A High Performance Distributed Optical Fiber Sensor Based on Φ-OTDR for Dynamic Strain Measurement

A high-performance distributed optical fiber sensor based on phase-sensitive optical time-domain reflectometry (Φ-OTDR) for dynamic strain measurement has been proposed. In this newly designed system, ultraweak fiber Bragg gratings (UWFBGs) are sparsely embedded in the sensing fiber. Through an unbalanced 3 × 3 coupler structure, the reflected lights from two adjacent UWFBGs would be mixed with each other and then split into three parts for phase demodulation. Then, a novelty table-look-up scheme is introduced to precisely demodulate the frequency, amplitude, and phase of dynamic strain. Rayleigh back-scattering light is utilized to identify and locate the accurate position of vibration event between two adjacent UWFBGs. The experimental results show that the proposed system is capable of reconstructing the vibration with a linear intensity response of R² = 0.9986 and a fiber length variation sensitivity of 117 pm/(Hz)^1/2. Meanwhile, a wide frequency response band from 50 to 2075 Hz is achieved with high signal-to-noise ratio above 56 dB.

SECTION 1. Introduction

Phase-sensitive optical time-domain reflectometry (Φ-OTDR) has been proved to be an efficient way to interrogate multi-point vibration events along the entire length of sensing fiber for fast response and high sensitivity [1]–​[3]. Therefore, it has been widely used in many applications, such as railway health monitoring, pipelines leak detection and intruder detection [4]–​[6]. Vibration events around the sensing fiber can induce dynamic strain to the fiber, resulting in the changes of refractive index and fiber length. Therefore, the variation of the phase difference (VPD) between the scattered lights will occur and the amplitudes of Rayleigh back-scattering (RBS) traces will fluctuate at the corresponding position. By measuring the fluctuation, the location and the frequency of the dynamic strain can be obtained by an Φ-OTDR system. However, due to the randomly distributed reflectivity and position of the Rayleigh scattering points in the fiber, there is no definite relationship between the strain value and the amplitude variation of RBS light [7]. Therefore, traditional Φ-OTDR sensing systems intrinsically suffer from the inability to reconstruct the dynamic strain.

Recently, several methods have been proposed to realize dynamic strain measurement [8]–​[13]. In these methods, two undisturbed fiber sections on both sides of the disturbed region are selected as reference sections. By measuring the VPD between the scatterings from the two reference sections, the fiber length variation induced by the dynamic strain could then be reconstructed. However, for in-field application, the reference section itself is not so easily isolated from external disturbance, which will degrade the performance of the measurement results. Meanwhile, the fading phenomenon of highly coherent scattering in an optical fiber may also make the RBS signal from some fiber sections fall into the destructive interference area, namely the dead zone [14]. Within the dead zone, the amplitude of noise could be comparable to or even stronger than that of RBS signal, leading to the failure of dynamic strain reconstruction.

Researchers have also made progress in high-precise measurement of dynamic strain based on fiber Bragg gratings (FBGs) [7], [15]–​[18]. In these literatures, fluctuant and weak RBS signals are replaced by stable and strong reflected lights generated by FBGs, where nϵ level accuracy has been successfully achieved. However, strain change could only be monitored at these positions where FBGs are installed, resulting in limited sensing points [15], [16]. Distributed sensing could be realized if the probe pulse covers two or more consecutive ultra-weak fiber Bragg gratings (UWFBGs) to generate the interference signal. However, in this case, spatial resolution would be equal to or greater than the interval of UWFBGs [7], [17]. If the UWFBGs are distributed with high density for high spatial resolution, the transmission loss will be high and the sensing length will be restricted [19]. Meanwhile, active laser frequency sweeping procedure consumes too much time for VPD demodulation, limiting the maximum detectable frequency of vibration events [7], [18].

In this paper, we propose a high performance distributed optical fiber sensor (DOFS) based on Φ-OTDR for dynamic strain measurement. In order to reduce the transmission loss, UWFBGs are sparsely embedded in a sensing fiber with equal interval. Through an unbalanced 3 × 3 coupler structure, the reflected lights from two adjacent UWFBGs would be mixed with each other and then are split into three parts for phase demodulation. Then, a novelty table-look-up scheme is introduced to precisely demodulate the frequency, amplitude and phase of dynamic strain. To obtain high accuracy of spatial orientation, RBS light is utilized to identify and locate the accurate position of vibration event between two adjacent UWFBGs. This newly proposed system will offer a versatile new option for dynamic strain measurement.

