1. Introduction

Distributed fiber optic transverse-force (TF) or -load sensing is important for multiple applications ranging from industrial and environmental structures to defense constructions [1–8], especially in pressure monitoring area, including oil/gas downhole and pipeline, geotechnical engineering, water distribution and sewerage utilities [8–12]. Fiber Bragg grating (FBG) can be used to implement TF or pressure sensing through adopting a special sensitivity-enhancement package [13,14], however only discrete multi-points or quasi-distributed fiber sensing with limited spatial resolution can be achieved [15,16]. In addition, a tradeoff between the sensing spatial resolution and the number of FBGs used must be considered. Compared with the numerous development efforts for distributed fiber optic strain and temperature sensing [17–23], the studies on distributed fiber optic TF sensing are just at an early stage, with few reports characterized by limited performances [3,5,8]. Reported demonstrations on distributed TF measurement were mainly focused on polarization maintaining fiber (PMF) based systems, either using distributed Rayleigh scattering analysis [3] or distributed polarization crosstalk analysis (DPXA) [2,4,6,7,24]. Reference [3] was claimed by the authors to be the first true distributed TF fiber sensing report in commercial Panda-type PMF with a spatial resolution of ∼2 cm. However, the measureable fiber length was limited to few tens of meters due to the difficulties inherent in the technique used. A much larger TF measurement range of 3.2 km was achieved with DPXA technique, with a slightly larger TF spatial resolution of ∼5 cm by some of the authors in this paper [6,7,25,26]. Unfortunately, using PMF as a sensing medium is always more expensive compared to using single-mode fiber (SMF) and requires complicated birefringence axis alignment in general [4,6,7,26].

From the numerous reports on distributed strain or temperature sening [17–23], it is not difficult to conclude that the standard SMF used for optical communications is an ideal low-cost and low-loss sensing medium, especially for the cases involving long sensing distances. Unfortunately, to the best of the authors’ knowledge, neither the distributed TF interrogation technique employing SMF as sensing medium has reached the level for practical applications, nor any direct demonstration was reported in literatures. Schenato et al. recently described a SMF-based distributed pressure sensing cable, capable of converting the transversal pressure into elongation, before being interrogated with any of the distributed strain sensing techniques, such as those based on Brillouin- and Rayleigh-scatterings [8]. Using a similar design idea of converting pressure to strain, C. Zhu et al. reported a distributed fiber pressure sensor based on Bourdon tubes using Rayleigh backscattering interrogated with optical frequency-domain reflectometry (OFDR) [12]. However, the use of such pressure-to-strain conversion mechanisms complicates sensing system designs and compromises sensing accuracies, especially for long fiber optic sensing systems.

Generally speaking, TF induces a local birefringence via the photo-elastic effect [27–30] when applied to a SMF, and therefore distributed fiber TF sensing can be achieved through accurately measuring the distance-resolved birefringence along the SMF. Several techniques based on optical time-domain reflectometry (OTDR) and OFDR for characterizing distributed birefringence of SMFs have been demonstrated, including homodyne Brillouin OTDR (BOTDR) [31], polarization OTDR (POTDR) [32,33], phase-sensitive OTDR (φOTDR) [34], chirped-pulse φOTDR (CP-φOTDR) [35,36], polarization-sensitive OFDR (PS-OFDR) [37,38], and polarimetric OFDR (POFDR) [5,39]. The homodyne BOTDR and POTDR both relied on indirect estimation to infer the local or average birefringence by analyzing the evolution of state of polarization (SOP) of backscattered signals via a certain mathematical analysis, which showed relatively high measurement uncertainty [31–33]. By calculating the spectral correlation between two groups of orthogonally-polarized measurements acquired by the φOTDR system, the distance-resolved phase birefringence measurement along a SMF could be achieved with a minimal measurable birefringence on the order of ∼10⁻⁷ over tens of kilometers detecting range [34]. However, such a small measureable birefringence can only be achieved by scarifying the spatial resolution (around 1 meter) and increasing the measurement time by carrying out a large number of repeated measurements and complicated averaging procedures [28]. By replacing the Gaussian-shaped pulses of traditional φOTDR with chirped pulses and significantly decreasing the measurement time and complexity of system [35], the CP-φOTDR enabled a direct measurement of position-resolved linear birefringence of SMFs in ∼1 sec, while maintained the spatial resolution and detecting range the same as those in φOTDR [36]. However, due to the limitation of minimum permissible optical pulse widths, all above OTDR-based distributed birefringence measurement techniques have a poor spatial resolution on the order of 1 meter.

