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Abstract
Phase-sensitive optical time domain reflectometry (Φ-OTDR) realizes quantitative measurement of the dynamic strain employing phase demodulation. Unfortunately, it is difficult to measure the large dynamic strain with the conventional Φ-OTDR due to the restriction of the unwrapping algorithm. In this work, an approach based on two-wavelength probe is proposed and demonstrated to improve the measurable range of the dynamic strain in Φ-OTDR. By utilizing the difference between the two phases acquiring with two different lasers, the large dynamic strain can be recovered. In experiments, dynamic strains with peak values from 10.32 uɛ to 24.08 uɛ are retrieved accurately, which cannot be recovered with the conventional Φ-OTDR. Moreover, the tunable sensitivity is also demonstrated through adjusting the wavelengths of the probe. With the increment of the wavelength interval from 9.06 nm to 23.06 nm, the normalized sensitivity increases from 0.4 to 1 accordingly. That agrees well with the theoretical prediction. Foreseeably, the proposed method will extend the scope of application fields for Φ-OTDR, which requires large dynamic strain recognition.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the increase of the application, distributed optical fiber sensors for measuring dynamic strain have been intensively studied over the past few decades [1,2]. To measure the dynamic strain, several techniques have been explored, including Sagnac interferometer (SI), Mach-Zehnder interferometer (MZI), Brillouin optical time domain analysis (BOTDA), polarization optical time domain reflectometry (POTDR) and phase-sensitive optical time domain reflectometry (Φ-OTDR) [3–8]. Among them, Φ-OTDR has been demonstrated as a promising technique owing to its capability of high sensitivity, accurate localization, broadband response and quantitative measurement [9–17]. Except for the academic research, Φ-OTDR has also been widely used in many application fields such as perimeter intrusion monitoring, pipeline safety monitoring, geological prospecting and acoustic detection [18–20].
In conventional Φ-OTDR, the intensity of the Rayleigh backscattered (RBS) signal is utilized to detect the perturbance [11–15]. Although the intensity demodulation discerns the perturbance locations precisely, it cannot distinguish the types of perturbances since the signal intensity is nonlinear to the external perturbance. To implement quantitative measurements, several schemes based on the similarity demodulation of measured backscattered traces are proposed [21–25]. Among them, the wavelength scanning based scheme is more robust than the one calculating the similarity with traces along the time axis [21–23]. But unfortunately, the schemes adopting wavelength scanning just measure the low-frequency vibrations, especially for the long-distance measurement. To improve the response speed, the chirped-pulse Φ-OTDR is proposed [24]. However, this scheme requires ultra-high sampling rate (up to several tens of GHz), hence it might be only suitable for the short-distance measurement [24,25]. Except for the similarity calculation, the quantitative measurements also can be realized with the phase extraction of the backscattered signals. Different form the signal intensity, the phase difference between two adjacent locations is linearly proportional to the external disturbance [26–28]. Therefore, the phase demodulation is proposed to retrieve the disturbance and it attracts much attention in recent years. Indeed, many researches validate the effectiveness of the phase retrieval to the disturbance recovery [26–31]. But it should be noted that all validations are performed with small dynamic strain (tens to hundreds of nano strains, nɛ). Restricted by the unwrapping algorithm, the phase retrieval is invalid for the large dynamic strain (uɛ), unless sacrificing the frequency response. Generally, the dynamic strains of tens to hundreds of microstrains need to be detected in many applications. To retain the frequency response and improve the measurable range, the improvement of the pulse repetition rate employing the temporally sequenced multi-frequency source is an alternative method [14]. However, the enhancement of measurable strain range is far less than the requirement and the system complexity increases sharply. Hence, it is necessary to explore a new approach to measure the large dynamic strain in phase demodulation based Φ-OTDR.
