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Abstract
High-scattering optical fibers have emerged as a key component in distributed sensing systems, primarily due to their capacity to enhance signal-to-noise ratio. This paper presents an experimental characterization of optical fibers doped with oxide nanoparticles for displacement sensing. They were manufactured using the phase-separation technique and different doping compounds, including calcium, strontium, lanthanum and magnesium. The Rayleigh backscattering (RBS) signatures in time and frequency domains were acquired using an Optical Backscatter Reflectometer (OBR). The maximum representative length, backscattering gain and strain sensitivity were evaluated. The results indicate that the fiber co-doped with magnesium and erbium chlorides offered the best compromise between strain sensitivity (0.96 pm/$\mu \epsilon$) and maximum length (17 m). For conditions of single and multiple perturbations, strain saturation was reached at ≥7000 μm and <1500 μm, respectively. In addition, the results reveal that, under a condition of variable temperature (30-60 °C), the sensor response becomes significantly nonlinear over length, requiring a technique for temperature cross-sensitivity mitigation that accounts for nonlinearities in sensitivity and hysteresis.
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1. Introduction
Advances in optical fiber fabrication allowed the achievement of low attenuation rates (0.35 dB/km at 1310 nm, and 0.2 dB/km at 1550 nm) and the interconnection of optical communication systems spread all around the globe [1]. Although it seems counterintuitive to propose optical fibers with enhanced propagation losses from the perspective of long-haul communications, the fields of optical sensing [2], fiber lasers and amplification [3] have been exploring this topic increasingly.
Several research works combine distributed sensing techniques with strategies to increase propagation losses, such as exposition of the fiber’s core to the surrounding environment [4], utilization of fibers destroyed by the catastrophic fuse phenomenon [5], inscription of weak fiber Bragg grating (FBG) arrays and ultralong FBGs [6], and exposition of fiber to UV light [7]. These strategies enhance the Rayleigh backscattering (RBS), yielding higher signal-to-noise ratio, measurement range and/or sensitivity [7,8]. They are often applied to standard single-mode fibers (SMF), however, another alternative consists of utilizing fibers doped with nanoparticles for RBS enhancement. In contrast to some special fibers (e.g. fibers made of alternative glasses), they combine the advantages of silica (cost, chemical and mechanical durability, transparency) with nanoparticles that contain different chemical compounds, such as magnesium, calcium and erbium, and act as scattering centers with customized RBS gain and attenuation coefficient [9,10].
With regard to optical sensing, fibers doped with oxide nanoparticles have been used as a key element in distributed systems [11,12]. Although these solutions generally have a limited sensing range on the order of tens of meters (e.g. $0.3$-$200$ m [13,14]) due to their higher propagation losses, they improve the signal-to-noise ratio [15]. In addition, they can be etched, giving rise to short-range distributed sensors with spatial resolutions as high as $1$ mm for refractive index [16,17], humidity [4] and biomarker monitoring [18]. In this context, nanoparticle-doped fibers have been explored in healthcare applications, including smart-home and smart-textiles monitoring [2,19]. In the field of structural health monitoring, distributed sensing can benefit from high-scattering fibers for the assessment of temperature, pressure, humidity, pH, vibration and deformation in concrete [20], vassels [21], wings and flaps of an aircraft [22], etc.
Coherent optical frequency domain reflectometry (OFDR) and optical backscattering reflectometers (OBRs) have been broadly combined with high-scattering medium. Optical fibers doped with magnesium oxide were analyzed with an OBR, and yielded temperature and strain sensitivities of $9.1$ pm$/^{\circ }C$ and $1.0$ pm$/\mu \epsilon$, respectively [15]. In addition, simultaneous multi-channel detection has been proposed by connecting a 1xN coupler to the OBR’s output for fiber multiplexing [10].
One of the existing methods for identifying variations in measurand using an OBR or an OFDR system consists of calculating the shift between the reference and measured RBS spectra [23]. However, a drawback of this technique is the cross-sensitivity between strain and temperature, which can cause significant measurement errors when not properly taken into account [24]. A common approach for cross-sensitivity mitigation is to utilize two optical fibers with different temperature and strain sensitivities (e.g. an SMF and a reduced-cladding SMF) [25]. In this scenario, SMFs are a straightforward choice as they have constant temperature and strain responsiveness over length [25]. By contrast, some properties of nanoparticle-doped fibers may change due to the doping solution composition and nonuniformities in the nanoparticles distribution, shape and size [26]. Therefore, to improve the measurement quality and expand the scope of some cross-sensitivity mitigation techniques to doped fibers, it is necessary to conduct studies to identify the behavior of the measurand response along doped fiber length, as well as its nonlinearities.
