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Abstract
A fiber Bragg grating (FBG)-based multi-point sensing system for the simultaneous measurement of strain and temperature is proposed, with a Fabry-Perot interferometer (FPI) consisting of low reflective FBGs inscribed inside a polarization-maintaining (PM) fiber is introduced as a sensor head. A multi-point sensing method with high dynamic range and short measurement time can be realized by analyzing the reflection spectrum of low reflective FBG-FPIs, and a simultaneous measurement of strain and temperature using two orthogonal polarization modes is enabled by the high birefringence of a PM fiber. An experimental demonstration of multi-point measurement utilizing the proposed system is reported.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber optic sensors have several significant advantages over conventional electrical sensors, such as explosion proof, immunity to electromagnetic interference, small size and lightweight allowing access into normally inaccessible areas [1,2]. Thus, they are expected to be used in various applications as the replacements for electrical sensors.
Among many fiber optic sensor types, sensors using fiber Bragg grating (FBG) have some wonderful characteristics: being easy to embed into structural materials, localization of the sensor head, high compatibility with the transmission optical fibers, and wide measurement range with high measurement resolution [2,3]. In addition, FBG sensors can be used to measure many physical quantities, notably strain and temperature. Therefore, they have been used in smart structure technology, real-time structural measurements, and many other engineering fields as well as numerous medical applications.
One of the major attractions of FBG sensors is that multi-point sensing can be performed simply by installing multiple FBGs on a single optical fiber. There are two conventional methods for multiplexing of FBG sensors: wavelength division multiplexing (WDM) [4–7] and time division multiplexing (TDM) [8–11]. However, the number of points that can be measured by FBG multi-point sensors using these methods is limited by various factors. In the sensing methods based on WDM, the number of measurement points is in a trade-off relationship with the dynamic range of measurement. On the other hand, in the sensing methods based on TDM, the number of measurement points is in a trade-off relationship with measurement time.
In order to solve the problem mentioned above, we have previously reported another method for FBG-based multi-point sensing, in which a Fabry-Perot interferometer consisting of two low reflective FBGs (a low reflective FBG-FPI) is used as a sensor head [12]. In the reported method, the dynamic range of the measurement is irrelevant to the number of measurement points, and the measurement time does not become prolonged in proportion to the number of measurement points. Therefore, a sensor array composed of low reflective FBG-FPIs is expected to have a capability of multipoint measurement with high speed and wide dynamic range. Moreover, in our proposed method, the signals from each sensor are differentiated based on the lengths of the interferometers. This is different from methods such as TDM, in which the sensors are differentiated based on the optical path lengths from the detecting system to the sensors. While methods such as TDM basically require the sensors to be evenly spaced to achieve the maximum number of measurable sensors, our proposed method does not require the sensors to be evenly spaced, and therefore the distance between the sensors can be freely selected. Note that a distributed sensor using ultra-weak intrinsic Fabry-Perot interferometer (IFPI), which has a quite similar structure to the low reflective FBG-FPI, has been reported by Chen et al. [13]. The reported method can realize distributed sensing with extremely high spatial resolution in a certain area. However, in the reported method, it is difficult to increase the distance between the sensors, and thus it is difficult to realize sensing of multiple measurement points at distant positions as intended by our proposed method.
Another common problem of conventional FBG sensors is the cross-sensitivity between applied strain and temperature changes. Since an FBG sensor responds in the same way to strain and temperature changes, it cannot be used in a condition where both strain and temperature change simultaneously. To overcome this issue, various measurement methods have been presented [14–17]. We have also previously introduced a method that utilizes a Fabry-Perot interferometer constructed with two FBGs written in a polarization maintaining fiber (PM-FBG-FPI) as a sensor head [18]. The introduced method can be used to measure simultaneously temperature and static strain with high resolution.
