By both simulation and experiment, we studied the relationship of the measurement accuracy and the birefringence of the distributed simultaneous strain and temperature sensor using polarization-maintaining fiber Bragg gratings (PANDA-FBGs). The PANDA-FBGs were applied to an optical frequency domain reflectometry (OFDR) which is capable of distributed measurement at high spatial resolution and sampling rate. The simulated results had agreement with the experimental results that the measurement accuracy of both strain and temperature were improved by increasing the birefringence. Additionally, the efficiency of the accuracy improvements decreased when accuracy increased.
© 2017 Optical Society of America
Recently, optical fiber sensors (OFSs) for strain measurement have been widely used in many fields including structural health monitoring (SHM) [1–3]. They offer the capability of distributed sensing, and can be conveniently embedded in structures with minimum perturbation to the structural strength. Among OFSs for SHM, fiber Bragg grating (FBG) sensors have attracted many attentions [4–6]. FBG can give absolute measurement of variation of environment (strain, temperature, etc.) by detecting the wavelength shift caused by them [7, 8]. Although, FBG sensors were essentially used for point sensing, in 2008, Igawa et al demonstrated distributed strain measurement using a long length FBG . It has proven the capability of FBG sensors for full distributed measurement. Furthermore, FBG sensors have sufficient accuracy at high spatial resolution of millimeter or sub millimeter order, which is important for SHM [10–12].
However, for strain measurement, large temperature variations are common in practical applications. The measurement accuracy will be reduced by the cross-sensitivity of temperature and strain in the sensing head. Thus, a compensation of the influence caused by temperature variation is required. Conventionally, in addition to the strain sensor, which is sensitive to both strain and temperature, a reference FBG in stress-free condition is used as temperature sensor . Since the reference FBG is parallel located in the same environment as the strain sensor, the error of strain induced by temperature variation can be compensated by subtracting the wavelength shift of temperature sensor from the wavelength shift of the strain sensor. However, it is complicated to keep the reference FBG free-stress. And the reference fiber will degrade the strength of host structure for embedded sensing. What’s worse, for distributed sensing, it is very difficult to avoid the misplacement between the reference FBG and strain sensing FBG that will introduce extra sensing errors, especially when high spatial resolution is required. Hence, techniques of simultaneous strain and temperature with one single FBG are under development. Echevarria et al discriminated strain and temperature by measuring the first and second order diffraction wavelength of an FBG . Sudo et al inscribed an FBG into a polarization maintaining (PM) fiber and realized simultaneous point sensing of strain and temperature . In 2011, Wada et al applied a PANDA-FBG to an optical frequency domain reflectometry (OFDR), and succeeded in simultaneous distributed measurement of strain and temperature , which was an important advance for SHM.
In this paper, we studied the properties of PANDA-FBGs for simultaneous strain and temperature distribution measurement, and established a numerical model for the estimation of measurement accuracy. Meanwhile, we applied multi-types of PANDA-FBGs to the measurement and evaluated their performance practically with specific equipment. According to the results, the simulation and experiments had agreement in the relationship between the measurement accuracy and the birefringence of PANDA fibers. This work might help in the design of this type of FBG sensors. Once the accuracy required for a specific application is known, the model helps to know which should be the value of birefringence for achieving the desired result.
2. Principle of simultaneous strain and temperature measurement using PANDA-FBG
PANDA fiber is a type of polarization maintaining optical fiber, where the propagating mode in it will split into two orthogonal polarized mode (fast and slow modes) due to the property of birefringence . The strength of birefringence is defined as18]. The PANDA-FBG indicates the FBG inscribed on the PANDA fiber, as shown in Fig. 1. Due to the birefringence, it has two distinct Bragg wavelength which can be expressed as 19].
Since each Bragg wavelength has different response to external variation of strain and temperature, we can determine the strain and temperature changes at the same time by measuring the two Bragg wavelength [15, 20]. Their relationship is expressed as
3. Numerical model of simultaneous strain and temperature measurement using PANDA-FBGs
In order to investigate the influence of birefringence in the measurement accuracy of strain and temperature we made a numerical model and simulated the simultaneous measurement, as shown in Fig. 2. The simulation consists the calculation of matrix K, the simulation of calibration, the simulation of simultaneous measurement, and the estimation of measurement accuracy.
