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Abstract
Quasi-distributed acoustic sensing (Q-DAS) based on ultra-weak fiber Bragg grating (UWFBG) is currently attracting great attention, due to its high sensitivity and excellent multiplexing capability. Phase-sensitive optical time-domain reflectometry (Φ-OTDR) based on phase demodulation is one of the most promising interrogation schemes for Q-DAS. In this article, a novel interleaved identical chirped pulse (IICP) approach is proposed on the basis of pulse compression Φ-OTDR with coherent detection. Different from the frequency-division-multiplexing (FDM) method, the identical pulses are used for multiplexing in the IICP scheme, and the mixed reflection signals can be demodulated directly, so the inconsistent phase offsets in FDM can be avoided. As a result, this scheme can enlarge the measurement slew-rate (SR) of Q-DAS by times compared with traditional single pulse scheme. In the proof-of-principle experiment, the SR of 28.9 mɛ/s has been achieved with an 860 m sensing range, which is 5 times as that of the traditional single pulse scheme; meanwhile, the response bandwidth has been enlarged by 5 times. The 277 kHz response bandwidth has been achieved, with 5 m spatial resolution and 2.8 ${{p\varepsilon }/\sqrt{\textrm{Hz}}}$ strain sensitivity.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
By measuring the variation of the lightwave parameters (intensity, phase, wavelength, etc.) propagating in optical fiber, optical fiber sensors (OFS) can be used to measure many physical quantities around the sensing fiber. The sensing medium, optical fiber, has many advantages compared to traditional electronic sensors, such as small size, lightweight, anti-electromagnetic interference and so on. As a result, OFS has been extensively studied and applied in many fields, such as seismic wave detection, pipeline security, intrusion monitoring, etc. [1–6].
Phase-sensitive optical time-domain reflectometry ($\Phi$-OTDR), as a critical branch of OFS, has many well-performed applications in recent years, due to its long sensing distance [7], high sensitivity [8] and good capability of dynamic detection [9]. According to different sensing mechanisms, $\Phi$-OTDR can be used for both distributed acoustic sensing (DAS) and quasi-distributed acoustic sensing (Q-DAS). The DAS systems are based on Rayleigh backscattering (RBS) of single-mode fiber (SMF), the phase and intensity of RBS light will change with external perturbation, from which the external perturbation can be inferred. However, due to the randomness of Rayleigh scattering, the fading phenomenon could cause sensing failure in many positions [10]. Moreover, the amplitude of RBS lightwave is very weak and unpredictable, which somehow limits the sensing performance of DAS.
Different from DAS, Q-DAS is based on the reflected lightwaves of ultra weak fiber Bragg grating (UWFBG) array, which can offer controllable and stable reflection [11]. Therefore, Q-DAS system can easily avoid the effects of interference fading and provide high sensitivity, making it a preferred choice in some applications [12–14].
To promote the applications of Q-DAS, researchers have improved the system performance in various aspects, such as sensitivity, signal-to-noise ratio (SNR), and sensing bandwidth. In terms of the system sensitivity, a Q-DAS system based on the Michelson interferometer has been demonstrated, which applied a 3$\times$3 coupler to demodulate the acoustic signal, achieved a high acoustic pressure sensitivity [15,16]. Y. Shan et al. proposed a self-heterodyne detection method to retrieve phase information; this scheme applied encapsulated fiber as a reference to reduce the phase noise of the system, which improved the sensitivity performance of the system [17]. In the performance of SNR, chirped pulses can be applied to the Q-DAS system with the pulse compression technique, allowing the system to measure the fiber with a high-energy pulse much wider than the spatial resolution [18]. In the sensing bandwidth of the system, the frequency division multiplexing (FDM) technique has been applied in the Q-DAS system [19], the 440 kHz frequency of vibration can be detected over 330 m fiber, which triples the sensing bandwidth.
