Multiple vibrations measurement using phase-sensitive OTDR merged with Mach-Zehnder interferometer based on frequency division multiplexing

Haijun He; Li-Yang Shao; Bin Luo; Zonglei Li; Xihua Zou; Zhiyong Zhang; Wei Pan; Lianshan Yan

doi:10.1364/OE.24.004842

1. Introduction

Distributed optical fiber sensing (DOFS) technology attracts wide attention due to its capability of long-distance monitoring. At the beginning the studies on DOFS focused on the static measurand such as temperature and static strain [1,2 ]. But in the health monitoring of large-scale structures, not only the location information but also the frequency information of the vibration is necessary, such as leakage of pipelines, vibration of engines, and crack of bridges.

In general, there are mainly two typical sensors for dynamic measurement in DOFS. One is optical interferometer sensors, and the other is optical time domain reflectometry based on backscattering. The interferometer sensors include Mach-Zehnder interferometer (MZI), Sagnac interferometer and Michelson interferometer [3–5 ]. Among them, the maximum frequency response reaches up to hundreds of kHz or even to tens of MHz, which is mainly restricted by the sampling rate of data acquisition device. However, they are not capable to determine the position of vibration, because the CW probe light does not carry location information. To locate the vibration, a variety of configurations integrating two interferometers were proposed, including Michelson merged with a Sagnac interferometer [6], dual Mach-Zehnder interferometers [7], and variable-loop Sagnac interferometer [8]. Generally, the spatial resolution of these hybrid-interferometers is only tens of meters because of the change of polarization state and correlated noise, which is not enough to locate the position of intrusion precisely.

In another sensing mechanism of DOFS, the backscattering of optical pulses is utilized to realize the dynamic measurement. It can achieve a satisfied spatial resolution, which is mainly determined by the optical pulse width. Brillouin-OTDR has been proposed to obtain the location and frequency of vibration with the spatial resolution of 3m and the detectable frequency of 98 Hz [9]. Then a polarization-OTDR scheme based on spectrum analysis has improved the frequency response up to 5 kHz [10]. However, only the first vibration point (first from the light source) can be discerned effectively based on polarization-OTDR. With the capability of telling the type and exact position of multiple intrusions simultaneously, the phase-sensitive optical time domain reflectometry (Ф-OTDR) has attracted much attention since its invention [11]. 5-m spatial resolution and 2.25-kHz frequency response has been reported in [12]. Unfortunately, in every OTDR systems, the longer sensing distance gives rise to the lower detectable frequency [13]. This tradeoff between the sensing distance and the detectable frequency limits the field applications such as crack of civil structures and leakage of high pressure gas/water pipelines of long distance.

To enhance the frequency response of Ф-OTDR system, a scheme integrating Ф-OTDR system and MZI structure was demonstrated [14]. The maximum detectable frequency reaches up to 3 MHz, but the increase in frequency response deteriorates the signal to noise ratio (SNR). After that, another scheme based on time-difference pulses was put forward [15]. But it is complex to control the timing sequence and process the data. Although the above solutions can locate the positions of multiple vibrations, there is a dead zone in detectable frequency range and they cannot tell the frequency corresponding to each vibration. Then several alternative Ф-OTDR schemes utilizing multiple-frequency pulses have been demonstrated [16,17 ], which increase the sample rate in one cycle and realize multiple vibrations measurement. However, the cost increases rapidly since more modulators are necessary in the system.

In this work, we propose a modified structure combining Ф-OTDR and MZI based on frequency division multiplexing (FDM), which benefits the advantages of both structures. The two different frequency signals in Ф-OTDR and MZI structure can be easily separated by passing through filters with different pass-band after being detected by the photo detector. The vibration frequency is obtained by demodulating the interference signal obtained by MZI structure, and the vibration position is located by the Ф-OTDR system. With well control of the power ratio between local light and the CW probe light, high-frequency vibration can be detected with satisfying SNR. The spatial resolution of 10m over 3km sensing fiber and the maximum frequency response of 40 kHz (restricted by the vibration actuator) have been realized in the experiment. More importantly, there is no dead zone in the detectable frequency range.

