High-sensitivity distributed measurement of hydrostatic pressure is experimentally demonstrated by optical time-domain analysis of Brillouin dynamic grating (BDG) in polarization maintaining fibers (PMF’s). The spectral shift of the BDG in four different types of PMF’s are investigated under hydrostatic pressure variation from 14.5 psi (1 bar) to 884.7 psi (61 bar) with less than 2 m spatial resolution. The pressure sensitivity of BDG frequency is measured to be ‒1.69, + 0.65, + 0.78, and + 0.85 MHz/psi for a PM photonic crystal fiber (PM-PCF), two Bow-tie fibers, and a PANDA fiber, respectively, which is about 65 to 169 times larger than that of Brillouin frequency-based pressure sensing.
© 2016 Optical Society of America
Detection of unintended inner obstacles or leak of a pipeline has been a significant issue in oil and gas industries and one of possible approaches is to monitor the variation of local pressure. Several types of fiber optic sensors have been demonstrated for measuring hydrostatic pressure on the basis of superstructure fiber grating, silica diaphragm, fiber Bragg grating (FBG) and photonic crystal fiber (PCF), in the form of a point sensor [1–5]. For distributed sensing of hydrostatic pressure Brillouin optical time-domain analysis (BOTDA) has been applied by measuring pressure-dependent variation of Brillouin frequency shift (BFS) . The discrimination of pressure and temperature dependencies of the BFS was also reported using the BOTDA . The reported pressure sensitivity of the BFS is about 0.7 MHz/MPa (or 0.07 MHz/bar) without coating and 1.5 MHz/MPa with outer coating in conventional single-mode fibers [8,9], which, however, is too low to be used for practical applications considering the measurement accuracy (~1 MHz in general) of Brillouin sensors. Recently, Brillouin dynamic grating (BDG) has attracted considerable attention in photonic societies and the researches on its application to distributed temperature and strain sensors have been conducted with various types of polarization maintaining fiber (PMF), single-mode fiber (SMF), and few-mode fiber (FMF). In principle the reflection spectrum and center frequency of the BDG in a PMF depend on local birefringence and have proven to show much higher sensitivities (by several tens of times) to temperature and strain variation compared to the BFS [10–14].
In this paper, we propose and experimentally demonstrate a distributed hydrostatic pressure sensor based on the BDG in PMF. Several types of PMF’s are tested including Bow-tie PMF, PANDA PMF, and PM photonic crystal fiber (PM-PCF), and the spectral shift of the BDG is characterized as a function of pressure by optical time domain analysis using the double modulation scheme of a single light source . Distributed measurements are performed with 1.0 – 1.8 m spatial resolution under hydrostatic pressure of atmospheric pressure (1 bar) to 884.7 psi (61 bar). The pressure sensitivity of the BDG frequency is measured to be −1.69, + 0.65, + 0.78, and + 0.85 MHz/psi for four different types of PMF’s (PM-PCF, two Bow-tie fibers, and PANDA fiber), respectively, which is about two orders of magnitude larger than that of the BFS-based method. The relation between the strain and pressure dependencies of the BDG frequency is also confirmed by analyzing the measurement data of two bow-tie fibers with different cladding diameters from the same manufacturer.
The BDG in a PMF represents an acoustic phonon generated by the stimulated Brillouin scattering (SBS) between counter-propagating pump waves, which is used to reflect a probe wave orthogonally polarized to the pump . Figure 1 shows the schematic of the BDG operation based on a PMF where the frequency offset (νD) between the pump1 (ν1) and the probe (ν2), called BDG frequency, is determined by the local birefringence (Δn) as follows:11].
When axial strain is applied to a PMF lateral stress is induced at the interface between the cladding and embedded stress members by the difference of Poisson’s ratio. The strain-induced birefringence Bst in the PMF is represented by :16]. Temperature-dependent variation of the birefringence in a PMF can be also attributed to thermally induced strain . Difference of thermal expansion coefficients between cladding (α1) and stress member (α2) induces thermal strain under ambient temperature variation which is given by18]. It should be noted that T is generally negative (since Tf is much larger than Tc) in silica fibers. The temperature coefficient of νD was measured to be negative in previous works , which means that the absolute magnitude of BT decreases as temperature increases. This feature is explained by the decrease of T in Eq. (3) with the increase of temperature. The opposite sign of strain and temperature coefficients of νD indicates that the terms (α1 – α2) and (μ1 – μ2) have the same sign.