SECTION 2. Principle of Dynamic Strain Measurement

When only reflected light generated by sparse UWFBGs array is utilized as the sensing signal, the spatial resolution of the system would be equal to the interval of UWFBGs, which is inferior to the typical performance of a traditional Φ-OTDR system. To realize high spatial resolution monitoring, RBS light between two adjacent UWFBGs is observed with traditional Φ-OTDR scheme. Although traditional Φ-OTDR fails to realize dynamic strain measurement, it could be used to identify and locate the vibration event with high accuracy and robustness. Then the dynamic strain induced by the corresponding vibration event could be obtained by VPD demodulating between adjacent UWFBGs.

As shown in Fig. 1(a), in the proposed method, identical UWFBGs are embedded in the fiber with equal interval L. The interval L is several orders of magnitude larger than the desired spatial resolution, determined by the width of probe pulse. The generated probe pulse is launched into the UWFBG array through a circulator. The reflected pulses go through the same circulator and are split into two paths by a 3 dB coupler. A delay fiber is inserted into the upper-path to make the pulses reflected from adjacent UWFBGs mix with each other. Any dynamic strain change on the fiber within two adjacent UWFBGs will lead to the variation of optical path difference (OPD) and create a linear monotonic phase change of interference signal. Through a 3 × 3 coupler, the interference lights are further split into three parts for VPD demodulation.

Fig. 1.

(a) Schematic diagram of the sparse UWFBG array system. APD_1∼3: Avalanche photodiode. (b) Schematic diagram of two adjacent UWFBGs. (c) Time series of reflected lights and the reflected lights after the delay.

To simplify the model, we only take two adjacent UWFBGs into account, as shown in Fig. 1(b). The electric fields of the reflected pulses from UWFBG1 and UWFBG2 are given by \begin{align} \left\{ \begin{array}{l} {E_{R1}} = {a_{1}}\;{\rm{cos}}\left[ {\omega t + {\varphi _0}} \right]\\ {E_{R2}} = {a_2}\;{\rm{cos}}\left[ {\omega t + {\varphi _0} + \frac{{4\pi n}}{\lambda }\left({L + \Delta L} \right)} \right] \end{array} \right. \end{align}where $a_{{1}}$ and $a_{{2}}$ are the amplitudes of the two reflected light pulses, ω is the angular frequency of the reflected light, $\varphi _{{0}}$ is the phase of the reflected light from UWFBG1, λ is the wavelength of the reflected light, ΔL is the interval variation induced by dynamic strain, and n stands for the refractive index of optical fiber core, having a typical value 1.46 for normal single mode fiber.

The time domain relationship of the reflected light pulses from different optical path is shown in Fig. 1(c). Ignoring the attenuation of the delay fiber, the electric fields of pulse1_D and pulse2 from the upper path and lower path, respectively, are given by \begin{align} \left\{ \begin{array}{l} {E_{{{1}_{{D}}}}} = {a_1}{\beta _1}\;{\rm{cos}}\left[ {\omega t + {\varphi _0} + \frac{{4\pi n}}{\lambda }L^\prime} \right]\\ {E_{2}} = {a_2}{\beta _2}\;{\rm{cos}}\left[ {\omega t + {\varphi _0} + \frac{{4\pi n}}{\lambda }\left({L + \Delta L} \right)} \right] \end{array} \right. \end{align}where $\beta _{{1}}$ and $\beta _{{2}}$ are the coupling ratios of 3 dB coupler $(\beta _{{1}}^{2}\,+ \,\beta _{{2}}^{2}\,= \,1,\,\beta _{{\rm{1,2}}}^{2}\,\in \,[ 0,\,1])$.Considering that the difference between L' and L is less than half of the spatial resolution, pulse 2 and pulse 1_D could overlap halfway with each other to guarantee the performance of demodulation. The intensity of the photocurrent generated by the interference signal between pulse 2 and pulse 1_D can be expressed as \begin{align} &I \propto {a_1}^2\beta _1^2 + {a_2}^2\beta _2^2 + 2{a_1}{a_2}{\beta _1}{\beta _2}\cos \left[ {\frac{{4\pi n}}{\lambda }\left({L - L^\prime + \Delta L} \right)} \right] \nonumber\\ & \quad = D + E\cos \left[ {{\varphi _{1^\prime 2}} + \Delta \varphi } \right],\;{\rm{with}}\;D = {a_1}^2\beta _1^2 + {a_2}^2\beta _2^2,\;E = 2{a_1}{a_2}{\beta _1}{\beta _2} \end{align}where $\varphi _{{\rm{1^\prime \,2}}}$ is the phase difference between pulse2 and pulse1_D, which is induced by OPD when no disturbance is applied on the sensing fiber. Δϕ is the VPD created by the variation of ΔL. The relationship between ΔL and Δϕ can be written as \begin{align} \Delta L = \frac{\lambda }{{4\pi n}}\Delta \varphi. \end{align}

