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Abstract
It is an enormous challenge for optical fiber sensors to intuitively achieve the simultaneous measurement of both gas pressure and temperature with high sensitivity. To address this challenge, the Fabry–Perot interferometer (FPI) based on high-order harmonic Vernier effect is combined with the fiber Bragg grating (FBG). A novel fiber sensor built with a cascaded FPI and an FBG for the simultaneous measurement of gas pressure and temperature is designed and experimentally investigated by virtue of the temperature sensing property of FBG and its independence on gas pressure-induced refractive index change, where a high-order harmonic Vernier effect was utilized to boost the gas pressure sensitivity of the sensor. As gas pressure increases from 0 to 1 MPa, the internal envelope of composite FBG and FPI based 10-order harmonic Vernier effect exhibits redshift with maximal sensitivities of 146.64 nm/MPa and a high magnification factor of 43. FBG is insensitive to gas pressure change, whereas, the spectral response of the internal envelope 10-order harmonic Vernier effect and FBG monotonously move and undergo blueshift and redshift as the temperature increases from 30 °C to 120 °C with maximal sensitivities of −0.48 and 0.011 nm/°C, respectively. Therefore, the distinct sensitivities of FBG and FPI to gas pressure and temperature result in extraction of both gas pressure and temperature information simultaneously by constructing measurement matrixes.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Harmonic Vernier effect, as a newly developed tool for sensitivity magnification, is popularly developed and utilized in the field of optical fiber sensing such as temperature sensing [1,2], refractive index (RI) sensing [3], strain sensing [4], and relative humidity (RH) field [5] because of its better fabrication tolerances and higher performance advantages. Harmonic Vernier effect was firstly proposed by André D. Gomes in 2019, whose generation comes from the optical path length (OPL) of one of the interferometers is increased by a multiple (i-times) of the OPL of the second interferometer [6]. Gas pressure sensing is an important application field of fiber optic sensors. Nowadays, various fiber sensor structures for gas pressure measurement have been developed and applied including Mach–Zehnder interferometer (MZI) [7,8], microfiber [9], and Fabry–Perot interferometer (FPI) [10,11]. Among them, optical fiber interferometer structures, especially FPIs were the most widely applied structure in gas pressure sensing. However, the gas pressure sensitivity of the optical fiber sensor is relatively low. For example, Yang et al. proposed an in-fiber integrated gas pressure sensor based on a hollow optical fiber with two cores with a gas pressure sensitivity of only 4.2 nm/MPa [12]. At present, there are mainly two schemes proposed for improving sensitivity. The first method is by employing the traditional Vernier effect or harmonic Vernier effect to “amplify” the sensing signal to achieve a high-sensitivity [13]. Typically, the traditional Vernier effect occurs when the optical path length of two interferometers is very close but not identical. The periodic envelope will be generated in the spectrum by the superposition of both interferometers’ spectra. The sensitivity can be amplified by tracking the position of the envelope [14]. For example, Lin et al. developed an ultra-highly sensitive gas pressure sensor based on dual side-hole fiber interferometers with the traditional Vernier effect, where a sensitivity of∼-60 nm/MPa and an amplification factor of 7 times has been experimentally achieved within a pressure range from 0 to 0.8 MPa [15]. Li et al. demonstrated a gas pressure fiber probe composed of two cascaded FPIs with micro-channel based on the traditional Vernier effect with a high gas pressure sensitivity of 80.3 nm/MPa. However, a costly high-frequency CO2 laser is required for manufacturing the side-opened gas micro-channel [16]. Zhao et al. cascaded two fiber MZIs to form the traditional Vernier effect, which has gas pressure sensitivity as high as −73.32 nm/MPa in the pressure range of 0–0.8 MPa, 8.5 times higher than that of the single MZI sensor with an opening in the HCF. One potential disadvantage is the cost in employing expensive femtosecond laser equipment to construct the connection channel between the air hole of one HCF and the external environment [17]. Traditional Vernier effect has a harsh optical path length matching condition and high sensitivity magnification is still usually limited because of inevitable matching errors from practical preparation processes such as fiber cleaving, splicing, and etching [18]. The harmonic Vernier effect breaks the limitation of the strict optical path length matching condition in a traditional Vernier effect and allows larger tolerances in fabrication without sacrificing sensitivity [2]. The second method is coating of highly sensitive material [19]. Compared with the second method, the first method has the superiorities of structural diversity, and simple operation.