Theoretically, the strain response arises because of both the physical elongation of the sensor, and the change in effective refractive index, neff, due to photo-elastic effects. Meanwhile, the temperature response arises due to the inherent thermal expansion of the optical fiber material and the temperature dependence of neff . The shift in Bragg wavelength with strain and temperature for single mode FBG can be expressed using4].
For PANDA-FBGs, we assumed that the strain and temperature response of fast and slow mode are independent. Thus, in Fig. 2: Step 1, the elements of matrix K were calculated as
Meanwhile, as shown in Fig. 3, the PANDA fiber consists of core, cladding and stress applying parts (SAP). Thus, the total thermal expansion coefficient can be calculated as
The values of the parameters in the numerical model were based on FUJIKURA Co., Ltd. PANDA fiber (SRSM15-PS-Y15), as given in Table 1. In this study, we assumed that the refractive index is linear related to temperature in the annealing process. Thus, dneff/dT were considered as constant.
In the model of calibration, Fig. 2: Step 2, we set the variations of strain and temperature as
Then, we introduced random errors to strain, temperature and Bragg wavelength shift, which are expressed asTable 2. They are based on the experimental equipment in this research which will be introduced in Section 4.
Then we conducted linear fitting in order to obtain the error introduced matrix K which is denoted by
In Fig. 2: Step 3, we simulated the process of simultaneous measurement. Firstly, we input the strain (Δεi) and temperature (ΔTi) variation into Eq. (3), and calculated the corresponding wavelength shifts as
Then, we introduced random errors to the wavelength shifts and recovered the output strain and temperature changes by the error introduced matrix (Eq. (19)), , which is expressed as
Finally, in Fig. 2: Step 4, the estimated accuracy of strain (±aε) and temperature (±aT) were calculated as
In this simulation, we input Case1: Δεi = 100 με, ΔTi = 95°C, Case2: Δεi =500 με, ΔTi = 130°C, and the variation from Case 1 to Case 2: Δεi = 400 με, ΔTi = 35°C, respectively. Then, we increased birefringence from 3.0 × 10−4 to 3.2 × 10−3 by the interval of 1 ×10−4 and obtained the simulated relationship of measurement accuracy (absolute value) and birefringence, as shown in Fig. 4. The simulation showed that the measurement accuracy was improved by increasing the birefringence of PANDA fiber.
Additionally, the influence to the accuracy of other independent parameters were investigated by the numerical model. Taking FUJIKURA Co., Ltd. PANDA fiber SRSM15-PS-Y15 (B = 5.2 × 10−4) as reference, we assumed that a FBG of which the period is 531 nm was inscribed with phase mask and UV beam. Then we introduced the perturbation from −20% to 20% to birefringence (B), period (Λ), and thermal expansion coefficient (α), respectively, and calculated the corresponding changes of the estimated accuracy. According to the results, the increase of birefringence and period can make efficient improvements of the accuracy, as shown in Fig. 5. Considering the accuracy and attenuation, Λ = 531 nm of which the Bragg wavelength (~ 1550 nm) is in the C band (1530 ~ 1565 nm) was chosen. Within C band, the maximum period of ~ 536 nm can only bring the improvement of ~ 0.7 µε and ~ 0.1°C, compared with the reference fiber. However, it is available to increase the birefringence to over 10 × 10−4 with current technology . As estimated in Fig. 4, the potential accuracy improvements by increasing birefringence are more than ~ 22 µε and 2.4°C, more efficient than increasing the period. In this study we examined the dependence of measurement accuracy on the birefringence in experiments.
In order to evaluate the measurement accuracy of PANDA-FGBs in simultaneous strain and temperature measurement practically, we conducted a series of experiments using various PANDA-FBGs. All the FBGs were tested under similar external environment.
4.1. Experimental arrangement
In the experiment, we applied quantifiable strain and temperature variation to the fiber under testing (FUT). The principle of the experimental equipment is to heat the FUT at sensing part and stretch it with special tools. At the same time, we monitor the applied strain and temperature simultaneously by sensors other than OFS.