In this work, we utilize a two-wavelength probe to improve the measurable range of the dynamic strain in Φ-OTDR. Through elaborately selecting the wavelengths of the probe, the large dynamic strain can always be retrieved. Experimental results show that 200-Hz dynamic strains with peak amplitude from 10.32 uɛ to 24.08 uɛ are measured accurately, which cannot be retrieved with the conventional Φ-OTDR. Restricted by the vibration transducer, the maximum strain is only 24.08 uɛ but it should be noticed that the larger dynamic strain can also be recovered. Benefiting from the relation between the phase change and the wavelength of the probe, the system sensitivity is tunable. With the increment of the wavelength interval, the peak-to-peak value of the phase change increases accordingly, indicating the improvement of the system sensitivity.
2. Principle
In Φ-OTDR, the phase of the Rayleigh backscattered (RBS) signal is an equivalent value, which is composited by a lot of scattering units [21,26–28]. Moreover, the difference of the adjacent phases is linearly proportional to the external disturbance, hence the exact disturbance can be retrieved with phase demodulation [27–34]. In the phase retrieval scheme, an unwrapping algorithm and differentiate operation are needed to process the demodulated phase consecutively [21,26–28]. Here, the differentiate operation is implemented between two adjacent phases of φA and φB, as illustrated in Fig. 1(a), the distance Δz between their corresponding positions of zA and zB (Δz = zB-zA) must be larger than the pulse width. The phase difference Δφ=φB-φA is expressed by
where n is the effective refractive index of the sensing fiber, λ is the wavelength of the probe light, Δz is the fiber interval between two locations of zA and zB. It can be seen that the phase difference is codetermined by n, Δz and λ. Among the three variables, n and Δz are the fiber’s properties and they vary with the external disturbance. Different from them, λ is independent from the fiber state so that the sensitivity can be adjusted through tuning the wavelength.
Fig. 1. (a) The schematic diagram of the differential operation; (b) the schematic of the unwrapping algorithm, the phase is retrieved exactly when all |Δ| are smaller than π (the upper illustration, actual phase: blue-dot line, demodulated phase: red line) otherwise it is distorted (the lower illustration).
Figure 1(b) depicts the schematic diagram of the unwrapping algorithm. Especially, only the absolute value of the phase jump between two consecutive points (|Δ|) is smaller than π, the phase can be recovered exactly with the unwrapping algorithm [27]. Otherwise, the demodulated phase is distorted. As shown in the right side of Fig. 1(b), the upper and lower illustrations are the results demodulating at the conditions of |Δ|<π (all |Δ|) and |Δ|≥π (part of |Δ|), respectively. Here, the blue-dot line and red line denote the actual phase and the demodulated phase, respectively. Obviously, the actual phase cannot be retrieved when |Δ|≥π. Considering that most of |Δ| are larger than π when large dynamic strain is applied on the sensing fiber, the conventional method does not work for the phase retrieval. Although the phase response to the external disturbance is tunable (through tuning wavelength), it is difficult to retrieve the actual value for the strong disturbance if we just adjust the wavelength of the probe light. To break this limitation and measure large dynamic strain, a modified scheme based on two-wavelength probe is proposed. Due to the probe light is consist of two different wavelengths of λ1 and λ2, two corresponding phase differences of Δφ1 and Δφ2 are acquired at the same position z, as depicted in Fig. 2(a). The modified phase difference Δφ12 is obtained with second-order difference (Δφ12=Δφ1-Δφ2, as illustrated in Fig. 2(a)) and is described as
Fig. 2. The schematic diagram. (a) the actual phase change and the actual phase difference Δφ12; (b) the demodulated results with the conventional approach and the demodulated Δφ12 with the proposed method.
Owing to (λ2-λ1)/λ1<<1, Δφ12 is much smaller than Δφ. That makes the large dynamic strain can be exactly retrieved with Δφ12 although it cannot be recovered with Δφ, as shown in Fig. 2(b). Compared with the actual phase changes (the blue and red lines in Fig. 2(a)), the conventional method cannot retrieve the large dynamic strain no matter what wavelength we choose. Different from the conventional approach, the modified phase difference (Δφ12) obtaining with the two-wavelength probe is identical to the actual value, the green lines shown in Figs. 2(a) and 2(b). Therefore, the large dynamic strain can be retrieved by adopting the proposed approach. Note that, a theoretical simulation is performed to acquire the schematic diagram depicted in Fig. 2.
