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Abstract
In this study, the distributed temperature and strain sensing with an annealed single mode gold-coated optical fiber over a wide temperature range up to 1000 °C is demonstrated by using the differential pulse pair (DPP) Brillouin optical time domain analysis (BOTDA). Owing to the protection provided by the gold coating, the fiber can withstand high temperature environments and maintain a high strength, which enables the gold-coated fiber acting as a repeatable high-temperature sensor. After annealing twice to remove the internal stress, the temperature coefficient of the gold-coated fiber is stable and consistent with a nonlinear function. Owing to the residual stress accumulated during the cooling process of coating and the low yield strength of gold, a pre-pulling test is essential to measure the strain of a gold-coated fiber. An equal axial force model is used to recalculate the strain distribution induced by the large temperature difference within the furnace. The high-temperature strain coefficient of an annealed gold-coated fiber decreases with temperature, i.e. from ~0.046 MHz/με at 100 °C to ~0.022 MHz/με at 1000 °C, mainly due to the increase in Young’s modulus of silica with temperature. To the best of our knowledge, this is the first time that an annealed gold-coated fiber has been applied for distributed high-temperature strain sensing, which demonstrates the potential applications for strain monitoring in complex, high-temperature devices such as jet engines or turbines.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Among the distributed fiber sensing techniques that have been widely studied in the past two decades, Brillouin optical time domain analysis (BOTDA) is a representative sensing method used to retrieve the temperature/strain distribution in many applications (such as bridges, railways, pipelines etc.) due to its advantages such as long sensing range [1] and high spatial resolution [2,3]. There are two main lines for developing the BOTDA technique: the development of new optical modulation techniques and the development of new kinds of optical fibers. On one hand, the state of art techniques used include pulse coding technique [4], Raman/Brillouin assistant amplifying technique [5,6], differential pulse pair (DPP) technique [7], and fast measurement technique [8–10], which could either increase the number of sensing points or reduce the measuring time; on the other hand, new kinds of optical fibers include polymer optical fibers (POF) for large-scale strain sensing [11,12], few-mode fibers (FMF) or polarization-maintaining optical fibers (PMF) for sensing of multiple parameters [13,14], and the fundamental mode excited by multimode optical fibers for bend-insensitive sensing [15], which could further extend the scope of applications of the Brillouin-based optical fiber sensing technique.
Recently, our group researched the high temperature distribution of Brillouin sensing based on a single mode fiber and a photonic crystal fiber [16], whose results concurred with Y. BAO’s work [17]. Although this demonstrates the ability of a polymer (single or double layer acrylate) coated fiber to sense high temperatures, one of its drawbacks is that the polymer coating would burn at ~300 °C, thus exposing a bare silica fiber to the high-temperature environment, subsequently degrading the fiber’s optical properties and causing it to lose most of its mechanical strength due to hydrogen ingression [18] and the crack growth of pre-existing flaws on the glass surface [19]. If left untouched, such fibers could survive temperatures as high as 1000 °C; however, any subsequent handling makes the fiber vulnerable to breakage because it becomes extremely brittle.
Sealing the fiber with a hermetic metal coating could prevent the diffusion of H2 molecules or H2O molecules in order to avoid high-temperature fiber fatigue and maintain the fiber strength close to melting temperature of the metal [20]. R. Ruiz-Lombera used a multimode gold-coated fiber to demonstrate high-temperature distributed sensing with BOTDA at 600 °C [21]. However, compared to single mode gold-coated fiber, the multimode gold-coated fiber is not an ideal candidate for sensing due to the inevitable sensing error induced because of mode coupling [15]. Nonetheless, gold coating could help a silica fiber survive at high temperatures because it has a higher melting point (1064 °C) and better hermeticity when compared with the other metal. Moreover, gold coating does not react chemically with silica at high temperature, indicating that it could retain higher fiber strength at high temperature, thus demonstrating the potential application of distributed high-temperature strain sensing that haven’t reported before.