According to the sampling theory [18], the real and fake frequency information measured by MZI and Ф-OTDR structure has a certain mathematical relation (explained in section 2). Besides, Ф-OTDR structure can locate the position of multiple vibrations precisely. Therefore, by mapping the real frequencies to the vibration points, multiple vibrations with high frequency will be measured exactly. In the experiment, two vibrations with frequency of 23 kHz and 40 kHz have been adopted to prove the concept.

2. Theory for frequency mapping with over/under-sampling

The principle for determining the frequency of multiple vibrations at different positions is to find the relation between the real and displayed frequency spectrum measured in over-sampling and under-sampling, respectively.

According to the explanation in [18], the essential steps of sampling theory are shown in Fig. 1 . The red line in Fig. 1(a) represents the target signal X_a(t). Assuming the bandwidth of a band-limited signal is f₀, the Fourier transform of the X_a(t) is illustrated in Fig. 1(b). They are described as.

Fig. 1 The evolution of sampling theorem. (a) The time domain of the band-limited signal and (b) the frequency spectrum with band width of f₀; (c) The time domain signal of the sampled function and (d) the frequency spectrum with repetition of f_s; (e) and (f) the time domain signal and the frequency spectrum of the obtained signal, respectively.

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X_{a} (t) \to X_{a} (f)

X_a(t) and X_a(f) are the time domain signal and the corresponding frequency spectrum calculated by the Fourier transform, respectively.

As shown in Fig. 1(c), the unit impulse sequence function P_δ(t) is used to sample the target signal. Its corresponding frequency domain P_δ(f) is illustrated in Fig. 1(d). They can be described as.

P_{δ} (t) = \sum_{n = - \infty}^{\infty} δ (t - n T) \to P_{δ} (f) = \frac{1}{T} \sum_{k = - \infty}^{\infty} δ (f - k f_{s})

where n and k belong to the set of integers, f_s equals to 1/T.

The sampling is performed in time domain by multiplying the function X_a(t) by P_δ(t) to yield the function S(t). The obtained signal S(t) and the corresponding frequency spectrum S(f) are illustrated in Figs. 1(e) and 1(f), respectively. As shown in Fig. 1, the frequency spectrum S(f) is the shift of the X_a(f) with the repetition of f_s. All of them can be expressed by.

S (t) = \sum_{n = - \infty}^{\infty} X_{a} (t) δ (t - n t) \to S (f) = \frac{1}{2 π \cdot T} \sum_{k = - \infty}^{\infty} X_{a} (j f - j k f_{s}) k \in z

As all known, these repetitions will overlap if the sample rate is lower than the Nyquist rate of 2f₀ (called by under-sampling). Moreover, the frequency spectrum calculated by the Fourier transform (FFT or DFT) only shows the frequency range from -f_s/2 to f_s/2. Meanwhile, the frequency with range from -f_s/2 to 0 and range from 0 to f_s/2 is about the Y axial symmetry. Thus, only the frequency range from 0 to f_s/2 is useful to obtain the frequency information.

The high frequency in the spectrum moves to the range from -f_s/2 to f_s/2 with the repetition kf_s, where k is an integer. For the under-sampling, although the frequency beyond the f_s/2 cannot be displayed as its real value, there is a certain mathematical relation between the real and the displayed frequency. Generally, the vibration frequency is a band-limited signal with a narrow bandwidth, which is shown in Fig. 2(a) . Its frequency spectrum will move to the range from -f_s/2 to f_s/2 when it is sampled by a unit impulse sequence function. And the yellow portion is the region we concern. If the frequency within the range from kf_s-f_s/2 to kf_s or kf_s to kf_s + f_s/2, the frequency spectrum does not overlap, which are illustrated in Figs. 2(b) and 2(c), respectively. As shown in Fig. 2(d), the frequency spectrum will overlap if the signals with frequency range from kf_s-f₁ to kf_s + f₂. Thus, the amplitude corresponding to the frequency in aliasing part becomes the summation of the amplitude of aliasing frequencies, as illustrated in Fig. 2(e). Similarly, Fig. 2(f) shows the frequency spectrum when the frequency range of the signal is from kf_s-f_s/2-f₁ to kf_s-f_s/2 + f₂.