According to Eq. (2) and Eq. (3), Δφ12 and (λ2-λ1)/λ1 can be tuned through changing the wavelengths of the probe. Benefiting from this property, the necessary condition of |Δ|<π can be satisfied no matter how strong of the dynamic strain in practical applications, hence the phase change (induced by the disturbance) can always be retrieved accurately. Moreover, this approach has a remarkable advantage of no frequency response loss.
3. Experimental setup
Experimental demonstration is implemented with the setup shown in Fig. 3. A tunable laser source (TLS) with linewidth of 100 kHz and a narrow linewidth laser (NLL, Koheras BasiK E15) with linewidth less than 1 kHz are employed as the light source. The output peak power and center wavelength of the NLL are 13 dBm and 1550.66 nm, respectively. In experiment, the center wavelength of TLS needs to be tuned and its peak power is fixed at 14.5 dBm. The output CW light from TLS is split into two branches through a 90:10 optical couplers (OC1). Here, the 10% branch is served as the local light to implement the heterodyne detection. Similarly, the CW light generating by NLL is also split by a 90:10 coupler (OC2). The both 90% branches are combined with a 3-dB coupler (OC3). Subsequently, the combing light is modulated into an optical pulse with an acoustic optical modulator (AOM, whose frequency shift is 200 MHz). The width and period of the probe pulse are 100 ns and 40 us, respectively. After being amplified by an erbium doped fiber amplifier (EDFA), the pulse probe light is injected into 1.7-km sensing fiber via an optical circulator (Cir). Noticed that, the coherent detection is adopted in our experiment and the power of the local light is much larger than the power of the scattered light. Hence, we do not use any optical filter considering that the amplified spontaneous emission (ASE) noise introduced by the EDFA has almost no influence on the quality of the electrical signal [11]. In order to compensate the phase drift induced by the lasers’ frequency drift, two weak reflecting points at the end of the fiber are used to acquire the reference phase [32–34]. In experiment, the fiber distance between the two reflecting points is set as 32 m. The backscattering Rayleigh light is divided into two parts through a 3-dB coupler (OC4). At the receiver end, after adjusting the state of polarization, the local light with wavelength of λ1 (blue line) and one part of the backscattering Rayleigh light are mixed in OC5. After that, the output of OC5 is converted into electrical signal at a balanced photodetector (BPD1, 200-MHz bandwidth). In the lower branch, the rest backscattering Rayleigh light is mixed with another local light (whose center wavelength is λ2, red line) and detected by BPD2. The beating signals are collected by an oscilloscope (OSC) with sample rate of 1 GS/s. Considering that the bandwidth of the BPDs, BPD1 and BPD2 extract the information carried on λ1 and λ2, respectively. At last, the phase is retrieved from the collected radio frequency (RF) signals.
Fig. 3. Experimental setup. TLS: tunable laser source; OC: optical coupler; AOM: acoustic optical modulator; AFG: arbitrary function generator; EDFA: erbium doped fiber amplifier; Cir: optical circulator; FUT: fiber under test; WRPs: weak reflecting points; NLL: narrow linewidth laser; PC: polarization controller; BPD: balanced photodetector; OSC: oscilloscope; PR: phase retrieval.
In the phase retrieval module, two demodulation methods can be utilized to acquire phase difference φ12. One of the methods retrieves φ12 with Hilbert transform and RF mixing, as depicted in Fig. 4(a). Here, S1(t) and S2(t) are the RF signals obtaining with λ1 and λ2, respectively. With this method, only φ12 is obtained and the measurable dynamic stain must be strong. Figure 4(b) shows the schematic of the other approach, the digital IQ demodulation is used to obtain φ1 and φ2 simultaneously. φ12 is calculated with subtraction operation between φ1 and φ2. In this method, the local signal SLO(t) is needed and its frequency (fLO) equals to the frequency shift of AOM. Compared to the first approach (shown in Fig. 4(a)), the second one is more complicated but it retains φ1 and φ2 except for φ12. φ1 and φ2 are the demodulation results employing the conventional methods and they are sensitive to the external disturbance. Hence, the demodulation approach shown in Fig. 4(b) can measure the small and large dynamic strains simultaneously. To reduce the computational complexity, the first method is adopted in our work.