By inscribing a low reflective FBG-FPI into polarization maintaining fiber, we have a new sensor head called low reflective PM-FBG-FPI. Since a low reflective PM-FBG-FPI is a combination of low reflective FBG-FPI and PM-FBG-FPI, it is possible to realize simultaneously high-speed multi-point measurement of temperature and strain. An experimental demonstration of simultaneous multipoint measurement of strain and temperature using three low reflective PM-FBG-FPIs was presented in [19]. In this extended paper, the experimental results of measurements utilizing one and two low reflective PM-FBG-FPIs are additionally provided. Based on the additional results, the measurement resolutions in the case of one-point sensing and the qualitative relationship between the increase in the number of measurement points and the measurement resolutions are evaluated.
2. Principles
An FBG can be fabricated by generating periodic refractive index changes in the core of an optical fiber along the longitudinal direction [20,21]. The FBG reflects only light of a specific wavelength, which is called the Bragg wavelength, and transmits other light. The Bragg wavelength λB is given by
where neff is the effective refractive index in the fiber core, and Λ is the period of the refractive index change. When strain is applied to the FBG or the temperature around the FBG changes, the Bragg wavelength shifts according to the relationship shown byA Fabry-Perot interferometer (FPI) is an interferometer composed of two parallel mirrors [22]. In this interferometer, light of a wavelength satisfying the resonance condition is strongly transmitted. In the case of normal incidence, the resonance wavelength λR is given by
where nF is the refractive index of the medium, LF is the interferometer length, m is an integer, and ϕm is a phase shift involved by the reflection of the mirrors. The difference between adjacent resonance wavelengths can be approximated byAn FPI composed of two FBGs as the mirrors is called an FBG-FPI. An FBG-FPI consisting of high reflective FBGs has a reflection spectrum with sharp transmittance peaks, and these sharp peaks can be used for high-resolution measurement [18,23–26]. However, a high reflective FBG-FPI reflects almost all light at and around the Bragg wavelength due to its high reflectance. Therefore, if multiple high reflective FBG-FPIs with the same Bragg wavelength are installed on a fiber, only one of them can be used as a sensor and thus multi-point sensing cannot be performed. If high reflective FBG-FPIs with different Bragg wavelengths are used, a WDM-based multi-point sensing can be realized, but the number of measurable points in that case will have a trade-off relationship with the dynamic range, as in conventional WDM-based FBG sensing methods. On the other hand, a low reflective FBG-FPI has a sinusoidal-shape reflection spectrum, as mentioned above. When strain is applied to the FBG-FPI or the temperature around the FBG-FPI changes, the effective refractive index and the interferometer length change as well. As a result, the reflection spectrum shifts in wavelength corresponding to the changes. The wavelength shift amount of the reflection spectrum can be derived in the same manner as the Bragg wavelength and is given by
In addition, it can be seen from Eq. (5) that the period of the sinusoidal wave in the reflection spectrum of low reflective FBG-FPI depends on the interferometer length of the FPI or, in this case, the spacing between two FBGs. In other words, low reflective FBG-FPIs with different spacing between FBGs will have sinusoidal reflection spectra with different periods. As a result, if multiple low reflective FBG-FPIs with different spacing between FBGs are installed in series on a single fiber, the total reflection spectrum structure will be a combination of sinusoidal waveforms with different periods (or frequencies). When the Fourier transform is applied to this total reflection spectrum, multiple amplitude peaks corresponding to the frequencies of sinusoidal waveforms can be detected, and therefore these peaks correspond one-to-one to the FBG-FPIs. By reading the phase changes at these peak positions, the wavelength shift amount corresponding to each FBG-FPI can be obtained independently. The relationship between the phase change ΔΦj and the wavelength shift amount Δλj corresponding to the jth FBG-FPI (j is integer) is given by
where ωj = 2πfj, and fj is the frequency of the sinusoidal reflection spectrum of the jth FBG-FPI [27]. This way, a multi-point sensing with a large number of measurement points can be realized. The number of measurement points is determined by the wavelength resolution of the reflection spectrum measurement and the peak width in the Fourier transform result of the reflection spectrum, which depends on the bandwidth of the reflection spectrum [27]. It is worth noting that each PM-FBG-FPI structure represents a measurement point, and therefore the spatial resolution of the multi-point measurement can be defined as the total length of a PM-FBG-FPI.A low reflective FBG-FPI inscribed in polarization maintaining (PM) fiber is called a low reflective PM-FBG-FPI. Due to the high birefringence in the core of polarization maintaining fiber, a low reflective PM-FBG-FPI has two reflection spectra corresponding to two orthogonal polarization components (slow-axis polarization and fast-axis polarization). These two reflection spectra shift in wavelength with different strain and temperature dependencies. Let Δλs be the wavelength shift amount of the reflection spectrum corresponding to slow-axis polarization, and Δλf be the wavelength shift amount of the reflection spectrum corresponding to fast-axis polarization. Base on Eq. (7), the relationship between Δλs, Δλf, applied strain ε and temperature change ΔT is given by
3. Experiments and results
Three low reflective PM-FBG-FPIs were fabricated for the experiments, with the spacing between two FBGs being 30 mm for the first one (PM-FBG-FPI1), 25 mm for the second one (PM-FBG-FPI2), and 20 mm for the third one (PM-FBG-FPI3). The fabrication of each PM-FBG-FPI was performed by exposing ultraviolet light onto a PANDA fiber (Fujikura SM15-PS-U25A) with a phase mask. Each FBG had a physical length of approximately 1 mm and a reflectance of about 1%. The Bragg wavelength was about 1550 nm. The reflection spectra corresponding to two polarization components of a single PM-FBG are shown in Fig. 1.
