1. Introduction

Distributed dynamic fiber optic sensors enable measurement of fast-changing parameters over an extended region and can be employed in a number of environmental and structural health monitoring systems. Even though high SNR measurements have been done using advanced sensing schemes based on Brillion scattering in silica fibers in the past, recently coherent Rayleigh scattering has become the phenomenon of choice as it enables using relatively less complex setups to make continuous real-time measurements. Specifically, Distributed Acoustic Sensing (DAS) is becoming a ubiquitous technique which has attracted significant attention from the fiber sensing community due to its capacity to monitor safety, security and integrity in among others oil & gas, transportation, and geophysical systems [1]. A recent global report on DAS shows that its market value is expected to maintain a steady compound annual growth rate (CAGR) of 20.2% during the period 2017-2025, and to surpass $ 2bn by 2025 [2]. So far, the implementation of DAS has been made using schemes which use time, frequency and correlation-domain techniques. The time domain technique typically involves a scheme known as Phase-sensitive Optical Time Domain Reflectometry (ϕ-OTDR), where a pulse of coherent light is sent into the probing fiber and the coherent Rayleigh backscattering traces from the fiber are used to measure vibration or temperature changes, thanks to the dependence of the amplitude and phase of the traces on the local variations of these parameters. Simple ϕ-OTDR systems involve measuring the frequency of vibration with acquisition of consecutive traces and observations of local intensity changes, while those for more accurate quantitative measurement of the frequency and amplitude of perturbations require more advanced techniques. Such dynamic ϕ-OTDR schemes are based on either use of phase demodulation techniques or multi-frequency probing pulses [3,4].

So far, enhancement of measurements in phase-OTDR has been made by either changing the configurations of the optical setup or using advanced signal processing techniques at the receiver. The techniques used include optical pulse coding [5], chirped pulse amplification, the use of high extinction ratio pulses employing the nonlinear Kerr effect [6] or an efficient filtering and modulation scheme [7,8]. However, most of these methods do not mitigate the limitation of the very low intensity of the Rayleigh backscattering coming from conventional fibers which results in noisy measurements without filtering or amplifications circuitry, or without using methods which incur changes in the setup or mechanism of the measurement. However, it is possible to use Ultra-Weak Fiber Bragg Gratings (UWFBGs) to obtain enhanced intensity of the backscattering signal coming from the fiber [9–11]. Each of these gratings has very low reflectivity values of typically less than −40 dB, which is significantly higher than the Rayleigh intensity level in a typical singlemode fiber. Thus, such transducers offer a great improvement in measurement SNR as many of them can be implemented in a single fiber at a spacing equivalent to the spatial resolution in distributed vibration sensing without incurring significant cumulative power loss.