Most of the optical sensors can only measure a single physical parameter, which cannot satisfy the requirement of simultaneous measurement of both gas pressure and temperature due to the existence of crosstalk. There are two typical methods for distinguishing the impact of two different parameters. A straightforward method is to monitor two or more wavelength shifts (peak or dip) with different responses to the two or even multiple-parameters in the surrounding environment. For example, Zhang et al. achieved simultaneous measurement of RI and temperature by designing a side-polished fiber MZI whose two dips have different responses to RI and temperature [20]. Zhou et al. constructed an internal-and-external-cavity FPI, which was used for simultaneous measurement of RI and temperature because the envelope and fine fringes of sensors have different RI and temperature sensitivities [21]. Urrutia et al. presented a half-coated long-period grating for the simultaneous measurement of RH and temperature because the attenuation bands corresponding to the coated and uncoated gratings have different spectral responses to RH and temperature [22]. Another method is to use a fast Fourier transform (FFT) algorithm to extract signals from hybrid spectra to distinguish the influence of two parameters. For example, Li et al. filled polymer materials named polydimethylsiloxane (PDMS) and polyvinyl alcohol (PVA), respectively into the C-shaped fiber to form dual FPIs for simultaneously measuring RH and temperature. The wavelength changes in FFT-filtered spectra of the two FPIs vary for different RH and temperatures [23]. Wang et al. employed optical adhesive and four-hole suspended-core fiber to fabricate a hybrid FPI. Owing to two FP cavities with different RH and temperature sensitivities, the phase-shift tracking scheme in FFT spectra was adopted to simultaneously demodulated both RH and temperature information [24]. Fu et al. tracked the Fourier phase response based on an inline multimode interferometer formed by the single-mode fiber (SMF) offset-splicing structure to realize the simultaneous measurement of strain and temperature [25]. Compared with the second type, the first type is more intuitive and simple, which does not require complex data processing operations such as spectral extraction. Gas pressure and temperature have a significant impact on the performance of the sensor [26]. It is well-known that the application of FBG is extremely extensive [27] and FBG is an attractive device for a variety of applications, especially for multiparameter sensing [28,29]. Cascading the FBG with other fiber interferometers is a common method to realize the simultaneous measurement of both gas pressure and temperature. Because the FBG is sensitive to temperature but insensitive to gas pressure change, which can act as temperature supervision and compensation in measuring gas pressure [30,31].
In this study, a new optical fiber sensing platform composed of a FBG and an FPI with high-order harmonic Vernier effect, is constructed and experimentally explored for the simultaneous measurement of gas pressure and temperature. High-order harmonic Vernier effect is employed to achieve the sensitivity magnification of gas pressure and temperature measurement. Three composite FBG and FPIs with different order (10th, 4th, and 6th order) are fabricated to investigate the influence of detuning ratio, and optical path difference (OPD) on sensitivity. Because the internal envelope and FBG of the proposed sensor exhibit different sensitivities to gas pressure and temperature, which can achieve simultaneous measurement of both gas pressure and temperature provided sensitivity matrix is determined. In addition, the repeatability, reversibility, and stability of the combined FBG and FPI sensor were experimentally investigated.