From (3) and (4), we can see that Δϕ leads to the variation of interference intensity. However, due to the non-monotone of cosine function, it would be impossible to obtain Δϕ directly from the power of interference signal. Therefore, a 3 × 3 coupler is introduced to generate three interference signals with different phase offset. To obtain the fiber length variation, interference signals are received by APDs for further demodulation.

The procedure of demodulation is shown in Fig. 2. Sampled traces of three APDs' outputs consist of several rectangular pulses, which are the reflections of rectangular probe pulse along the fiber. In order to obtain better signal-to-noise ratio (SNR), matched filter is utilized to convert rectangular pulses into triangular pulses, which is the optimum filtering system for receiving a pulse signal in additive white Gaussian noise [20]. We sample the peak value of triangular pulses for demodulation and the intensities of sampled peak would be \begin{align} {I_N}\left(t \right) = \ p{R_N}{\alpha _N}\left\{ {D + E{\rm{cos}}\left[ {\varphi \left(t \right) + {\varphi _{LFD}}\left(t \right) + \frac{{2\pi }}{3}\left({N\; -\; 2} \right)} \right]} \right\}{+\rm{ }}{I_{Nnoise}}(t) \end{align}where N = 1, 2, 3, p is the intensity gain factor of matched filter, $R_{N}$ is the responsivity of the Nth APD, $\alpha _{N}$ is the coupling ratio of Nth channel of the 3 × 3 coupler $(\alpha _{{1}}^{2}\,+ \,\alpha _{{2}}^{2}\,+ \,\alpha _{{3}}^{2}\,= \,1,\,\alpha _{{\rm{N}}}^{2}\,\in \,[ 0,\,1])$, ϕ(t) is the VPD induced by dynamic strain, $\varphi _{LFD}(t)$ is the phase noise generated by the laser frequency drifting (LFD), and $I_{Nnoise}(t)$ is the intensity noise caused by APD and data acquisition device. The intensity noise mainly comprises the dark current of APD, the offset current of trans-impedance amplifier and the offset voltage of ADC.

Fig. 2.

Flow chart of digital signal process for VPD demodulation.

The traditional 3 × 3 coupler demodulation scheme [21] can be implemented in two ways: analog circuit [22] or digital circuit [12], [13], [17], which is established on the condition that signals are noise free or the SNR is extremely high. Although the analog one has fast process speed, the use of amplifiers brings extra offset noise, degrading the performance of demodulation. The digital one replaces the derivative and integral process in analog circuit by differencing and cross-multiplication algorithm. Although the demodulation of the digital one could be easily realized by sequential logic circuit, the result tends to be a little worse than that of analog circuit. If $R_{N}$, $\alpha _{N}$ are not compensated and $I_{Nnoise}(t)$ cannot be neglected, the accuracy of the traditional 3 × 3 coupler demodulation scheme will be affected. To overcome this problem, we propose a novelty demodulation method, denoted as table-look-up scheme.