Some work has been done to use distributed schemes for interrogation of UWFBG arrays. In one such system, a wavelength division multiplexing (WDM) technique whereby each ultra-weak grating has an identical center wavelength and the interrogation is made using active laser sweeping and phase-unwrapping algorithms has been demonstrated [12]. The combination of the two techniques incurs inevitable delay due to source sweeping and further computations from the phase unwrapping, making the implementation of the method for dynamic measurements challenging. Another distributed configuration based on a TDM scheme using a combination of a pair of reference and measurement filters to convert wavelength variations to intensity variations has also been proposed and demonstrated [13]. A demodulation technique using ϕ-OTDR for interrogation of a UWFBG array with identical central wavelength for static temperature measurements has also been demonstrated using a charge coupled device (CCD) with a gating element whose delay is adjusted to choose the location of the sensing per measurement round [11]. A configuration similar to the ones used in conventional DAS based on 3x3 couplers [14], and subsequent signal processing for phase change retrieval involving a table lookup has also been proposed [15]. The use of the 3x3 coupler results in a duplication of components necessitating three independent photodiodes working in full synchronization, while the table lookup operation incurs further delays which reduce the dynamic performance. Optical hydrophones using Phase Matched Differential Interferometry (PDMI) have also been proposed including, among others, the measurement of cross-talk between sensor elements using a 4-element Fabry-Perot interferometeric sensor array based on fiber ring reflectors with reflectivity in the range of 1-2% [16] and a method for determining the reflectance distribution of FBGs in a fiber-optic interferometric system with a TDM scheme in two hydrophones [17]. Other ϕ-OTDR configurations for phase demodulation such as coherent or I-Q demodulation can be employed for interrogation of UWFBGs for dynamic measurements. However, most of them involve the use of phase unwrapping computations. Phase unwrapping in one dimension is computationally-intensive and a number of independent studies were made in order to come up with an effective algorithm [18]. In distributed dynamic sensing, unwrapping of the phase at each spatial location translates to similar computations at each point of the sensor giving rise to more complex two-dimensional phase unwrapping, the same as the ones present in image processing [19,20], seriously limiting the development of such measurement schemes. Other systems which do not require phase unwrapping include the use of a Phase-Generated Carrier (PGC) differentiate-multiply-square (PGC-DMS) which involves division operations requiring mechanisms to handle zero-crossing of the denominator [21]. In addition, a critical issue hampering the development of DAS schemes is the lack of cost-effective interrogation schemes for dynamic measurements which can be candidates for practical realization via scalable commercialization by paying proper attention to the impact of the specific type of signal processing used to retrieve phase change due to an external impact [22,23]. Hence, a system which addresses the issues of duplication and synchronizations of photodetection and automatically avoids computationally demanding phase-unwrapping operations, while maintaining the simplicity and scalability of the optical configuration for UWFBG interrogation, is highly desirable.

In this paper, we propose and experimentally demonstrate a high-SNR DAS based on ϕ-OTDR, using an array of identical UWFBG gratings as a transducer and employing a delayed interferometry technique exhibiting phase modulation in one arm and delay on the other, together with a scalable interrogation scheme based on the PGC demodulation with the Differentiate and Cross-Multiply (PGC-DCM) algorithm. The demonstrated scheme is suitable for distributed sensing as the phase retrieval mechanism uses a single narrowband receiver in direct detection with a single pin photodiode while automatically avoiding the necessity to use computationally intensive phase-unwrapping algorithms. The specific demodulation technique is also robust against harmonic distortions and, most importantly, division-by-zero errors in continuous real-time measurements. In addition, the computations involved in the technique are ordinary integration and differentiation operations which, thanks to the rich set of techniques for fractional order calculus, can be efficiently executed in a scalable manner with multi-channel FPGA devices and/or analogue processing circuits which are candidates for small-scale integration. We demonstrate the proposed DAS scheme using a sensing fiber with 200 UWFBGs each with a reflectivity of ∼-43 dB, spaced at intervals of 5 m via measurement of a generic phase fluctuation induced by a 2.5 kHz vibration on a piezoelectric (PZT) transducer placed at 1 km, with an SNR of ∼34.52 dB.

In the following sections, we first discuss the mechanism of demodulation in a delayed interferometric sensor and present the mathematical background of the demodulation technique used in our scheme in section 2. Section 3 is dedicated to the experimental setup used to demonstrate the technique and, in section 4, results of back-reflection from UWFBGs and their comparison with the use of standard singlemode fiber operation are given including the output of the interferometer, the intermediate signals used in the demodulation and the retrieved dynamic phase from a generic vibration source.

2. Delayed interferometer in ϕ-OTDR for interrogation of UWFBG array

The mechanism of measurement in the proposed sensing system is shown in Fig. 1, where the generic case of the interrogation of an array of N identical UWFBG_i: i ∈ [1,N] with equal spacing of $\Delta z$is considered. A narrow pulse of a generic shape from a laser with emission at the center wavelength of the gratings is sent into the array. Subsequently, a carefully chosen delay is applied to the response of the UWFBG array such that the reflections from two consecutive UWFBGs overlap in time, and the delayed and normal responses mix at the interferometer. The resulting beating at the photodiode will exhibit a characteristic which can be employed in measuring perturbations happening between adjacent UWFBGs at a resolution corresponding to their spacing.