However, for all of these schemes, the phase variation range will be within [-$\pi$, $\pi$] unless introducing phase unwrapping [20]. Even with this algorithm, the maximum phase difference between two adjacent sampling points is within $\pi$[21], otherwise the unwrapping will fail. If the unwrapping of a wrapped phase signal is failed, there will be some discontinuities in the demodulated signal [22], therefore its real amplitude and frequency won’t be accessible. This will limit the application of Q-DAS in case where the large dynamic strain measurement is required. A dynamic strain level of 656 ${n\varepsilon }$ has been achieved in Q-DAS [23], but due to the use of phase unwrapping, for high-frequency signal, the measurable amplitude of the vibration is restricted [20].
Since Q-DAS and DAS are mainly built for dynamic measurement, slew-rate (SR) is a proper indicator for the maximum measurable phase/strain change, which is the product of scan-rate and the maximum phase or strain change during two adjacent measurements [21]. Therefore, there are two directions to enlarge SR of the system: one is to enlarge the maximum-measurable phase/strain change during two measurements, and the other is to increase the scan-rate. For the former direction, Z. Zhong et al. proposed a new process of phase unwrapping with an auxiliary channel in DAS, in which a disturbance signal which induces a maximum phase jumping of 3.7 rad is well reconstructed [24], but each sensing point has only 50% probability to truly reconstruct large strain signal. Recently, a dual-wavelength scheme was proposed [25] to improve the measurable strain range in DAS system, while two laser sources and two detection channels are necessary. Another method based on complementary frequency was proposed in [26], which can improve the measurable strain range effectively. However, all these papers are in the fields of DAS, and to the best of the authors’ knowledge, no papers has described the improvements of SR for phase demodulated Q-DAS.
FDM is a direct method to increase the scan-rate [19], however, due to the probe pulses are in different frequency bands, the reflected signals from different pulses must be demodulated separately and then combined. This demodulation process in conventional FDM system will scramble the phase relationship between adjacent channels, which eventually leads to the failure of phase unwrapping. This phenomenon in DAS system has been introduced in [26]. For the similar reason, the conventional FDM scheme isn’t an efficient way to enlarge the SR of the phase-demodulated Q-DAS. The SR and critical limitation of conventional FDM scheme in Q-DAS will be discussed in detail in the second section. In our previous work [27], the scan-rate has been increased by times based on chirped pulses; however, the multiplexed probe pulse are different, for the same reason as FDM, the SR can’t be enlarged effectively.
In this paper, we proposed a novel interleaved identical chirped pulses (IICP) method to significantly enlarge the SR of Q-DAS systems. With the use of identical chirped pulses, the mixed reflected signals can be demodulated directly without recombining signals from different frequency bands. This feature brings a benefit that the measurable strain range can be enlarged while the scan-rate is increased. The principle of the proposed scheme is elaborated in detail and the experimental demonstration is given. In the proof-of-principle experiment, the SR and the response bandwidth can be simultaneously increased by 5 times as those of traditional single pulse scheme, the 277 kHz response bandwidth has been achieved on an 860 m fiber under test (FUT), with 5 m spatial resolution and 2.8 ${{p\varepsilon }/\sqrt{\textrm{Hz}}}$ strain sensitivity.
2. Principle
In this section, the SR and the critical limitation of the conventional FDM scheme in Q-DAS will be discussed, then the principle of IICP will be described, finally different Q-DAS systems will be compared, and the advantages of IICP over other schemes will be discussed.