2. Sensor preparation and simulation
2.1 Sensor fabrication
A schematic diagram of the sensor structure based on composite FBG and FPI with harmonic Vernier effect is shown in Fig. 1(a). The hollow core fiber (HCF) is sandwiched between an FBG and four-hole fiber (FHF) without capillary collapse to form three FPs through three reflective surfaces air-silica interfaces named air cavity (FP1), silica cavity (FP2), and hybrid cavity (FP3). The lengths of FP1, FP2, FP3, and the RI of FP1 and FP2 are labeled as ${L_1}$, ${L_2}$ ${L_3}$ and ${n_1}$, ${n_2}$, respectively. The value of ${n_1} $ changes from 1 to 1.0026635 as gas pressure increases from 0 to 1 MPa calculated by equation (Eq). (1) [32]:
where four air holes of FHF act as natural gas inlet channels. The RI of FHF’s core (${n_2}$) is 1.45. ${n_{air}}$, p, and T in Eq. (1) represent the RI of air, air pressure (Pa), and temperature (°C), respectively. The FBG was inscribed by a 193 nm excimer laser at the SMF with a core diameter of 8.5 µm and a cladding diameter of 125 µm. The test report and corresponding reflection spectrum of fabricated FBG are presented in Table 1 and Fig. 1(g). The center wavelength, 3 dB bandwidth, signal-to-noise ratio (SNR), and the length of FBG are 1535 nm, 0.2 nm, 17 dB and 15 mm, respectively. According to the references [33], the relationship between the OPD of FP1 ($OP{L_2}$) and FP2 ($OP{L_1}$) must meet the Eq. (2) to produce the harmonic Vernier effect by precisely cleaving the lengths of HCF and FHF under an optical microscope. A high- precision six-dimensional translation stage platform supported with an optical microscope is used to precisely control the cutting length of the fiber.
Fig. 1. (a) Schematic diagram of sensor structure; Microscopic images of fabricated FPIs: (b) S−1; (c) S−2; (d) S−3; Microscopic images of cross section: (e) HCF; (f) FHF; (g) Spectral monitoring of fabricated FBG.
Table 1. FBG parameters
2.2 Theoretical simulation
First of all, the gas pressure sensitivities of S−1, S−2, and S−3 are theoretically simulated. The detailed parameters in numerical simulation are as follows: The values of ${L_1}$, ${L_2}$ are 59.3, 439.3 µm; 134, 443 µm; 100.6, 378.6 µm when optical fiber sensors are S−1, S−2, and S−3, respectively. The RI (${n_2}$) of FHF core is set as 1.45. The value of ${n_1}$ increases from 1 to 1.0026635 with an equal interval of 0.00013317 when gas pressure increases from 0 to 1 MPa. In addition, the transmission losses of FP1 and FP2 are the same with the value of 0.5. For i-order harmonic vernier effect, the internal envelope was drawn by fitting the peak or dip of high-frequency fringes with (i + 1) peaks or dips as intervals, which is called the internal envelope fitting method. The reflected spectra of S−1, S−2, and S−3 are presented in Fig. 2(a-c), which are 10th, 4th, and 6th order harmonic Vernier effect, respectively. As shown in Fig. 2(a-c), the free spectral range (FSR) of the simulated spectra’s internal envelope is too large to track easily. However, rich internal envelope and intersection points are provided by the high-order harmonic Vernier effect. The wavelength shift of target measurand can be obtained by tracking the intersection points of two internal envelopes. The simulated gas pressure sensitivities of S−1, S−2, and S−3 including the upper envelope and internal envelope are summarized in Fig. 2(d). Clearly, the simulated gas pressure sensitivities of S−1, S−2, and S−3 based on the upper envelope are 3.43, 3.37, and 3.39 nm/MPa. The simulated gas pressure sensitivities of S−1, S−2, and S−3 based on the internal envelope are 147.89, 84.99, and 37.8 nm/MPa. Therefore, the magnification factor (M) of S−1, S−2, and S−3 are calculated as 43.12, 25, and 11.15, which are consistent with results obtained by Eq. (4) [34]:
where $FS{R_{{\mathop{\rm int}} }}$, $FS{R_{upp}}$ are the FSRs of the internal envelope and upper envelope, respectively. The detailed parameters of fabricated three composite FBG and FPIs are summarized in Table 2.Table 2. Parameters of fabricated three composite FBG and FPIs