Fig. 4. Schematic diagrams of the phase retrieval. (a) Hilbert transform and RF mixing; (b) digital IQ demodulation and phase difference.
4. Experimental results and discussion
4.1 Phase drift compensation with weak reflecting points
Generally, NLL with tiny frequency drift is necessary to realize precise measurement in Φ-OTDR. According to the operation principle, two NLLs with different center wavelengths are required in our work. However, to verify the tunable sensitivity, one of the NLLs is replaced by a TLS. Compared to NLL, TLS has wider adjustable range of the wavelength so that it demonstrates the tunability preferably. But unfortunately, TLS has much larger frequency drift (compared with NLL) and it introduces a random phase error to the measured phase difference ΔφM. To realize accurate measurement, the phase drift must be eliminated and two weak reflecting points at the end of the fiber are deployed to acquire the reference phase (ΔφR), as depicted in Fig. 3. Through subtracting ΔφR from ΔφM, the actual phase variation ΔφV induced by the dynamic strain can be achieved (ΔφV=ΔφM-ΔφR).
In this section, the center wavelengths of TLS (λ1) and NLL (λ2) are assigned as 1527.6 nm and 1550.66 nm, respectively. In experiments, we firstly verify the effectiveness of the compensation method and a vibration with frequency of 400 Hz is applied on the fiber. A cylindrical PZT acts as the vibration actuator and 3-m bare fiber is coiled over it at the location of 700 m. Since the preset distance between two reflecting points is 32 m, the same fiber interval of 32 m is adopted in the differential operation. Figure 5(a) shows the evolution of the reference phase ΔφR, which is calculated with the two reflecting points. Owing to the large frequency drift of TLS, ΔφR1 (blue line) changes significantly within 20 ms. Conversely, ΔφR2 acquiring with NLL (red line) keeps constant. Except for the slow drift, rapid fluctuation exists in ΔφR1 and ΔφR2, as shown in Fig. 5(a). To reduce the compensation error, smooth processing is executed to extract the reference phase ΔφR, the purple and green lines illustrated in Fig. 5(a). Meanwhile, the phase fluctuations are estimated through subtracting the corresponding smooth curves from ΔφR1 and ΔφR2. Due to influence of the lasers linewidth [35], the phase jitter measured with TLS (ΔφR1) is much larger than the one adopting NLL (ΔφR2), as illustrated in Fig. 5(b). The standard deviations of ΔφR1 and ΔφR2 are 0.186 and 0.014, respectively. Figure 5(c) depicts the measured phase (ΔφM) and the reference phase (ΔφR) simultaneously. Obviously, the vibration-induced phases (blue and red lines) have the same drifts as the corresponding reference phases (purple and green lines). After compensating the phase drift, the real phase variation (ΔφV) induced by the vibration is depicted in Fig. 5(d). Except for the phase offset, the same phase changes are achieved for both lasers. That proves the vibration-induced phase can be corrected with the compensation method.
Fig. 5. (a) The phase drift measured with the auxiliary reflecting points; (b) the phase jitters adopting the two different lasers; (c) vibration measurement with both lasers; (d) the compensated results.