2.1 SR of the $\varPhi$-OTDR
In phase demodulation $\Phi$-OTDR, the phase of the measured signal will be in the range of [-$\pi$, $\pi$] rad. Though a larger phase can be retrieved through phase unwrapping, the phase change between two adjacent measurements for the same sensing point should not exceed $\pi$ rad [20]. When the disturbance signal is large enough, the true maximum phase change that it causes will be much larger than $\pi$ rad. Without loss of generality, assuming this disturbance is a sinusoidal signal, the induced actual phase change within a gauge length is
where $\phi _A$ and $f$ represent the amplitude and frequency of $S$. Then the measured phase change is where $i$ is the ordinal number of measurement, and $k_i$ is a integer such that $S_i$ within [-$\pi$, $\pi$]. The S can be retrieved through $S_i$ with phase unwrapping, and the following rule should be met: Since $\phi _A$ is larger than $\pi$, there must be at least one measurement point between the minimum and maximum phase change in one period of $S$, i.e., more than two measurement points are needed in one whole period of $S$, which means the decreasing of sensing bandwidth. The larger the $\phi _A$ is, the more points are needed. Therefore, the sensing bandwidth is inversely proportional to the amplitude of the disturbance signal [20]. In conclusion, phase unwrapping is only an efficient way to enlarge the maximum measurable strain for the low-frequency disturbance. To enhance the strain range of full-band disturbance, the most effective way is to enlarge the SR.In DAS/Q-DAS system, the maximum measurable strain is determined by the SR [21], which is defined by
where $\Delta \varepsilon _{max}$ is the maximum-measurable strain-change between two adjacent measurements, c is the light speed in vacuum, and $T_{rep}$ is the measurement period.Even the phase unwrapping algorithm is applied in phase-demodulated $\Phi$-OTDR, the maximum measurable phase difference between two adjacent sampling points should not exceed $\pi$ rad, corresponding to a optical path change of $\lambda /2$, where the $\lambda$ is the wavelength of sensing lightwave. Therefore the SR satisfies
where $\Delta \varepsilon _{max,\phi }$ is $\Delta \varepsilon _{max}$ in phase demodulation scheme, $G_L$ is the gauge length when calculating differential phase, and $n$ is the refractive index of fiber.The SR is a constant for a given system and doesn’t relevant to disturbance feature, but it will be influenced by the noise level in the phase demodulation scheme. The reason is that the noise will influence the phase unwrapping process, which in turn makes the maximum-measurable phase-difference between adjacent two sampling points decrease from $\pi$ [20]. Finally, the $\Delta \varepsilon _{max,\phi }$, or the SR will be reduced with the increase of noise.
In general, $\Delta \varepsilon _{max,\phi }$ is a constant for a phase demodulated Q-DAS if the noise level is determined, thus an efficient way to enlarge SR, i.e., the maximum measurable strain, is to reduce the $T_{rep}$.
2.2 Critical limitation of the conventional FDM scheme in the Q-DAS
The FDM is a direct method to increase the scan-rate, i.e. reduce the $T_{rep}$. In general, the conventional FDM isn’t a fully efficient way to enlarge the SR. This phenomenon in DAS has been discussed in [26], and the proof of it in phase demodulated Q-DAS is detailed as follows.
In the phase demodulated Q-DAS system, the lightwave reflected from the $i^{th}$ UWFBG can be expressed as
After $E$ is beat with local oscillator (LO), detected by photodetector and field retrieving through Kramers-Kronig relation [28], the Eq. (6) becomes
It can be found in Eq. (9) that there is a phase offset $\phi _{PO}=2\pi f\Delta \tau$. In FDM based Q-DAS, the difference of phase offsets between different channels is
where the $\Delta f$ is the frequency interval between two FDM channels.For a Q-DAS system, the time width ($\tau$) and bandwidth ($B$) product of the probe pulse satisfies the uncertainty principle, i.e. $\tau \cdot 2\pi B\geq 2\pi$ [29]. Even for a chirped probe pulse, the time width after pulse compression still satisfy this relationship. The frequencies interval in FDM should be larger than $B$, and the $\Delta \tau$ should be larger than $T$ since the UWFBG interval is longer than half of the pulse width (the $\Delta \tau$ should be longer than the time width after pulse compression in chirped case). Therefore, the phase offset $\phi _{PO}$ varies among channels with a magnitude larger than $2\pi$ in FDM scheme. This phase offset will scramble the relationship between two adjacent demodulated phases of different FDM channels, and eventually lead to the failure of phase unwrapping.