This paper presents an experimental characterization of optical fibers doped with oxide nanoparticles for distributed displacement sensing. They were fabricated using the phase-separation technique, and four different doping compounds, namely calcium, strontium, lanthanum and magnesium, were comparatively analyzed by means of an OBR. The fibers signature in time and frequency domains, maximum length, cross-correlated spectral shift, displacement and temperature sensitivities and hysteresis are evaluated in this paper. Similar works in the literature have characterized the strain and temperature responses of a MgO-doped fiber for different applications and network configurations [12,15,27]. Different doping compounds have been exploited using the Transmission-Reflection Analysis (TRA) technique for characterization of strong disturbances at multiple fiber positions [28]. However, due to the simplicity of this technique, strain on fiber did not produce a detectable output. To the best of our knowledge, this is the first time that several doping compounds are comparatively analyzed in a scenario of distributed strain sensing. In addition, nonlinearities associated with temperature changes and multiple disturbances are also analyzed, highlighting that the adoption of a single characterization point may lead to measurement errors. The objective of this study is to enhance the comprehension of how displacement and temperature affect the RBS in nanoparticle-doped fibers.
2. Theoretical background
Figure 1 shows a typical example of a Rayleigh backscattering signature of a doped optical fiber. The gain in power $G$ at the fiber-head interface varies depending on the fiber under test (FUT), as well as the attenuation slope $2\alpha$ (i.e. the fiber attenuation coefficient multiplied by 2). Assuming that the attenuation coefficient is variable along the length of the doped optical fiber, the backscattering power $P$ at a known location $z$ can be calculated as,
where $P_{0}$ represents the backscattering power of the standard SMF used as patch cord immediately before the fiber-head interface. In Fig. 1, a colored line represents the $i$-th discrete section in length ($i=1,\ldots,N$), used to estimate $\alpha (\Delta z_i)$ as, where $\Delta P_i$ and $\Delta z_i$ represent the variation in location and power along the $i$-th interval, respectively. Thus, for an RBS signature expressed in dB, the attenuation coefficient can be determined by calculating its derivative along $i$ discrete intervals [15]. In many cases, $2\alpha$ can be assumed to be constant over length, being specified as the mean of $2\alpha (\Delta z_i)$ for $i=1,\ldots,N$. However, for RBS signatures that decay exponentially, the least-squares algorithm and the model described in Eq. (3) can be used to determine $\alpha (z)$ for arbitrary locations outside the range of $z_0$ - $z_N$.In Eq. (3), $A$ and $B$ are the coefficients estimated by the least-squares algorithm, and $\alpha _s$ is the minimum attenuation coefficient. As depicted in Fig. 1, the slope of the measured RBS signature starts to smooth when the signal-to-noise ratio (SNR) becomes very small until it reaches approximately $0$. Therefore setting $\alpha _s=0$ simulates saturation due to the noise floor of the distributed measuring system. Equation (1) can be manipulated to quantify the maximum representative length of the doped fiber ($l_{max}$) for an acceptable minimum value of optical power $P_{th}$ (or a minimal SNR) detected by the interrogation system, resulting in the following expression,
The temperature and strain sensitivities can be obtained by monitoring the variation in optical power $P(z)$, or by determining the spectral shift between the reference and measured spectra by means of cross-correlation [25]. The latter strategy will be adopted here, since it has shown higher linearity in a similar work [15]. During characterization of sensitivity, hysteresis can be calculated as,
where $\Delta S$ is the variation in spectral shift for a specific fiber sample at a given deformation and location and $(S_{max}-S_{min})$ is the difference between the maximum and minimum values of spectral shift in a full loading/unloading cycle.3. Optical fiber fabrication
The silica FUTs were prepared using the phase-separation technique and its fabrication procedure is thoroughly outlined in [26]. However, a brief review of fabrication is provided as follows. At first, a germanium-doped silica porous layer is deposited inside a silica tube via the Modified Chemical Vapor Deposition process. For G18 and G21, phosporous was added too in the porous layer. Then, the preform’s core is soaked with the doping solution, i.e. an alcoholic solution containing alkaline earth and lanthanide ions. The names of the different fiber and their composition are depicted in Table 1. After drying, the preform’s core sinters down to a denser glass layer, and collapses becoming a solid rod at high temperatures (>$2000^{\circ }$). For I29, after the sintering of the silica porous layer doped with Mg ions, additional silica layers were deposited before deposing new porous layer doped with Al and Er ions. For this fiber (I29), the nanoparticles are located in a ring around the core. For all the other fibers, the nanoparticles are into the core. Then, the solid preform is moved to a draw tower, giving rise to an optical fiber with cladding and core diameters of $125\,\mu$m and $8\,\mu$m, respectively. During the drawing, the FUTs are coated with a polymer material for enhancing robustness.