Fig. 2 The evolution of under-sampling. (a) The frequency spectrum of the band-limited signal X_a(f) with a narrow bandwidth; (b) the frequency spectrum with range from kf_s-f_s/2 to kf_s; (c) the frequency spectrum with range from kf_s to kf_s + f_s/2;. (d) the evolution of the frequency spectrum with range from kf_s-f₁ to kf_s + f₂ when the signal is sampled by an unit impulse function; (e) the frequency spectrum with range from kf_s-f₁ to kf_s + f₂; (e) the frequency spectrum with range from kf_s + f_s/2-f₁ to kf_s + f_s/2 + f₂.

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According to the sampling theorem, the mathematical relation between the real and the displayed frequency can be expressed by.

f_{d i s p l a y} = | f_{r e a l} - k \cdot f_{s} | (k \in z, | f_{r e a l} - k \cdot f_{s} | < f_{s} / 2)

where f_real is the real frequency and f_display is the frequency displayed in the spectrum correspondingly. k is an integer, which makes f_real move to the frequency range from –f_s/2 to f_s/2.

Meanwhile, multiple real frequencies are mapped to one displayed frequency because of aliasing. Thus, the amplitude corresponding to the displayed frequency equals to the sum of those real frequencies. It can be rewritten as

A_{f_{d i s p l a y}} = {\sum A}_{f_{r e a l_d i s p l a y}}

where A_fdisplay is the amplitude of the displayed frequency in the spectrum, A_{freal_display} is the amplitude of the real frequency correspondingly.

In order to obtain the real frequency spectrum, over-sampling is used to sample the target signal generally. However, the sample rate in some systems is restricted less than the Nyquist sample rate, where the frequency information cannot be detected precisely. But there is a certain relation between the real and the displayed frequency spectrum. To verify this relation, the over-sampling and under-sampling cases are simulated by software (Matlab) and the results are shown in Fig. 3 . In the over-sampling case, all the results are simulated with the sample rate of 800 MS/s and the highest frequency response reaches up to 400 MHz, which are shown in Figs. 3(a), 3(c), and 3(e). Simultaneously, this target signal is sampled with sample rate of 100 MS/s and the detectable frequency range is from DC to 50 MHz, which are illustrated in Figs. 3(b), 3(d), and 3(f). A target signal with a single frequency is sampled with the above sample rates and the frequency spectrum with the peak of 320 MHz and 20 MHz are shown in Figs. 3(a) and 3(b), respectively. That means the frequency of the target signal is moved to the frequency range from DC to 50 MHz. After that, a band-limited signal with center frequency of 285 MHz is simulated to verify the description in Fig. 2. The frequency spectrum of the target signal is shown in Fig. 3(c). As illustrated in Fig. 3(d), the displayed frequency spectrum without overlap is the results moving the real one according to the repetition of 100*k MHz, where k is an integer. The real frequency spectrum and the aliasing results are shown in Figs. 3(e) and 3(f), respectively. It is obvious that the amplitude of displayed frequency in Fig. 3(f) is the summation of the corresponding frequencies (illustrated in Fig. 3(e)). Evidently, all the simulation results satisfy the relation expressed in Eq. (4) and Eq. (5).

Fig. 3 Simulated results in over-sampling and under-sampling. (a) The real and (b) the displayed frequency spectrum with a single peak of 320 MHz and 20 MHz, respectively; (c) the real frequency spectrum of band-limited signal with center frequency of 285 MHz; (d) the displayed frequency spectrum in under-sampling, which corresponds to (c); (e) the real frequency spectrum and (f) the aliasing one.

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Although the MZI structure can obtain the real frequency spectrum for the high-frequency vibration, it does not carry the location information. When multiple vibrations occur simultaneously, there are multiple peaks in the frequency spectrum, which cannot be distinguished. Fortunately, the corresponding frequency spectrum at the vibration position is obtained with under-sampling rate by the Ф-OTDR system. Therefore, by mapping the displayed frequency spectrum in under-sampling to the real one, the position and high frequency of the multiple vibrations can be measured accurately.