 

Fig. 1 Schematic of the operating principle of delayed interferometry to interrogate identical UWFBGs using a pulse of narrowband light.

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The use of a delayed interferometric system in a ϕ-OTDR for measurement of perturbations can be clearly understood from the schematic given in Fig. 2, which shows two consecutive points along the fiber corresponding to the position of two adjacent weak gratings in the middle of which an external perturbation is applied. At the receiver the backscattering signal from a grating is delayed, and allowed to beat with the one from an adjacent grating in an interferometer while a phase of $\Delta \delta (t)$is applied in one arm using a phase modulator. If the phase change induced by the external perturbation$\xi (t)$is$\varphi \text{'}(t)=f(\xi (t)),$and considering it will appear in the contribution of the point z_k while not being included in z_m, the electric fields of the individual signals in the two arms become:

 

Fig. 2 Schematic of a double pulse ϕ-OTDR showing the backscattering from two adjacent points.

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where$E_{m,k}$stand for the amplitudes of the two fields and${\delta }_{m,k}(t)+{\phi }_{m,k}$are the individual phases in the two locations,${\phi }_{m,k}$being constants denoting initial phases. Due to the coherence of the source used to interrogate the array, at the photodiode, the two fields in (1) will interfere, giving rise to an intensity whose expression is given by:

where$\varphi (t)$is the measured phase change due to the external impact, $\Delta \delta (t)=C\cos {\omega }_{0}t$,$C$being the phase modulation depth and ${\omega }_o$ the angular frequency of phase, is the phase modulation in one arm.

3. Phase generated carrier differentiate and cross-multiply (PGC-DCM) demodulation mechanism

The demodulation technique in our sensor employs the PGC-DCM algorithm. In a typical interferometric configuration using PGC demodulation, a phase modulation is applied to one arm of the interferometer and its mixing with another signal composed of a delayed version of the input signal results in a beating which contains the phase modulating signal as a carrier for externally induced relative phase changes between the two arms [24–26]. Considering the generic case in which the beating has the phase change term$\theta (t)=C\cos {\omega }_{0}t+\varphi (t)$, while C is the modulation depth and an external impact induces a phase change of $\varphi (t),$the expression for the output of the interferometer has the form:

After using Bessel function expansion in Eq. (3), it can be shown that the second term contains two orthogonal components centered at the even and odd multiples of${\omega }_0$, which means the mixing of the interferometer signal at the receiver with ${\omega }_0$ and 2${\omega }_0$(which are the lowest odd and even components) followed by low-pass filtering can be used to obtain the two components s₁(t) and s₂(t) as shown in Fig. 3. In the mixing of the received signal given in Eq. (2), assuming the amplitudes of the local oscillators for the two mixers are G and H respectively, the two intermediate components become:

 

Fig. 3 Mixing and low-pass filtering to obtain the intermediate signals used in PGC demodulation (LPF: Low-pass Filter).