After that, small dynamic strains (vibrations) with increasing intensities are used to calibrate the sensor response of the conventional Φ-OTDR. That acquires the relation between the applied voltage and the dynamic strain simultaneously. The amplitude of the vibration increases from 1 to 5 V (peak-to-peak value) with a step of 1 V. With the strengthening of the vibration, the peak-to-peak value of the measured phase increases for both lasers, as shown in Figs. 6(a) and 6(c). To evaluate the vibration response exactly, the corresponding frequency spectra of Figs. 6(a) and 6(c) are calculated and the results are illustrated in Figs. 6(b) and 6(d), respectively. The power at 400 Hz is extracted and great linearities are obtained for both lasers, as depicted in Fig. 6(e). Here, the slope of the response curve (fitting curve) represents the sensor sensitivity. It can be seen that the sensitivity obtaining with TLS (blue line) is slightly larger than the one achieving with NLL (red line). According to Eq. (1), the results are reasonable because of λ1<λ2. In the test results, the peak-to-peak value of the phase change is about 30.75 rad for the 5-V driving voltage, which corresponds to ∼860 nɛ.
Fig. 6. The measurement of the vibration response. (a) Time domain signals and (b) the corresponding frequency spectrums of the vibrations with different amplitudes by adopting λ1; (c) time domain signals and (d) the corresponding frequency spectrums of the vibrations with different amplitudes by adopting λ2; (e) the evolution of the peak power with the increment of the vibration amplitude.
4.2 Verification of the large dynamic strain measurement
To validate the feasibility of the large dynamic strain measurement, a violent vibration driven by a sine function is applied on the sensing fiber. The frequency and amplitude of the driving function are 200 Hz and 130 V (corresponding to a maximum strain of 22.36 uɛ), respectively. In this section, λ1 and λ2 are also assigned as 1527.6 nm and 1550.66 nm, respectively. Figure 7(a) shows the demodulation results with the conventional method and the actual vibration cannot be retrieved with single phase difference (Δφ1 or Δφ2). On the contrary, the modified phase difference Δφ12 is in consistent with the applied vibration, as illustrated in Fig. 7(b). Furthermore, the phase jitter is calculated by subtracting its smooth curve and the result (green line) is shown in Fig. 7(c). For comparison, the phase fluctuations resulting from the lasers are also computed, the blue and red lines illustrated in Fig. 7(c). The standard deviations of Δφ1, Δφ2, and Δφ12 are 0.179, 0.019 and 0.181, respectively. Hence, the phase fluctuation of Δφ12 is codetermined by the two lasers. Especially, the phase jitter of Δφ12 is mainly caused by TLS in our work. In practical applications, the wavelengths of the lasers can be predetermined so that the phase jitter can be greatly reduced by replacing TLS with a NLL. Besides, the power spectral density (PSD) of the signal in Fig. 7(b) is calculated and illustrated in Fig. 7(d). The SNR of the measured vibration is over 40 dB. The noise level is about −50 dB rad2/Hz, corresponding to 3.2×10−3 rad/√Hz.
Fig. 7. The comparison between the conventional and the proposed methods. (a) The dynamic measurement with the conventional method; (b) the measurement with the proposed method; (c) the comparison of the phase jitters; (d) the power spectral density of the vibration signal.
In addition, a frequency-chirped vibration with frequency from 0.2 kHz to 2 kHz is applied on the fiber. The voltage of the driven signal is 100 V, corresponding to 17.2 uɛ. Figure 8(a) depicts the time domain signal and the corresponding time-frequency spectrum is calculated with the short-time Fourier transform, as illustrated in Fig. 8(b). It can be seen that the frequency-chirped signal can be retrieved excellently, indicating that this approach has the capability of measuring the special strain.
Fig. 8. The measurements of the frequency-chirped vibration. (a) The measured time domain signal and (b) the corresponding time-frequency spectrum.
In theory, the modified phase difference Δφ12 is also proportional to the strain intensity. To verify the response property of this method, large dynamic strains (driven by sine function) with increasing amplitudes are applied to the sensing fiber. The amplitude of the vibration increases from 60 V to 140 V with a step of 10 V, which corresponds to a peak strain from 10.32 uɛ to 24.08 uɛ accordingly. Figures 9(a) and 9(b) depict the time domain signals and the corresponding frequency spectra, respectively. With the increment of the dynamic strain, the peak-to-peak value of the phase change enhances. We extract the power at 200 Hz from Fig. 9(b) and the peak power is linearly proportional to the vibration intensity, as illustrated in Fig. 9(c). That is in good consistent with the theoretical analysis. Restricted by the permissible voltage of PZT, the maximum dynamic strain is only 24.08 uɛ. But it must be noted that the larger dynamic strain still can be retrieved.