In this paper, the distributed temperature and strain sensing in a wide temperature range of 1000 °C is demonstrated by using annealed single mode gold-coated fibers via DPP-BOTDA. Owing to the protection provided by the gold coating that prevents hydrogen penetration, the fiber can survive in high temperature environments and maintain a high fiber strength, which enables the gold-coated fiber acting as a repeatable high temperature sensor. The high-temperature coefficient of the annealed gold-coated fiber is stable at each temperature after annealing twice to remove the internal stress. Owing to the residual stress accumulated during the cooling process of coating and the low yield strength of gold, a pre-pulling test is essential to measure the strain of a gold-coated fiber. An equal axial force model is used to recalculate the strain distribution induced by the large temperature difference within the furnace. The high-temperature strain coefficient of an annealed gold-coated fiber decreases with temperature, i.e. from ~0.046 MHz/με at 100 °C to ~0.022 MHz/με at 1000 °C, mainly due to the increase in Young’s modulus of silica with temperature.
2. Experimental setup
The DPP-BOTDA experimental setup is shown in Fig. 1. Based on the BOTDA-type system, DPP-BOTDA injects two separated pump lights with different pulse-widths ( and ) into the fiber and subtracts their time domain waveforms of Brillouin signals at each scanned frequency to acquire the differential BGS [7]. The resulting equivalent pulse-width difference () can be used to determine the minimum spatial resolution, provided that the rise/fall time of the pulse pair is shorter than the equivalent pulse-width difference.
Fig. 1 Experimental setup: C, coupler; PC, polarization controller; MZM, Mach-Zehnder modulator; DC, direct current; AFG, arbitrary function generator; RF, radio frequency; PS, polarization scrambler; EDFA, erbium-doped fiber amplifier; FBG, fiber Bragg grating; PD, photo detector; OSC, oscilloscope.
As shown in Fig. 1, the output of a distributed-feedback (DFB) laser is divided into two arms by a 3-dB optical coupler to provide two waves, i.e. the pulsed pump and the continuous probe. Two polarization controllers (PC) are used to control the polarization state of the pump and probe waves that are sent into the Mach-Zehnder modulators (MZM). An arbitrary function generator (AFG) is used to drive a high extinction-ratio (>40 dB) MZM to generate two pulses with different pulse-widths. A polarization scrambler is used to randomly change the polarization state of the pump pulse to reduce polarization-fading induced signal fluctuation by averaging a large number of signal traces; the number of times averaged in our experiment is 1000 times. The pump pulse is amplified by an erbium doped fiber amplifier (EDFA) and then inserted into the gold-coated fiber.
On the other branch, the continuous probe beam is modulated using the double-sideband technique, which involves a radiofrequency (RF) signal generated by a microwave generator that is added to the MZM to generate two sidebands and a suppressed carrier wave by adjusting the bias voltage of the MZM. An isolator is put between the gold-coated fiber and the MZM to isolate the pump pulse. Two beams interact inside the gold-coated fiber to generate stimulated Brillouin scattering. The Brillouin signal is filtered by a fiber Bragg grating (FBG) after passing through two optical circulators, and then detected by a 3.5 GHz bandwidth photo detector and recorded by an oscilloscope with a sampling rate of 10 GSa/s. LabVIEW software was used to complete the acquisition of the Brillouin signal and Brillouin gain spectrum (BGS) fitting by changing the probe frequency at a step of 4 MHz in the vicinity of Brillouin frequency shift (BFS) of gold-coated fiber. The peak power of pulsed pump was ~200 mW and the power of the probe was ~1 mW, which produced relatively high signal intensity. The measurement of high temperature for a gold-coated fiber was done via a chamber furnace (Chinese Academy of Science Instrument Department, SXL-1400C), whose temperature was monitored by an electrical thermocouple with a measuring accuracy of ± 1 °C.