Although the intensity noise for individual device is different from each other, the distribution of $I_{Nnoise}(t)$ could be described by Gaussian function in most cases and the maximum intensity of noise could be measured as $A_{Nnoise}$ by a long-term observation. Equation (5) can be simplified by setting $k_{N}\,= \,pR_{N}\alpha _{N}$. By long-term observation, the maximum and the minimum values in (5) can be obtained as \begin{align} \left\{ \begin{array}{l} {I_{Nmax}} = \ {k_N}(D + E){+\rm{ }}{A_{Nnoise}}\\ {I_{Nmin}} = \ {k_N}(D - E) - {A_{Nnoise}} \end{array} \right. \end{align}where $I_{Nmax}$ is achieved when the phase angles of pulse2 and pulse1_D are the same, and $I_{Nmin}$ is obtained when the phase difference between pulse2 and pulse1_D equals π. Then, (5) can be normalized as \begin{align} {{\bar{I}}_N}\left(t \right) &= ({I_N}(t) - {I_{Nmin}})/\left({{I_{Nmax}} - {I_{Nmin}}} \right) \nonumber\\ & = \ \frac{1}{2} + \frac{1}{2}\frac{{{k_N}E}}{{{k_N}E{+\rm{ }}{A_{Nnoise}}}}\cos \left[ {\varphi \left(t \right) + {\varphi _{LFD}}\left(t \right) + \frac{{2\pi }}{3}\left({N\; -\; 2} \right)} \right]{+\rm{ }}\frac{1}{2}\frac{{{I_{Nnoise}}(t)}}{{{k_N}E{+\rm{ }}{A_{Nnoise}}}}. \end{align}

We divide the phase range of −π∼π into M equal parts and set up a phase/intensity look-up table according to (7) . The table is given by \begin{align} {\tilde{I}_N}\left(m \right) = \frac{1}{2} + \frac{1}{2}\cos \left[ {{\varphi _m} + \frac{{2\pi }}{3}\left({N\; -\; 1} \right)} \right] \end{align}where $\varphi _{m}\,= \,(2\pi m/ M)-\pi $, m = 0, 1, 2… M-1. At time $t_{{1}}$, we calculate the correlation between ${\bar{I}_N}({{t_1}})$ and ${\tilde{I}_N}(m)$, that is the sum-of-squared difference between ${\bar{I}_N}({{t_1}})$ and each group ${\tilde{I}_N}(m)$ in look-up table. The process can be expressed by \begin{align} \mathop {\min }\limits_m \bigcup\limits_{m = 1}^M {\left[ {{{\sum\limits_{N = 1}^3 {\left({\overline I ({t_1}) - {{\widetilde I}_N}(m)} \right)} }^2}} \right]}. \end{align}

The minimum value is obtained when $m\,= \,m_{{1}}$. We have $\varphi _{m{1}}\,= \,\varphi (t_{{1}})\,+ \,\varphi _{LFD}(t_{{1}})$, which would be the best estimation to the phase at time t₁. After applying the demodulation method to all points, we can obtain the VPD value with an additive phase noise $\varphi _{LFD}(t)$ generated by LFD. Unfortunately, the results are wrapped into the range of (−π, π ) due to the non-monotonicity of cosine function. Phase unwrapping algorithm [7] can solve this problem as long as the phase difference between adjacent traces does not exceed the range of (−π, π). Therefore, the repetition rate of traces requires to be high enough to guarantee that the fiber length variation ΔL between adjacent traces falls into the range of (−λ/4n, λ/4n ), otherwise the algorithm will fail. Usually, the useful components of the vibration event are distributed in the high frequency band while the noise induced by LFD is around Hz or sub-Hz level [7] , [23]. Thus, a high-pass filter is applied to separate the noise $\varphi _{LFD}(t)$ from the useful signal ϕ(t) generated by the fiber length variation.

SECTION 3. Experimental Setup

The experimental setup of the newly designed system is illustrated in Fig. 3 . A NLL (RIO OrionTM Laser module) was selected as the light source whose output power was 7 dBm. The wavelength of the laser module was 1550.12 nm and its linewidth was 3.7 kHz. 10% of the CW light served as the local-oscillator light whose frequency was shifted by a 200 MHz AOM. While 90% of the CW light was converted into optical probe pulses by a high extinction ratio (ER) modulator. The ER of the modulator was higher than 65 dB for coherent noise suppression [24]. The pulse width was 100 ns, corresponding to a spatial resolution of 10 m. The peak power of probe pulse was amplified to 21 dBm by EDFA and then launched into a 2.4 km sensing fiber through a circulator.

Fig. 3.

