Distributed static and dynamic sensing is demonstrated with an ultra-short fiber Bragg grating (USFBG) array. The USFBGs serve as the sensors and reflection mirrors at the same time. Distributed static sensing is performed by demodulating the strain-induced or temperature-induced wavelength shift of each USFBG. Dynamic vibration sensing is realized based on phase variation between two adjacent USFBG reflected pulses. Static temperature and dynamic vibration are applied to the sensing ultra-short FBG array simultaneously. The experiments show that the temperature measurement from 30 °C to 80 °C is achieved successfully. And dynamic sensing of nε scale vibration and 12.5 kHz acoustic wave are demonstrated at a sampling rate of 50 kHz.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Fiber Bragg grating (FBG) sensors have been widely used in structure health monitoring  and mechanical fault diagnostics  for being compact, passive, non-conductive, stable, and multiplexing capable [3,4]. Because low reflectivity could reduce the crosstalk level in multiplexed FBG sensing system, the ultra-weak FBGs and the compatible interrogation techniques have drawn a lot of research interest in recent years. In , two semiconductor optical amplifiers (SOAs) are driven by the same electrical pulse trains with a controllable delay to demodulate a selected FBG in the array. Since the delay needs to be scanned for each FBG to be demodulated, the system has a long response time and low demodulation rate. A demodulation scheme based on optical low-coherence reflectometry (OLCR) is demonstrated . The demodulation rate is limited by the scanning speed of OLCR, and the system is vulnerable to external interference. To improve the demodulation speed, chromatic dispersion induced wavelength-to-time mapping is applied for wavelength demodulation . However, a 40 GS/s sampling rate is required to achieve wavelength resolution of more than 10 pm. With wavelength-sweep optical time-domain reflectometry, high speed demodulation of identical ultra-weak FBGs is demonstrated . Nonetheless, the spatial resolution is only 20 m due to the limited wavelength sweeping rate. The above technologies have defects in the realization of high-speed sensing, and the accuracy below 1 pm cannot be achieved.
High-sensitivity and high-speed vibration signal sensing is essential in some SHM scenarios, such as crack detection due to repeated loads, corrosion, and thermal shocks, which has trouble realizing by wavelength demodulation techniques. Phase demodulation is proven superior to wavelength demodulation in the measurement of dynamic signals . However, location of multi-disturbance is difficult based on traditional structures such as dual Mach-Zehnder or Michelson interferometers [10,11]. Phase-sensitive optical time-domain reflectometry (Φ-OTDR) has been investigated extensively for multi-disturbance sensing. Nonetheless, it is difficult for Φ-OTDR to realize a good signal-to-noise ratio (SNR), due to the ultra-weak intensity of the scattering light. By using an ultra-weak FBG as a “fiber mirror”, a reasonable reflectivity stronger than the Rayleigh scattering strength can be maintained, which leads to SNR improvement of Φ-OTDR. However, such techniques usually require the use of high-coherence light sources with kHz linewidth [12,13]. Additionally, multiplexing of the FBGs also facilitates multi-disturbance sensing of interferometers . Although phase interrogation is highly sensitive for vibration signal monitoring, its high susceptibility to environmental disturbance makes it unsuitable for static sensing.
In this paper, we propose a distributed static and dynamic optical fiber sensing system based on ultra-short fiber Bragg grating (USFBG) array. Two sets of laser pulses with wavelengths matching the two edges of the FBG reflection spectrum are used as the light sources. By using the spectral edges of the gratings, the wavelength shift is converted to the change of intensities at the two wavelengths. With a typical length of only hundreds or even tens of micrometers, USFBG has ultra-low reflectivity of about −40 dB and broad spectral width up to several or even tens of nm [15,16]. The wideband USFBG extends the detecting range of temperature to 50 °C. In our system, part of the reflected optical pulses is utilized for restoring weak vibration signal of nε based on phase demodulation. Owing to the features of 3 × 3 coupler, the intensity variation of the reflected optical pulses will not affect the results of dynamic phase demodulation. Acoustic wave of 12.5 kHz is measured successfully at a 50 kHz sampling rate. Through the combination of wavelength interrogation and phase demodulation, we facilitate high-stability static strain sensing and high-sensitivity dynamic vibration sensing at the same time. In addition, in contrast to the approach reported in [13,14], the interference structure enables the application of DFB laser of 10 MHz linewidth for phase detection.