3. High temperature measurement of gold-coated fiber
Distributed high temperature measurements of a 1-m gold-coated single mode fiber (FiberGuide AFS 9.0/125/155G) with 20-cm spatial resolution were conducted by selecting 2 ns as the pulse-width difference in the DPP-BOTDA system. The diameters of core, cladding and gold coating of gold-coated fiber are 9 μm, 125 μm, and 155 μm, respectively. The results of five repeated measurements at temperatures ranging from 100 to 1000 °C, with a step of 50 °C, can be seen in Fig. 2(a), where the BFS of the gold-coated fiber increases nonlinearly with temperature. It can also be observed that the BFS of the first two measurements vary greatly from the BFS of the last three measurements, which is much more significant in Fig. 2(b) that shows the BFS difference between two successive measurements. From the black columns that highlight the BFS difference between the first and the second measurements, it can be observed that the BFS difference first increases and then decreases with temperature, with the largest BFS difference being ~30 MHz at 700 °C, which is a temperature dependent behavior that can be referred to as internal stress relaxation [16]. From the red columns that highlight the BFS difference between the second and third measurements, the BFS difference is more than 10 MHz at 350 °C, even though the temperature error induced by the temperature fluctuation of the chamber furnace under 300 °C is ignored. Meanwhile, in the blue and pink columns, the BFS difference is bound by ± 2.15 MHz, which illustrates that the gold-coated fiber can reach a relatively stable state after annealing twice. Therefore, the third measurement of BFS with temperature is used for polynomial fitting:
where is the BFS in megahertz and is the fiber temperature in Celsius.Fig. 2 1000 °C repeated distributed high temperature measurements of 1-m-long gold coated fiber by DPP-BOTDA with 20-cm spatial resolution. (a) 5 measurements of a single sensing point from 100 to 1000 °C with a step of 50 °C, temperature coefficient of gold-coated fiber changes with temperature nonlinearly; (b) BFS difference between every 2 adjacent measurements, the maximum difference in the last 3 measurements is within ± 2.15 MHz (beyond 300 °C).
After annealed twice, the temperature coefficient of the gold-coated fiber has been enhanced below 300 °C due to the internal stress relaxation. Although such a phenomenon has been observed in polymer-coated fibers [16], it cannot be successfully implemented in practical applications because the fiber will become extremely fragile after one high-temperature (>1000 °C) annealing. Owing to the protection of gold coating, the annealed gold-coated fiber can maintain its fiber strength almost similar to the unannealed one, which means that the gold-coated fiber can be used as a repeatable sensor. The temperature and strain coefficients of the annealed and unannealed gold-coated fibers are experimentally tested and compared, as represented by the black and red points in Fig. 3, respectively. The temperature coefficients for unannealed and annealed gold-coated fibers are 1.13 MHz/°C and 1.35 MHz/°C respectively, while the strain coefficients are 0.0485 MHz/με and 0.053 MHz/με, respectively. An improvement of 19.5% and 9.3% in temperature and strain coefficients indicates that the annealed gold-coated fiber can be used for high accuracy distributed sensing.
Fig. 3 The temperature and strain coefficients of gold-coated fiber before and after annealing. (a) Temperature coefficient from room temperature to 90 °C; (b) strain coefficient at room temperature.
4. Effect of coating on strain measurement
Gold coating that is characterized as a genuine hermeticity protection enables the silica fiber to endure high temperatures by preventing hydrogen penetration. Silica fiber is coated with gold by a technique known as in-line freezing, which is an effective method to guarantee its hermeticity and fiber strength [22]. During the process of coating, the temperature of the fiber should be maintained at somewhat lower than the melting point of the gold so that the gold film can solidify on the surface of the fiber. Moreover, the contact duration of the fiber with the molten metal should be shorter than the duration between the heating of the fiber to the metal’s melting point in order to obtain a stable and uniform metallic film [23]. Owing to the large difference in the thermal expansion coefficients of silica (5.5 × 10−7/°C) and gold (14.2 × 10−6/°C), very high stresses can arise between the gold coating and silica fiber during cooling, which shows an effect on gold-coated fiber for strain sensing that cannot be ignored, as discussed below. Meanwhile, high stress induced micro-bending optical loss (15 dB/km) would limit the application of gold-coated fiber in some fields, such as intensity-based spectral-slope-assisted Brillouin distributed sensing techniques [24,25]. Nevertheless, it is not a challenge for BOTDA as it is a frequency-sweep based detection technique.