In the research, we employed a cylinder heater to apply temperature variation to FUT and applied strain by a stationary stage and a translation stage, as shown in Fig. 6.
The stages were fixed on the optical table. During the experiments, FUT was located on the mid axis and fixed by adhesive. The length of FUT, LFUT, was 1m. The displacement of translation stage, Ds, was measured by the laser displacement sensor. Thus the applied strain can be described as
The cylinder heater was located between the stages and fixed on the optical table as well. It consists of two semi-cylinder parts (Part A, Part B), and can be open and closed from the side, as shown in Fig. 7. In the heater, we installed 9 channels of thermocouples. Among them, Ch-0 was used for PID temperature control, the other 8 channels from Ch-I to Ch-VIII were used for monitoring applied temperature distribution. The position of Ch-I was set to be zero point. And the distance between adjacent channels were set to be 12 mm.
As shown in Fig. 8, the FUT was fixed to the stages, and the middle part of the PANDA-FBGs were inside of the heater, while the rest of them were outside of it. z represents the position. The area between Ch-II to Ch-VII was the Application Area where the characteristics and performance of PANDA-FBGs were tested. The specification of the equipment are shown in Table 3.
In the experiment, the uniform strain and temperature distribution were applied to the FUT in the Application Area of which the length is 60 mm. When the errors during the experiment are introduced, from Eq. (4) we can obtainEq. (3) and Eq. (4) into Eq. (26), we can obtain
From the second term of Eq. (27) at right hand side, we know that the measurement accuracy are related to the applied strain and temperature variation, and will be amplified by the matrix K. Thus, in order to obtain a general accuracy of distributed measurement and compare between different types of PANDA-FBG sensors, uniform strain and temperature should be applied. Otherwise, for each sensing point, the accuracy will be different.
In the experiments, the distributed wavelength shift were determined with the optical frequency domain reflectometry (OFDR) [9, 11, 16], as shown in Fig. 9. It is a combination of two interferometers. All the optical fibers and couplers were polarization maintaining. The clock signals observed by Detector 1 was used to trigger the sampling of Detector 2. And, the observed signals at Detector 2 were demodulated by short time Fourier transform (STFT). Since a polarization splitter was employed between Coupler 3 and Detector 2, the system was able to determine the wavelength of fast and slow mode individually. In the experiments, the settings of the OFDR are shown in Table 4. The sampling rate of OFDR was set to be 800 sps, the spatial resolution was about 5 mm, and the maximum measurement length was 1 m. Figure 10 illustrates the spectrogram of the full length of a PANDA-FBG under applied strain and temperature.
4.2. Calibration of strain and temperature sensitivities of PANDA-FBGs
In this research, four types of PANDA-FBG were calibrated before being applied to simultaneous strain and temperature measurement. Since different amount of B2O3 were doped in the SAPs of the PANDA fibers, they have different birefringence . The FBGs were inscribed with the same phase mask that the Bragg wavelength of slow mode were approximately the same. The dimensions of PANDA-FBGs are given in Table 5.
The PANDA-FBGs were calibrated under the similar environments by the same experimental equipment. In the calibration of strain sensitivities, we applied the strain variation to the FUT from ~ 50 µε to ~ 550 µε by the interval of ~ 50 µε at the constant temperature of 99.6°C (average value by thermocouple Ch-IV and Ch-V), as shown in Fig. 11(a). Meanwhile, the wavelength shifts were monitored by OFDR. For each strain, the corresponding wavelength shifts were averaged from 100 samplings at 800 sps of 13 positions between Ch-IV (36 mm) and Ch-V (48 mm) with the interval of 1 mm.
Figure 12 illustrates the strain response of PANDA-FBGs. As strain increases, the Bragg wavelength shift to longer wavelength. The strain sensitivities, as shown in Table 6, are indicated by the slopes from linear fitting of measured data. The results show good linear relationship between applied strain and Bragg wavelength during the experiment.