Table 1. Composition of the doping solution of the FUTs.
Throughout this procedure, amorphous nanoparticles with variable size, shape and composition are grown in situ in the silica preform. Nanoparticles size ranges from few nm up to hundreds nm [26]. Moreover, in the fiber, nanoparticles with several shape patterns can be identified, such as spheres, cylinders and irregular forms with different diameters along their lengths [29]. In addition, evidences suggest that the composition of the nanoparticle changes with their size [26]: concentration of phase separating elements such as Mg increases with size.
According to [29], the bigger the nanoparticle radius, the greater the Rayleigh scattering attenuation. In addition, big nanoparticles induce light interferences, invalidating the ’independent scattering regime’. The refractive index of a nanoparticle depends on its composition, which also affects light scattering [30]. For these reasons, assumptions made by the traditional Rayleigh scattering model for SMFs, such as constant attenuation coefficient, may become no longer valid. In this context, nonlinear behaviors have already been reported in research works that exploit nanoparticle-doped fibers for optical sensing. They include nonlinear attenuation/transmission with variable input power and modeling incompatibility when using some traditional equations that assume the Rayleigh regime in SMFs [31].
4. Experiments
The Rayleigh backscattered power of each FUT was acquired using an OBR (OBR4600, Luna Innovations, Virginia, EUA). The frequency sweeping was configured from $1525$ nm to $1610.17$ nm. The measurand sensitivity was obtained by calculating the spectral shift associated with the maximum cross-correlation between the reference undisturbed condition and the measurement condition, and the width of the cross-correlated data blocks was set to $1$ cm. The optical fibers listed in Table 1 were spliced to a single-mode fiber (SMF), which was connected to the OBR by means of an APC/FC connector, and glued to a linear translation stage at a distance $d \approx 5$ cm from the splice interface. All the optical fibers are coated with an acrylate layer, which was not stripped during the experiments for higher robustness. The manual micrometer of the translation stage was gradually adjusted until a maximum strain of $7000\,\mu \epsilon$ was reached, and then the axial deformation was gradually decreased back to its initial undisturbed condition. This procedure was repeated three times. In addition, an analysis of the fiber’s temperature response was also performed using a thermal chamber (Ethiktechnology, São Paulo, BR), where the temperature was linearly raised from $30\,^{\circ }$C to $60\,^{\circ }$C in steps of $10\,^{\circ }$C. The experimental setups for displacement and temperature monitoring are depicted in Fig. 2(a) and (b), respectively.
5. Experimental results and discussion
The fibers’ backscattering signatures are exhibited in Fig. 3. Notably, there are short fiber samples ($\sim 0.5$ m), causing an abrupt decrease in power immediately after the fiber-end interface. Fibers G18 and G21 exhibited a more linear RBS decay, whereas S22, S26 and I29 have a nonlinear RBS attenuation along their length.
Fig. 3. Rayleigh backscattering signature of doped optical fibers: (a) G21-01, (b) G18-01, (c) S26-01-P2, (d) S22-01-P2 and (e) I29.