A schematic diagram of experimental setup for the interrogation of PM-FBG-FPI sensor array is shown in Fig. 2. The PM-FBG-FPI sensor array consists one or more reflective PM-FBG-FPIs installed in series, and only one interrogator is required for the interrogation of the entire sensor array. A tunable semiconductor laser (Santec TSL-710) was used as a wavelength swept light source. The sweep range of the laser source was set to 1540∼1560 nm considering the center wavelength of the PM-FBG-FPIs was about 1550 nm, while the tuning interval was set to 0.004 nm. The light reflected from the PM-FBG-FPI sensor array consist two orthogonal polarization components. These polarization components are split by a polarization beam splitter and transmit through two legs of the beam splitter, then pass through two optical circulators to the respective photodetectors (Newport 2053FC-M). The laser source and photodetectors were connected to a computer with Santec Swept Test System (STS) software installed. The wavelength sweep and the measurement of the reflectance were performed by operating the Swept Test System software.
Figure 3 shows the measured reflection spectra corresponding to two polarization components of PM-FBG-FPI1. In these figures, it can be confirmed that the reflection spectrum corresponding to each polarization component has a substantially sinusoidal structure in the reflection band of the FBG. In addition, it can be seen that the reflection spectra of PM-FBG-FPI have envelopes with the same shape as the reflection spectra of a single PM-FBG. The measurement of the reflection spectra of PM-FBG-FPI2 and PM-FBG-FPI3 gave almost the same results, except that the periods of sinusoidal waveforms in the reflection spectra of these PM-FBG-FPIs were different to each other and different to the period of sinusoidal waveforms shown in Fig. 3. These results show that the period of the sinusoidal reflection spectra of a PM-FBG-FPI depends on the interval between two FBGs.
Fig. 3. (a) Reflection spectra of PM-FBG-FPI1 and (b) the enlarged view in the range from 1549.8 to 1550.2 nm.