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In Eq. (4), the mixing efficiency and amplitude of the interfering signal are assumed to be shared constant factors for the two intermediate components. The most straightforward way to obtain the phase from $s_1(t)$and $s_2(t)$would be to use the ratio of the two components and the arctan function for similar mixing efficiency and amplitude of the AC components [27–29]. However, this method, also known as the PGC-arctan demodulation technique needs the requirement of the modulation depth C such that$J_1^{}(C)=J_2^{}(C),$which happens for a modulation index of C = 2.63. Slight deviations of C from this value have been shown to result in a significant reduction of accuracy in the demodulated phase [27]. Besides, this value of the modulation depth is not the optimum one for reducing errors in demodulation [29]. Another critical aspect of the PGC-arctan is that it involves unwrapping the phase for values outside the range of the arctan function with a suitable unwrapping algorithm, and separate investigations have been dedicated to address this problem [18,19]. Namely, such algorithms are computationally heavy, especially in situation where the signal is noisy, and may lead to errors at low sampling rates. In the case of distributed measurement as in ϕ-OTDR, a similar computation needs to be made for each sensing point along the sensing fiber as per the measurement spatial resolution, giving rise to more complex two-dimensional unwrapping akin to the one in image processing systems [20]. In a typical long distance DAS which can be used for continuous real-time monitoring, a significant amount of data needs to be acquired and processed and this is one of the issues that need to be addressed in the development of DAS systems as per recent surveys [2]. Hence it is highly desirable to employ a demodulation technique which addresses this issue in dynamic measurements. For the interrogation of the UWFBG array, we propose and demonstrate the use of a technique known as PGC-DCM whose schematic is shown in Fig. 4. The phase obtained using this method starting with the intermediate components described in Fig. 3, becomes;

 

Fig. 4 Schematic of phase demodulation using PGC-DCM

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First, using trigonometric identity, the RHS of (5) becomes:

The demodulated phase can be obtained by integration of both sides of Eq. (6), which yields:

The parameters G and H in Eq. (7) are the amplitudes of the local oscillator used to obtain the intermediate signals s₁(t) and s₂(t) at the receiver. In our measurement, we used values of unity for both parameters and hence, G = H = 1. In addition, to account for any other intensity fluctuations in the interference signal, as the sum of squares of the cosine and sine in (4) sum to unity, normalization by s₁(t)² + s₂(t)² removes the effect of changes which appear in both components.

Thus the PGC-DCM does not require complicated phase unwrapping algorithms and hence it is suitable for distributed measurements. Studies have also shown that PGC-DCM is robust against undesirable harmonic distortions, which are high when using the PGC-arctan method and the modulation depth deviates from its nominal value [27]. Since there are no division operations, the method is also suitable for situations where one of the intermediate signals used to obtain the demodulated phase has several zero-crossing points thereby avoiding additional mechanisms to mitigate division-by-zero operations. The other interesting feature of the demodulation technique is that, the PGC-DCM algorithm also involves symmetric differentiation and integration operations which are particularly suitable for analogue processing systems. Thanks mainly to the rich set of techniques for fractional order calculus [30], which has applications in a number of control systems, efficient implementations of the integration and differentiation computations have already been implemented using FPGA and analogue processing systems [31]. In a distributed sensing scheme, FPGA-based signal processing can easily be implemented in an efficient system which involves concurrent computations on multiple channels corresponding to different sensing locations along the sensing fiber. These computations are also candidates for electronic integration as they can be realized with analogue processing systems using, among others, operational amplifiers built on CMOS platforms [32,33], single feedback amplifiers [34], and, more recently, ones with reduced circuit complexity [35]. Finally, another contribution to the practicality of the proposed interrogator comes from the compatibility of the integration of operational amplifiers for integration and differentiation with silicon photonics [36], which means that the proposed technique for measurements with analogue processing can be included in a cost-effective hybrid scheme by adding it to a receiver containing integrated photoreceivers [37].

Note that the contribution in [22] involves use of the double pulse to probe the fiber while the current one involves that of a single pulse. The part of the setup with coupling at the source looks similar to an interferometer since we used a more robust mechanism to generate the double pulse from a single one using a delay, thereby avoiding the burdens of delicate synchronization for easily selecting the pulse which should undergo phase modulation, as explained in the experimental section in [22]. The double pulse method is more resilient to imbalance at the interferometer compared to the single pulse one. In addition, the current contribution avoids the issue of phase-unwrapping by employing a different demodulation method (PGC-DCM) which doesn’t require explicit clauses for division-by-zero-operations thereby avoiding errors at zero-crossing points. On the other hand, the previous method in [22] used PGC DMS, which involves division operation and hence the demodulation is more prone to errors. Regarding the sensing mechanisms, the current contribution involves delay interfering of the backscattering from adjacent UWFBGs at the receiver, while the previous one involved interference of overlapped backscattering from adjacent points in the fiber coming from a double pulse probe. While the ultimate physical effects are similar, the individual mechanisms which give rise to them are different. Note also that the susceptibility of self-mixing methods to polarization fading is relatively less compared to schemes which employ a local oscillator for phase demodulation since the delay and mixing happen between back-reflections of adjacent points along the fiber.