3. Experimental characterization
A schematic diagram of experimental device is presented in Fig. 3. As shown in Fig. 3, the composite FBG and FPI is sealed in the gas pressure chamber and the pressure in chamber is controlled by a pressure pump (ConST-162), which is consisted of the alundum tube. It is worth mentioning that the alundum tube can withstand a high temperature of 1200°C and 10 MPa, which is placed in muffle furnace. Three ports of a circulator are connected to the proposed sensor, broadband light source (BBS, Purchased from Fiberlake Technology Co., Ltd, ASE-EB-D-2-2-FC/APC, wavelength range:600 nm-1700nm, average power:20 mw, max peak power:100 mw.), and optical spectrum analyzer (OSA, (AQ6370C)), respectively. The light emitted from the BBS is reflected by the composite FBG and FPI. The output light from the third port of the circulator is monitored by an OSA. The change of FP1’s RI results in spectral shift of composite FBG and FPI as gas pressure increases or decreases. The reflected spectra of the fabricated three samples (S−1, S−2, and S−3) are depicted in Fig. 4(a-c), respectively. The Spatial frequency spectra (SFS) based on linear-in-wavenumber resampling using FFT in Figs. 4(d-f) are obtained from Figs. 4(a-c), respectively, which revealed the cavities with distinct OPDs [35]. The three main frequency domain peaks correspond to the air cavity (peak1), silica cavity (peak2), and hybrid cavity (peak3), respectively. The composite FBG and FPI’s reflected spectrum presented in Fig. 4(a-c) primarily attributed to the contribution of peak1, peak2, and peak3.
Fig. 3. The schematic diagram of the experimental setup for simultaneously measuring gas pressure and temperature.
Fig. 4. The reflection spectra of fabricated FPI formed by HCF and FHF: (a) S−1; (b) S−2; (c) S−3; (d) SFS of S−1 based on FFT by the method of linear-in-wavenumber resampling in (a); (e) SFS of S−2 based on FFT by the method of linear-in-wavenumber resampling in (b); (f) SFS of S−3 based on FFT by the method of linear-in-wavenumber resampling in (c).
3.1 Gas pressure measurement
In the experiments, gas samples freely enter or leave the sensing cavity through the four air holes of FHF as open channels. The gas pressure value was designed to increase from 0 to 1 MPa with a step change of 0.05 MPa for four runs to evaluate the gas pressure sensing properties of the composite FBG and FPI. The corresponding reflective spectra were measured, as presented in Fig. 4(a-c). Clearly, the large FSR of the inner envelope caused low resolution and accuracy. Therefore, the intersection points (the red spots in Fig. 5(a)) of env7 and env10 in Fig. 4(a) were selected and tracked to monitor the wavelength shift of internal envelope for S−1. The reflected spectra of internal envelope and upper envelope for S−1 moved toward the long-wave direction when the gas pressure increased from 0 to 1 MPa as shown in Fig. 5(a-b). As presented in Fig. 5(c), the spectral response of FBG is insensitive to gas pressure, which is attributed to its negligible sensitivity to RI [36]. The average gas pressure sensitivities of internal envelope and upper envelope (single sensitive cavity) for S−1, S−2, and S−3 during the rising process were 146.64, 3.43 nm/MPa; 87, 3.78 nm/MPa; 38.23, 3.36 nm/MPa with M-factor of 43, 23, and 11 shown in Fig. 5(d-f). By comparison, experimental and theoretical results have excellent consistency. Besides, reversibility, as an important characteristic of a sensor, is experimentally investigated four times. As shown in Fig. 6(a-b), the reflected spectra of internal envelope and upper envelope for S−1 moved toward the short-wave direction as the gas pressure decreases from 1 to 0 MPa. As summarized in Fig. 6(c-e), high average gas pressure sensitivities are obtained. The sensitivities of internal envelope and upper envelope for S−1, S−2, and S−3 are 146.59, 3.39 nm/MPa; 89.57, 3.8 nm/MPa; 38.46, 3.32 nm/MPa with M-factor of 43, 24, and 11.6, which agree well with simulated results. In addition, experimental results show that composite FBG and FPI has excellent repeatability.
