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We demonstrate a distributed sensing network with 500 identical ultra-weak fiber Bragg gratings (uwFBGs) in an equal separation of 2m using balanced Michelson interferometer of the phase sensitive optical time domain reflectometry (φ-OTDR) for acoustic measurement. Phase, amplitude, frequency response and location information can be directly obtained at the same time by using the passive 3 × 3 coupler demodulation. Lab experiments on detecting sound waves in water tank are carried out. The results show that this system can well demodulate distributed acoustic signal with the pressure detection limit of 0.122Pa and achieve an acoustic phase sensitivity of around −158dB (re rad/μPa) with a relatively flat frequency response between 450Hz to 600Hz.
© 2015 Optical Society of America
1. Introduction
Fiber sensors have attracted considerable attention in recent years, particularly in acoustic measurement [1–3 ]. They have developed from single- or multi-point measurement to distributed measurement. For single- or multi-point measurement, large-scale fiber Bragg grating (FBG) network has attractive prospects for major engineer monitoring because of its low cost and high multiplexing capability [4,5 ]. Wavelength-division multiplexing (WDM) and time-division multiplexing (TDM) are two major multiplexing techniques for the expansion of the sensor network capacity [6,7 ]. For the WDM method, the maximum number of FBGs is restricted by the ratio of the source spectral width over the dynamic wavelength range of an individual FBG sensor. The TDM method utilizes different time delays between reflected pulses to distinguish sensors even with an identical wavelength and to relieve the spectral bandwidth issue. However, the multiplexing capacity is seriously limited by signal crosstalk among these normal FBGs [8]. The main challenge of large-scale FBG network is to massively multiplex FBG sensors and to quickly interrogate each FBG in the array. And due to the mass redundant data from no grating zones, the system has to adopt a low speed interrogation for precision [9,10 ].
For distributed measurement, distributed fiber sensors offer the capability of measuring at thousands of points simultaneously, using a simple, unmodified optical fiber as the sensing element. A promising technique is phase sensitive optical time domain reflectometry (φ-OTDR) of Rayleigh backscattering by using a narrow line-width laser [11,12 ]. Brillouin based long-range strain sensors have been researched [13]. Another hybrid interferometer-backscattering system is demonstrated [14]. But the major limitation of those distributed sensors above is that they are incapable of determining the full vector acoustic field, namely the amplitude, frequency and phase, of the incident signal, which is a necessity for seismic imaging.
Recently, the technique of on-line writing of ultra-weak fiber Bragg grating (uwFBG) arrays during drawing ordinary single mode fibers (SMF) has been realized [15]. This array has no fusion loss and therefore shows high mechanical stability, which opens new possibility for further application of large-scale FBG networks. In this paper, we demonstrate a distributed sensing network with 500 identical uwFBGs in an equal separation of 2m using balanced Michelson interferometer of φ-OTDR for distributed acoustic measurement. Phase, amplitude, frequency response and location information can be directly obtained at the same time by using the passive 3 × 3 coupler demodulation. The experimental results show that our system can well demodulate the acoustic signal with linear intensity response and has a relatively flat frequency response. Our system offers a versatile new tool for acoustic sensing and imaging, such as massive acoustic camera/telescope, which can be used for surface, seabed and downhole measurements.
2. OTDR-interferometry principle
To get distributed information along an identical uwFBG fiber, the reflection waves from each identical uwFBG are detected. Normally, φ-OTDR technique, where the system is probed with narrow coherent light pulses with direct detection [16,17 ], is used. Here we add a balanced Michelson interferometer to the output of the φ-OTDR. Figure 1 shows the schematic configuration of the φ-OTDR-interferometer of the uwFBGs. The reflection signals are injected into a classical balanced Michelson interferometer comprised of a coupler and two Faraday rotation mirrors (FRM). The interference signal at every certain time contains not only the information of the corresponding positions in the fiber but also the phase changes within the several adjacent identical uwFBGs for demodulation.