The strain dependence of low reflective PM-FBG-FPI was experimentally measured. In this experiment, to improve the measurement accuracy, only one of the fibers containing a PM-FBG-FPI was connected to the interrogation system at one time, and the dependence measurement of each PM-FBG-FPI was performed individually. One end of the fiber was bonded to a fixed stage and the other end was bonded to a movable stage. The fiber length between two ends before strain applying was 1335 mm for PM-FBG-FPI1, 1345 mm for PM-FBG-FPI2 and 1395 mm for PM-FBG-FPI3. Static strain was applied to each PM-FBG-FPI by moving the movable stage from 0 to 0.5 mm at an interval of 10 µm, which stretched the fiber containing it. Note that a fiber stretching amount of 10 µm corresponds to a strain amount of 7.49 µε for PM-FBG-FPI1, 7.43 µε for PM-FBG-FPI2 and 7.17 µε for PM-FBG-FPI3. Also, in the strain measurement experiments that will be described later, the manner of fixing the fibers is the same, and therefore the relationships between the amount of stage movements and the applied strain are the same. The wavelength shifts of the reflection spectra of PM-FBG-FPI1 in responses to applied strain are shown in Fig. 4. It can be seen that the reflection spectra of PM-FBG-FPI1 shifted to longer wavelengths in responses to the applied strain. The correlation coefficients of the measurement results were 0.99996 for both polarizations, implying that the responses were almost linear. In addition, it can be confirmed that the slow-axis polarization had larger wavelength shift amount than the fast-axis polarization in the case of strain applying, and the difference of wavelength shift amounts of two polarizations (wavelength shift amount of slow-axis polarization minus wavelength shift amount of fast-axis polarization) increased almost linearly. The ratio between the difference and the average of wavelength shift amounts of two polarizations was stable at around 0.7%, implying the high stability of the measuring system. The strain dependence coefficients of the wavelength shifts (i.e., the slopes of the response curves) were 1.22 pm/µε and 1.21 pm/µε for slow-axis polarization and fast-axis polarization, respectively. Note that the estimated values shown in Fig. 4(b) were calculated from these strain dependence coefficients. The strain dependence measurement of PM-FBG-FPI2 and PM-FBG-FPI3 gave almost the same results.
Fig. 4. (a) Wavelength shifts of the reflection spectra of PM-FBG-FPI1 in responses to strain applying and (b) the difference of wavelength shift amounts of two polarizations.
Next, the temperature dependence of low reflective PM-FBG-FPI was experimentally measured. In this experiment, only one of the fibers containing a PM-FBG-FPI was connected to the interrogation system at one time, and the dependence measurement of each PM-FBG-FPI was performed individually. The temperature around a PM-FBG-FPI was stabilized using a thermal insulation box and a thermoelectric heater/cooler, and monitored using a digital thermometer. The set temperature of the thermoelectric heater/cooler was changed from 21 to 40 °C in steps of 1 °C, which changed the temperature around the PM-FBG-FPI consequently. The wavelength shifts of the reflection spectra of PM-FBG-FPI1 in responses to temperature change are shown in Fig. 5. Note that the temperature values being used in the graph are the values measured by the thermometer. It can be seen that the reflection spectra of PM-FBG-FPI1 shifted to longer wavelengths in responses to the increase in temperature. The correlation coefficients of the measurement results were 0.99995 for both polarizations, showing the high linearity of the responses. In addition, it can be confirmed that the slow-axis polarization had smaller wavelength shift amount than the fast-axis polarization in the case of temperature increasing, and the difference of wavelength shift amounts of two polarizations decreased almost linearly. This is contrary to the case of wavelength shifts due to strain applying. The ratio between the difference and the average of wavelength shift amounts of two polarizations was stable at around 4%, again implying the high stability of the measuring system. The temperature dependence coefficients of the wavelength shifts, or the slopes of the response curves, were 10.1 pm/°C and 10.5 pm/°C for slow-axis polarization and fast-axis polarization, respectively. Note that the estimated values shown in Fig. 5(b) were calculated from these temperature dependence coefficients. Almost the same results were obtained in the temperature dependence measurement of PM-FBG-FPI2 and PM-FBG-FPI3.
Fig. 5. (a) Wavelength shifts of the reflection spectra of PM-FBG-FPI1 in responses to temperature change and (b) the difference of wavelength shift amounts of two polarizations.
There is a theory behind the fact that the difference of wavelength shift amounts of two polarizations show opposite trends when strain and temperature change, which bases on the effect of the stress applying parts in PM fiber. When strain is applied, the fiber expands in the longitudinal direction and simultaneously compresses in the axial direction. At this time, the compression in the axial direction of the stress applying parts is smaller than the normal cladding, and therefore the difference of the refractive indices of two polarizations increases. On the other hand, when the temperature rises, the fiber expands in both the longitudinal direction and axial direction. At this time, the expansion in the axial direction of the stress applying parts is higher than the normal cladding, and therefore the difference of the refractive indices of two polarizations decreases. This way, the difference of wavelength shift amounts of two polarizations changes reversely when strain and temperature change.