OFDR is capable of achieving extremely high spatial resolution, on the order of millimeters or even microns, with the potential to characterize a fiber length of tens of kilometers or even more than one hundred kilometers [22,40–43] with degraded spatial resolution of tens of meters, although the state-of-the-art commercial OFDR products only have a measurement range less than 100 meters in fiber due to the lack of long coherence length linearly swept laser sources or high speed digital circuits. Limited SOP analysis was introduced into the OFDR system, termed PS-OFDR, to enable a distributed characterization of fiber bending induced birefringence along SMFs [38]. However, such PS-OFDR was only demonstrated in fiber samples with a length less than 30 meters and a spatial resolution of 3 cm. In a previous publication [5], we demonstrated a polarization sensitive OFDR system (P-OFDR) based on polarization scrambling and analysis capable of measuring the local bending-induced birefringence along a SMF with a spatial resolution of 0.5 mm over 800 m, with an advantage that the system was robust against SOP variations caused by fiber movement during test. However, such a system can only measure the size of the birefringence, unable to determine its direction, because the birefringence in each segment inside the fiber was obtained by averaging 200 random polarization states and consequently the direction information of birefringence was lost. In addition, its birefringence measurement sensitivity may also need to be improved. Ding et al. described a P-OFDR system and developed a method for the distributed measurement of birefringence induced by bending, twist and TF, respectively, in a spun high-birefringence (HiBi) fiber and a standard SMF [39]. However, the authors mainly aimed to verify the potential of their P-OFDR system for evaluating and improving the quality of the spun HiBi fibers, but did not investigate its capability for distributed TF sensing.

In a previous publication [44], we reported a novel OFDR based distributed polarization analysis (DPA) system with full polarization analysis capability, called polarization-analyzing OFDR (PA-OFDR). Such a system incorporates binary magneto-optic (MO) polarization rotators to achieve high measurement accuracy [45,46]. Unlike the strain and temperature measurements with a regular OFDR which are relative with respect to a reference Rayleigh spectrum measurement, the birefringence measurements with our PA-OFDR are absolute and therefore exclude the inaccuracies of the references. In [44], we validated the birefringence measurement accuracy of our PA-OFDR using a non-distributed polarization analysis system with birefringence measurement accuracy traceable to a quartz standard [42] and obtained a relative error of 0.59%, a birefringence measurement resolution of <2×10⁻⁷ RIU (RIU: refractive index unit), a reflection spatial resolution of 10 µm, and a minimum detecting backscattering (reflectivity) of −130 dB. We pointed out that the system could be used for distributed TF sensing with high measurement accuracy and spatial resolution. Note that although Ref. [5] reported the measurement of bending-induced transverse stress and also pointed out its potential for TF sensing, the actual TF sensing was not demonstrated. In addition, Ref. [5] used a polarization scrambling based OFDR to obtain distance resolved birefringence induced by the transverse stress via the photo-elastic effect, while this paper uses a very different approach, the full Muller matrix analysis based PA-OFDR, to obtain the information. In addition, since the local birefringence information in Ref. [5] was extracted by averaging local scattering data from each fiber segment over 200 random polarization states, the birefringence measurement sensitivity is much lower than that obtained by the PA-OFDR in which the birefringence was obtained by using Muller matrix analysis with 6 distinctive SOP’s without any averaging over SOP’s.

In this paper, we report what we believe the first demonstration of a true direct distributed TF sensing along a SMF without the need of force-to-strain conversion using our PA-OFDR system of [44]. We show that the birefringence induced by the TF is linearly proportional to the transverse line-force (TLF) applied to the fiber, where the TLF is defined as TF divided by the length of fiber subject to the TF. We experimentally verify the linear relationship using the PA-OFDR and determine the proportional constant, which is defined as the TF measurement sensitivity. Using the TF sensitivity as the calibration factor of the system, we successfully demonstrate the distributed TF fiber sensing capable of detecting a weight of less than 0.68 g, yet having a dynamic range over 44 dB. In particular, we obtained a maximum detectable TLF of 16.8 N/mm, a minimum detectable TLF of 6.61×10⁻⁴ N/mm, a TLF measurement uncertainty of less than 2.432%, a TF sensing spatial resolution of 3.7 mm, and a TF sensing distance of 103.5 m. Finally, we experimentally investigated the influence of different fiber coatings on the TF sensing and found that the polyimide coating is a better choice due to its high TF measurement sensitivity and response speed, although the high residual birefringence in the polyimide coated SMF needs to be reduced in further development. We believe the findings reported in this paper are important for the implementation of the OFDR based technology for distributed TF sensing applications in practice.

2. Principle of distributed TF fiber sensing and experimental setup

2.1 Birefringence induced by TF in SMF

When a length of SMF is subject to a TLF f, the birefringence $\Delta n$ induced via the photo-elastic effect can be expressed as [27,47,48]:

2.2 Experimental setup

The experimental setup of distributed TF sensing using the PA-OFDR is shown in Fig. 1. The linewidth, frequency-sweep speed and sweep range of the tunable laser source (TLS, Yenista TUNICS T100S-HP) are ∼500 kHz, $2.5 \times {10^3}$ GHz/s (20 nm/s) and $1 \times {10^4}$ GHz (80 nm, from 1520 nm to 1600 nm), respectively. The TLS, with a power of 2 dBm, outputs a linear polarized light through a PMF jumper. 5% light is coupled out from an optical coupler (C1) to the auxiliary interferometer, termed as k-clock interferometer, for providing trigger pulses to the digital circuit to digitize the signal measured by the main interferometer with equal frequency spacing to reduce the nonlinearity of the frequency sweeping of the TLS [44]. Note that, since the TLS’s linewidth of ∼500 kHz corresponds to a coherence length of ∼600 m, so a delay-line of ∼250 m long SMF is used for the k-clock interferometer for ensuring a measurement distance of >100 m. Fast Fourier transform of the digitized signal reveals the distance-resolved information of backscattered and reflected light in the SMF under test (SMF-UT). The local birefringence $\Delta n(z )$ along the SMF-UT can be obtained from the following equation [44]