4. Experimental setup

The experimental setup used to implement the interrogation of the UWFBG array is shown in in Fig. 5. First, light from a narrowband tunable laser with a linewidth of 200 kHz is amplified using the Erbium-Doped Fiber Amplifier (EDFA) and filtered using an Optical Bandpass Filter (OBPF). The signal is then modulated using an Acousto-Optic Modulator (AOM) which generates probing pulses which are amplified and filtered using, respectively, a second pair of EDFA and OBPF. The pulses are then sent into the UWFBG array containing 200 UWFBGS written on a singlemode fiber at a spacing of 5 m, each having a reflectivity of ~-43 dB, using a three port optical circulator. The gratings have been inscribed using an on-line writing with a phase mask technique where the uniformity of the center wavelength of gratings is maintained using a suitable and stable tension during the drawing [38]. Specifically, a chirped phase mask technique has been employed for the array used in this experiment and the FWHM of the reflection spectrum of each grating is ∼3.4 nm. At the end of the array, a part of the fiber between two consecutive gratings is wound on a PZT actuator driven with a voltage amplifier connected to a waveform generator with which sinusoidal modulations of controlled frequency are applied.

 

Fig. 5 Experimental setup of the proposed ϕ-OTDR sensor: Erbium-Doped Fiber Amplifier (EDFA); Optical Band-Pass Filter (OBPF); Acousto-Optic Modulator (AOM), Digital Acquisition (DAQ); Phase Modulator (PM); Piezoelectric Actuator (PZT).

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The signal reflected from the ultra-weak gratings, each of which is centered at 1549.8 nm is fed through the return port of the circulator to the interferometer containing a passive optical fiber delay in one arm and a phase modulator (PM) on the other. The PM is modulated with sinusoidal inputs of typically 10 kHz with an arbitrary phase modulation depth, while the power level and state of polarization in one arm are adjusted to optimize the beating. The delay is carefully chosen in such a way that the back-reflections of two adjacent UWFBGs accurately overlap. The output of the interferometer which contains the beating is detected using a pin photodiode having a 125 MHz bandwidth.

The photodetected signal is directly acquired (with no averaging) at a repetition period of 20 μs with a real-time Digital Acquisition (DAQ) system with an embedded ADC whose triggering is synchronized with the Arbitrary Waveform Generator (AWGs) driving the AOM and PM. Typically, a single set of traces is acquired to check the backscattering signal from all UWFBGs and to compare the in-band reflections from the raw Rayleigh backscattering from the fiber. The Rayleigh back-scattering signal was also observed by tuning the seed laser & filters out of the reflection bandwidth of the UWFBGs so that the response is observed in the singlemode fiber equivalent of the sensing fiber. To measure phase changes induced by a generic dynamic vibration applied to the PZT over a relatively long period of time, thousands of consecutive traces are acquired. The signal processing scheme shown in Fig. 3, which includes mixing of the interference signal with a sinusoid at the phase modulation frequency${\omega }_0$and$2{\omega }_0$with subsequent low-pass filtering is used to obtain, for each point along the fiber, the two intermediate signals $s_1(t)$and$s_2(t).$These are then fed to the PGC-DCM algorithm to retrieve the demodulated phase, which is also allowed to pass through a High-Pass Filter (HPF) with a cutoff frequency of 1200 Hz to extract the dynamic vibration. It is worth noting that while many DAS systems for the interrogation of UWFBGS based on ϕ-OTDR schemes typically use narrowband lasers with very small linewidth values in the order of 10 kHz, we used a simple tunable laser with a linewidth of ~200 kHz.