To have a better and direct understanding, we use the one-dimensional impulse-response model of the multiple reflections to explain the system theoretically [18]. When we launch a coherent light pulse with a pulse width w and an optical frequency f into a fiber at t = 0, we obtain a reflection wave Er(t) at the input end of the fiber which is given by:
where em and τm are the amplitude and the delay of the mth uwFBG, N is the total number of uwFBG, c is the velocity of light in a vacuum, nf is the refractive index of the fiber, and rect[(t-τm)/w] = 1 when 0≤[(t-τm)/w]≤1, and is zero otherwise, indicating which uwFBGs are reflecting at a certain t moment. The delay τm corresponds to the distance lm( = ml 0, l 0 represents the distance between two nearest identical uwFBGs and obeys l 0≤cw/2nf so that the interference could happen) from the input end to the mth uwFBG through the relation τm = 2nflm/c. The term rect[(t-τm)/w] accounts for the change in the reflecting volume seen as the pulse propagates.Therefore the interference power I(t) associated with the reflection wave is given by:
where ϕmn = 4πfnf (ln-lm)/c.The quantity ϕmn denotes the phase difference between the reflection waves from the mth and nth uwFBGs. The interference term I(t) is a function of f, w, nf, and ϕmn. Moreover, ϕmn includes the acoustic responses between uwFBGs. When acoustic pressure affects the fiber, ϕmn will change via the elasto-optic effect as well as mechanical elastic effect of solid materials, and hence I(t) changes with them. Using this feature, we can measure the distributed acoustic responses by analyzing the measured interference power.
3. 3 × 3 demodulation method
For signal processing and demodulation part, here we use the passive 3 × 3 demodulation method [19], which consists of a simple balanced Michelson interferometer (Fig. 2 ) made by a circulator, a 3 × 3 coupler and two FRMs. This method can directly give the phase changes caused by the acoustic signal. Since no carrier wave is included in the modulating process, the accuracy requirement for the laser source is lowered. In general, its working mechanism is to produce modulated signals with certain phase shift for different arms. The demodulation principle is much simpler, and the burden carried by the demodulation calculation is reduced.
Theoretically, there is a 120° phase shift between two adjacent arms [19]. Accordingly, the outputs of the three arms can be expressed as:
where ϕ(t) = ϕs + ϕn + ϕ0. ϕs, ϕn and ϕ0 are respectively the signal phase to be detected, the noise and the intrinsic phase of the system. For each point on the detection fiber, ϕs is obtained after the demodulation process shown in Fig. 3 . It can directly demodulate all the information from the signal detected at the same time without any Fourier transformations.4. Experimental setup and results
The experimental setup of the φ-OTDR-interferometer with identical uwFBGs is shown in Fig. 4(a) . Five hundred identical uwFBGs, whose length of each is less than 1cm, are distinguished with an equal separation of 2m using the on-line writing technique mentioned [15] so that the total length of the identical uwFBG fiber is about 1km. The center wavelength of each identical uwFBG is 1540.05nm with the bandwidth of 0.18nm and the reflectivity is ~0.08%.
Fig. 4 (a) Experimental setup for φ-OTDR-interferometer with identical uwFBGs, DFB-FL: distributed feedback fiber laser; AOM: acoustic-optic modulator; F: optical fiber grating filter; FRM: Faraday rotation mirror; PD1~3: high-sensitive photodetectors. (b) Schematic diagram of underwater distributed acoustic testing experiment.
The light source is a narrow linewidth distributed feedback fiber laser (DFB-FL) with maximum output power of 50mW and linewidth of 5kHz. This 1540.05nm continuous wave light is injected into an acoustic-optic modulator (AOM) to generate the input pulse serial whose width is 50ns (which obeys the principle cw/2nf>2m) and the repetition rate is fixed at 20kHz. The time interval among the pulses should be larger than the round trip time that the pulses travel in the fiber to keep only one pulse inside the fiber. For the 20kHz repetition rate, the maximum fiber length is 5km theoretically which is determined by L≤c/2nf.
A filter (F) with very narrow transmission bandwidth from a π phase-shifted fiber grating is used to filter the possible noise of the pulses after AOM and then the filtered pulses are launched into the identical wFBG fiber by a circulator. The reflections of the uwFBGs is filtered (F) again to obtain better performance and then injected into a balanced Michelson interferometer which consists of a circulator (C), a 3 × 3 coupler and two FRMs. The final interference signals outputting from 3 × 3 coupler are collected by three highly sensitive photodetector (PD1~3) and then the signal processing scheme is accomplished by a software program. In our experiment, 2000 periods for scanning are recorded by a high-speed oscilloscope with 100MHz sampling rate and total data acquisition time is 0.1s.