 

Fig. 1. Schematic of experimental setup for distributed TF fiber sensing, with TF’s simultaneously applied at 10 different positions along the SMF-UT, using a PA-OFDR system. Different weights are placed on the top of a glass-slide for applying different TF’s onto the SMF-UT and the length of the glass-slide determines the force-applying length. A supporting-SMF, in parallel with the SMF-UT, is used for maintaining the balance of every glass-slide. The coatings of each fiber segment subject to the TF and the corresponding supporting SMF are removed. Inset shows measured birefringence versus distance along SMF-UT under a typical TF with a BSR of 0.25 mm for data processing. PMF: polarization maintaining fiber; TLS: Yenista T100S-HP tunable laser source; C1, C2, C3: PMF couplers; C4, C5: SMF couplers; PSG: polarization state generator; PSA: polarization state analyzer; CIR1, CIR2: optical circulators; BPD1, BPD2: balanced photodetectors; FRM1, FRM2: Faraday rotation mirrors; SMF-UT: SMF under test; PC: personal computer. Data acquisition and processing were implemented with a personal computer and a LabVIEW^TM based software.

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From Eq. (1), the distributed TF fiber sensing using a PA-OFDR system can be achieved with a sensitivity equal to the proportion constant $\zeta $. To demonstrate the distributed TF fiber sensing, we setup a simple experiment as shown in Fig. 1. The whole SMF-UT, with a length of ∼18 m, was placed on a stainless steel optical table, and affixed with soft adhesive tapes in order to avoid inducing undesired stress. Care was also taken to avoid twisting the fiber. In addition, any possible bending along the SMF-UT was assured to have a radius larger than 10 cm, for keeping bending-induced birefringence negligible [44]. We selected 10 fiber segments, as numbered in the figure, with an interval of ∼0.5 m from ∼11 m to ∼16 m along the SMF-UT, to apply transversal force along the SMF-UT. The buffer coatings of the 10 fiber segments were stripped carefully with no damage to the fiber itself. A TF was precisely applied to each fiber segment by putting one or more calibration weights stacked together on a glass-slide pressing on the SMF-UT. To keep each glass-slide balanced, a supporting-SMF, identical with the SMF-UT and with the coating removed, was used, and subsequently only half of the total weight was experienced by the SMF-UT. All the glass-slides had the same width of 2.5 cm but were cut into different lengths for changing the force-applying lengths onto the fiber. Therefore, the TLF f applied to a segment of SMF-UT can be expressed as:

In the inset of Fig. 1, a typical measured curve of birefringence along the SMF-UT, induced by a TF with a weight of 400 g and a force-applying length of 7.5 cm, is shown, obtained using a BSR of 0.25 mm for the data processing. In order to avoid the measuring uncertainties, we performed 10 repeated measurements and the curve represents the 10 times average. Note that the birefringence distribution inside the 7.5 cm force-applying length is expected to be uniform. The Gaussian-like distribution is mainly caused by the low-pass digital filtering during data processing and averaging of multiple data traces, including multiple frequency-scans in each measurement and 10 full measurements. Also, due to the above data processing, we find that the Gaussian-like peak has a full width at half maximum larger than the force-applying length. This issue can be solved by optimizing the data processing algorithm in the future.

3. Experiments and discussions

3.1 Calibration of TF measurement sensitivity

In order to demonstrate a true direct distributed TF fiber sensing, a calibration should be performed to determine the TF to birefringence conversion coefficient $\zeta $ or the TF measurement sensitivity of each SMF batch, although it can be estimated to be 8.559×10⁻⁸ ${{\textrm{RIU}} / {({{\textrm{N} / \textrm{m}}} )}}$ using Eq. (2) theoretically. In practice $\zeta $ may be slightly different from fiber batch to batch due to small variations in fiber dimensions and material properties. Since either the TF itself or the force-applying length can change the TLF f in Eq. (1), two groups of experiments with different force-applying lengths and different TF were conducted to minimize potential errors in the calibration process. Note that one may apply different TLF to a single segment of optical fiber to perform the calibration for obtaining $\zeta $, we choose to simultaneously apply different TLF to 10 different fiber sections to perform the calibration, which we believe can average out the slight position dependent variations, as will be shown below.

3.1.1 Calibration by changing force-applying length

We took the advantage of distributed measurement capability of our PA-OFDR system and carried out the first group of experiments by applying the same amount of calibration weight on 10 fiber segments along a SMF-UT with different force-applying lengths from 8 to 17 cm, with 1 cm increment, respectively, in a single measurement. For instance, we loaded a 400 g mass on each glass-slide by stacking 3 weights (200 g, 100 g and 100 g) on top of one another to obtain the birefringence curve along the SMF-UT with our PA-OFDR, as shown in Fig. 2(a), averaged over 10 repeated measurements. As can be seen, 10 TF-induced birefringence peaks with 10 different force-applying lengths were produced, with the corresponding force-applying length marked on each peak. These peaks are inversely proportional to the force-applying length, as expected from Eq. (1). Figure 2(a) also shows the residual birefringence (RB) of the fiber on the fiber section from 8 m to 11 m without applied force [44], which is mainly the results of inherent geometric asymmetry and internal stress of the fiber, with an average value of 1.707×10⁻⁷. This RB is smaller than our previous measured value in [44], probably due to the batch differences. In addition, a minimum RB of 9.172×10⁻⁸ was obtained, indicating that our PA-OFDR’s birefringence measurement resolution should be <1×10⁻⁷ RIU, improved from our previous record [44]. The RB is important because it sets the limit on the minimum measurable TLF, as will be shown in section 3.4.