Fig. 5. Gas pressure test during the rising process: (a) Spectral response of internal envelope for S−1 as gas pressure varies from 0 to 1 MPa; (b) Spectral response of upper envelope for S−1 as gas pressure varies from 0 to 1 MPa; (c) Spectral response of FBG as gas pressure varies from 0 to 1 MPa; Measured average gas pressure sensitivities of the internal envelope and upper envelope for four runs: (d) S−1; (e) S−2; (f) S−3.
Fig. 6. Gas pressure test during the falling process: (a) Spectral response of internal envelope for S−1 as gas pressure decreases from 1 to 0 MPa; (b) Spectral response of upper envelope for S−1 as gas pressure decreases from 1 to 0 MPa; Measured gas pressure sensitivities of the internal envelope and upper envelope for four runs: (c) S−1; (d) S−2; (e) S−3. Insets: enlarged view of error bar.
Sensing performance of S−1 is compared with S−2, and S−3 to analyze the role of order i. According to experimental results, detuning ratio and order of harmonic Vernier effect are two main factors, which influence the gas pressure sensitivity. Furthermore, the lower the detuning ratio, the higher the harmonic order, and the higher the sensitivity. In a word, a small detuning ratio and a large order render a high sensitivity. Although the detuning ratios of S−1 and S−2 are similar with value of 25.8% and 20.9%, the order of S−1 is much higher than S−2 and S−3. Therefore, the gas pressure sensitivity and M-factor of S−1 is the highest among the three samples. On the basis of experimental analyses, M-factor can be further improved by increasing the order of harmonic Vernier effect if the different FPIs have similar detuning ratios. From the Eq. (2), we can conclude that adjusting the ratio of the sensing cavity and reference cavity’s lengths (L1 and L2) can obtain the optimal order of the harmonic Vernier effect. Clearly, although L2 of S−1 and S−2 is basically the same with value of 439.3 and 443 µm, the order of harmonic Vernier effect for S−1 (10-order) is higher than S−2 (4-order) by changing the value of L1. The detuning $\Delta $ of S−2 and S−3 is 28 µm and 54 µm. The detuning $\Delta $ of S−3 is about twice that of S−2. Compared with S−2 and S−3, although the order of S−3 is higher than S−2, the detuning ratios of S−3 is larger than S−2. Thus, the gas pressure sensitivity and M-factor of S−2 is higher than S−3.
The stability of the S−1 at 0.1 MPa was experimentally investigated for 480 min, and then the gas pressure value was adjusted to 0.5, 0.9 MPa for another 480 min. The wavelength shifts of the composite FBG and FPI were automatically recorded every 20 min. The internal envelope and upper envelope of for S−1 are lastly monitored and plotted in Fig. 7(a) and (c). As demonstrated in Fig. 7(b) and (d), the fluctuations of wavelength drifts were relatively small at 0.1, 0.5, and 0.9 MPa. The maximum wavelength shifts of internal envelope and upper envelope for S−1 were ±0.22 and ±0.09 nm, respectively. Therefore, the proposed optical fiber sensor has relatively good stability.
Fig. 7. Stability test: (a) Spectral response of internal envelope for S−1 at 0 min and 480 min when gas pressure is 0.1, 0.5, and 0.9 MPa, respectively; (b) The wavelength shifts of internal envelope for S−1 at 0.1, 0.5, and 0.9 MPa; (c) Spectral response of upper envelope for S−1 at 0 min and 480 min when gas pressure is 0.1, 0.5, and 0.9 MPa, respectively; (d) The wavelength shifts of upper envelope for S−1 at 0.1, 0.5, and 0.9 MPa.