Here we use a water tank system to test the demodulation capability of our φ-OTDR-interferometer network with identical uwFBGs [Fig. 4(b)]. Two underwater speakers are placed at the bottom of the tank and driven by a function generator. The identical uwFBG fiber attached to the demodulation instrument is placed above the speakers by 5cm along the water tank so that the sound wave produced by the speakers can be directly transmitted to the fiber. A commercial piezoelectric hydrophone with the response factor of 300Pa/V is also placed close to the fiber directly above underwater speaker 1 to measure the acoustic pressure amplitude. The function generator is used to drive the two underwater speakers with two separate sinusoidal signals. They have the same frequency of 550Hz, but different amplitudes of 1V and 2V, respectively. The global demodulation result of 1km fiber is given in Fig. 5(a) . It can be clearly seen that there exist two phase changes located within the green frame in Fig. 5(a) between 250m to 350m. Figure 5(b) shows the 3D diagram of the demodulated phase change between 250m and 350m. Our system locates two demodulated phase change peaks at 273m with the width of about 4m and 327m with the width of about 5m, respectively. First we compare the demodulated acoustic data acquired by our system with those by the piezoelectric hydrophone for the 1V signal at underwater speaker 1. The results from spectral analysis via fast Fourier transform (FFT) are shown in Fig. 5(c). Here for wave shape details we just show the time response data from 0s to 0.03s. The demodulated 1V signal given by our system fits well with the piezoelectric hydrophone one, which has a good sinusoidal shape with the amplitude of about −8.025dB [ = 20log(Asignal), 0.397rad] on average. But the demodulated signal our system gives contains the second harmonic peak at 1100Hz mostly due to our asymmetry splitting ratio of the 3 × 3 coupler by numerical simulations. Then we extract time domain signals at both peaks in Fig. 5(b) and give their instantaneous frequencies from spectral analyses, as shown in Fig. 5(d). The demodulated 2V signal at 327m also has a sinusoidal shape and the amplitude is about −1.783dB (0.814rad) on average. The demodulated amplitude ratio, A2V/A1V( = 0.814/0.397≈2.05), nearly equals to the ratio of generating signal amplitudes, 2. The background noise floor, which is determined from the data at 273m when the function generator is off, is about −56dB on average – indicating that the phase detection limit is 1.585 × 10−3rad. The result indicates that our φ-OTDR-interferometer network with identical uwFBGs can properly demodulate the instantaneous frequency and spectral property of distributed sound signals via phase changes.
Fig. 5 (a) Demodulated scalogram of the 550Hz acoustic signal with an amplitude of 1V along the total 1km fiber. (b) 3D demodulated phase changing diagram between 250m and 350m [red area in Fig. 5(a)]. (c) Time and frequency responses of our system at 273m and the piezoelectric hydrophone. (d) Time and frequency responses of the demodulation results at 273m, 327m and background.
We also use different generating voltages at 550Hz to test the demodulating accuracy of the amplitude proportions. The generating amplitudes are set from 0.5V to 4V. The demodulation results are shown in Fig. 6 . The amplitude of 4V demodulated signal A4V( = 1.664rad) is almost eight times larger than that of 0.5V demodulated signal A0.5V( = 0.211rad), indicating that our φ-OTDR-interferometer network with identical uwFBGs can well recreate the phase change of a variable acoustic signal with a good linear property. Though we only test 550Hz property, the linear demodulation of our system could cover a much wider frequency range due to the passive demodulation.
Then to prove our system can demodulate different sound waves, we set function generator to output one sinusoidal wave with the same 1V amplitude but different frequencies to underwater speaker 1. Figure 7 is the instantaneous demodulated phase changes and the spectral analysis at underwater speaker 1 with different acoustic frequencies from 450Hz to 600Hz. Here for wave shape details we also show the time response data from 0s to 0.03s. The average peak amplitude of the demodulated signals are −8.135dB (0.392rad) at 450Hz, −8.499dB (0.376rad) at 500Hz, −8.025dB (0.397rad) at 550Hz, and −8.629dB (0.371rad) at 600Hz, although the second and third harmonic peaks are existed. These results indicate that our system can also demodulate the signals at different frequencies.