3. Experimental setup

Figure 4 shows the setup for the proposed system integrating Ф-OTDR with MZI based on the FDM. A DFB laser with narrow linewidth of ~100 kHz is used as the light source, which generates CW light with center wavelength of 1550.12 nm and the output peak power is 100 mw. The laser is then divided into three parts through a fiber coupler1 (0.1:90:9.9). The first part is a CW light where its frequency is f, acting as the probe signal in MZI structure. The second part is modulated into narrow pulse (100 ns) by an acoustic-optic modulator (AOM) with frequency drift of 200 MHz. After that, the optical pulses are injected into the sensing fiber from port1 of circulator with repetition rate of 25 kHz. The backscattering light will be collected through the port3. The last part (CW light) is used as reference light, acting as the local oscillator in the Ф-OTDR structure and forming the balanced MZI structure with the CW probe light as well. To form the balanced MZI, the length of the reference fiber must be equal to the sensing fiber. The Rayleigh backscattering light (with frequency of f + 200MHz) and the CW probe light (with frequency of f) will beat with the reference light when they fall on the balanced photodetector (BPD), there are two different frequency signals in the output of the BPD. Then, it is divided to two branches by a 3dB electrical power divider after amplifying by a low noise amplifier (LNA). The upper branch is filtered by a low-pass filter (LPF) with cutoff frequency of 10MHz. The signal in lower branch passes through a band-pass filter (BPF), where frequency response range is from 150MHz to 250MHz. At last, these signals will be acquired by a two channel oscilloscope whose highest sample rate is 2.5 GS/s. The interference signal sampled in upper branch is calculated with fast Fourier transform (FFT) to obtain the vibration frequency spectrum. And the Ф-OTDR signal in lower branch is processed by the self-mixing demodulation method.

Fig. 4 Experimental setup of phase-sensitive OTDR merged MZI system. NLL: narrow linewidth laser; AOM: acoustic-optic modulator; AFG: arbitrary function generator; PC: polarization controller; FUT: fiber under test; BPD: balanced photo detector; LNA: low noise amplifier; BPF: bandpass filter; LPF: lowpass filter; OSC: oscilloscope.

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An optical pulse is injected into sensing fiber from the port1 of the circulator. When the pulse travels in fiber, the backscattered signal E_R(t)expi(2π(f_c + ∆f)t + φ(t)) returns to the port3 and interferes with CW reference light E_L(t)expi(2πf_ct) at coupler2. Then it is received by a BPD, and the output of the BPD can be expressed by.

I (t) \propto E_{R} {(t)}^{2} + E_{L O} {(t)}^{2} + 2 E_{R} (t) E_{L O} (t) \cos θ_{R L} \cos (2 π Δ f t + φ (t))

where θ_RL and φ(t) are the relative polarization angle and phase between backscattered light and reference light, respectively. f_c is the center frequency of the laser. ∆f is the drift frequency introduced by AOM, which is 200 MHz in this experiment. E_R(t) and E_Lo(t) are the amplitudes of backscattering light and CW reference light, respectively.

Meanwhile, the interference results from CW probe light E_M(t)expi(2πf_ct + φ(t)) and reference light can be described as.

I_{M} (t) \propto E_{M} {(t)}^{2} + E_{L O} {(t)}^{2} + 2 E_{M} (t) E_{L O} (t) \cos θ_{M L} \cos φ (t)

where θ_ML is the relative polarization angle between the CW probe light and reference light, E_M(t) is the amplitude of the CW probe light. According to Eq. (6) and Eq. (7), the two signals in the output of BPD can be easily distinguished by passing through filter with different pass-band.

However, signals from first part will also beat with the one from second part, and the beating result is expressed by.

I_{n o i s e} (t) \propto E_{R} {(t)}^{2} + E_{M} {(t)}^{2} + 2 E_{R} (t) E_{M} (t) \cos θ_{R M} \cos (2 π Δ f t + φ_{n o i s e} (t))

The AC component of Eq. (8) has the same frequency as the AC component of Eq. (6). The AC component of the obtained signal carries the vibration information, which is described as.

S (t) \propto 2 E_{R} (t) [E_{L O} (t) \cos θ_{R L} \cos (2 π Δ f t + φ (t)) + E_{M} (t) \cos θ_{R M} \cos (2 π Δ f t + φ_{n o i s e} (t))]

where θ_RL is relative polarization between backscattered light and reference light, θ_RM is relative polarization between backscattered light and CW probe light. Although the signal and the noise cannot be separated by passing through filter, the vibration signal can be detected with satisfying SNR if controlling the power ratio between E_Lo(t) and the E_M(t) well (such as E_Lo(t)/E_M(t) > 20 dB).