3.2 Temperature sensing
The wavelength shift of the proposed sensor upon temperature change is not negligible because of the thermo-optic and thermal expansion effects of silica. Thus, the temperature-sensing characteristics was experimentally investigated. Gradually increase the temperature from 30°C to 120°C at a step change of 10°C, and stabilize at each temperature value for 1 h to ensure the accuracy of data. The temperature experiment was tested four times to investigate the repeatability of the temperature sensor. Here, the intersection points of env4 and env8 were chosen to monitor wavelength shifts caused by temperature change. This is because the relative position of the internal envelope does not change when the RI changes, so tracking the intersection points of the internal envelope is equivalent to tracking the internal envelope. Fig. 8(a) shows the spectral response of the internal envelope with wavelength blue shifts trend as the temperature increased from 30°C to 120°C by tracking the intersection points. As depicted in Fig. 8(b), the spectra of FBG shift towards to longer wavelength direction when the temperature changes from 30°C to 120°C. As illustrated in Figs. 8(c) and (e), the average temperature sensitivities of internal envelope and FBG for S−1, S−2, and S−3 during the rising process are −0.48, 0.011 nm/°C; −0.28, 0.0109 nm/°C; and −0.091, 0.0112 nm/°C with a small error bar and excellent linear correlation coefficients, respectively. Therefore, the internal envelope and FBG have different sensitivities to changes in the external temperature. Because S−1 has a higher i-th order with a value of 10 and the smaller $\Delta $ (15.3 µm), the temperature sensitivity of S−1 is the highest. In addition, multiple experimental results show that the average temperature sensitivity of FBG is about 0.011 nm/°C.
Fig. 8. Heating process; (a) The spectral response of internal envelope for S−1 by tracking the intersection point; (b) The spectral response of S−1’s FBG; The average temperature sensitivities: (c) S−1; (d) S−2; (e) S−3. Insets: enlarged view of error bar.
In addition, the reversibility of temperature is experimentally demonstrated in Fig. 9. As shown in Fig. 9(a-b), the spectral responses of internal envelope and FBG for S−1 have a red-shift trend and blue-shift trend, respectively during the cooling process. The average temperature sensitivities of internal envelope and FBG for S−1, S−2, and S−3 are −0.47, 0.0116 nm/°C; −0.283, 0.0105 nm/°C; and −0.09, 0.0111 nm/°C plotted in Fig. 9(c-e), which agree well with the heating process.
Fig. 9. Cooling process; (a) The spectral response of internal envelope for S−1 by tracking the intersection point; (b) The spectral response of S−1’s FBG; The average temperature sensitivities: (c) S−1; (d) S−2; (e) S−3. Insets: enlarged view of error bar.
Additionally, the stability is experimentally explored to evaluate the performance of the proposed sensor. The reflected spectrum was lastly monitored for 480 min by automatically recording experimental data every 20 minutes as an interval while the temperature remained at 30°C, 70°C, and 120°C, respectively. As shown in Fig. 10(a), the internal envelope has almost no wavelength shift after 480 min. The summarized wavelength variation of the tracked internal envelope is depicted in Fig. 10(b). The maximal dip wavelength fluctuation within 480 min was 0.23 nm, revealing that the proposed sensor has relatively good stability and practical application value.
Fig. 10. Stability test: (a) Spectral monitoring within 480 min;(b) Measured wavelength shifts of internal envelope at 30°C, 70°C, and 120°C within 480 min.
The reproducibility of the sensor was studied by characterizing three sensors S−1, S−2, and S−3 for gas pressure and temperature measurements, each for four times. The experimental results of the three sensors have excellent consistency and relatively small standard deviation, proving that the sensor has excellent reproducing performance. In addition, the good agreement between the simulation results and experimental results indirectly reflects the sensor's good reproducibility.