A detailed explanation of phase offset in scrambling the phase relationship is shown in Fig. 1. The red line is the desired measured phase without offsets, while the blue line is the actual phase retrieved based on the red line through phase unwrapping. For a signal that satisfies the condition of phase unwrapping, the phase change between two adjacent measurements should within $[-\pi ,\pi ]$. Therefore, if there is a phase difference beyond this section, just like the point A and B in Fig. 1, it can be concluded that there must be a wrapped phase of 2$\pi$. Then the real phase at B$_1$ can be retrieved by adding a 2$\pi$ phase change to B. After that, the phase difference between A and B$_1$ is within $[-\pi ,\pi ]$. Then the same process will be applied between the newly point B$_1$ and C, and the point C$_1$ is obtained. After do this unwrapping process to all the measurement points, the actual phase will be obtained as the blue line.
However, if the phase offsets of different frequencies are considered, the measured phase of 3-channels FDM scheme will performance like the yellow line in Fig. 1. The phase points measured by the same frequency still keep their own relationship in difference since they will have the same phase offset. But the phase difference between the points measured by different frequencies will be changed, since the phase offsets are different. As an example, the offsets of frequencies f2 and f3 are respectively negative and positive, which cause the point A and B changes to A$_2$ and B$_2$ respectively. The phase difference here goes from bigger than $\pi$ to smaller than $\pi$, and the phase unwrapping algorithm does nothing here. Finally, the actual phase signal couldn’t be retrieved with the yellow line.
Figure 1 only gives an example of the possible phase offsets combination among three different frequencies. The full possible combinations between two frequencies were discussed in [24], which shows that there is only a 50% probability that the actual phase change can be retrieved. Moreover, this probability is decreased with the increasing number of FDM channels. Therefore, the conventional FDM scheme is not a fully efficient method to enlarge the SR of Q-DAS systems.
2.3 Principle of IICP
Unlike the SMF, the UWFBG array has a series of fixed-spaced reflection points, so the space between two reflected points can be used to insert and multiplex pulses [27]. The principle of IICP is shown in Fig. 2, three evenly spaced probe pulses are injected into the UWFBG array in a round-trip. Without loss of generality, as an example of 4 UWFBGs, R1, R2, R3 respectively stand for the reflected signals of 3 multiplexed pulses through the FUT, which has many randomly distributed Rayleigh scatters and four UWFBGs, with the perturbation applied between the last two UWFBGs. R represents the actual detected mixed reflection signals of 3 multiplexed pulses. The peak with different numbers represents reflected lightwave of the i-th UWFBG reflection. By precisely adjusting the repetition period of pulses, the reflected lightwaves of different UWFBGs are separated from each other in the time domain, as shown by R in Fig. 2. In the space between the two reflected peaks of the first pulse reflected by UWFBG3 and UWFBG4, the two peaks reflected by the second pulse and the third pulse through UWFBG2 and UWFBG1 are inserted. Since these peaks are separated, the perturbation information can be recovered from the reflected signals of the three pulses with negligible crosstalk, and the scan-rate of this system can be increased by three times.
It’s obvious that the pulse width should be much smaller than UWFBG interval to keep the separation of the reflection peaks, and the larger the multiplexing number, the smaller the pulse width. Because the noise power in the demodulated signal is inversely proportional to the pulse width [18], the decrease of pulse width will result in the reducing of the SNR.
However, since the chirped pulse is used as probe lightwave, its width can be compressed through matched filtering, i.e. cross-correlation with the original chirped pulse, and the width after compressing is only determined by the chirped bandwidth [18,30]. Therefore, just make sure that the cross-correlation peaks of the reflection lightwave satisfy the separation relationship shown in Fig. 2, the IICP method is efficient when the width of chirped pulse is longer than the UWFBG interval. As a result, the pulse width needn’t to be decreased with the increasing of multiplexing number, and the SNR will not be sacrificed with the increase of multiplexing number.