Here, the maximum representative length of the optical fiber is considered the location $l_{max}$ where the optical power $P(l_{max})$ becomes close to the OBR noise floor, i.e. the location where the SNR declines to nearly $0$ dB. To overcome the constraint of identifying the maximum length using short fiber samples, the attenuation coefficient was divided into spatial intervals and the fiber’s signature was modeled to estimate $l_{max}$. Figure 4(a) shows the measured backscattered power of I29. The colored lines represent the discrete $i$ intervals utilized to calculate $\alpha (\Delta z_{i})$. Differently from the G21-01 and G18-01 whose signatures decay almost linearly, the RBS of the I29 has a nonlinear behavior (Fig. 4(b)). Notably, $2\alpha$ increases exponentially until it reaches full saturation at the OBR noise floor. Thus, Eq. (3) is adopted to model the fiber attenuation coefficient, since it describes a typical exponentially saturated model. The markers in Fig. 4(b) represent the attenuation coefficients at each discrete interval, whereas the dotted line is the fitted results obtained using the least-squares algorithm and the model described in Eq. (3). Here, $\alpha _s$ is $0$. The extended Rayleigh backscattering signature was calculated by replacing the estimated $2\alpha (z)$ in Eq. (2), and is exhibited in Fig. 4(c) along with the measured results. The maximum length was determined by identifying the distance $l_{max}$ where the estimated signature becomes equal to $P_{min}$ + $\Delta \sigma /2$, where $P_{min}$ is the mean noise floor, and $\Delta \sigma$ is the maximum noise amplitude.
Fig. 4. Estimation of the attenuation coefficient and Rayleigh backscattering signature of I29: (a) estimation intervals $z_i$, (b) estimated attenuation coefficient over length, and (c) estimated backscattering signature.
Table 2 exhibits the gain $G$, the average attenuation coefficient $2\bar {\alpha }(z)$ (calculated by determining the mean of the first five discrete coefficients $2\alpha (z_i)$, $i=1,2,\ldots,5$, over the range of [$0-0.45$ m]) and the maximum length $l_{max}$ of all fiber samples. Two G18 samples with lengths of $0.64$ m and $8.1$ m were connected to the OBR to calculate the relative error between the estimated and measured values of $l_{max}$. The attenuation coefficients of the shortest fiber sample were calculated at each $i$-$th$ interval, resulting in Fig. 5(a). Unlike the I29, the RBS signal of the G18 decays linearly, causing $2\alpha (z)$ to be approximately constant over length. The fitted results considering a linear and an exponential RBS decay are plotted in Fig. 5(a) as patterned curves. The last round marker is an outlier and represents the smoothing of the RBS signature at lower SNR values, preceding signal saturation at the OBR’s noise floor. Figure 5(b) depicts the signature of both G18 samples, as well as the estimated results using the shortest sample for estimation of $2\alpha (z)$. For higher SNR values, the estimation error is minimized by assuming $2\alpha$ constant. However, the exponential model depicted in Eq. (3) is adopted here, as it results in a lower error for sensing scenarios that can explore RBS signals with very low SNR for extraction of information. In this context, the estimated $l_{max}$ and its relative error are $1.0$ m and $2.3$ mm, respectively, as shown in the inset in Fig. 5(b). For sensing conditions that require high SNR, a target value can be established and $2\alpha$ can be assumed constant for fibers G18 and G21, e.g. for a target SNR of $10$ dB, the maximum representative length of the G18 is $0.72$ m.
Fig. 5. (a) Estimated attenuation coefficient of G18-01, and (b) relative error between the estimated and measured values of $l_{max}$.
Table 2. Gain, attenuation coefficient and maximum length of the FUTs.
The frequency domain response was also analyzed and Fig. 6 shows the 2-way losses in backscattering power. They were obtaining by subtracting the reflected signals measured at the fiber-end and fiber-head, which were spaced by a distance $l$. Then, the results were downsampled and filtered using a low-pass Butterworth filter (5th order, normalized cutoff frequency of 0.05 [15]) to mitigate noise. Due to erbium absorption, all doped optical fiber have a higher attenuation around $1530$ nm, which increases with the fiber length [15]. The G18-01 exhibits the highest mean attenuation ($44$ dB), whereas the I29 has the smaller attenuation over the wavelength range of $1525-1570$ nm (on average $-9.2$ dB as depicted in the inset in Fig. 6), even though it has the longer fiber length ($l=7.8$ m). The S22-01-P2 exhibits a strong attenuation peak of approximately $28$ dB over the wavelength range of $1525-1570$ at position $l = 7.3$ m.