In a cylindrical material the axial strain induces the contraction in the radial direction and the hydrostatic pressure in the radial direction axially stretches the length of the material . When an optical fiber is used as a pressure sensor the pressure in the axial direction is cancelled and the pressure in the radial direction (P) is directly converted to the axial strain (ε) by the following relation:Eqs. (1) - (4) as follows:Equation (5) is valid in a bare fiber without coating which can have additional influence on the pressure dependence. Considering the positive strain coefficients of νD in previous works  it can be predicted that the hydrostatic pressure tends to increase the birefringence (and νD) of Bow-tie and PANDA PMF’s [20,21].
Figure 2 shows the experimental setup for distributed measurement of hydrostatic pressure using BDG in PMF’s. The insets A, B, and C depict the configurations for two Bow-tie fibers, PANDA fiber, and PM-PCF, respectively, used for fiber under test (FUT).
A distributed feedback laser diode (DFB-LD) at the wavelength of 1550 nm was used as a light source, and the output was modulated at fm1 with carrier suppression to generate two first order sidebands for pump and probe waves by an electro-optic modulator (EOM) and a microwave generator (MGW1). Two sidebands were amplified by an Er-doped fiber amplifier (EDFA) and the amplified spontaneous emission (ASE) noise was removed by using the optical tunable filter (OTF) before the pump and probe waves were separated by a FBG. The pump wave was divided by a 3 dB coupler, and one of the outputs was modulated by a single sideband modulator (SSBM) and MGW2 to generate a continuous wave (CW) pump2. The modulation frequency (fm2) of pump2 was set equal to the νB of FUT to maximize the BDG reflection. The other output was modulated as a 20 ns bell-shaped pulse for pump1 by an EOM and a pulse generator. The probe wave was also modulated as a pulse by an EOM and the pulse generator, the duration of which was 10 ns for PMF-1 and PMF-2 (Bow-tie fibers, HB1500 and HB1500G by Fibercore) and PMF-4 (PM-PCF, PM-1500-01 by NKT photonics), and 18 ns for PMF-3 (PANDA fiber, SM15-PS-U25A by Fujikura). The pump waves were amplified by EDFA’s and counter-propagated in the FUT with the polarization alighted parallel to the slow axis. The probe wave was launched to the FUT in the direction of the pump1 with the polarization aligned parallel to the fast axis through a polarization beam splitter (PBS) after being amplified by an EDFA. The timing of the pump1 and probe pulses was controlled to maximize the reflection signal from the BDG (i.e. the probe pulse lags by 10 ns). The reflection signal from the BDG was amplified and filtered by an EDFA and a FBG, respectively, and recorded by a 125 MHz photo detector and an oscilloscope. The BDG spectrum of each FUT was obtained with 4 MHz step by sweeping fm1 in the vicinity of the half of νD. Each trace was averaged 256 times for noise suppression and the hydrostatic pressure on the test section of FUT was varied from 1 bar (14.5 psi) to 61 bar (884.7 psi) using a stainless steel pressure chamber.
For removing the effect of temperature change on νD the temperature of pressure chamber was monitored which was used to compensate the measured νD according to the reported temperature coefficients . The time required for distributed measurement at each pressure was less than 1 minute during which the temperature variation was suppressed to be less than ± 0.1 °C, and long-term variation of the ambient temperature during the total measurement time was less than 2 °C for each FUT. Insets ‘A’, ‘B’, and ‘C’ in Fig. 2 show the structures of FUT which are two Bow-tie fibers (PMF-1 and PMF-2), a PANDA fiber (PMF-3), and a PM-PCF (PMF-4), respectively. The length of the fiber section inside the pressure chamber was 3 m for PMF-1, PMF-2, and PMF-3, and 2.5 m for PMF-4 which is larger than the spatial resolution determined by the duration of probe pulse.