4. Experimental results and discussion

4.1 The results of single vibration

A piezoelectric transducer (PZT) with the maximum vibration frequency response of 40 kHz is used as the vibration actuator in the experiment. A single vibration is added to the position of 2.04 km of sensing fiber. One hundred consecutive traces in Ф-OTDR system were recorded by one channel of the oscilloscope. The demodulating traces and the details at the position of the vibration are shown in Figs. 5(a) and 5(b) , respectively. It is obvious that there is an intensive change at the vibration position. By subtracting the amplitude traces from the first trace and computing the relative amplitude change, the vibration point will show at 2.04 km clearly, as illustrated in Fig. 5(c). Figure 5(d) shows the spatial resolution of ~11m, which is slightly larger than the theoretical value.

Fig. 5 (a) The Ф-OTDR traces demodulate form the raw data; (b) The detail of the vibration position; (c) Superimposed differential signals of 100 traces at 2.04 km; (d) the spatial resolution of vibration detection with 100 ns modulated pulses.

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Restricted by the length (~3.1 km) of sensing fiber, pulse repetition rate of 25 kHz was implemented in this experiment. That means the detectable frequency range is from DC to 12.5 kHz. In order to measure the vibration with frequency beyond 12.5 kHz, MZI structure has been integrated to the Ф-OTDR system. As shown in Figs. 6(a), 6(c), and 6(e) , the time domain signals with vibration frequency of 20 kHz, 30 kHz and 40 kHz have been obtained, respectively. By calculating the time domain signal with the algorithm of FFT, three corresponding frequency spectrums with evident peak of 20 kHz, 30 kHz and 40 kHz are illustrated in Figs. 6(b), 6(d), and 6(f), respectively.

Fig. 6 (a) The time domain signal and (b) frequency spectrum of the vibration with the peak of 20 kHz; (c) The time domain signal and (d) frequency spectrum of the vibration with the peak of 30 kHz; (e) The time domain signal and (f) frequency spectrum of the vibration with the peak of 40 kHz.

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According to the explanation in [14] and [15], there is a dead zone with frequency range from 12.5 kHz to 25 kHz. Obviously, it has been removed since the vibration with frequency of 20 kHz has been detected in the experiment.

4.2 The results of double vibrations

The high-frequency vibration measurement has been demonstrated in previous reports [14,15 ]. The position and frequency spectrum of vibration were measured by Ф-OTDR and MZI structure, respectively. The position of two vibrations is shown in Fig. 7(a) clearly, where the two peaks are called by vibration point A and vibration point B, respectively. The frequency spectrum with peak of 23 kHz and 40 kHz is illustrated in Fig. 7(b). For the previous studies [14,15 ], where the vibration with frequency of 23 kHz occurs (the vibration point A or point B) cannot be determined since the two signals in frequency spectrum were obtained simultaneously.

Fig. 7 (a) The locating signal of two vibrations; (b) the frequency spectrum of the vibrations with the peak of 23 kHz and 40 kHz.

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According to the sampling theorem [18], although a sample rate is not enough to obtain the real vibration frequency, there is a certain mathematical relation between the obtained and the real frequency spectrum. In this experiment, the actual and displayed (fake) vibration frequency spectra are detected by MZI and Ф-OTDR structure, respectively. Besides, the displayed frequency spectrum measured by Ф-OTDR structure is obtained at the vibration location. The frequency spectrum measured by Ф-OTDR structure is obtained according to its vibration location. And its vibration frequency is only determined by the location where the vibration occurs (not affected by other position). Thus, by mapping the displayed frequency to the correct one according to the certain mathematical relation, the position and the corresponding real frequency of the multiple vibrations can be determined precisely.

Two vibrations with frequencies of 23 kHz and 40 kHz are applied to the test fiber at the position of 2.04 km and 2.76 km, respectively. Figure 8(a) shows the superimposed signals of 100 consecutive Rayleigh backscattering traces demodulating by the self-mixing method. To show the amplitude changes caused by PZT at location of 2.04 km and 2.76 km (circled in red and pink dashed lines, respectively), the zoomed in vibration positions are shown in insets of Fig. 8(a). Moreover, the vibrations at the position of 2.04 km and 2.76 km are named by the vibration point A and point B, respectively. By subtracting the amplitude traces from the first trace and computing the relative amplitude change, the double vibration points appear at 2.04 km and 2.76 km clearly, as illustrated in Fig. 8(b). In addition, the SNR of locating signal does not deteriorate with the increase of frequency response because the SNRs at the two vibration points are almost equal.