3.3 Simultaneous measurement of both gas pressure and temperature
The internal envelope and FBG of the proposed sensor have different gas pressure and temperature sensitivities based on the experimental results, which mean simultaneous measurements of both gas pressure and temperature can be realized through the following coefficient matrix, Eq. (5) [37]:
Here, $\Delta {\lambda _{\textrm{int}}}$ and $\Delta {\lambda _{\textrm{FBG}}}\; $ represent the wavelength shifts of sensor’s internal envelope and FBG caused by changes in temperature $\textrm{(}\Delta {T)}$ and gas pressure $\textrm{(}\Delta \textrm{G)}$, respectively. $\textrm{ }{S_{int,T}}$, $\textrm{ }{S_{FBG,T}}$, $\textrm{ }{S_{int,G}}$, and $\textrm{ }{S_{FBG,G}}$ indicate the temperature and gas pressure sensitivities of the internal envelope and FBG, respectively. These parameters can be calibrated/measured using the proposed sensor. The matrix can be inversely transformed to obtain the following measurement matrix, Eq. (6) [38]:
Table 3 lists the performance comparison of different optical fiber sensor structures for the measurement of temperature and gas pressure including sensor types, gas pressure sensitivity (G. sens.), temperature sensitivity (T. sens.), and the ability to realize the simultaneous measurement. As shown in Table 3, traditional optical fiber gas pressure and temperature sensors such as FPI [40,41], MZI [42], and optical fiber grating [43] have relatively low sensitivity. According to the references [44,45,46,47], the conclusion can be drawn that the harmonic Vernier effect or traditional Vernier effect is an effective method to achieve sensitivity improvement. However, the 1st and 2nd -order harmonic vernier effects are adopted and the large advantage of the high-order harmonic Vernier effect has not been fully developed [44]. Fabry-Perot silica-microprobe [45] and cascaded MZIs [47] could have higher sensitivity, however expensive equipment, such as a femtosecond laser is required to fabricate such sensor devices. By contrast, the sensitivity of the composite FBG and FPI for the measurement of gas pressure and temperature is the highest by employing the 10th-order harmonic Vernier effect. Furthermore, our proposed sensor has good repeatability and stability. Therefore, the proposed composite FBG and FPI with 10th-order harmonic Vernier effect has better performance advantages than those summarized in Table 3.
4. Conclusion
In summary, a new sensor compose of a cascade FBG and FPI for simultaneous measurement of both gas pressure and temperature was proposed and experimentally investigated. High gas pressure and temperature sensitivity and M-factor are obtained with the help of the high-order harmonic Vernier effect with values of 146.615 ± 0.025 nm/MPa, −0.475 ± 0.005 nm/°C, respectively. The internal envelope and FBG of the composite interferometer have different sensitivities to gas pressure and temperature, indicating simultaneous measurement of both gas pressure and temperature can be achieved by constructing a sensitivity matrix. In addition, the order and detuning ratio of the harmonic Vernier effect’s influence on sensitivity are experimentally investigated by preparing three composite FBG and FPI samples with large fabrication tolerance. Furthermore, further increasing the order of the harmonic Vernier effect and reducing the detuning ratio is the indicator to develop the optical fiber sensor with higher sensitivity. Besides, the proposed composite FBG and FPI with high-order harmonic Vernier effect exhibited good reversibility, repeatability and stability, which have potential applications in the measurement of environmental, biological, and other temperature and gas-sensing fields.
Table 3. Sensing performance comparison of different types of optical fiber sensors for measurement of gas pressure and temperature
Funding
Shenzhen Science and Technology Innovation Program (GXWD20201230155427003-20200731103843002, JCYJ20190806143818818, RCYX20221008092907027); National Natural Science Foundation of China (61675055, 62105080).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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