The schematic of the distributed optical static and dynamic sensing system is shown in Fig. 1. The light source is composed of two DFB lasers, two semiconductor optical amplifiers (SOAs) and an optical coupler (OC1). The two DFB lasers are thermally tuned to emit at two different wavelengths λ1 and λ2. Since direct pulse modulation will induce a strong chirp at the laser output, two SOAs are driven by the same electrical pulse train for the generation of nanosecond optical pulses. The electrical pulse train has a period of 2Ts. By tuning the electrical delay, the pulses at the two wavelengths are time-interleaved to form a pulse train with a period of Ts. The output from OC1 is amplified by an erbium-doped fiber amplifier (EDFA) and launched into the uniformly distributed USFBG array under test by a circulator. The reflected optical pulses are divided into two parts by an optical coupler (OC2). One part is detected by a photodetector (PD1) to measure the wavelength shifts of the USFBGs, which are induced by the static strain. The other part is directed to an unbalanced Mach-Zehnder interferometer (MZI) for dynamic measurement, which restores the phase variation caused by weak vibration. The unbalanced MZI is formed by a 2 × 2 optical coupler (OC3) and a 3 × 3 optical coupler (OC4). The 3 × 3 optical coupler could eliminate the influence from intensity fluctuations at the input to the interferometer. The three outputs of OC4 are detected by three photodetectors. The serial data from the four detectors are collected by a high-speed data acquisition system (DAQ).
Based on the edge filtering technique, the wavelength shifts of USFBGs are demodulated for high-stability distributed static strain measurement. The main lobe of the reflection spectrum of a FBG can be modeled as a Gaussian function , shown as:
The pulse intensities are affected by the loss mechanisms in the sensing fiber, such as fiber bending loss. However, the logarithmic ratio between the two shifted Gaussian functions results in a linear function of the center wavelength λ0 ,Eq. (4), this linear function of P(λ0) is independent of the intensities of the two pulses. Once the output wavelengths of the two DFB lasers are properly tuned, the static signal applied to the USFBGs can be measured. In addition, since the pulse trains are time interleaved, they can be distinguished in the time domain when serial intensity measurement is performed. Such arrangement could facilitate easy online processing of the collected intensity data. Each two sets of reflected optical pulse arrays can interrogate the Bragg wavelength of all USFBGs.
Apart from static strain sensing, the reflected pulses are also sent to an unbalanced MZI for phase demodulation, which realizes distributed dynamic sensing . According to unwrapping algorithm , the phase shifts are recovered from λ1 and λ2 respectively. Since the pulse source is formed by time-interleaved pulses at λ1 and λ2, the phase shifts recovered at the two different wavelengths are combined to generate the final phase demodulation results. The relative difference of the phases measured at the two different wavelengths is thus less than 0.001 since the difference of λ1 and λ2 is only 1 nm. Thus, the error introduced by this method can be ignored because it is much smaller than system noise. Even though the intensity of each reflected pulse changes along with the Bragg wavelength shift of the corresponding USFBG, the phase shift between the consecutive pulses can be demodulated accurately with the 3 × 3 coupler design. In Fig. 2, the temperature or strain around USFBG#1 is drifting slowly and the fast sinusoidal vibration is applied at the sensing fiber between USFBG#1 and USFBG#2. The Figs. 2(a), 2(b) and 2(c) plot the reflected intensity of USFBG#1 and the results of phase demodulation at three different sections, disturbance 1 only, disturbance 2 only and simultaneous disturbance 1 & 2. At the ideal split ratio, the output of the 3 × 3 coupler can be expressed as:Fig. 2(b), the phase information can be restored accurately when the reflected intensity is stable. However, in Fig. 2(a), IA is drifting slowly with the wavelength shift of USFBG caused by temperature or strain. The AC component of changed outputs can be expressed as:19], the results processed by derivation, subtracting and summing can be expressed as:Eq. (7) by the Eq. (8), the intensity fluctuation I’AIB is removed, the same phase information can be restored. Thus, the wavelength shifts of USFBGs don’t influence the phase demodulation, as shown in Fig. 2(c), which guarantees the feasibility of simultaneous static and dynamic sensing.