Fig. 8 (a) Superimposed signals of 100 consecutive traces with amplitude change at the position of 2.04 km and 2.76 km (the insets show the details of the vibration information); (b) Superimposed differential signals of 100 traces at 2.04 km and 2.76 km;

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The temporal signal of two vibrations measured by MZI structure is illustrated in Fig. 9(a) . The corresponding frequency spectra in Fig. 9(b) shows two evident peaks at 23 kHz and 40 kHz, which agrees well with the applied ones. The simulated results with the sample rates of 1 MS/s and 25 kS/s are shown in Figs. 9(c) and 9(d), respectively. The real frequency of 23 kHz and 40 kHz are mapped to the fake frequency of 2 kHz and 10 kHz respectively. That coincides with the Eq. (4) in section 2 perfectly. Simultaneously, as shown in Figs. 9(e) and 9(f), the frequency spectrum with two peaks of 2 kHz and 10 kHz are detected at the position of vibration point A and point B (through the OTDR traces), respectively. Obviously, the frequency values are identical with the simulation results shown in Fig. 9(d). The procedure of frequency mapping method is as followed. Firstly, calculating the displayed frequency spectrum with the real one (measured by MZI structure) according to the theory in section 2; then, comparing the fake frequency spectrum (measured by Φ-OTDR structure) with the calculated one. Only if the calculated frequency is equal to the fake one, one can confirm the real frequency occurs at the position where the fake frequency appears (in Ф–OTDR trace). The peak in Fig. 9(e) equals to the calculated frequency of 2 kHz = |25-23| kHz, and the other one in Fig. 9(f) equals to another calculated frequency of 10 kHz = |50-40| kHz. So the vibration with frequency of 23 kHz and 40 kHz occur at the position of point A and point B, respectively. All of them are in good agreement with the relation mentioned in section 2.

Fig. 9 (a) The time domain signal measurement by MZI structure; (b) the frequency spectrum of the vibrations with the peak of 23 kHz and 40 kHz; (c) and (d) the simulation results with sample rate of 1 MS/s and 25 kS/s; (e) and (f) the frequency spectrum of test point A (2 kHz) and B (10 kHz) measured by Ф-OTDR traces, respectively.

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Another two vibrations with single frequency of 29 kHz and 39 kHz have been tested at the same positions. The original interference waveform detected by MZI structure and their corresponding vibration frequencies of 29 kHz and 39 kHz are shown in Figs. 10(a) and 10(b) respectively. Figures 10(c) and 10(d) show the simulation results with sample rate of 1 MS/s and 25 kS/s, respectively. Meanwhile, the frequency spectrum with peak of 4 kHz and 11 kHz, calculated by the OTDR traces at the position of point A and point B, are shown in Figs. 10(e) and 10(f), respectively. They also satisfy the mathematical relation mentioned in section 2.

Fig. 10 (a) The time domain signal of double vibrations measurement by MZI structure; (b) the frequency spectrum of the vibrations with the peak of 29 kHz and 39 kHz; (c) and (d) the simulation results with sample rate of 1 MS/s and 25 kS/s; (e) and (f) the frequency spectrums of test point A (4 kHz) and B (11 kHz) measured by Ф-OTDR traces, respectively.

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Unfortunately, it is possible that the aliasing/displayed frequencies induced by different real frequencies appear at the same frequency point in the spectrum. That makes multiple vibrations cannot be discerned. If the frequency of signals is in range from 0-f_s/2, the Ф–OTDR system can measure them accurately. Note that, the f_s equals to the repetition of probe pulses. When the frequency of signals is in the range from f_s/2 to f_s, there is one-to-one correspondence between the real frequency spectra (f_s/2-f_s) and the fake frequency spectra (0-f_s/2), so they also can be measured precisely. For a signal with frequency beyond f_s, there are multiple frequencies mapping to a same frequency point (in the frequency range from 0 to f_s/2). And the number of mapping to the same frequency increases with the increase of vibration frequency. To completely avoid this situation in multiple vibrations measurement, this system works without mistake when the vibration frequency range is from 0 to f_s. That means this system doubles the detectable frequency range in multiple vibrations measurement compared to Ф–OTDR system. In addition, if taking good control of the relation between fiber length and the maximum response frequency, multiple vibrations with higher frequency can be measured.