The photoelastic coefficient of optical fibers doped with different oxides may change with their composition and concentration [32]. To analyse the displacement sensitivity, axial deformations with variable intensities were applied to all fiber samples under constant room temperature ($23\,C^{\circ }$). The resulting spectral shift is exhibited in Fig. 7(a). Notably, the spectral shift increases linearly with strain, and the smaller R-Squared $R^2$ value (0.9991) is associated with the SP22-01-P2. This fiber sample also exhibited the highest hysteresis ($3.31$%), whereas the G18-01 presented a minimum hysteresis of $0.4$%. It is noteworthy to mention that the SMF strain sensitivity ($1.1$ pm/$\mu \epsilon$) is in accordance with [15], where a value of $1.0-$ pm/$\mu \epsilon$ was reported. With the exception of the SMF, the highest sensitivity was achieved by the I29 ($0.12$ GHz/$\mu \epsilon$ or $0.96$ pm/$\mu \epsilon$). Differences in sensitivity between the SMF and the I29 may be justified by small variations in the thickness of the protective coating layer.
Fig. 7. System’s response to variable displacement. (a) Spectral shift induced by displacement in fiber and (b) displacement sensitivity versus maximum fiber length.
The strain sensitivity versus maximum length is represented in Fig. 7(b). Ideally, the optical fiber that offers the best compromise between sensitivity and length is located at the southeast extremity of the graph. However, there are some short-range applications that require sensing ranges of the order of centimeters and could benefit from the enhanced SNR offered by the G18-01, G21-01 and SP26-01-P2, such as 3D-shape sensing systems for monitoring of smart objects [33], quench detection in high temperature superconductors [34], and humidity mapping and liquid-depth measurements [4]. On the other hand, the I29 is a good choice for applications that require longer fibers (of the order of meters) such as smart textiles for gait analysis [35] and 3D-shape reconstruction [36]. The shaded areas in Fig. 7(b) represent intervals containing values of strain sensitivities currently reported in the literature. A typical strain sensitivity of a common FBG on a standard SMF is around $1.1$ pm/$\mu \epsilon$ [37]. FBGs with enhanced strain sensitivity often achieve values that range from $2$ pm/$\mu \epsilon$ to tens or hundreds of pm/$\mu \epsilon$ [37,38]. With regard to fully distributed sensors based on OFDR and OBR, values such as $1.0$ pm/$\mu \epsilon$ [10], $1.20$ pm/$\mu \epsilon$ [39] and $1.24$ pm/$\mu \epsilon$ [40] can be found in the literature.
Further experiments were conducted with the I29 due to its longer spatial coverage and higher strain sensitivity. Homogeneous displacements were applied along five deformation regions spaced $0.5$ m apart, each with a length of approximately $0.26$ m. At each region, the first fiber extremity was glued to a fixed point whereas the second was glued to a manual translation stage. During this process, different initial condition were applied to the fiber: the 1st and 2nd regions were slightly tensioned, the 3th region was kept loose and the 4th and 5th regions were kept slightly loose. This was performed to assess the how saturation affects each region independently. A distance $d=3$ m was arbitrarily chosen as the beginning of the first deformation region. At all regions, the position of the manual micrometer was simultaneously incremented from 0 to $400$ $\mu$m in steps of $50$ $\mu$m, and then decreased back to $0$ $\mu$m.
The spectral shift measured at each region is depicted in Fig. 8(a). It is worth mentioning that, regarding the conditions of single and multiple deformations, the sensitivity changed from $0.96$ pm/$\mu \epsilon$ (Fig. 7(b)) to a mean value of $1.02\pm 0.05$ pm/$\mu \epsilon$. This small difference may be due to optical fiber splicing, which may lead to variations in launched optical power, causing a non-linear change in RBS [31]. In addition, variations in sensitivity per deformation region could also be justified by the differences in fiber alignment on the translation stage. The increase in hysteresis can also be justified by fiber alignment, causing slight variations in fiber settling during two distinct cycles of variable strain.
Fig. 8. Analysis of multiple perturbations on the I29 fiber. (a) Characterization of displacement sensitivity at each deformation region, and (b) reference and estimated displacements.