 

Fig. 2. (a) Measured birefringence curve along a SMF-UT with a 400 g weight applied onto 10 fiber segments with different force-applying lengths shown on each peak. Averaging of 10 repeated full measurements was performed for curve plotting. The residual birefringence (RB) of the SMF-UT was obtained from fiber section without any applied load from 8 m to 11 m with the maximal fluctuation range of RB (f_RB) and the minimum RB value shown in the figure. (b) TF-induced birefringence as a function of transverse line-force (or TLF) f. Error-bars are plotted in pink to show the variations of 10 repeated measurements.

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The peak values of the TF-induced birefringence as a function of TLF is plotted in Fig. 2(b), with the error bars from the 10 repeated measurements shown on each data point with short pink lines. The values of TLF in the horizontal axis were obtained with Eq. (4). It is evident that our sensing system has an excellent birefringence measurement repeatability. Curve-fitting of the averaged data point with Eq. (1) yields the TF sensitivity (TLF to birefringence conversion coefficient) to be 9.162×10⁻⁸ ${{\textrm{RIU}} / {({{\textrm{N} / \textrm{m}}} )}}$, with the goodness of fit (Adj. R-Square) of 0.99495, in good agreement with the theoretically estimated value of 8.559×10⁻⁸ ${{\textrm{RIU}} / {({{\textrm{N} / \textrm{m}}} )}}$. The slight deviation is expected, because the theoretical value was calculated with parameters of bulk fused silica mentioned previously, but the experimental data were obtained with real fiber having a core and cladding, in addition to the measurement uncertainties, such as the nonuniformity of the contact length between the fiber segment and the glass-slide. Additionally, the RB of 1.604×10⁻⁷ obtained from the curve-fitting is very close to the directly measured average value of 1.707×10⁻⁷, validating again that our PA-OFDR system is capable of performing high accuracy distributed measurement of SMF’s RB for determining the minimum detectable TLF.

In addition to loading the fiber segments with 400 g weight, we applied different weights of 200 g, 300 g, 500 g and 600 g to obtain the TF measurement sensitivity, which are listed in Table 1, together with the corresponding RB obtained from curve-fitting. As can be seen, the TF sensitivity values are highly consistent, but the RBs have relatively larger variations.

Table 1. TF Sensitivity and RB Values Obtained with Varying Force-Applying Lengths under Different Loading Weights

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3.1.2 Calibration by changing applied TLF

In this group of experiments, we applied different amount of TF to 10 different fiber sections along the SMF-UT, all with the same length of glass-slide, to measure the induced birefringences in a single measurement. For instance, using a force-applying length of 12 cm, we obtained the birefringence distribution along the SMF-UT as shown in Fig. 3(a) by taking 10 repeated measurements and averaging them. The corresponding TLF is calculated using Eq. (4) and marked on each peak. As expected from Eq. (1), the TF-induced birefringence increases proportionally with the applied TLF along the fiber. The peak values of the TF-induced birefringence as a function of TLF are plotted in Fig. 3(b) with the error-bars representing the measurement uncertainty of the 10 measurements. Curve-fitting the experimental data to Eq. (1) yields the expression given in Fig. 3(b), with an Adj. R-Square value of 0.99853. Using the expression, a TF sensitivity of 9.132×10⁻⁸ ${{\textrm{RIU}} / {({{\textrm{N} / \textrm{m}}} )}}$ and a RB of 1.489×10⁻⁷ are obtained and listed in Table 2. To verify the measurement repeatability of our PA-OFDR system, we performed similar experiments using different force-applying lengths of 8 cm, 10 cm, 14 cm and 16 cm respectively and obtained the corresponding TF sensitivities and RBs via curve-fitting, with the results listed in Table 2. Similar to those in Table 1, the TF sensitivity values are highly consistent with one another, indicating an excellent sensing repeatability.

 

Fig. 3. (a) Measured birefringence curve along the SMF-UT with 10 different TF’s applied onto 10 different fiber segments using the same length of glass-slides (12 cm) obtained with 10 repeated measurements. The TLF f applied to each fiber segment is calculated using Eq. (4). (b) TF-induced birefringence as a function of TLF f. The error-bars are plotted in pink to show the measurement repeatability of our PA-OFDR system.