Fig. 9. Large dynamic strain driven by sinusoidal functions (from 10.32 uɛ to 24.08 uɛ). (a) Time domain signals and (b) the corresponding frequency spectra; (c) the relationship between the peak power at 200 Hz and the vibration amplitude.
4.3 Tunable sensitivity through adjusting the wavelengths
According to Eq. (2), the sensitivity of the dynamic strain can be adjusted through tuning the wavelengths of the two lasers. To verify this characteristic, we perform experiments through adjusting λ1 from 1527.6 nm to 1541.6 nm (with a step of 2 nm) and fixing λ2 at 1550.66 nm simultaneously. Two types of driving functions (including sine and triangle functions) are implemented to ensure the reliability of the measurements. Here, the frequency and amplitude of the both driving functions are fixed at 200 Hz and 140 V, respectively. Figures 10(a) and 10(b) show the time domain signals and the corresponding frequency spectrums of the sine vibration, respectively. Obviously, the peak-to-peak value of the phase variation is proportional to the wavelength interval, which agrees well with the theoretical analysis. Similarly, the measured results enhance with the increment of the wavelength interval for the vibration driven by triangle function, as illustrated in Figs. 10(c) and 10(d). To analyze the relation between the sensitivity and the wavelength interval clearly, the power at 200 Hz is extracted and linear fitting is executed. As depicted in Fig. 10(e), the sensor sensitivity increases with the wavelength interval for both driving functions. Compared to the sine function (blue dots), smaller power is obtained at each wavelength interval for the triangle driving function (red dots). Theoretically, sine function just contains a single frequency tone and all energy is concentrated at 200 Hz, as shown in Fig. 10(b). However, triangle function is composed of multiple tones (including basic frequency and harmonics, 200 Hz, 600 Hz and 1000 Hz etc.) so that the energy is distributed in all frequencies, as depicted in Fig. 10(d). Therefore, smaller power is acquired at 200 Hz (basic frequency) for the triangle driving function. To evaluate the relation between the sensitivity and wavelength interval more exactly, the theoretical prediction is calculated (according to Eq. (3)) to contrast with the measured results. Here, the normalized processing is required to compare them in the same scale. The results in Fig. 10(e) and the theoretical values are normalized with their corresponding peak values obtaining at 23.06-nm interval, as illustrated in Fig. 10(f). It can be seen that the measured response is in good agreement with the theoretical calculation and the sensitivity can be adjusted very well.
Fig. 10. The measurements of the tunable sensitivity with different wavelength intervals. (a) Measured time domain signals and (b) the corresponding frequency spectra driven by sine function; (c) measured time domain signals and (d) the corresponding frequency spectra driven by triangle function; (e) the evolution of the peak power (at 200 Hz) with the increment of the wavelength interval; (f) the comparison of the normalized sensor responses.
5. Conclusion
In this work, a two-wavelength probe has been proposed to enhance the measurable range of the dynamic strain in Φ-OTDR. Different from the conventional method, the large dynamic strain can always be retrieved through elaborately selecting the wavelengths of the probe. The dynamic strains with increasing peak amplitudes are measured accurately and the measured phase change is proportional to the strain intensity with a great linearity. Moreover, this approach has an advantage of tunable sensitivity and this property is demonstrated through adjusting the laser wavelengths. The test result is in good consistent with the theoretical prediction. It should also be noted that there is no frequency response loss of this approach, indicating its feasibility over other enhanced methods.
Funding
National Natural Science Foundation of China (61735015); Key Project of Sichuan Provincial Science and Technology Plan (2017GZ0091).
Disclosures
The authors declare no conflicts of interest.
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