillouin scattering have been extensively studied for structural health monitoring owing to their capability of distributed strain and temperature measurement. Although a higher signal-to-noise ratio (leading to high spatial resolution and high-speed measurement) is generally obtained for two-end-access systems, they reduce the degree of freedom in embedding the sensors into structures, and render the measurement no longer feasible when extremely high loss or breakage occurs at a point of the sensing fiber. To overcome these drawbacks, a one-end-access sensing technique called Brillouin optical correlation-domain reflectometry (BOCDR) has been developed. BOCDR has a high spatial resolution and cost efficiency, but its conventional configuration suffered from relatively low-speed operation. In this paper, we review the recently developed high-speed configurations of BOCDR, including phase-detected BOCDR, with which we demonstrate real-time distributed measurement by tracking a propagating mechanical wave. We also demonstrate breakage detection with a wide strain dynamic range.

Strain Dynamic Range Enlargement of Slope-Assisted BOTDA by Using Brillouin Phase-Gain Ratio

A novel technique to enlarge the dynamic range of strain measurement for slope-assisted Brillouin optical time domain analysis (SA-BOTDA) is proposed by introducing a new parameter called Brillouin phase-gain ratio, which combines Brillouin phase shift and Brillouin gain. With the new technique, the dynamic range of strain measurement can be enlarged, and the pump-power-dependency problem mitigated. In the experiment, a 100-MHz frequency span of linear slope is demonstrated with a 25-ns pump pulse, which is 3.3 times of that in conventional SA-BOTDA, and a dynamic strain with a large amplitude of about 1000 μe is successfully measured.

Single-end-access distributed strain sensing with wide dynamic range using higher-speed Brillouin optical correlation-domain reflectometry

Single-end-access real-time fiber-optic distributed strain sensing has recently been demonstrated using an ultrahigh-speed configuration of Brillouin optical correlation-domain reflectometry (BOCDR). Its extremely high sampling rate was, however, achieved at the cost of a limited strain dynamic range (<0.2%). Here, by employing a noise-floor compensation technique, we develop a new cost-effective higher-speed configuration of BOCDR with a wide strain dynamic range (up to 2.0%; evaluated by static strain measurement). This value is larger than that of any other BOCDR configuration. Using this configuration, we demonstrate some fundamental distributed strain measurements and breakage detection.

Ultrahigh-speed distributed Brillouin reflectometry.

Optical fibre sensors based on Brillouin scattering have been vigorously studied in the context of structural health monitoring on account of their capacity for distributed strain and temperature measurements. However, real-time distributed strain measurement has been achieved only for two-end-access systems; such systems reduce the degree of freedom in embedding the sensors into structures, and furthermore render the measurement no longer feasible when extremely high loss or breakage occurs at a point along the sensing fibre. Here, we demonstrate real-time distributed measurement with an intrinsically one-end-access reflectometry configuration by using a correlation-domain technique. In this method, the Brillouin gain spectrum is obtained at high speed using a voltage-controlled oscillator, and the Brillouin frequency shift is converted into a phase delay of a synchronous sinusoidal waveform; the phase delay is subsequently converted into a voltage, which can be directly measured. When a single-point measurement is performed at an arbitrary position, a strain sampling rate of up to 100 kHz is experimentally verified by detecting locally applied dynamic strain at 1 kHz. When distributed measurements are performed at 100 points with 10 times averaging, a repetition rate of 100 Hz is verified by tracking a mechanical wave propagating along the fibre. Some drawbacks of this ultrahigh-speed configuration, including the reduced measurement accuracy, lowered spatial resolution and limited strain dynamic range, are also discussed.

Frequency-Scanning BOTDA With Ultimately Fast Acquisition Speed

A polarization-independent fast and distributed frequency-scanning Brillouin optical time-domain analysis (BOTDA) technique is presented, capable of acquiring the full Brillouin gain spectrum at a speed limited only by the fiber length and the employed frequency scanning granularity. For a 145-m long fiber and 71 interrogating frequencies, the ultimate measurement speed of 9700 [full-fiber-Brillouin-gain-spectra]/second is demonstrated, covering a strain dynamic range of 4200 με with an accuracy of ±10 με. Dynamic measurements with a spatial resolution of 10 cm are also demonstrated by combining the technique with the double pulse pair BOTDA method.