Figure 8(b) shows the strain over length, calculated by multiplying the measured spectral shift of a deformation region by its respective displacement sensitivity (obtained through the previous characterization exhibited in Fig. 8(a)). In Fig. 8(b), the solid lines represent the half-cycle with increasing strain, whereas the dotted lines are related to half-cycle with decreasing strain. Notably, at a specific intensity, the system stops responding linearly with strain, and the fiber’s sensitivity achieves saturation, showing no substantial difference when the manual micrometer is incremented. This condition affects regions under different deformations (e.g. 1st and 3rd regions in Fig. 8) at the same time, being associated with the the global system instead of a local threshold strain value per deformation region.
For a single-deformation condition, linear displacements up to $7000$ $\mu \epsilon$ resulted in a linear spectral-shift response, which indicates that the measurement range is $\geq 7000$ $\mu$m. However, due to saturation, the sensing range changed when multiple displacements were applied simultaneously to the sensing fiber, achieving values within the interval of $960-1350$ $\mu \epsilon$. Therefore, the presence of multiple perturbations diminished the measurement range. This may affect applications that require the detection of multiple high-intensity deformations in fiber, such as multi-user smart carpets that analyze gate. It is worth to mention that the system’s spatial resolution is not affected by the presence of single or multiple deformation regions, but by the laser frequency sweeping interval in conjunction with the length of data block used for cross-correlation. Smaller blocks imply higher spatial resolution, however the results are more prone to noise and outliers (such as the one visible in the 4th deformation region exhibited in Fig. 8(b)).
To quantify the influence of temperature on the spectral shift, the I29 was positioned inside a thermal chamber. An SMF was used as reference to measure the temperature gradient along the fibers’ length. Figure 9 shows the spatially-resolved spectral shift over a $20$-cm interval, and the solid and dotted lines are related to positive and negative temperature steps, respectively. They depict the mean of three complete thermal cycles, whereas the shaded areas represent the maximum and minimum measured deviations from the mean. In Fig. 9, the SMF has an almost flat response (maximum standard deviation of $\pm 0.32\,^{\circ }$C), and maximum hysteresis of $4.13{\% }$ (corresponding to a maximum difference in temperature of $0.95\,^{\circ }$C), indicating that the temperature distribution did not change considerably over the longitudinal axis. On the other hand, the I29 exhibits a high hysteresis (maximum amplitude difference of $7.15\,^{\circ }$C), and a non linear response (maximum standard deviation of $4.32$ GHz). Doped optical fibers fabricated by the phase-separation technique have been proved to contain nanoparticles with variable sizes, compositions and spatial distribution [26,29], justifying the irregular spectral shift response over length for different temperatures.
The influence of temperature on the backscattering power of nanoparticle-doped fibers has been broadly addressed in the literature [12,27]. Figure 10 shows the temperature sensitivity of the SMF and I29 at different positions: $0.95$, $1.00$, $1.05$, $1.95$, $2.00$ and $2.05$ m. The patterned curves represent the fitted results considering the average of the points measured at $1\pm 0.05$ and $2\pm 0.05$. Regarding the SMF, the mean temperature sensitivity is $0.6$ GHz/$^{\circ }$C ($9.6$ pm$^{\circ }$C) and the maximum standard deviation at different positions is $\pm 0.48$ GHz, occurring at $50\,^{\circ }$C. With respect to the I29, the mean sensitivities over the regions of $1\pm 0.05$ m and $2\pm 0.05$ m are $1.61$ GHz/$^{\circ }$C and $1.35$ GHz/$^{\circ }$C, respectively. Therefore the temperature sensitivity decreases by $16.15{\% }$ over a $1$-m range. The standard deviation of sensitivity increases with temperature, achieving a maximum values of $\pm 7.80$ GHz/$^{\circ }$C at $60\,^{\circ }$C. These results emphasize the need to utilize a nonlinear technique for mitigation of temperature cross-sensitivity in distributed strain sensors consisting of nanoparticle-doped optical fibers.
To analyze the variability of the temperature response over time, different measurements were collected over three consecutive days. At each day, three temperature cycles were performed, whose mean results are shown in Fig. 11. As can be noted, fiber S22-01-02 presented the best repeatability over a three-day period. Table 3 lists the mean absolute errors in GHz between two different days, highlighting that fibers S22-01-02 and I29 presented lower mean absolute errors during the aforementioned period.
Table 3. Mean absolute error (GHz) between days.
Although the goal of this study is mainly to provide a characterization of different nanoparticle-doped fibers for distributed sensing, Table 4 provides some results that can found in the literature for systems based on OBR and OFDR.