The strain measurements of unannealed and annealed gold-coated fibers at room temperature were investigated, as shown in Fig. 4. The annealing process of gold-coated fiber is described as follows: first, the temperature of the furnace is increased at a rate of 10 °C/min until it reaches 1000 °C; next, the gold-coated fiber is kept at 1000 °C for a duration of 2 hours; finally, the temperature of the furnace is cooled down to room temperature at a rate of 5 °C/min. Figure 4(a) shows the strain measurements of unannealed gold-coated fiber with a strain step of 770 με, with the strain coefficient being 0.0485 MHz/με in the first measurement. For next measurements, the BFS of gold-coated fiber at 0 strain is elevated for ~18 MHz, which indicates that BFS is independent on the first step strain after the first measurement. While Fig. 4(b) shows the strain measurements for an annealed gold-coated fiber with a strain step of 1140 με, the BFS at 0 strain is also elevated for ~14 MHz after the first measurement. The phenomenon mainly stems from the fact that a thermally-induced residual compressive stress remains in the gold-coated fiber, which is due to fast cooling process of gold coating that has solidified on silica fiber. Three more measurements are conducted after the first measurement in order to confirm that the gold-coated fiber is stable. It can be seen in Fig. 4 that all the measurements coincide with each other at a coefficient variation of < ± 0.2%.
Fig. 4 Four strain measurements at room temperature. (a) Unannealed and (b) annealed gold-coated fiber, the BFS at 0 strain is elevated after the 1st measurement.
To demonstrate the effect of coating on strain sensing more clearly, the relationship between the increase in BFS of annealed gold-coated fiber and the imposed strain in the first strain measurement was investigated. The increase in BFS is recorded when the annealed gold-coated fiber returns to its original position from the position of imposed strain, whose values are 1934 με, 3868 με, 5802 με, and 7736 με respectively, as shown in Fig. 5. When the strain is 3868 με and 7736 με, the increase in BFS is ~19 MHz and ~26 MHz, respectively. The increase in BFS grows with the imposed strain, implying that plastic deformation occurs in the gold-coated fiber in the first strain measurement due to the release of residual compressive stress and the low yield strength of gold. From Figs. 4 and 5, it can be concluded that the gold-coated fiber would first experience plastic deformation followed by elastic deformation in the first strain measurement. Hence, it is necessary to subject the gold-coated fiber to a pre-pulling test before using it for strain sensing.
Fig. 5 The increase in BFS of annealed gold-coated fiber with the imposed strain in the first strain measurement.
5. Measurements and discussions of strain at high temperatures
Figure 6 shows the experimental setup of a gold-coated fiber for high-temperature strain measurement. The gold-coated fiber is adhered to stainless steel via a high-temperature-resistant inorganic adhesive. One section of the stainless steel is inserted into the muffle furnace (Carbolite Gero Ltd.) through an outlet of the horizontal tube and the other section is fixed outside the furnace. The two outlets of the horizontal tube of the muffle furnace are sealed with asbestos to keep the internal temperature stable. As the strength of inorganic adhesive deteriorates with an increase in temperature, and there is a region of temperature transition from room temperature to the setting temperature of muffle furnace, it is necessary to select an appropriate position at which the temperature is not too high so that the inorganic adhesive could maintain enough strength to pull the fiber. Meanwhile, the fiber is placed within a uniform temperature region of the muffle furnace because of the uneven temperature distribution in it. In the experiment for measuring strain, a gold-coated fiber with a span of 45 cm was installed in the middle of the muffle furnace by adjusting the position of the adhesive accordingly. The high-temperature distributed strain measurements were performed by pulling the stainless steel outside the muffle furnace, and the temperature was monitored via a high accuracy thermocouple of ± 1 °C. The spatial resolution was 5 cm by selecting 0.5 ns as the pulse-width difference and the sampling rate was at 10 GSa/s.