In the wavelength demodulation, multiple average can suppress the intensity fluctuation of laser to improve the precision of quasi-static signal monitoring. When the average number is 2000 and the pulse repetition rate fτ is 50 kHz, the quasi-static signal with the frequency of DC to 12.5 Hz can be demodulated. As for phase modulation, the detectable frequency is limited by the highest sampling frequency and the frequency response of interferometer. The phase shift φ, which is caused by external vibration, can be expressed as:Eq. (9) into Eq. (5), and setting the index i to 1, the intensity variation IAC can be expanded as
In order to restore the valid vibration signal, the bandwidth of the receiver system should be broad enough to recover all the harmonic components with the Bessel values greater than 0.1. In practical engineering applications, the value of D is determined by the sensitivity characteristics of the sensor. Here, we do not discuss the sensitivity enhancement or weakening, so the analysis of detectable frequency is carried out considering D = 1. According to the Nyquist sampling theorem, the sampling frequency must be at least twice the receiver bandwidth to avoid spectrum aliasing. Therefore, if the vibration signal has a frequency of fs, the required sampling frequency (the pulse repetition rate fτ) is at least 4fs. Meanwhile, in an OTDR-based distributed sensor, there is a trade-off between the required sampling frequency fτ and the sensing distance L, which is that fτ*L must be less than half of the light velocity in the fiber c/(2n0). When the sensing distance is about 2 km, the detectable frequency of the system reaches 12.5 kHz with a required sampling rate of 50 kHz. As is known to all, due to environmental sensitivity of coherence detection, it cannot achieve a stable static measurement. The combination of wavelength demodulation and phase interrogation compensates for this deficiency and facilitates the detectable frequency range of DC to 12.5 kHz theoretically.
3. Experimental setup for distributed static and dynamic sensing
As a proof-of-concept experiment, 964 identical wideband USFBGs are distributed over ~2 km long fiber with a fixed grating spacing of 2 m. The USFBGs have a uniform Bragg wavelength of 1549.8 nm, ultra-short grating length of 1mm, reflection bandwidth of 1.7 nm, and reflectivity of ~0.01% (−40 dB). The wide bandwidth of the USFBGs increases the measuring range of the static physical quantity and improves the fault tolerance for dynamic measurement when the Bragg wavelengths of individual FBGs are shifted by the localized strain or temperature variation. The two DFB lasers (LUCENT D2526T31, 10 MHz linewidth) are tuned to 1549.3 and 1550.3 nm to match the reflection spectrum of the USFBG. The optical pulse train has a repetition rate of 50 kHz and a pulse width of 10 ns. Static and dynamic experiment is conducted by sensing the static temperature and dynamic vibration at the same position simultaneously, as shown in Fig. 1(a). We put the USFBG #250 in a thermotank, and the temperature at USFBG#250 is increased from 30 °C to 80 °C with a step of 3 °C. At the same time, PZT is driven by the sine-wave with voltage of 6 V and frequency of 1 kHz.
Figure 3 shows the results of dynamic measurement at different temperatures. The reflected optical pulse arrays (at 30 °C) at two different probe wavelengths are shown as Figs. 3(a) and 3(b). The intensity of reflected optical pulse will change suddenly when the probe wavelength switches from λ1 to λ2. Meanwhile, the Bragg wavelength shift at different temperatures will cause the intensity variation. Nevertheless, 3 × 3 coupler can eliminate the influence of optical intensity variation in phase demodulation. The results of static temperature measurement are shown as Figs. 3(c) and 3(d) and we can find the temperature measurement range is up to 50 °C and the linearity of measurement curve is up to 0.9976. Figure 3(e) shows the results of phase demodulation at two different probe wavelengths. And in Fig. 3(f), the dynamic signals detected at 30 °C and 54 °C are plotted clearly. Thereby, the static and dynamic signal can be monitored simultaneously.
In order to evaluate the influence of the Bragg wavelength shift on the dynamic measurement, the temperature at USFBG #250 is varied from 30 °C to 80 °C to introduce a gradually increased the Bragg wavelength shift. The results are obtained from the average of 100 measurements at each temperature. As shown in Fig. 4(a), the 1 kHz vibration is clearly identified by the strong peaks in the frequency spectrum for both temperatures. The demodulated signals at different temperatures have similar harmonic suppression ratio. As for the amplitude of the dynamic strain, the standard deviation is 2.518 nε, as shown in Fig. 4(b). The results verify that the wideband USFBG guarantees the wide range of static measurement and stability of dynamic measurement.