5. Experimental results and discussions

The first set of measurements done is to observe the intensity of the backscattering of the UWBG gratings. The passbands of the tunable filters after the two EDFAs are adjusted to maximize the 1% tap of the pulse sent into the fiber as observed in a probing oscilloscope. The wavelength of the tunable laser and the center of the reflection bandwidth of the weak gratings are also aligned by looking at the maximum intensity of the traces on the oscilloscope.

A sample set of traces is given in Fig. 6, which shows all the back-reflections from each grating from the UWFBG array. The reflections are more clearly observed in two different zones representing the response of the near-end of the sensing fiber given in Fig. 7(a) and that of its far-end in Fig. 7(b). From the consistent overlap of subsequent traces, it can be clearly seen that the reflection has a stable pattern with high SNR, which can enable measurements even when the input peak power has been significantly reduced. A comparison of the response of the UWFBG array with the coherent Rayleigh backscattering signal from the fiber without the effective presence of the array, which is equivalent to the case where the interrogation is that of a standard singlemode fiber (SMF), has also been made for a closer observation of the gain in the back-reflection intensity. This was done by keeping all the conditions of the ϕ-OTDR scheme fixed while shifting the wavelength of the seed laser and the passband of the tunable filters shown in Fig. 5, so that the probing pulse lies outside the narrow reflection bandwidth of the ultra-weak gratings, all of whom are centered at a similar wavelength.

 

Fig. 6 500 raw traces showing reflections from the UWFBG array.

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Fig. 7 Back-reflection from 500 raw traces showing reflections from different parts of the (a) near end, (b) far-end of the UWFBG array.

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The difference in the back-reflection intensity is due to non-uniformities of reflectivity during manufacturing of gratings. A comparison of the reflections for the case of UWFBG operation using 20 ns and the coherent Rayleigh backscattering from the fiber for both 20 ns and 120 ns have been done showing that the SMF operation at 20 ns does not enable measurement as the intensity of the trace at the end of the sensing fiber overlaps with the noise of the measurement. Similarly, the SMF operation at 120 ns gives rise to higher intensity; however, note that since the spacing between each grating is 5 m, using such a pulse width would mean the reflections from adjacent gratings overlap even without delay and mixing and hence it is not suitable for phase change measurements. Since the 20-ns probe in singlemode operation shows noisy traces which do not enable measurement, a quantitative comparison of the SNR for the SMF and UWFBG cases has been done by calculating the SNR of a measured vibration using UWFBG as will be given in a subsequent plot. Note that, since the interest so far is in observing the response of UWFBG to the ϕ-OTDR probe, direct measurement of the coherent Rayleigh backscattering traces of the fiber was made by disconnecting one arm of the interferometer, and hence no phase modulation has been applied.

The next set of measurements was performed using the full interferometric setup at the receiver as shown in Fig. 5. A sinusoidal vibration of 2.5 kHz was applied to the PZT, around which a piece of fiber between two gratings at the end of 1 km has been wound, and a number of raw traces (10,000) were acquired in real-time with no averaging performed. The phase modulator was driven with a sinusoidal RF input of 10 kHz. To confirm the presence of the beating between the back reflections of adjacent UWFBGs, we have reported in Fig. 8 the output of the interference signal for a section at the end of the fiber, which is also clearly seen upon visual observation of the back-reflections from the UWFBGs on a real-time oscilloscope. As can be clearly seen in the diagram, unlike the case in Figs. 6 and 7, where traces without the presence of the interferometer nearly overlap, here the reflections from adjacent gratings exhibit a beating.

 

Fig. 8 Overlapped output of the interferometer near the position of PZT showing beating of reflections from adjacent UWFBGs.