Before experimentally conducting simultaneous multi-point measurements, we confirmed the performance of low reflective PM-FBG-FPI in a one-point measurement of strain and temperature. Only PM-FBG-FPI1 was used for this measurement. The fiber containing PM-FBG-FPI1 was bonded to two stages as in the strain dependence measurement. Also, the temperature around PM-FBG-FPI1 was controlled by a thermoelectric heater/cooler and measured by a digital thermometer, as in the temperature dependence measurement. In the experimental procedure, at first, the set temperature of the thermoelectric heater/cooler was set to 20 °C. Then, strain was applied to PM-FBG-FPI1 by moving the movable stage by 50 µm at 10 µm intervals. After that, the set temperature of the thermoelectric heater/cooler was raised up to 30 °C at 1 °C intervals, and the movable stage was moved by 50 µm at 10 µm intervals each time the temperature rose. The reflection spectra of PM-FBG-FPI1 were measured during the temperature change and strain applying. The strain and temperature changes were calculated by substituting the wavelength shift amounts of these reflection spectra and the obtained dependence coefficients into Eq. (10). Figure 6 shows the strain and temperature measured by PM-FBG-FPI1, along with the estimated strain values and the temperature values measured by the thermometer as reference values. The estimated strain values in Fig. 6(a) were calculated using the original length of the fiber and the shift amount of the movable stage (i.e., the extended amount of the fiber length). It can be seen that the strain and temperature values measured by PM-FBG-FPI1 were almost the same as the reference values. The root mean squares (rms) of the differences between the values measured by PM-FBG-FPI1 and the corresponding reference values were calculated to be about 1.1 µε for the strain and about 0.1 °C for the temperature. These values can be considered as the measurement errors of one-point sensing using a low reflective PM-FBG-FPI. On the other hand, according to previous studies the measurement errors of one-point sensing using a high reflective PM-FBG-FPI sensor, which was proposed for high-resolution measurements, were 0.8 µε and 0.1 ° C for the strain and temperature respectively [26]. Comparing these results, it can be seen that the low reflective PM-FBG-FPI can also be used for high-resolution measurements of strain and temperature in the case of one-point sensing.
Finally, simultaneous multi-point sensing of strain and temperature utilizing low reflective PM-FBG-FPIs was experimentally demonstrated. Two experiments, including a two-point measurement and a three-point measurement, were conducted. A schematic diagram of experimental setup for the two-point sensing experiment is shown in Fig. 7. For the three-point sensing experiment, the fiber containing PM-FBG-FPI3 was connected to the system via the fiber containing PM-FBG-FPI2. In the experimental procedure, the set temperature of the thermoelectric heater/cooler was raised from 20 °C up to 30 °C at 1 °C intervals, and the fibers containing PM-FBG-FPIs were stretched by moving the movable stages by 50 µm at 10 µm intervals each time the temperature rose. The fibers were stretched in the order of PM-FBG-FPI1, PM-FBG-FPI2 (and PM-FBG-FPI3, in the case of three-point sensing experiment). In short, while strain was applied to all two (or three) PM-FBG-FPIs in turn, only the temperature around PM-FBG-FPI1 was controlled and changed intentionally. Since PM-FBG-FPIs other than PM-FBG-FPI1 were placed in a room temperature environment without temperature stabilization, the temperature around them was not monitored by any thermometer. The reflection spectra of PM-FBG-FPI sensor arrays were measured while strain was being applied and temperature around PM-FBG-FPI1 was being changed.
Figure 8 shows the results of applying the Fourier transform on the obtained reflection spectra. It can be seen that in the two-point sensing experiment two amplitude peaks corresponding to two PM-FBG-FPIs were detected, while in the three-point sensing experiment three amplitude peaks were detected. The phase changes at the positions of these peaks were read out simultaneously but independently for the conversion to the wavelength shift amounts of each PM-FBG-FPI’s reflection spectra using Eq. (8). It is worth noting that if the reflectance of a PM-FBG-FPI is too low, the amplitude of the peak corresponding to that PM-FBG-FPI will be too small. Consequently, the phase change will become difficult to be read out correctly, which induces the large errors in the wavelength shift amount and the final measurement result. However in these experiments, the amplitudes of the peaks are considered to be large enough to extract the phase changes.