As analyzed in last section, due to the different phase offsets for signals of different frequencies, it is difficult for the FDM to enlarge the SR of the signal. Since the identical chirped pulses are used, the IICP scheme can directly demodulate the mixed reflected signal, while avoiding the unstable phase offset in FDM scheme. Therefore, the SR of this system can be effectively enlarged.
Although these cross-correlation peaks are separated from each other in the time domain, there is still some crosstalk due to the RBS lightwave and the sidelobes (or even the edge of main lobe), as shown in Fig. 2(a) and the blue line in Fig. 2(b). The cross-correlation peaks of the other two pulses reflected by UWFBG1/UWFBG2 locate between the peaks of first pulse reflected by UWFBG3 and UWFBG4. Therefore, the disturbance information carried in the signals reflected by the first pulse through UWFBG3, UWFBG4 and the nearby Rayleigh scatters will have crosstalk signals at UWFBG1 and UWFBG2, which called mapping zones. The crosstalk from RBS lightwave is inevitable, while that from other UWFBGs are controllable.
To solve this problem, these methods are effective like increasing the distance between UWFBGs that the interval between peaks becomes larger, or increasing the bandwidth of the chirped pulses that the cross-correlation peaks can be narrowed. On the other hand, the sidelobes can be suppressed through adding the time-domain window to the signal [30], or using nonlinear frequency modulated (NLFM) probe pulse [32]. As shown in Fig. 2(b), the sidelobes can be suppressed effectively with different sidelobe suppression method (adding Hanning/Hamming window in time domain or using NLFM probe pulse), but the the main lobe will be enlarged by about 1.5 times. As a result, the crosstalk can be suppressed if the interval between two correlation peaks is bigger than the 1.5 FWHM of the original correlation peak. Therefore, the system bandwidth can be saved since the crosstalk of sidelobes can be ignored. In this paper, the Hamming window was chosen for its narrower main lobe than Hanning window and easier processing procedure than NLFM scheme.
Table 1 compares the several important parameters of different Q-DAS systems based on phase demodulation. The rectangular pulse scheme with phase noise compensation (PNC) is the representative of traditional Q-DAS using a common rectangular pulse. The strain range $@c/4nL$ means the strain range at the disturbance frequency of $c/4nL$. It can be clearly seen that, compared with traditional Q-DAS using rectangular pulse and chirped pulse, the scan-rate and SR of IICP scheme increase by $M$ times, where $M$ is the number of multiplexing channels. Compared with FDM scheme, the SR, thereby strain range, of the proposed scheme is enlarged by $M$ times.
Table 1. The comparison of different Q-DAS systems
The frequency of $c/4nL$ was chosen because it is a critical point. When the frequency is lower than $c/4nL$, the strain ranges of the first three methods in Table 1 are inversely proportional to the disturbance frequency. When the frequency is higher than $c/4nL$, the first two Q-DAS schemes without multiplexing in Table 1 are no longer applicable. Although the FDM method can measure the frequency of signals higher than $c/4nL$, the strain range remains the same as at $c/4nL$, which is explained in the last subsection. Different from other schemes, the IICP satisfies the inverse relationship between the disturbance frequency and the strain range, in the entire measurable frequency band. When the disturbance frequency lower than $c/4nL$, the strain range of the proposed scheme is M times than that of other schemes; when the disturbance frequency higher than $c/4nL$, not only can it retrieve signals in this frequency range, but also enlarge the strain range.