Local BDG spectra measured at different hydrostatic pressures are presented in Figs. 3(a) – 3(d) for PMF-1 to PMF-4, respectively. The pressure step between BDG spectra in Figs. 3(a)–3(c) is 217.6 psi (15 bar), and that between two BDG spectra of PMF-4 (PM-PCF) is 870.2 psi (60 bar) where multiple peaks appear spanning 1.5 GHz. It is notable that the BDG frequency increases along with the increase of hydrostatic pressure in Bow-tie and PANDA fibers as expected in Eq. (5), while it decreases in PM-PCF. The multiple peaks and the broad spectra in Figs. 3(c) and 3(d) could be attributed to the non-uniformity of birefringence in the FUT sections. The distribution maps of BDG frequency shift (ΔνD) with different hydrostatic pressures in the test section are shown in Figs. 4(a)–4(d) for PMF-1 to PMF-4, respectively, where one can confirm the shift of νD by local change of hydrostatic pressure. It is worth mentioning that ΔνD was calculated by applying the cross-correlation fitting of two BDG spectra for accurate determination of the spectral shift in a multi-peak spectrum  with the spectra at 14.5 psi as the reference.
Figures 5(a) – 5(d) plot ΔνD as a function of hydrostatic pressure with a step of 72.52 psi (5 bar) where the pressure coefficients of νD are + 0.78, + 0.65, + 0.86, and −1.69 MHz/psi for PMF-1 to PMF-4, respectively, by the linear fit. The data of 14.5 psi (1 bar) and 884.7 psi (61 bar) in all FUTs was measured several times for the confirmation of reproducibility. The frequency deviation from the linear fit in cases of PMF-1 to PMF-3 was within ± 6 MHz which corresponds to the hydrostatic pressure of ± 9.3 psi. We think this deviation could be attributed to temperature fluctuation (~0.1 °C) inside the pressure chamber considering the accuracy of pressure gauge (0.1%) and the temperature sensitivity (~50 MHz/°C) of the BDG frequency reported in our former work . The measurement of PMF-4 (PM-PCF) provides higher accuracy with the frequency deviation less than ± 2 MHz as confirmed in the zoomed view presented in Fig. 6, which corresponds to the pressure error of ± 1.2 psi. This enhanced accuracy originates from the fact that the temperature sensitivity of νD in the PM-PCF is negligible above room temperature . When the pressure was changed from 1 to 61 bar slight increase (~1°C) of the chamber temperature was observed as a result of adiabatic process. This temperature variation was compensated at the final stage using the reported temperature coefficient of νD. In the former work the pressure sensitivity of BFS in a coated optical fiber was reported to be 1.5 MHz/MPa (i.e. ~10 kHz/psi) . Therefore one can obtain 65 (PMF-2) to 169 (PMF-4) times higher pressure sensitivity with this BDG-based pressure measurement when compared to the BFS-based scheme.
Table 1 lists the specifications and the sensitivities of νD to strain (Δε), temperature (ΔT) and hydrostatic pressure (ΔP) for the PMF’s used in this work according to the results of previous and current works. PMF-1 and PMF-2 are Bow-tie fibers made by the same company with similar cross-sections but different cladding diameters. It is notable that the ratio of Δε-dependence to ΔP-dependence is about 1.64 in PMF-1 and 1.63 in PMF-2. This similarity can be explained by the similar mechanical properties (i.e. Poisson ratio and Young’s modulus) of two fibers according to Eq. (4). The ratio in PMF-3 (PANDA fiber) is about 1.29, different from PMF-1 and PMF-2, which is attributed to the different geometrical structure. Additionally, the ratio of ΔT-dependence to ΔP-dependence is about −72.8 in PMF-1 and −71.4 in PMF-2, less than 2% difference, which is smaller in PMF-3 (−67.3). Among the Bow-tie and PANDA fibers the one with larger νD shows larger Δε-dependence of νD, while the PANDA fiber (PMF-3) shows larger ΔT- and ΔP-dependence of νD than Bow-tie fibers.
We have proposed and experimentally demonstrated the distributed measurement of hydrostatic pressure on the basis of BDG in various PMF’s. The pressure sensitivities ranging from 0.65 (Bow-tie fiber) to 1.69 (PM-PCF) were obtained, which is about 65 to 169 times larger than that of BFS in a single-mode fiber. For practical applications of the BDG-based pressure sensor, however, it is critical to separate the effects of temperature and strain from pressure due to the large sensitivities of BDG frequency to all of them. We think one of possible approach is to measure Brillouin and Raman scatterings together with the BDG spectrum for complete discrimination of temperature, strain and hydrostatic pressure. The use of PM-PCF also looks promising by its negligible temperature dependence above room temperature, which, however, may suffer from larger noise coming from the reflection at splicing points as well as high cost.
National Research Foundation of Korea (NRF) (NRF-2015R1A2A2A01007078). Chung-Ang University Excellent Student Scholarship.
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