In the calibration of temperature sensitivities, we kept the FUT under stress-free condition, and changed the temperature at midpoint (average value by thermocouple Ch-IV and Ch-VI) from ~ 100 °C to ~ 160 °C by the interval of ~ 20°C. The temperature condition generated stable temperature distribution, as shown in Table 3, at the same time, reduced the influence of nonlinear sensitivity . The monitored temperature and strain are shown in Fig. 11(b).
The temperature response of PANDA-FBGs are shown in Fig. 13. The temperature sensitivities are also indicated by the slopes from linear fitting of measured data, as given in Table 7. The result shows good linear relationship between applied temperature and Bragg wavelength during the experiment.
4.3. Simultaneous measurement of strain and temperature
We respectively applied PANDA-A, B, C, D to the OFDR system and conducted experiments. In the experiment, we applied the strain and temperature variation simultaneous, as shown in Table 8. The relative strain and temperature from Case 1 to Case 2 (denoted by Case 2 - Case 1) were also examined. Meanwhile, the measured strain and temperature variation were recovered from the wavelength change byTables 6 and 7. In this research, the measured data points were readout by the interval of 1 mm within Application Area (12 mm ~ 72 mm, as shown in Fig. 8). For each measurement, we obtained the wavelength distribution for 2 s at the sampling rate of 800 sps. The measurement results for 1 sampling of PANDA-B and PANDA-D are shown in Fig. 14.
In this research, we assumed that the applied strain were uniform along the FUT. Meanwhile, we assumed that the temperature distribution between two adjacent channels were linear. Then, we used root mean square deviation (RMSD) at positions to represent the accuracy of simultaneous distributed strain and temperature measurement in Application Area, which are expressed asFig. 15. According to the results, the accuracy of both strain and temperature measurement were improved while the birefringence was increased.
4.4. Results and discussion
We plotted the simulated and experimental results in the same figure, as shown in Fig. 16. According to the figure, the simulation has agreement with experiment that higher birefringence leads to better measurement accuracy. Among the testing, in Case 2 - Case 1, under small temperature span, the measurement accuracy had the best agreement with the simulation. Relative bad accuracy in Case 2 might be caused by the amplification effect by the second term of Eq. (27) at right hand side. Additionally, for the large temperature span in Case 2 (~ 130°C), errors from the nonlinear temperature sensitivities could also lead to some disagreement between the experimental results and simulation based on linear approximation. Also, with higher temperature in Case 2, larger errors might be introduced by the instability of air flow. Although in this study, the influence of nonlinear sensitivities is limited, it is worth noting that when the measurement accuracy becomes higher, the ratio of nonlinear error to the total error will gradually become significant. Thus, high order coefficients should be taken into account in high accuracy measurement, and the linear K matrix method should be replaced by nonlinear analysis.
Additionally, we described the efficiency of improving accuracy by increasing the birefringence asFig. 17, while the birefringence increases, the efficiency of the improvement for both strain and temperature decrease. Additionally, the efficiency are much lower at high birefringence than low birefringence. For example, the efficiency at B = 1.4 × 10−3 is about 1/10 of the efficiency at B = 4 × 10−4.
In the experiment, PANDA-D achieved the best accuracy at the spatial resolution of 5 mm and the sampling rate of 800 sps in measuring the variation from Case 1 to Case 2 (Case 2 - Case 1: ±16.7 µε and ±1.9°C).
5. Conclusion and future works
In this work, we have built up a numerical model to estimate the accuracy of simultaneous distributed strain and temperature measurement PANDA-FBG sensors and study its dependence on the birefringence. The simulated results had agreement with the experimental results that the measurement accuracy of both strain and temperature were improved by increasing the birefringence. Meanwhile, we have found that the efficiency of the improvement were reduced when the birefringence were increased. Further more, the numerical model has been validated by the experiments. According to the results, once the accuracy required for an specific application is known, the model helps to know the birefringence for achieving the desired result.
In the future, we will investigate the influences of other parameters to the measurement accuracy by simulation and validate them by experiments. Additionally, under large temperature span, nonlinear analysis are expected to bring better measurement accuracy instead of linear K matrix method.
We would like to thank Mr. Makoto KANAI for his support in the preparation of the experiments.
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