3. Experimental setup and results
The proof-of-principle experimental setup is shown in Fig. 3. A narrow bandwidth laser is divided into two parts by a 1:9 coupler. The 10% part is the LO, and the 90% part generates chirped pulses with a pulse width of 0.1$\mu$s and a bandwidth of 300 MHz through the IQ modulator. Taking multiplexing 5 pulses as an example, considering the fiber length and the separation of cross-correlation peaks after matched filtering, the repetition period is adjusted to 1.805 $\mu$s, which is about 1/5 of the round-trip $T_R$ of Q-DAS systems. After amplified by the EDFA, these chirped pulses are injected into the fiber under test (FUT), which consists of 171 UWFBG with 5 m interval. The fiber between the 169th FBG and the 170th FBG is wrapped on a piezoelectric transducer (PZT) to employ the external disturbance. After passing through the circulator, the reflected signals from the FUT combine with LO in a 1:1 coupler and is detected by BPD.
Fig. 3. Experimental setup. AWG: arbitrary waveform generator; EDFA: erbium doped fiber amplifier; PC: polarization controller; VOA: variable optical attenuator; OSC: oscilloscope; BPD: balanced photodetector.
3.1 SR improvement verification of IICP and the comparison to the FDM scheme
Taking into account the linear relationship between the SR of the disturbance signal and the number of multiplexed pulses, the trapezoidal signal is used as the disturbance signal at first to verify the SR improvement ability of the system. The results of the single pulse scheme are first displayed, the repetition period of chirped pulses is 9.025$\mu$s, the disturbance of 200 Hz trapezoidal signal was applied to the PZT, and the measured time domain of disturbance signals are shown in Fig. 4. In Fig. 4(a), the peak to peak value is 68.3 rad (corresponding to 1.68 $\mu \varepsilon$), the maximum phase difference between the two adjacent points is 3.05 rad. When continuing to increase the voltage applied to the PZT, the threshold is exceeded, as shown in Fig. 4(b). In the areas enclosed by the dashed line, the phase has jumps, which indicates that the phase unwrapping algorithm has failed. Thus, in the absence of multiplexing, the maximum-measurable phase-difference between the two adjacent points is about 3.05 rad, corresponding a SR of 33.8$\times$10$^{4}$ rad/s (or 5.7 $m\varepsilon$/s). The phase difference, 3.05 rad, is a little smaller than $\pi$ rad, which is due to the influence of noise and signal distortion produced by PZT. Since the PZT used in the experiment has a resonance peak at around 13 kHz, the demodulated trapezoidal perturbation signal has some shakes at the top and bottom.
Fig. 4. The disturbance signal restored by single chirped pulse. (a) Within the unwrapping threshold; (b) exceeding the unwrapping threshold.
Then a series of IICP was injected into the fiber with the repetition period of 1.805 $\mu$s, which means five pulses were multiplexed within a pulse round-trip in the fiber. The disturbance signal restored by the IICP scheme is shown in Fig. 5(a). The peak to peak value is 326.7 rad (corresponding to 8.06 $\mu \varepsilon$), the maximum phase difference between the two adjacent points is 3.1 rad, corresponding to the SR of the scheme is 171.75$\times$10$^{4}$ rad/s (or 28.9 $m\varepsilon$/s), which is about 5 times than that of the single pulse scheme.
Fig. 5. The disturbance signal restored by IICP scheme (a), and the angles of baseband optical fields at UWFBGs in (b) IICP and (c) FDM schemes.
The disturbance signal demodulated by the FDM scheme is also demonstrated as a comparison. The center frequencies of 5 multiplexed probe pulses are 180 MHz, 240 MHz, 300 MHz, 360 MHz, and 420 MHz, with a bandwidth of 60 MHz. The disturbance signal applied to the PZT has the same frequency and voltage as the IICP scheme.