Three-dimensional optical coherence elastography by phase-sensitive comparison of C-scans.

We present an acquisition method for optical coherence elastography (OCE) that enables acquisition of three-dimensional elastograms in 5 s, an order of magnitude faster than previously reported. In this method, based on compression elastography, the mechanical load applied to the sample is altered between acquisitions of consecutive optical coherence tomography volume scans (C-scans). The voxel-by-voxel phase difference between the volumes is used to determine the axial displacement and determining the gradient of the axial displacement versus depth gives the local axial strain. We demonstrate sub-100-microstrain sensitivity and high contrast in elastograms, acquired in 5 s, of structured phantoms and freshly excised rat muscle tissue that are comparable in strain sensitivity and dynamic range to our previously reported B-scan-based method. The much higher acquisition speed may expedite the translation of OCE to clinical and in vivo applications.

Strain estimation in phase-sensitive optical coherence elastography

We present a theoretical framework for strain estimation in optical coherence elastography (OCE), based on a statistical analysis of displacement measurements obtained from a mechanically loaded sample. We define strain sensitivity, signal-to-noise ratio and dynamic range, and derive estimates of strain using three methods: finite difference, ordinary least squares and weighted least squares, the latter implemented for the first time in OCE. We compare theoretical predictions with experimental results and demonstrate a ~12 dB improvement in strain sensitivity using weighted least squares compared to finite difference strain estimation and a ~4 dB improvement over ordinary least squares strain estimation. We present strain images (i.e., elastograms) of tissue-mimicking phantoms and excised porcine airway, demonstrating in each case clear contrast based on the sample’s elasticity.

A Wide Dynamics and Fast Scan Interrogating Method for a Fiber Bragg Grating Sensor Network Implemented Using Code Division Multiple Access

We propose and demonstrate a fiber Bragg grating (FBG) sensor network employing the code division multiple access (CDMA) technique to identify information from individual sensors. To detect information without considering time delays between sensors, a sliding correlation method is applied, in which two different signals with the same pseudo-random binary sequence (PRBS) pattern, but slightly different frequencies, are applied to the source and detector sides. Moreover, for time domain detection, a wavelength-to-time conversion technique using a wavelength dispersive medium is introduced. The experimental results show that the proposed sensor network has a wide strain dynamic range of 2,400 με and a low crosstalk of 950:1.

Investigation of parametric spectral estimation techniques for elasticity imaging

Several autoregressive (AR) and autoregressive moving average (ARMA) parametric spectral estimators were evaluated for use in tissue strain estimation. Using both 1-D simulations and in vitro phantom experiments, the performance of these parametric spectral strain estimators were compared against both a nonparametric discrete Fourier transform (DFT) spectral strain estimator and a coherent elastographic technique. Parametric spectral estimator model orders were selected based on a modified strain filter approach. This technique illustrated the trade-offs between different signal-processing parameters and a strain estimator performance measure, namely the area under the strain filter (using applied strain dynamic range of 0.1 to 50%). The Yule-Walker AR spectral strain estimator outperformed all other parametric methods evaluated, but failed to outperform the DFT-based approach. Furthermore, both these spectral strain-estimation techniques exhibit an elastographic signal-to-noise ratio ( SNR e ) and strain estimation dynamic range not achievable using conventional elastography without global stretching. (E-mail: flemming.forsberg@jefferson.edu)

Vascular intramural strain imaging using arterial pressure equalization

Peripheral vascular strain imaging has limited strain dynamic range because arterial wall deformations only exhibit small strains under physiologic pressures. A noninvasive freehand ultrasound (US) scanning procedure was performed to apply external force, comparable to the force generated in measuring a subject's blood pressure, to achieve higher strains by equalizing the internal arterial baseline pressure. When the applied pressure matched the internal baseline diastolic pressure, intramural strain and strain rate increased by a factor of 10 over a cardiac cycle. Radial arterial strain was assessed within the vessel wall over the entire deformation procedure using a phase-sensitive 2-D speckle-tracking algorithm. The feasibility of this technique to assess vascular nonlinear elastic properties is demonstrated in an ex vivo experiment and further supported by in vivo measurements. With some uncertainty associated with the elastic properties of surrounding tissue, an elastic modulus reconstruction procedure was developed to estimate the nonlinear elastic properties of the vascular wall. (E-mail: kangkim@umich.edu)