Experimental setup of the combined system. NLL: narrow linewidth laser; CW: continuous waveform; ER: extinction ratio; EDFA: erbium-doped fiber amplifier; AOM: acoustic-optic modulator; BPD: balanced photodetector; BPF1∼2: Band-pass filter; LNA: low-noise amplifier; APD_1∼3: avalanche photodiode; OSC: oscilloscope; PZT: piezoelectric transducer; FUT: fiber under test; R_1∼3: reflector (UWFBG).

As a proof-of-concept experiment, three UWFBGs with reflectivity of −35.8 dB, −33.3 dB, and −37.5 dB were placed at the end of a 2155 m single mode fiber, called ${\rm{R}}_{{1}}$, ${\rm{R}}_{{2}}$ and ${\rm{R}}_{{3}}$, respectively. The central wavelength of the embedded UWFBGs was 1550.12 nm, coincident with the laser source in our experiment. The 3 dB bandwidth of UWFBGs was 5 nm to make the reflectivity insensitive to strain and temperature change. The interval between adjacent UWFBGs was 99 m. A cylindrical piezoelectric transducer (PZT) was twined with a 10 m fiber to create controllable dynamic strain by stretching, which was located between ${\rm{R}}_{{1}}$ and ${\rm{R}}_{{2}}$. The distance between R₁ and the middle of the 10 m stretching region was 67 m. Since the power of reflected pulses was dozens of times stronger than that of RBS light, 90% of the backscattered light was combined with the local-oscillator light through a 3 dB coupler. Then the heterodyne signal centered at 200 MHz was received by a BPD (Thorlabs, PDB430C, 40 dB gain, 350 MHz bandwidth) for identifying and locating the vibration. 10% of the backscattered light was injected into the unbalanced 3 × 3 coupler structure with $2L^\prime \,= \,{\rm{198\,m}}$. Then the interference lights were received by three APDs (60 dB gain, 20 MHz bandwidth) for VPD demodulation. Outputs of the BPD and three APDs were synchronously recorded by an oscilloscope (Lecroy WaveRunner 610Zi). The trace repetition rate was 25 kHz, which was the maximum capturing rate of oscilloscope.

SECTION 4. Experimental Results and Discussions

In our experiment, PZT was first driven by a cosine signal of 100 Hz with the amplitude of 13 V. BPD traces were continuously recorded by OSC with 1GSa/s for 40 ms. The heterodyne signal of BPD consisted of jagged RBS traces and saturated rectangular reflected lights. After extracting the envelope of each trace, we could identify and locate the position of vibration event with differential method. Fig. 4(a) illustrated the waterfall plot of RBS envelope traces around the PZT position. The region marked in the black rectangular frame contained a repetitive event with a period of 10 ms, which was coincident with the vibration event applied by the stretching of PZT. Three red rectangular regions with saturated light intensities were recognized as reflected light pulses of UWFBGs. The positions of the tri-UWFBGs were 2161 m, 2260 m, 2358 m. The differential results of RBS envelope traces were exhibited in Fig. 4(b), showing that 4 peaks located at the positions of 2161 m, 2228 m, 2260 m, and 2358 m. Compared with the locations of UWFBGs in Fig. 4(a), three weaker pulse peaks were recognized as reflections from UWFBGs and the maximum pulse peak at 2228 m was identified as the vibration event created by PZT. Except for the vibration zone, the intensities of differential RBS signals were lower than that of three weaker pulse peaks. This is because the intensities of reflected pulses were several times as stronger than that of RBS signals, and so were the differential results. Although the amplitudes of three weaker pulse peaks were stronger than RBS signal, identifying that the vibration location was not affected owing to their unchangeable positions. The SNR of disturbance event induced by PZT exceeded 10 dB, which was good enough to guarantee the accuracy of locating. In our setup, the middle position of the PZT stretching region was located at the position of 2227 m, so the error of event locating was 1 m compared with the measured position of 2228 m.

Fig. 4.

(a) Waterfall plot of differential Φ-OTDR envelope traces around the PZT position. (b) Differential Φ-OTDR traces around the UWFBGs region.