Fig. 6 Experimental setup of gold-coated fiber for high-temperature strain measurement with a spatial resolution of 5cm.
After the pre-pulling test, the distributed strain measurements were conducted from 100 to 1000 °C in a strain range of <3500 με, and the distributed BFSs of annealed gold-coated fiber at 400 °C, 600 °C, 800 °C, and 1000 °C can be seen in Fig. 7. It was observed from Fig. 7 that the temperature varies along the fiber and the asymmetric temperature distribution. By comparing BFS along the annealed gold-coated fiber, it was observed that the left end was closer to the middle part than the right end because the left wall of the muffle furnace had a better thermal insulation property when compared to the right wall. It can also be observed that the BFS increased linearly with strain at 400 °C, whereas from 600 to 1000 °C, the increase in BFS at the beginning of several strain steps became increasingly smaller. For example, the BFS did not increase linearly with strain until the sixth step (1333.2 με) at 1000 °C, as shown in Fig. 7(d). This is because the thermal expansion of the gold-coated fiber at high temperature counteracts part of the tensile strain. The lowest curve (strain = 0) at each figure represents the temperature distribution in the muffle furnace. It can be observed from Fig. 7 that there is a temperature stable region of 25 cm where the maximum BFS difference is < 20 MHz which can be used to characterize the strain coefficient of the annealed gold-coated fiber, as discussed below.
Fig. 7 The distributed high-temperature strain measurements post the pre-pulling test with a step of 222 με at (a) 400 °C, (b) 600 °C, (c) 800 °C and (d) 1000 °C.
It is common knowledge that the Young’s modulus of silica increases with temperature [26] while that of gold decreases [27]. Apart from this, the non-uniform temperature distribution also contributes towards the variation of stiffness of the gold-coated fiber. Correspondingly, the strain distribution along the fiber is not constant when the outer surface of the stainless steel is subjected to a constant strain. If the strain is assumed to be constant along the fiber, a calculated error will have to be introduced into the strain coefficient, especially for high temperatures. An equal axial force model that excluded this error was proposed to calibrate the strain distribution of the annealed gold-coated fiber.
The gold coating and the silica fiber can be considered to be deformed as a whole without relative displacement. Based on the equilibrium, an equal axial force acting internally can be assumed along the fiber. As shown in Fig. 8(a), the gold-coated fiber can be divided into N parts, where the length of each part is equal to the equivalent length of sampling rate (10 GSa/s) used in the experiment. At the measurement of each strain step, the total elongation of the gold-coated fiber is equal to:
Where represents the elongation of each part, then:where is the strain, is the axial force which is the sum of all forces acting on the cross-section, and are the equivalent Young’s modulus and cross-sectional area of the fiber, which are functions of the axial coordinal because of the non-uniform temperature. Being neglected the relative displacement between the silica and the gold coating, tensile rigidity can be written as: is the Young’s modulus of silica, which can be calculated from BFS [28,29]; is the Young’s modulus of gold, which can be obtained from [27]. As shown in Fig. 8(c), and are the areas of silica and gold which can be determined by using their diameters, 125 μm and 155 μm, and thermal expansions, 5.5 × 10−7/°C and 14.2 × 10−6/°C, respectively.The process to derive strain distribution is as follows: firstly, the temperature distribution is derived from the BFS of the lowest curve of Fig. 7 by using Eq. (1). Secondly, the tensile rigidity is obtained from Eq. (4). Thirdly, according to the equal axial force model, , the axial force can be obtained from Eqs. (2) and (3) for the total measured displacement due to extension, which is 100 μm in this case. Finally, the strain distribution is calculated by using:
The equal axial force model is further applied to analyze the strain distribution of the gold-coated fiber with an elongation of 1000 μm at 1000 °C, as shown in Fig. 9. It can be observed that the strain varies along the annealed gold-coated fiber due to the non-uniform temperature distribution. In the region where the temperature is stable, the strain is larger than the average value (dash line), whereas the strain is lower than the average value in other parts of the fiber.