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Using the data in Table 1 and Table 2, we obtained average values of TF sensitivity $\zeta $ and RB of 9.223×10⁻⁸ ${{\textrm{RIU}} / {\left( {{\textrm{N} / \textrm{m}}} \right)}}$ and 1.325×10⁻⁷, respectively, and the corresponding equation relating the TF-induced birefringence with the TLF f as:

Table 2. TF Sensitivity and RB Values Obtained with Varying TF on Different Force-applying Lengths

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3.2 Validation of distributed TF fiber sensing

With the TF sensitivity $\zeta $ obtained in Eq. (5), we now proceed to validate TF sensing by first measure the birefringence and then calculate the TLF f using

We performed two TF sensing experiments (Experiment I and Experiment II), the first one with a set of TLFs of ∼20.1 N/m applied onto 10 fiber segments (sequentially numbered ① to ⑩) in a sensing SMF-UT (Exp. I) from the same fiber spool as that in Figs. 2 and 3 (identical production batch), and the second one with a set of TLFs of ∼98.5 N/m applied onto the 10 fiber segments (No. ① ∼ ⑩) in a second sensing SMF-UT (Exp. II) from the same fiber spool. Note that the force-applying lengths for the TF loads on the 10 fiber segments were purposely chosen to have five different lengths of 8, 9, 10, 11, and 12 cm to show that our measurement accuracy is independent of the force-applying lengths. Table 3 lists the applied TLF and the corresponding force-applying length on each fiber segment in the two experiments.

Figure 4 shows the measured TLF f as a function of fiber distance by first obtaining the TF induced birefringence $\Delta n$ and then converting it to f using Eq. (6). 10 repeated measurements were averaged for each curve. Table 3 lists the measured TLFs for the 10 fiber segments in the two experiments. The relative errors between the applied TLFs and the measured TLFs are also listed in Table 3. As can be seen, the maximum relative errors are 12.769% for the case of ∼20.1 N/m applied TLFs in Experiment I and 2.432% for the case of ∼98.5 N/m applied TLFs in Experiment II. In addition, the relative errors obtained in Experiment I for the smaller applied TLFs are all much larger than those obtained in Experiment II for the larger applied TLFs. Clear, the RB has a larger impact on the measurement accuracy for the case of smaller applied TLF, consistent with one’s expectations. Other factors affecting the measurement accuracy include system noises and the uncertainty of the contact lengths between the glass and the fiber which affects the accuracy of the force-applying length.

 

Fig. 4. Measured TLF curves from two separate experiments (Exp. I and Exp. II) with different TLF applied onto 10 fiber sections along two SMF-UTs with different force-applying lengths. Red: ∼98.5 N/m TLF applied. Blue: ∼20.1 N/m TLF applied. 5 different force-applying lengths were chosen to apply the TLF on the fiber sections. The RB equivalent TLF (RBF) on the fiber section without the applied TLF are also shown on the left side of the curve from 8 to 11 m, with the maximum RBF_max of 3.130 N/m and 4.280 N/m for the two experiments, respectively.

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Table 3. Comparison of Applied and Measured TLF with Our PA-OFDR Sensing System

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The RB equivalent TLF (RBF), which is the RB converted to TLF using Eq. (6), is shown on the left hand-side from 8 m to 11 m in Fig. 4. The maximum values of RBF (RBF_max) corresponding to the two fibers in two experiments are 3.310 N/m (Exp. I) and 1.198 N/m (Exp. II), respectively, and the minimum values of RBF (RBF_min) are 1.198 N/m (Exp. I) and 0.543 N/m (Exp. II), respectively. In practice, it is feasible to perform a RB measurement of the entire sensing fiber to determine the RBF as a function of distance along the fiber so that the minimum detectable TLF can be determined for every position of the fiber.

3.3 Maximum detectable TLF

The maximum TLF detectable value f_max is an important parameter of a distributed TF fiber sensing system. Considering that the accumulative retardation induced by the TF over the range of BSR of the DPA system cannot be over π to avoid phase wrapping problem, according to Eq. (3), the maximum TF-induced $\Delta n$ must satisfy:

3.4 Minimum detectable TLF

The minimum TLF detectable value f_min is another important parameter for distributed TF sensing. Here we define f_min as the applied TLF for inducing a birefringence twice of the RB or 3 dB above the RB, as shown in the inset of Fig. 5(a). To determine f_min, we located a fiber segment with low RB and applied weights from 5 g to 65 g with an increment of 5 g over a glass-slide having a length of 7.5 cm (the force-applying length) to measure the TF induced birefringence , with the results shown in Fig. 5(a). For each data point, 6 repeated measurements were averaged, with the error-bars representing the maximum data variations, indicating an excellent repeatability of our measurement system. Curve-fitting of the experimental data obtained a straight line with a superb goodness of fit of 0.99930. As a reference, the RB is also plotted in the figure. It is evident from the fitted line that the minimum detectable TLF, f_min, is 0.634 N/m.

 

Fig. 5. (a) TF-induced birefringence as a function of applied TLFs generated by loading different weights from 5 g to 65 g with 5 g increment onto a fiber segment via a glass-slide of 7.5 cm for determining f_min. Inset shows the birefringence distributions along the fiber segment under test with 0 g, 5 g, 10 g and 15 g weight on the force-applying glass-slide, respectively. Inset also illustrates the 3-dB criteria for determining f_min. (b) Minimum detectable TLF induced birefringence as a function of force-applying length. For both figures, 6 repeated measurements were averaged for each data point.