In UWFBG array, intensities of three APDs' outputs were continuously recorded with 100 MSa/s for 0.16 s, displayed in Fig. 5(a). In Fig. 5(b), rectangular pulses were converted to triangular pulses after matched filtering. The triangular pulse was much higher than the rectangular one at the same position, whereas noise floor in Fig. 5(b) was lower than that in Fig. 5(a). Therefore, if the data was extracted at the peak of triangular pulse, the SNR would be further improved, better than that of rectangular pulses. According to the experimental setup, the interference of pulses from ${\rm{R}}_{{1}}$ and ${\rm{R}}_{{2}}$ formed the second triangular pulse, denoted as position2. The peaks of position2 from each sweeping trace were extracted to demodulate VPD.

Fig. 5.

(a) Output intensities of three arms. (b) Output intensities of three arms after matched filtering.

With the parameters obtained from pre-calibration, we could normalize the extracted data as shown in Fig. 6. Observations of normalized data from three arms revealed that periodical signals were of the same frequency, with fixed phase differences between each other. Due to the non-monotone of cosine function, the phases of a single arm data were folded, which could only reconstruct the VPD with low reproduction quality.

Fig. 6.

Normalized intensities of three arms at the position2.

Then the correlations between normalized results of three arms and look-up table were carried out. Fig. 7(a) was the waterfall form of Fig. 6. In Fig. 7(b), each column contained an integrated period of cosine function corresponding to (8), which had a phase difference of 2π/3 with each other. As shown in Fig. 7(c), the demodulated VPD changed as a cosine wave wrapped into the range of (−π, π ), which was similar to the PZT stretching signal applied. After phase unwrapping, the VPD was processed as continuous signal, and high-pass filtering was implemented to eliminate low frequency noise. The results were demonstrated in Fig. 8. The trace in Fig. 8(a) was the raw data of phase variation, presenting as a cosine wave biased with low frequency drifting. The offset drifting should be induced by LFD as we explained in (5). The trace in Fig. 8(b) was the filtering result of the raw data. The cut-off frequency of the high-pass filter applied was 10 Hz. According to (4) and the parameters used in the experiment, the measured sensitivity of ΔL was 84.5 nm/rad, denoted as S. Considering the stretched length of PZT was 10 m, the dynamic strain sensitivity of the experiment was 8.45 nϵ/rad (S divided by 10 m). The red one was a pure cosine wave consistent with the PZT stretching signal applied. The peak-to-peak value of the VPD was about 4.24 rad, Therefore, the amplitude of the applied dynamic strain should be 35.83 nϵ.

Fig. 7.

(a) Waterfall plot of normalized intensities of three arms at position2. (b) Waterfall plot of look-up table. (c) Time response of VPD without unwrapping algorithm.

Fig. 8.

(a) Time response of unwrapped VPD at position2. (b) Time response of unwrapped VPD after high-pass filtering at position2.

As shown in Fig. 5(b), although the peaks at position2 and position3 both fluctuated, the origins of fluctuations were different. To certify it, the VPD at position3 was compared with that at position2. Fig. 9 shows the power spectrum of unwrapped VPD without high-pass filtering at position2 and position3 obtained by fast Fourier transform (FFT), whose vertical coordinate was logarithmic calculated (The solid line wave was the spectrum of the VPD at position2, and the dot line wave was the one at position3). There was a clear peak at 100 Hz on the solid line wave and the SNR was about 61.83 dB compared with the far end white noise floor. The sensitivity of the fiber length variation induced by strain change for the proposed system was calculated to be ${\rm{117\,pm/ (Hz)}}^{1/ 2}$ by $S\,^{\ast} (S_{n}/ B)^{1/ 2}$, where $S_{n}$ was the sum of noise power spectrum density and B was the bandwidth of observation. The dot line wave was exactly similar to the solid one except for these regions around the 100 Hz fundamental wave and its higher order harmonics. It means that the vibration applied between ${\rm{R}}_{{1}}$ and ${\rm{R}}_{{2}}$ would not influence the fiber between ${\rm{R}}_{{2}}$ and ${\rm{R}}_{{3}}$, confirming that our system has the ability of multi-points detecting. Measuring the power spectrum of cosine signals applied on the PZT, the power differences between the higher order harmonics and 100 Hz fundamental wave were similar. So the higher order harmonics was induced by the PZT drivers, rather than the process of phase demodulation. At low frequency band, the power intensity of both spectrums raise up with the same tendency. According to the discussion on Fig. 8(a), we deduce that these similar spectrum components at lower frequency band were mainly caused by LFD, which was the origin of fluctuation at position3 in Fig. 5.