Fig. 8. Results of applying the Fourier transform on the reflection spectra of PM-FBG-FPI sensor arrays in case of (a) two-point sensing and (b) three-point sensing experiments.
The strain and temperature changes at the position of each PM-FBG-FPI were calculated using the wavelength shift amounts of the reflection spectra and the obtained dependence coefficients. The strain and temperature changes measured by PM-FBG-FPIs along with the reference values are shown in Fig. 9 and Fig. 10 for the two-point sensing experiment and the three-point sensing experiment, respectively. Note that since the temperature changes around PM-FBG-FPI2 and PM-FBG-FPI3 were not monitored by any thermometer, there were no reference values of temperature for these PM-FBG-FPIs. Therefore, the temperature changes measured by PM-FBG-FPI2 and PM-FBG-FPI3 are shown but the measurements errors for these measurement results are not evaluated here. In addition, since PM-FBG-FPI2 and PM-FBG-FPI3 were placed in a room temperature environment without any temperature stabilization, the temperatures around these PM-FBG-FPIs might vary largely, inducing the large uncertainties of measured temperature values. It can be seen from the figures that the strain and temperature values measured by PM-FBG-FPIs were close to the reference values, if applicable. The rms of the differences between the values measured by PM-FBG-FPIs and the corresponding reference values were calculated and considered to be the measurement errors. In the two-point sensing experiment, the strain measurement errors of both PM-FBG-FPI1 and PM-FBG-FPI2 were about 4 µε, and the temperature measurement error of PM-FBG-FPI1 was about 0.4 °C. In the three-point sensing experiment, the strain measurement errors of all PM-FBG-FPIs were about 7 µε, and the temperature measurement error of PM-FBG-FPI1 was about 0.6 °C. These results have experimentally demonstrated that simultaneous multipoint sensing of strain and temperature using low reflective PM-FBG-FPIs can be realized. However, it is observed that the measurement errors increased as the number of PM-FPG-FPIs increased in the experiments.
As the strain and temperature changes are given by Eq. (10), we try estimating the uncertainty of the measured quantities with respect to the uncertainty of the measured wavelength shift amounts using the condition number of the matrix. The elements of the vector on the left side of Eq. (10) represent two physical quantities with different dimensions. Therefore, we define the following vector
4. Conclusion
A sensing system utilizing Fabry-Perot interferometers consisting of low reflective FBGs inscribed inside polarization maintaining fiber (low reflective PM-FBG-FPIs) as sensor heads was proposed for simultaneous high-speed multi-point measurement of strain and temperature. The dependences of the fabricated low reflective PM-FBG-FPIs on strain and temperature were measured experimentally, and the dependence coefficients required for sensing were obtained. After that, the performance of a low reflective PM-FBG-FPI on simultaneous measurement of strain and temperature was confirmed in a one-point sensing experiment. The experimental results show that a low reflective PM-FBG-FPI has measurement resolutions of 1 µε and 0.1 °C in the case of one-point sensing. Finally, simultaneous multi-point measurements of strain and temperature using low reflective PM-FBG-FPIs were performed in a two-point sensing experiment and a three-point sensing experiment. The strain and temperature changes measured by PM-FBG-FPIs were close to the reference values, with measurement errors being 4 µε and 0.4 °C in the two-point sensing experiment, as well as 7 µε and 0.6 °C in the three-point sensing experiment. These results allow a conclusion that simultaneous multi-point measurement of strain and temperature utilizing low reflective PM-FBG-FPIs is possible.
In the experiments, the measurement errors increased as the number of PM-FPG-FPIs increased. Since this issue may become a limiting factor for multi-point sensing, it should be further considered in future work. Particularly, the number of measurement points should be further increased to confirm if the measurement errors continue increasing or stop increasing. The confirmed relationship between the number of measurement points and the measurement errors would help to find the causes and solutions for the issue.
Funding
Japan Society for the Promotion of Science (JP18K04190).
Acknowledgments
The authors would like to thank K. Omichi (Fujikura Ltd.) for fabricating the PM-FBG-FPIs.
Disclosures
The authors declare no conflicts of interest.
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