In order to compare the phase offset characters of IICP and FDM schemes, the angels of the first five baseband traces in the two schemes are shown in Fig. 5(b) and 5(c), respectively. It should be noted that only the angles at the UWFBG positions are plotted. The baseband trace is the retrieved optical fields after shifting to the baseband, and the first five traces in FDM are measured by different-frequency pulses. It’s clear that the five angle traces of IICP well matched with each other except the disturbed area. This is because that they were sensed by the same probe pulse, and therefore have the consistent phase offsets on the same UWFBG. However, since the five traces in FDM were obtained with different probe pulses, the angle traces are different. This difference will result in the unwrapping failure, which is illustrated in Fig. 6.
Fig. 6. The disturbance signal restored by FDM scheme for comparison. (a) Failed signals retrieved by five frequencies respectively; (b) the combined signal.
Figure 6(a) shows the disturbance signals which are retrieved for each of the 5 frequencies, and the combined signal is shown in Fig. 6(b), where the inset part of which shows the details of the combined signal. Since the phase offset is different for each frequency, it leads to the failure of the phase unwrapping, and the signal is not retrieved correctly. It can be seen that the typical FDM scheme cannot enlarge the SR of the system.
3.2 Sensing bandwidth and performance of the IICP based Q-DAS
Since the IICP scheme increases the system’s frequency response while enlarging the SR of system, the frequency of perturbation signal applied on the PZT is increased to 250 kHz, which has exceeded the maximum response bandwidth of the single pulse scheme. The harmonics of the trapezoidal signal are affected because the frequency is too high, so the sinusoidal signal is used instead of the trapezoidal signal. As shown in Fig. 7(a), the 250 kHz sinusoidal disturbance signal is accurately retrieved, with a strain sensitivity of 2.8 ${{p\varepsilon }}/\sqrt{\textrm{Hz}}$. The perturbations with different frequencies of 50 kHz, 100 kHz , 150 kHz, and 200 kHz are also applied to the FUT and are detected successfully, their SNRs are all about 40 dB according to power spectra density shown in Fig. 7(b).
Fig. 7. (a)The PSD of 250 kHz disturbance signal restored by IICP scheme; (b) The PSD of disturbance signal at multiple frequencies by IICP scheme.
Figure 8 shows the disturbance induced phase change along the 860 m FUT. The disturbance zone can be clearly identified in the range of 845 m to 850 m and the phase change in the undisturbed zone is almost zero, which proves that the crosstalk of mapping zones can be successfully reduced in this system. The inset of Fig. 8(b) shows the time-domain trace of the demodulated disturbance.
The linearity of the strain response is very important for a quantitative measurement system. To verify the response linearity of IICP system, the amplitude of the driving signal applied to the PZT is varied from 100 mV to 20 V (corresponding to 5.1 ${n\varepsilon }$ to 1.07 ${\mu \varepsilon }$), with the frequency of 10 kHz. The linearity of the strain response is shown in Fig. 9. From the fitting results, the linear coefficient R$^{2}$=0.99997, so this IICP system has a good linear strain response capability.
3.3 Discussion
For a fixed UWFBG interval, the sweep bandwidth of probe pulse determines the width of main lobe, which in turn limits the multiplexing number of IICP. While the frequency-domain resources should be carefully considered. When selecting multiplexing number and system bandwidth, two mainly factors, system reliability and crosstalk, should be taken into account.
Firstly, the reliability of the sensing system is considered. Figure 10(a) gives the simulated correlation peak of five chirped pulses (150 MHz bandwidth, with Hamming window in time domain) reflected by the UWFBGs at the disturbed and the mapping areas. There is 1 m spatial interval between every two adjacent pulses, which is the same as the experimental setup (There are four peaks from mapping areas locate in a 5 m UWFBG interval, thus the interval between every two adjacent peaks is 1m). The red dashed line shows the Rayleigh scattering level, which is about 20 dB lower than the correlation peak. If the orange peak is what we concerned, the other four peaks and the Rayleigh scattering lightwave will give it crosstalk. It’s clear that there is only one optimal point, at where the optimal crosstalk suppression ratio can be achieved. However, this optimal point may be missed during the ADC sampling process.