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As an alternative, we performed another set of experiments with different force-applying lengths of 1 cm, 2 cm, 3 cm, 4 cm, 5 cm, 6 cm and 7 cm, respectively, and obtained the minimum detectable TF-induced birefringence as a function of force-applying length as shown in Fig. 5(b). For each force-applying length, the corresponding total weight on the fiber is also given. As can be seen, the minimum detectable TLFs, varying from 0.576 to 0.790 N/m, are all close to the average of 0.661 N/m (or 6.61×10⁻⁴ N/mm). The result indicates that our system is highly sensitive to the TF. Taking a conservative estimate by assuming a force-applying length of 5 mm, our system is capable of sensing a weight as small as 0.68 g from the f_min obtained above, which is about 1/4 the weight of a US penny, to put in perspective. Additionally, according to the obtained f_max of 16.8 N/mm and f_min of 6.61×10⁻⁴ N/mm, a TF sensing dynamic range of our system is calculated to be over 44 dB.

3.5 Spatial resolution and maximum sensing distance

Spatial resolution and the maximum measurement distance are other two important parameters for TF sensing. To determine the spatial resolution, we apply a single-point TLF on a fiber segment using a digital force gauge (DFG, Sundoo Instrument, model SH-50), as shown in Fig. 6(a). In the experiment, a total length of ∼6.3 m SMF-UT was used and the fiber segment with its buffer coating removed was fixed between two micro-translation stages with soft adhesive tapes. In addition, the BSR of the PA-OFDR system is selected to be 0.25 mm, which is the fiber length over which the retardation was accumulated and calculated in data processing. The contact length of the DFG’s force-applying head against the fiber was 1.0 mm, resulting in a TF-applying length of 1.0 mm. Ideally, a TF-applying length less than the BSR of 0.25 mm should be used to determine the TLF spatial resolution, unfortunately, 1.0 mm is the smallest force-applying head available for the DFG. We therefore expect that the TLF spatial resolution obtained with the 1.0 mm force-applying head is the upper limit of the true spatial resolution. In order to obtain the TF measurement spatial resolution, we first applied a certain TF to the fiber segment with the DFG and measured the TLF distribution along the fiber as shown by the blue solid-line (Test-1) in Fig. 6(b). We then adjusted the two translation stages to move the contact point of the fiber segment with the force-applying head of the DFG step by step with an increment of 0.1 mm and measured the corresponding TLF distribution along the fiber after applying the same amount of TLF by the DFG as shown by the red dashed-line (Test-2). Figure 6(b) shows the measured two TLF curves with a spatial separation of 3.7 mm, and the combined curve was also plotted. As can be seen that the central dip in the combined curve just disappears with the 3.7 mm separation, which therefore can be considered as the TF measurement spatial resolution of our PA-OFDR system following the Sparrow criterion [51,52], although the 3-dB width of the TLF response curve is ∼5 mm. Note that 10 repeated measurements were averaged for each curve plotting in Fig. 6(b). Here, although we used the single-point TF-loading to carry out the spatial resolution measurement shown in Fig. 6(a), the system is capable of distributed and multi-point TF sensing, as shown in Figs. 2, 3, and 4.

 

Fig. 6. (a) Experimental setup of single-point TF loading and measurement with a digital force gauge. (b) Two measured TLF curves along SMF-UT with a spatial separation of 3.7 mm. The combined curve indicates a spatial resolution of 3.7 mm using the Sparrow criterion. Note that the 3-dB width of each TLF curve is about 5 mm.

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According to the Nyquist sampling theorem, the length of delay-line of the k-clock interferometer in Fig. 1 should be at least 2 times longer than the maximum fiber length to be measured by the OFDR system. In order for the maximum TF sensing distance longer than 100 m, the delay-line used in the k-clock interferometer must be longer than 200 m theoretically. In our PA-OFDR system, we choose the delay-line used in the k-clock interferometer to be 250 m to ensure a >100 m measurement range, although the coherence length of the tunable laser used is around 600 m. In order to verify the TF measurement range, we first applied a TLF on a fiber segment in a SMF-UT with a length around 6.3 m using a DFG with the setup in Fig. 6(a) and obtained a TLF peak (Peak-1) with our PA-OFDR system at the location of 5.652 m, as shown in Fig. 7(a) with the blue line. We then inserted a SMF with a length ∼97.2 m before the first 6.3 m fiber, which would effectively move the location of the TF application point around 97.2 m away from the OFDR exit reference point and extend the total fiber length to 103.5 m. We next took another measurement using the PA-OFDR and indeed saw the TF peak moved to 102.865 m (Peak-2), as shown with the red curve in Fig. 7(a). With this operation, the fiber segment and the TF applied to the fiber segment were not changed. Note that the inserted 97.2 m fiber was from the same fiber batch as the first 6.3 m fiber and the data shown in Fig. 7(a) is the average of 10 repeated measurements. The average values of Peak-1 at 5.652 m and Peak-2 at 102.865 m are 21.179 N/m and 21.685 N/m, respectively, with excellent agreement.

 

Fig. 7. (a) TF sensing with a 6.3 m SMF-UT (blue) and a 103.5 m SMF-UT (red). Peak-1 at 5.652 m and peak-2 at 102.862 m were produced with a DFG. Inset displays the enlarged local position of peak-2 to show the maximum measurement distance of 103.5 m. 10 repeated measurements were averaged for each curve. (b) Location uncertainties of peak-1 and peak-2 obtained from10 repeated measurements.