Other experiments are demonstrated to verify measurement performance. We established a strain experimental setup to evaluate static resolution, as illustrated in Fig. 1(b), since realizing accurate temperature control is difficult. To put the USFBG#964 in the linear range of static strain measurement, 411 με is applied by adjusting the coarse stage. The high precision adjuster which has 0.3 mm travel at 0.5 μm resolution is employed to change the displacement between two stages with the step of 0.5 μm. The total strain variation applied to USFBG#964 is 29.4 με with the step of 294.5 nε. Figure 5 shows the good linearity of 0.9850 within the range of 100 data. The RMSE of experimental data and fitted data is 0.05367 dB, which gives the uncertainty of the static measurement. The increasing rate of the fitted line model is 0.0148 dB per 294.5 nε. Thus, the resolution in the static measurement is ~1 με (The resolution can be obtained through RMSE divided by the model increasing rate).
To evaluate the deviation of vibration amplitude measurement, a standard MZI is applied for calibration , as shown in Fig. 6. The optical switch is used to select the calibration standard MZI structure or our system. The PZT is driven by a 1 kHz sine-wave whose amplitude increased from 1.2 V to 12 V. The vibration is measured with our system and the calibration component, respectively. Because the calibration system and our system both have dithering, the results are averaged for 5 times to compare the detection error. Figure 7(a) shows the result of the deviation of amplitude measurement. Compared with the calibrated values from calibration component, the maximum measuring error is only 3.12 nε. It can be found that the measured and calibrated values show a linear relationship, and the linearity of curving fitting is 0.9875. To estimate the stability, only PZT is driven by the sine-wave with voltage of 6 V and frequency of 1 kHz. The dynamic strain is measured for 200 times, with an interval of 10 minutes. As shown in Fig. 7(b), the standard deviation of the system is 1.689 nε. Actually, the amplitude of the PZT generated vibration is not absolutely stable, which is partially responsible for the small system instability.
The acoustic signal under water is then detected to verify the detectable frequency of the dynamic sensing system. An underwater speaker (WBT-22) is fixed at the bottom of the water tank and driven by a signal generator. The sensing fiber section is placed above the speaker by 5 cm. A hydrophone (RHSA-20) with response factor of 350Pa/V is placed close to the sensing fiber for calibration. In order to guarantee that the hydrophone and the sensing fiber are detecting the same acoustic wave, they are installed as close to each other as possible. The 2-m sensing fiber is wound on a spool to make it a point sensor. Both the hydrophone and the sensing fiber are placed 5 cm away from the underwater speaker (WBT-22). The driving signal frequency is set at 12.5 kHz, which is the highest detectable frequency restricted by the 50 kHz sampling rate. The frequency response of the transducer also influences the detectable frequency of system. The result verifies the effect of repetition rate fτ of the light source in this experiment. As shown in Fig. 8, the distinct peak at 12.5 kHz clearly verifies the capture of the acoustic signal under water.
Motivated by the potential for distributed static-dynamic sensing, we have proposed and demonstrated a wavelength-phase interrogation system for a USFBG array based on edge filtering and Mach-Zehnder interference. The USFBGs are adopted as sensors and fiber mirrors. A wide static temperature detection with the ranges of 50 °C and dynamic sensing of nε vibration are realized simultaneously. The linearity of static and dynamic measurement are 0.9976 and 0.9875, respectively. In addition, the resolution of 1 με is demonstrated in the static measurement. The maximum measuring error of dynamic sensing is only 3.12 nε compared with standard Mach-Zehnder interferometer. The system exhibits high speed, high sensitivity, good fault tolerance, low requirement for the laser linewidth, and wide static measurement range, indicating remarkable application prospect in the pipeline leak monitoring and structure inspection.
National Natural Science Foundation of China (Grants 61735013 and 61575149), the Natural Science Foundation of Hubei Province of China (Grant No. 2018CFA056) and the Excellent Dissertation Cultivation Funds of Wuhan University of Technology (2017-YS-057).
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