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For a closer analysis of overlapped traces for the position corresponding to the location of the PZT, a raw time domain evolution at the point of the vibration is shown in Fig. 9(a). The power spectra of this signal, reported in Figs. 9(b) and 9(c), shows that it has components centered at 10 and 20 kHz, which are at${\omega }_0$and$2{\omega }_0$of the 10 kHz phase modulating signal applied in one arm of the interferometer, at a spacing of 2.5 kHz, consistent with the expected spectrum of a phase modulated signal.

 

Fig. 9 Evolution of the signal at the point of vibration: (a) Raw time domain beating signal near the point of vibration and, power spectra of intermediate signals for: (b) component centered at ω₀ and (c) component centered at 2ω₀.

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Consequently, the demodulation of the phase change induced by the vibration of the PZT was made by first obtaining the intermediate components from the interference signal given in Fig. 9, via a mixing of the received signal with sinusoids at the frequencies corresponding to${\omega }_0$and$2{\omega }_0,$and subsequent low-pass filtering as shown in Fig. 3. The PGC-DCM demodulation scheme depicted in Fig. 4 is then employed to obtain the final demodulated response. The plot given in Fig. 10 shows both intermediate signals and the final demodulated signal before and after high-pass filtering.

 

Fig. 10 Intermediate components and the demodulated signal before and after high-pass filtering.

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It can be clearly seen that, before high-pass filtering, the demodulated phase follows the random fluctuations caused by the slow drift of the response of PZT while also capturing the applied dynamic vibration, demonstrating that the proposed technique can be used to measure a generic phase change from a perturbation source. The results show consistent and stable demodulation of the phase change induced by the vibration for the entire duration of a 200 ms measurement which involves 500 cycles of the 2.5 kHz vibration.

The instantaneous variations of the unfiltered phase change demonstrates capability of sensing of slow drifts in addition to the fast vibration, something which is desirable in many structural health monitoring applications. Note that techniques other than the PGC-DCM which avoid phase unwrapping require division-by-zero operations, which are prone to errors introduced by the zero-crossing points one of the intermediate signals. The filtered dynamic response of the 2.5 kHz vibration (which has a 0.4 ms cycle) is shown in Fig. 11, showing consistent dynamic retrieval.

 

Fig. 11 PGC-DCM demodulated dynamic responses of a 2.5 kHz vibration at two different instances.

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The spectrum of the phase is also depicted in Fig. 12 and the SNR of the measurement is calculated to be 34.52 dB, which is equivalent to the gain obtained by using the UWFBGs compared to standard singlemode operation since the latter yields traces which are at the level of the system noise floor for the same conditions.

 

Fig. 12 Power spectrum of demodulated response of a 2.5 kHz PZT vibration.

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6. Summary

In conclusion, we have proposed and experimentally demonstrated a DAS technique for the measurement of dynamic phase changes based on the interrogation of identical UWFBGs using a ϕ-OTDR with a simple tunable narrowband laser as a seed for the probing pulses and an interferometer with a direct detection receiver using a simple pin photodiode. The traces acquired from the a 1 km array of 200 identical UWFBGs, each with reflectivity of ~-43 dB and FWHM of ~3.4 nm inscribed at intervals of 5 m, exhibit high intensity levels at lower peak-power levels compared to standard singlemode fibers, confirming suitability of the transducer for measurement with higher SNR. A piece of fiber between two adjacent gratings at the end of the sensing fiber has been wound around a PZT and the beating between the back-reflections from two UFBGs after delay and mixing has been observed while applying 500 cycles of a generic dynamic vibration. Subsequent results show extraction of the intermediate signals from the output of the interferometer and consistent retrieval of the dynamic response induced by the vibration for all cycles of the measurement including at zero-crossing points using the PGC-DCM algorithm, which automatically avoids phase unwrapping operations. The generic slow varying and dynamic response of a 2.5 kHz PZT vibration applied at the end of the 1 km UWFBG array has been retrieved with an SNR of ~34.52 dB.