Fig. 9.

Frequency responses of VPD without high-pass filtering at position2 and position3 (the third triangular pulse in Fig. 5(b)). SNR is calculated as Ps-Pn, where Ps is the logarithmic power of the signal, and Pn is the mean logarithmic power of the remote noise floor.

To verify the linear response of the proposed system, the frequency of cosine signal applied on PZT was still fixed at 100 Hz, but the voltage amplitude was changed from 4 V to 20 V. Fig. 10(a) exhibited the dynamic strain of different magnitudes at the position2 after signal conditioning. Measured strain waves remained the shape of cosine wave without distortion as the stretching of PZT increased. In Fig. 10(b), the blue points were the amplitudes of different strains and the red dash line was the fitting line of the amplitudes. The R-square of the fitting line was 0.9986, which confirmed a high level of linearity.

Fig. 10.

(a) Detected dynamic strains of different voltages at position2. (b) Amplitude of dynamic strain V.S. different PZT voltages at 100Hz and its fitting line.

Furthermore, to investigate the measurable frequency range of the proposed system, we tuned the tone of the cosine signal applied on the PZT while its amplitude was fixed at 13 V. The tested frequencies were 50 Hz, 100 H, 500 Hz, 1000 Hz and 2075 Hz. The results after high-pass filtering were shown in Fig. 11 . Five peaks were 50 Hz, 100 H, 500 Hz, 1000 Hz and 2075 Hz with the SNRs of 57.29 dB, 65.65 dB, 56.24 dB, 60.27 dB, and 59.35 dB, respectively. Dynamic strain measurements with high SNR have been obtained over a wide frequency range, which was a significant improvement compared with the results reported by previous literatures [7], [12], [17].

Fig. 11.

Frequency responses of detected dynamic strain with different frequencies at position2.

In our system, since the dynamic range of APD could not cover both RBS light and UWFBG array reflected lights, BPD was utilized to identify and locate the accurate position of vibration. If we could fabricate UWFBG array with much lower reflectivity, the complexity and the expense of the system would be further reduced since single APD detector would be enough to cover both the UWFBG reflections and RBS signals. The frequency resolution and repetition rate of current demonstration were limited by the performance of the oscilloscope. As a replacement, an acquisition card with FPGA or DSP could realize real-time phase demodulation.

It is worth to discuss the ability of detecting multiple vibrations between two UWFBGs. It is true that for the vibrations with same frequency, out system cannot identify the amplitude of each individual vibration between two UWFBGs. However, such situations are extremely rare for in-field applications. As long as the vibration events are of different frequencies, they could still be roughly identified by the conventional Φ-OTDR function in our system and the amplitude of each individual vibration can then be distinguished by filtering method.

Another fact need to be emphasized is that although the phase noise $\varphi _{LFD}(t)$ generated by LFD can be easily eliminated by high-pass filter, it would influence the ability of detecting low frequency dynamic strain for the proposed system. Meanwhile, the similar spectrum components at lower frequency band in Fig. 9 indicated that the impacts of LFD on different positions were approximately consistent. Supposing there exists one position that is isolated from external disturbance, its VPD could then be used to eliminate the low frequency phase noise $\varphi _{LFD}(t)$ of all the other UWFBG pairs along the sensing fiber. More experiments will be carried out to verify the feasibility of light source frequency compensation in the future.

SECTION 5. Conclusion

In this paper, a high performance DOFS based on Φ-OTDR for dynamic strain measurement has been demonstrated. In the newly designed system, vibration event is identified and located by the Φ-OTDR scheme while an unbalanced 3 × 3 coupler structure with table-look-up scheme is introduced to demodulate the VPD between adjacent UWFBGs. The experimental results show that the proposed system is capable of reconstructing the vibration with a linear intensity response of R² = 0.9986 and a fiber length variation sensitivity of 117 pm/(Hz)^1/2 . Meanwhile, a wide frequency response band from 50 Hz to 2075 Hz is achieved with high SNR above 56 dB. The proposed system offers a versatile new option for dynamic strain measurement, which extends the potential application realm of the DOFS technologies.