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Figure 7(b) shows the location uncertainties of the measured TLF peak for Peak-1 and Peak-2, respectively, with 10 repeated measurements. As can be seen, a maximum variation of 1.23 mm was obtained for peak-2, as compared with a maximum variation of 0.83 mm for peak-1, much smaller than the validated spatial resolution of 3.7 mm. Therefore, we can confidently conclude that the TF sensing range of our PA-OFDR is at least 103.5 m, which can be extended by using a longer delay-line in the k-clock interferometer and a data acquisition card with higher speed.

It is important to note that, since the polarization scrambling method described in Ref. [5] is not sensitive to fiber motion induced polarization variations, it is easier to achieve a measurement range of 800 m by using a TLS with a linewidth sufficiently narrow. On the other hand, the full polarization analyzing method in this paper requires the SOP to be stable along the SMF-UT during each measurement. Lights scattered further down in the fiber is more susceptible to SOP disturbances by vibration and temperature, limiting the accuracy of sensing in longer fibers. In order to extend the measurement range of our PA-OFDR to 800 m as in Ref. [5], the measurement speed of the system should be significantly improved to minimize the effects of fiber disturbances, which in turn require the tunable laser, as well as the data acquisition and processing electronics, to have much faster speed than what we are currently using. Unfortunately, we don’t have such high speed laser and electronics available in our lab.

3.6 Influence of SMF buffer coating on TF sensing

A standard SMF for optical communications generally has a buffer coating with a thickness of 62.5 µm made of polyacrylate material with a small Young’s modulus to protect it against external stresses, and therefore not suitable for TF sensing. In our experiments above, the polyacrylate coating of SMF-UTs at the places for applying TF was removed. However, in practical TF fiber sensing applications, the SMF should have a suitable coating, which allows the efficient force transmission onto the fiber but in the same time can protect the fiber. Therefore, it is crucial to investigate the influences of different buffer coatings of the SMF on TF sensing applications.

In a previous work [7], we found that a thin polyimide coating with a large Young’s modulus can efficiently transfer an external TF onto a polarization maintaining fiber. Here we use a standard SMF with polyacrylate coating and a polyimide coated SMF (YOFC HT-9/125-14/155) with a core, cladding, and coating diameters of 9 µm, 125 µm, and 155 µm, respectively, to measure the TF sensitivity and the RB of the fiber using the same methodology as in section 3.2. The polyimide coated SMF has the same index profile of silica glass as those of the standard SMF, but with a polyimide coating thickness of 15 µm. In each type of fiber, TF’s were applied to 10 different fiber segments similar to the experiment in 3.1.3, but without removing the fiber coating. Figure 8(a) shows the measured birefringence distributions as a function of fiber distance when 10 different segments were subject to TLFs of ∼98.5 N/m. For comparison, the corresponding curve measured using a length of fiber with the coating removed as that in section 3.2 was also plotted here. As can be seen, with the TLFs of ∼98.5 N/m applied to the 10 fiber segments with either the polyacrylate or the polyimide coating, no TF-induced birefringence peaks can be observed, indicating that they were buried under the RB of the corresponding fiber and the applied TLF were not sufficient to induce observable induced birefringence. In addition, one can observe that the standard SMF’s with and without the polyacrylate coating have the same RB level, however, the polyimide-coated SMF has much higher RB distribution along the fiber, indicating that the polyimide coating induced much higher internal stress, similar to what was observed in polyimide-coated PMF [7]. To further validate our observation, we fusion spliced a length of standard polyacrylate-coated SMF with a length of polyimide-coated SMF as a new fiber sample, and measured its RB distribution with our PA-OFDR system, with the results shown in Fig. 8(b). As can be seen from the blue-solid line, the RB increased sharply beyond the splicing point and had a much larger fluctuation in the section of the polyimide-coated SMF. We next removed the polyimide coating of the polyimide-coated SMF following the splicing point from 6.6 m to 9.5 m and measured the RB distribution again, with the results displayed by the red dashed-line in Fig. 8(b). The polyimide coating of the fiber from 9.5 m to 11 m was not removed. As expected, the RB of the fiber section with the polyimide coating removed decreased to the same level as that of the polyacrylate-coated SMF. We can therefore conclude that the polyimide coating is the sole reason for the increased RB and that such a high RB level will significantly limit the minimum detectable TLF.

 

Fig. 8. (a) Birefringence distributions as a function of fiber distance measured with PA-OFDR system, when TLFs of ∼98.5 N/m applied to 10 fiber segments along SMF-UTs without coating (blue dashed-line), with polyacrylate coating (magenta dotted-line) and with polyimide coating (red solid-line), respectively. (b) RB distributions as a function of fiber distance of a polyacrylate-coated SMF (from 0 m to 6.6 m) fusion spliced with a polyimide-coated SMF (from 6.6 m to 11 m); Blue solid line: without polyimide coating removed; Red dashed-line: Polyimide coating was removed in the section from 6.6 m to 9.5 m and the coating remained on the rest of the fiber.