Fig. 7 Time and frequency responses of the demodulated phase changes with 450Hz, 500Hz, 550Hz and 600Hz acoustic signals of 1V at underwater speaker 1.
Moreover, we use the hydrophone signal to relate the phase measurement with acoustic pressure. So the acoustic pressure amplitudes at different frequencies are measured using the piezoelectric hydrophone, and the phase-pressure sensitivity of our φ-OTDR-interferometry sensing network with identical uwFBGs is calculated. Table 1 shows the phase-pressure data and results of our system. The acoustic pressure amplitudes are all around 30Pa at all four frequencies. Then the phase-pressure sensitivities are calculate using the changed phase amplitude our system demodulated divided by the actual acoustic pressure amplitude the piezoelectric hydrophone detected, which are almost the same [S450Hz = 13.11mrad/Pa (−157.6dB, re rad/μPa), S500Hz = 12.6mrad/Pa (−158dB), S550Hz = 13.18mrad/Pa (−157.6dB), S600Hz = 12.65mrad/Pa (−157.9dB)], indicating that our identical uwFBG fiber can well demodulate the amplitude, frequency and phase of the variable acoustic signals with a relatively flat frequency response. Though the bandwidth of our experiment only covers 450Hz to 600Hz, the frequency response of our system could be much wider due to the passive demodulation. The pressure detection limit of our system is also estimated, which is around 0.122Pa (1.585 × 10−3rad divided by 13mrad/Pa) from the phase detection limit of our system.
Table 1. Experimental Data of Sensitivity at Different Frequencies
5. Further discussions
The polarization of the reflection signals of the uwFBGs may be important to our sensing network. Further experiment will be done to determine whether the polarization affects our system and, if necessary, how to eliminate the possible influence. However the polarization of the interferometer is not a critical issue and its polarization is generally stable and well maintained since it is not used as the sensing element and path length is not long. The spatial resolution of our system is determined by the pulse width w according the relation: cw/2nf. But in order to produce the interference signal, the pulse width should cover at least two nearest uwFBGs (cw/2nf>2m) so that the spatial resolution of our system has a inherent minimum value. It can be improved by smaller separation of uwFBGs and shorter pulse width. As for the cross-talk, we haven’t observed any significant cross-talk effect between our uwFBGs because of their ultra low reflectivity (~0.08%). We also build the mathematical model and determined the conditions to limit the first level cross-talk of FBG. And the simulation results indicate that the cross-talk effect can be ignored when the reflectivity of FBG is less than 0.1%.
Compared to the backscattering-type distributed sensing system like the one in [20], our identical uwFBG system has its own advantages. While both systems use one single fiber as the detection probe, the intensity of the uwFBG reflection is much stronger and more stable than that from the backscattering. Thus our system significantly relaxes the requirement on multiple amplifiers to increase the signal and filters to suppress the background noise. Although the system performance is quite modest by now, there are potential to be improved. The mapping of acoustic events, which directly gives what is happening around the detecting area, is very important. The φ-OTDR-interferometry with identical uwFBGs could be a versatile new tool for acoustic mapping and imaging with one single optical fiber used as massive acoustic camera/telescope, optical hydrophone or directional accelerometer arrays in many fields such as vertical seismic profiling and surface seismic surveys.
6. Conclusion
In this paper, we demonstrate a distributed acoustic sensing scheme network of 500 identical uwFBGs with an equal separation of 2m using φ-OTDR-interferometer technique. Phase, amplitude, frequency response and location information can be directly obtained simultaneously by using the passive 3 × 3 coupler demodulation. Experiments on detecting acoustic signals in water tank are carried out. The results show that our system can well demodulate the distributed acoustic signals with the pressure detection limit of 0.122Pa and have an acoustic phase sensitivity of around −158dB (re rad/μPa) with a relatively flat frequency response between 450Hz to 600Hz. This sensing network offers a versatile new tool for acoustic sensing and imaging which could be useful for surface, seabed and downhole seismic measurements.
Acknowledgments
This work was supported by the International Science and Technology Cooperation Program of China (2012DFA10730), Natural Science Foundation of Shandong Province (ZR2010FM039) and Science and Technology Development Project of Shandong Province (2014GGX103019).
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