Compared to previous reports [12–15 ], this system realizes multiple vibrations measurement and doubles the detectable frequency in Ф–OTDR system.

Two vibrations with band-limited frequencies have been tested by the function generator working in the sweep-frequency mode. Two signals with frequency range of 27.5-29.5 kHz and 36-38 kHz were applied at the vibration point A and point B, respectively. The test result measured by MZI structure is shown in Fig. 11(a) , where the insets show the detail of the two signals. To verify the function of this system, two similar signals with the real signals have been simulated. Note that, the simulation signal merely has the same frequency range with the obtained signal illustrated in Fig. 11(a).The results simulated with sample rate of 1 MS/s and 25 kS/s are exhibited in Figs. 11(b) and 11(c), respectively. The test results measured by Ф–OTDR structure at point A and point B are illustrated in Figs. 11(d) and 11(e), respectively. Obviously, the bands of the signal with frequency range from 36 to 38 kHz are overlapped. But the overlapped frequency can be deduced according to the Eq. (4) and Eq. (5) in section 2, and the simulation results (shown in Fig. 11(c)) proves it to be effective. Compared to the simulation results shown in Fig. 11(c), there is a little difference between experimental and simulated results. But the location and bandwidth shown in spectrum is almost same. Considering the difference between real and simulation signal, especially the outline of the two spectra, the difference is acceptable. The procedure measuring the band-limited signal is as follows, firstly, calculate the displayed frequency spectrum with the real frequency spectrum according to Eq. (4) and Eq. (5) in section 2; then, compare the calculated frequency spectrum with the fake frequency spectrums measured by Ф–OTDR structure. If the two comparative frequency spectrums are located in same position in spectrum, and an extremely similar outline is illustrated simultaneously, can determine the real frequency occurs at the position where the fake frequency appears (in Ф–OTDR trace).

Fig. 11 (a) The real frequency spectrum of two vibrations measured by MZI structure; (b) and (c) the test results simulated with sample rate of 1 MS/s and 25 kS/s, respectively; (d) and (e) the fake frequency spectrums detected by Φ-OTDR structure at the point A and point B, respectively.

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Similar to the above explanation, this system works without mistake when the maximum frequency of the signal is lower than f_s. If the frequency of a vibration signal is over f_s, the reliability of this system decreases with the increase of vibration frequency. That means there is a tradeoff between the maximum detectable frequency and the reliability when the system’s maximum detectable frequency over f_s. Certainly, in multiple vibrations measurement, this system can double the detectable frequency in Ф–OTDR system.

5. Conclusion

In this work, a cost-effective scheme integrating Φ-OTDR system with the MZI structure has been proposed to detect the multiple high-frequency vibrations. The spatial resolution of 10 m over 3 km sensing fiber and the maximum detected frequency of 40 kHz (restricted by the vibration actuator) have been realized in the experiment. Compared to previous investigations, the SNR of locating signal does not deteriorate with the increase of the maximum detectable frequency. Besides, it is simple to control the timing sequence and process the data. And most importantly, the dead zone in the detectable frequency range has been eliminated in this system.

According to sampling theory, there is a certain mathematical relation between the displayed and the real vibration frequency spectrum. The relation is utilized to realize the multiple high-frequency vibration measurement in DOFS. Mapping the fake frequency to the real high frequency, multiple high-frequency vibrations can be measured exactly. The position and corresponding frequency spectrum of two vibrations have been measured precisely in the experiment.

Acknowledgments

The research is supported in part by the International Science and Technology Cooperation Program of China (2014DFA11170), the National Natural Science Foundation of China (NSFC) (No. 61475128), the Key Grant Project of Chinese Ministry of Education (No.313049) and the Fundamental Research Fund for the Central Universities (2682014RC22).

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Multiple vibrations measurement using phase-sensitive OTDR merged with Mach-Zehnder interferometer based on frequency division multiplexing

Abstract

1. Introduction

2. Theory for frequency mapping with over/under-sampling

3. Experimental setup

4. Experimental results and discussion

4.1 The results of single vibration

4.2 The results of double vibrations

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (11)

Equations (9)

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