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To obtain and compare the TF measurement sensitivities $\zeta $ of SMFs with the polyacrylate coating and polyimide coating, we prepared another length of fiber by fusion spliced the two types of fiber together. We chose two segments, one located in the polyacrylate-coated SMF section and the other in the polyimide-coated SMF section with a low RB, and applied different TLF on each segment with a same force-applying length of 7.5 cm starting from 100 N/m. Figures 9(a) and (b) show the measured birefringence variations as a function of TLF. As can be seen, the minimum detectable TLFs are 200.000 N/m and 146.667 N/m, for SMFs with polyacrylate coating and polyimide coating, respectively, indicating that the polyimide coating has better force transmission property in comparison. Beyond the minimum detectable TLF, the TF-induced birefringence starts to increase with TLF for both types of fiber, as shown in Figs. 9(c) and (d) respectively. Curve-fitting the experimental data in Fig. 9(a) and 9(b) yields the TF sensitivities of 5.839×10⁻⁸ ${{\textrm{RIU}} / {({{\textrm{N} / \textrm{m}}} )}}$ and 8.707×10⁻⁸ ${{\textrm{RIU}} / {({{\textrm{N} / \textrm{m}}} )}}$ with a goodness of fit of 0.97112 and 0.99074, respectively. For comparison, we listed the measured TF sensitivities for different types of SMFs in Table 4. It is evident that the TF sensitivity of polyimide-coated SMF is much closer to the measured value of the SMF without coating, as well as to the theoretical value. On the other hand, the SMF with polyacrylate coating significantly reduces the TF sensitivity compared with that of a naked SMF.

 

Fig. 9. TF-induced birefringence variations as a function of TLF using SMFs with polyacrylate coating (a) and polyimide coating (b), respectively. TF sensitivities of both SMFs were obtained via curve-fitting of the experimental data. Variations of TF-induced birefringence against applied TLF for SMFs with polyacrylate coating (c) and polyimide coating (d), respectively, together with the RB of each fiber type. (e) TF-induced birefringence as a function of time when a 200 N/m TLF applied to the SMFs with polyacrylate coating (blue squares) and polyimide coating (red triangles).

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Table 4. Different SMF-UT’s TF Sensitivity ζ Measured with PA-OFDR System

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We also investigated the response time of the two types of fibers under a same TLF of 200 N/m and a same force-applying length of 7.5 cm as shown in Fig. 9(e). As can be seen, the response time for the polyimide-coated SMF to react to the TF is too fast to be measureable with our PA-OFDR system. In contrast, the time takes for the polyacrylate-coated SMF to produce a stable TF-induced birefringence is ∼6 minutes due to the large thickness (62.5 µm) and small Young’s modulus of the coating, which is not desired for TF sensing in real time.

From the experimental data one may conclude that the polyimide coated fiber is a good candidate for distributed TF sensing for its large TF sensitivity and fast response time. However, the large RB associated with polyimide coating is a drawback which limits the minimum detectable TLF. Further development is required to reduce the stress of the polyimide coating on the fiber and therefore the RB. As an added advantage, with the capability to measure coating stress induced RB, our OFDR will prove useful for evaluating and improving the coating quality of optical fibers.

4. Conclusions

We demonstrate the first direct distributed TF sensing along SMFs, with a polarization analyzing OFDR system which has been validated to be capable of measuring distance-resolved birefringence distribution of SMFs in our previous work. We show that our PA-OFDR system can perform absolute measurement of TF-induced birefringence, avoiding the need for complicated force-to-strain converting mechanism. By applying different TLFs on 10 fiber segments with different force-applying lengths along a standard SMF, we obtain the TF measurement sensitivity of the fiber, a calibration constant relating the measured birefringence with the applied TLF, to be 9.223×10⁻⁸ ${{\textrm{RIU}} / {({{\textrm{N} / \textrm{m}}} )}}$, highly consistent with the theoretically estimated value of 8.559×10⁻⁸ ${{\textrm{RIU}} / {({{\textrm{N} / \textrm{m}}} )}}$. We obtain a minimum RB of 9.172×10⁻⁸, indicating that our PA-OFDR system has a measurement resolution better than 1×10⁻⁷. We show that our system is capable of sensing a weight of merely 0.68 g but yet has a large dynamic range of over 44 dB, with a maximum and minimum detectable TLF of 16.8 N/mm and 6.61×10⁻⁴ N/mm respectively, a TLF measurement uncertainty of <2.432%, a TF sensing spatial resolution of 3.7 mm and a TF sensing distance of 103.5 m. The TF sensing spatial resolution can be improved further by optimizing the data processing algorithm, and the measurement distance can be further enlarged by increasing the fiber delay in the k-clock interferometer and the speed of the data acquisition. Note that, in Ref. [44], our main focus was to validate our distributed polarization analysis system, the associated birefringence calculation algorithm, and the accuracy of birefringence measurement, while in this paper we focus on using the PA-OFDR system to demonstrate the distributed TF sensing and determine the achievable sensing parameters, such as the minimum detectable TF, the maximum detectable TF, the TF sensing accuracy, the spatial resolution, and the sensing range. The work here is an important continuation of our work in Ref. [44] and paves the way for the practical application of the system and the algorithm developed in Ref. [44], especially considering that the superb performance data on OFDR based TF sensing achieved in this paper was never reported previously by anyone in the field.

We also investigated the influence of different fiber coatings on the performance of TF sensing, and found that a polyimide coating is a good candidate due to its high sensitivity and fast response time towards TF. However, further development is required to reduce the relatively high RB in the polyimide coated SMF.

Finally, the results reported in this paper are beneficial for engineers and scientists to implement the PA-OFDR technology for TF sensing with low cost SMFs, and provided important guidelines for the manufacturing, evaluating, and improving of SMFs for distributed fiber optic TF sensing in the future.