Table 4. Comparison of different results found in literature for distributed strain sensing using an OBR or OFDR-based system.
To mitigate the cross-sensitivity between temperature and strain, an SMF and a reduced-cladding (RC) SMF were applied along with a traditional signal processing technique based on the coefficients matrix [25]. The RC SMF yielded high temperature sensitivity ($3.47$ GHz/$^{\circ }$C). A thorough characterization of a MgO-doped optical fiber has been provided by [10]. The multiplexing of several optical fibers has been proposed to improve the compromise between sensing range and spatial resolution. In [41], an optical fiber containing densely spaced weak gratings was utilized to increase the RBS and sensing range. A strain sensitivity of $0.15$ GHz/$\mu \epsilon$ was obtained along a 200-m fiber.
An optical fiber based on a silica/silica/polyamide structure was utilized by [39] and combined with a novel signal processing technique to extend the temperature sensing range and improve accuracy. In [42], a nanoparticle-doped fiber was used in conjunction with an FBG for distributed temperature sensing, which allows to tag a specific sensing point as reference and to decouple the strain and temperature responses. Notably, the optical sensing system proposed in this paper has a strain sensitivity close to the average results described in Table 4. In addition, it has high temperature sensitivity, which points out the feasibility of its application as a thermal sensor. The spatial resolution could be further improved by adjusting the OBR parameters, and values of the order of $\mu$m can achieved at the cost of increasing the measurement noise.
6. Conclusions
This paper presented the characterization of optical fibers doped with nanoparticles for distributed displacement sensing. Here, different doping solutions containing calcium, strontium, lanthanum and magnesium oxides were analyzed. Experiments with variable strain ($0-7000\,\mu \epsilon$) and temperatures ($30-60\,^{\circ }$C) were conducted and the RBS intensity was acquired using an OBR. In addition, a method for estimating the maximum sensing length considering a nonuniform attenuation coefficient was introduced. Results indicate that, among all fiber samples, the I29 offered the best compromise between strain sensitivity and maximum length ($17$ m). However, it presented higher hysteresis ($3.31{\% }$) when subjected to cycles of linear displacement variations under constant room temperature. In contrast, fiber samples doped with calcium and strontium oxides produced hysteresis as low as $0.4{\% }$.
Experiments with single and multiple perturbations were performed using the I29. Under a condition of a single disturbance, variations from $0$ to $7000\,\mu \epsilon$ caused linear shifts in spectrum. By contrast, saturation was reached for displacements as small as $1000\,\mu$ when multiple perturbation were induced on fiber. Nevertheless, within the unsaturated working region, the I29 could successfully measure five different displacements over a $3.5$-m range, with a sensitivity of $\sim 1$ pm/$\mu \epsilon$ ($\sim 0.13$ GHz/$\mu \epsilon$). For experiments with variable temperature and null deformation, the I29 exhibited high hysteresis and nonlinear spectral shift over length (maximum standard deviation $\sigma$ of $\pm 4.32$ GHz in contrast to $\sigma = \pm 0.48$ GHz for the SMF). In addition, the temperature sensitivity changed along the optical fiber length, decreasing by $16.15{\% }$ over a $1$-m range. These findings highlight the necessity of applying a method for temperature cross-sensitivity mitigation that takes into account the nonlinearities introduced by hysteresis and nonuniform sensitivity. Future works include the investigation of stimulated Brillouin scattering using the nanoparticle-doped fibers, as well as the study of machine learning techniques and nonlinear signal equalization for minimizing the temperature cross-sensitivity. In addition, studies of different doping compounds, such as Al$_2$O$_3$, will be addressed in the future.
Funding
Fundação para a Ciência e a Tecnologia (LA/P/0037/2020, PTDC/EEI-EEE/0415/2021, UIDB/50011/2020, UIDB/50025/2020, UIDP/50011/2020, UIDP/50025/2020); Financiadora de Estudos e Projetos (0036/21, 0322/23, 2784/20); Fundação de Amparo à Pesquisa e Inovação do Espírito Santo (1004/2022 P, 316/2023, 458/2021, 629/2022); Conselho Nacional de Desenvolvimento Científico e Tecnológico (310709/2021-0, 405336/2022-5, 440064/2022-8).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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