If the sweep bandwidth of chirped pulse is changed to 300 MHz, as shown in Fig. 10(b), there will be an optimal region which mainly affected by Rayleigh scattering. A wider region can guarantee that more points with the best crosstalk suppression ratio can be picked. In the case of the 300 MHz, the width of this region occupies more than 95% of the chirped-pulse interval. A system bandwidth within 150$\sim$300 MHz is acceptable if a fewer sampling point with optimal crosstalk suppression ratio is needed.
Secondly, the crosstalk is taken into account. It’s clear that the wider the chirped bandwidth, the narrower the correlation peak, the higher the crosstalk suppression ratio. When the correlation peak is narrow enough, the Rayleigh scattering light becomes the main source of crosstalk, just like the optimal region in Fig. 10(b). Then the crosstalk changes slowly with the increase of chirped bandwidth.
In order to investigate the influence of bandwidth, IICP experiments with different chirped bandwidths were carried out. Figure 11 illustrates the PSDs of demodulated signals measured with different chirped bandwidth. The blue lines in Fig. 11 are the disturbances demodulated at the perturbation area, and all the other lines are the signals obtained at the mapping areas. The crosstalk suppression ratio in disturbance is marked in the subfigure of Fig. 11, and the trendline of it varying with bandwidth is shown in Fig. 12(a). It can be found that the crosstalk suppression ratio improves at first with the increase of chirped bandwidth, and then becomes steady after 300 MHz. This trend is consistent with the trend in Fig. 12(b), which is the simulated intensity signal suppression ratio between peaks at disturbed and mapping area. The intensity suppression ratio is calculated as the ratio between the intensity of correlation peak within 3 dB width of the peak and the intensity of crosstalk within the same range.
Fig. 12. The crosstalk suppression ratio varies with chirped bandwidth. (a) The experimental result of the disturbance suppression ratio between the disturbed and mapping area. (b) The simulated intensity signal suppression ratio between the disturbed and mapping peaks.
Taking all these factors into account, a bandwidth of 300 MHz was chosen in the demonstration experiment. However, a narrower chirped bandwidth is acceptable to realize 5-channels IICP with 5 m UWFBG interval, if a narrower optimal region and higher crosstalk are acceptable.
Compared to FDM scheme with chirped probe pulse [33] and Orthogonal FDM (OFDM) [34], a higher system bandwidth was used in the demonstration experiment to optimize the reliability and crosstalk. However, this requirement can be reduced according to the analysis above. Moreover, it is predictable that with the increasing number of multiplexing channels (system bandwidth increases simultaneously in the same proportion), the ratio between the necessary system bandwidths of IICP scheme and chirped-FDM/OFDM method keeps unchanged, while the factors of slew-rate-improvement keeps increasing.
4. Summary
In conclusion, a novel IICP method to enlarge the slew-rate of Q-DAS is proposed, based on pulse compression $\Phi$-OTDR and coherent detection. Compared with FDM scheme, since identical probe pulses are used, this system can directly demodulate the mixed reflected signal. Therefore, the frequency-related unstable phase offset is avoided, and the slew-rate is multiplied. As a result, the sensing bandwidth and the measurable strain range can be multiplied simultaneously. In the proof-of-principle experiment, the response bandwidth and the slew-rate of the system are both enlarged by 5 times compared to those in traditional single pulse scheme. If the chirped signal with wider bandwidth and FBGs with larger spatial intervals are used, more multiplexing numbers can be achieved, which will result in a even larger strain range and wider response bandwidth. The work provides new insights into enhancing the performance of quasi-distributed sensing based on phase demodulation.
Funding
National Natural Science Foundation of China (62075030, 41527805, 61731006); Sichuan Provincial Project for Outstanding Young Scholars in Science and Technology (2020JDJQ0024); The 111 Project (B14039).
Disclosures
The authors declare no conflicts of interest.
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