Fig. 9 Strain distribution along the 45-cm-long gold-coated fiber with an elongation of 1000 μm at 1000 °C.
Next, the dependence of BFS on strain for the center position of 3.6 m in Fig. 7 is investigated at different temperature. Figure 10(a) shows the variation of BFS with strain calibrated by using the equal axial force model for different temperatures, ranging from 100 to 1000 °C. The BFS generally increases linearly with temperature, except when the temperature is between 500 to 1000 °C, where the BFS shows no response to the first several strain steps due to thermal expansion of annealed gold-coated fiber, which agrees well with Fig. 7.
Fig. 10 High-temperature strain coefficients of annealed gold-coated fiber from 100 to 1000°C. (a) BFS with strain at a position of 3.6 m as shown in Fig. 7; (b) strain coefficients for all the data in a span of 25 cm as indicated in Fig. 7.
The strain coefficient of the annealed gold-coated fiber at different temperatures is calculated by using the BFS of annealed gold-coated fiber that varies linearly with strain, as shown in Fig. 10(b). The error bar is calculated from the relatively stable temperature region 25cm (3.47 m to 3.72 m) shown in Fig. 7, based on the fact that the maximum variation of strain in this region is < 1% (as shown in Fig. 9), thus indicating that the influence of temperature variation on the strain coefficient can be neglected. In Fig. 10(b), the maximum error bar is 0.0029 MHz/με at 100 °C, which is mainly due to the temperature fluctuation of the furnace. Meanwhile, the maximum relative coefficient error is ± 4.34% at 1000 °C, where the strain coefficient encounters a sharp decrease. The error bar at each temperature probably occurs due to the non-uniform coating thickness created by the coating process ( ± 16μm). It was observed that the strain coefficient of the annealed gold-coated fiber decreased with temperature, which coincided with an increase in the Young’s modulus of silica with temperature [26]. Although the Young’s modulus of gold shows an opposite trend of variation with temperature, this is not significant. Hence, the decrease in the strain coefficient of gold-coated fiber is mainly due to the increase in Young’s modulus of silica with temperature.
6. Conclusions
In conclusion, the distributed optical fiber temperature and strain sensing up to 1000 °C was demonstrated with an annealed single mode gold-coated fiber via the DPP-BOTDA method. The annealed gold-coated fiber can also be used as a repeatable high-temperature sensor due to the protection provided by the gold coating that also maintains fiber strength. The temperature coefficient of the gold-coated fiber is stable and consistent with a nonlinear function after annealing twice to remove the internal stress. Owing to the residual stress accumulated during the cooling process of coating and the low yield strength of gold, a pre-pulling test is essential for the gold-coated fiber to measure strain. The high-temperature strain coefficient of an annealed gold-coated fiber decreases with temperature, i.e. from ~0.046 MHz/με at 100 °C to ~0.022 MHz/με at 1000 °C, which mainly occurs due to the increase in Young’s modulus of silica with temperature.
Funding
National Key Scientific Instrument and Equipment Development Project of China (2017YFF0108700); National Natural Science Foundation of China (NSFC) (61575052).
Acknowledgments
The authors would like to thank Long Wang, Yue Pan and Chao Pang for the assistance of high temperature experiment; the authors would like to thank Chen Chen for the assistance of high-temperature strain experiment; the authors would like to thank Dengwang Zhou and Benzhang Wang for the discussion.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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