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Abstract
As a high-precision fiber optic sensor, a single optical fiber Fabry Pérot interferometer (FFPI) sensor is often used to measure parameters such as temperature or strain. However, the use of combined FFPIs to measure multiple parameters simultaneously has rarely been reported. In this paper, a compact Tri-FFPI sensor consisting of three series-connected FFPIs is proposed to measure high temperature, high acceleration, and large strain. The total length and diameter of the sensing part are only 2558.9 µm and 250 µm, respectively. One of the FFPIs, FFPI-1, contains a cantilever beam structure to measure vibration acceleration. FFPI-2 is used to measure temperature and the temperature compensation of the strain measurement. FFPI-3 is used to measure strain. To ensure that the sensor has high measurement sensitivity, two demodulation methods are used: the light intensity demodulation method for vibration acceleration and the wavelength demodulation method for temperature and strain. The sensor is capable of withstanding ultrahigh temperatures up to 1000°C.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As important parameters in health monitoring of equipment, research on vibration acceleration, temperature, and strain measurement [1–4] has never stopped, especially in aircraft engines, space satellites and other technology-intensive fields. The measurement environment can be harsh. For example, F.R. Ismagilov et al. [5] designed a highly efficient high-temperature starter generator to meet the development needs of aircraft engines. Part of the generator needs to work at 700°C. Therefore, for the measurement of this generator, the sensor needs to be able to withstand 800°C. In addition to high temperatures, harsh environments also include the presence of corrosive gases, corrosive liquids, or electromagnetic interference. In such cases, fiber-optic sensors with the advantages of high temperature resistance, corrosion resistance, and immunity to electromagnetic interference have been favored by researchers. Among them, optical fiber Fabry Pérot interferometer (FFPI)-based fiber optic sensors with simple structures and high measurement accuracy have developed into an important branch of fiber optic sensors.
To achieve temperature, acceleration, and strain measurements, many researchers have performed excellent researches. Wei et al. [6] proposed an FFPI based on a photonic crystal fiber with a sensitivity of 13 pm/°C. The sensor can be used in the range of 40–480°C. Zhenshi et al. [7] fabricated a high-temperature FFPI sensor that can withstand a high temperature of 1000°C. The sensor was made by core-dislocation fusion of a fine optical fiber and a single-mode optical fiber. In terms of vibration acceleration measurements, Dong et al. [8] proposed an FFPI sensor that measured vibration at 500°C. Their test showed that the sensitivity of the sensor reached 11.57 mV/g. However, its resonance frequency was only 165 Hz, which cannot meet the needs of aircraft engines. Bin et al. [9] proposed a high sensitivity FFPI vibration sensor by splicing two different types of fibers. Their tests showed that the vibration sensitivity of the sensor was 60.22 mV/g at 100 Hz. However, its working frequency range is from 40 Hz to 500 Hz. In terms of strain measurements, Teng et al. [10] proposed a wide-range strain sensor based on an FFPI, a fiber Bragg grating (FBG), and a 3D printed spring. With the elasticity of the spring, the strain measurement range of the sensor was up to $1.5 \times {10^7}\mathrm{\mu \varepsilon }\textrm{.}$ Yanping et al. [11] fabricated an FFPI by repeating arc discharge on an optical fiber, achieving the advantages of small size and high strength. Their test results showed that a wide measurement range of 9800 µɛ was achieved. Jing et al. [12] proposed an FFPI strain sensor by core-dislocation fusion of two optical fibers, which were etched at the end faces to form circular cavities. Their test results showed that the core-dislocation fusion improved the strain sensitivity of the FFPI strain sensor from 1.67 pm/µɛ to 3.14 pm/µɛ. Yong et al. [13] fabricated a 35 µm-long rectangular FFPI using a high-precision fiber cutting platform, which improved the precision of the fabrication of FFPIs.
Researches about multi-parameter measurements have also been reported in recent years. Yuzhu et al. [14] proposed a sensor based on two FFPIs connected in series to measure strain and temperature. The sensing principle of the sensor were based on different sensitivities of the two FFPIs. However, the temperature sensitivities of the two FFPIs were very similar, which led to larger measurement errors. By chemical etching, Paula A.R. Tafulo et al. [15] proposed an FFPI sensor to measurement high temperature and strain. This sensor can withstand high temperature of up to 700°C.
However, there are few reports on compact sensors that are able to measure temperature, vibration acceleration, and strain simultaneously. The accurate measurement of these three parameters is the basis of health monitoring. For aircraft engines and space satellites, the small size and lightweight of compact sensors can effectively save the internal space and reduce the weight of devices, which can further improve their performance and reduce the operating cost. Therefore, a compact FFPI sensor for simultaneously sensing high temperature, acceleration, and strain is urgently needed. In this research, a compact Tri-FFPI sensor consisting of three series connected FFPIs was designed and developed for sensing temperature, vibration acceleration, and strain, simultaneously. The light intensity demodulation method was used to demodulate acceleration. The wavelength demodulation method was used to demodulate temperature and strain. The experimental results show that the designed Tri-FFPI sensor has a sensitivity of 1.55 nm/°C, a measurement linearity of 99.99%, and a measurement error of 0.59% F.S. in the temperature measurement up to 1000°C. The measurement sensitivity, linearity, and error of the acceleration measurements are 1.87 mV/g, 99.98%, and 1.44% F.S., respectively, in the range of 0–100 g. In the strain measurement, the sensitivity, linearity, and measurement error are 9.52 nm/µɛ, 99.99%, and 1.03% F.S., respectively, in the range of 0–2500 µɛ.
2. Designed sensor
2.1 Design of the compact Tri-FFPI sensor
A diagram of the designed compact Tri-FFPI sensor is shown in Fig. 1. The sensor was designed with three FFPIs, a support sleeve and an encapsulation sleeve. The encapsulation sleeve and support sleeve are made of hollow capillary glass tubes of different sizes. The encapsulation sleeve protects the sensor. The encapsulation sleeve and the fiber are connected by a support sleeve. The sensing part of the sensor mainly consists of two air cavities and a quartz cavity on the fiber. One of the air cavities contains a cantilever, as shown in Fig. 1(b). The cantilever is comprised of a fine fiber and a fiber mass. The fiber mass is made from a small piece of single-mode fiber flat at both ends. The fine fiber is obtained by etching the single-mode fiber, a mold field diameter of 10 µm at a wavelength of 1550 nm and a cladding diameter of 125 µm, with 10% hydrofluoric acid (HF). The fine fiber and the fiber mass are connected and fixed using a fusion splicer (FITEL-S178A). The end facing RS-1 and RS-2 form FFPI-1 for acceleration sensing in the ${D_2}$-direction. The two end faces of the fiber mass, RS-2 and RS-3, form FFPI-2 for temperature sensing. The end faces RS-3 and RS-4 form FFPI-3 for temperature sensing and strain sensing in the ${D_1}$-direction. The dimensions of the sensor are labeled and represented as shown in Fig. 2 and Table 1.
Fig. 1. Diagrams of the designed Tri-FFPI sensor. (a) Outlook of the sensor; (b) Section view of the sensor along the axis; (c) Cantilever structure; (d) End view of the sensor.
Fig. 2. Size of the designed Tri-FFPI sensor. (a) Section view of the designed Tri-FFPI sensor along the axis; (b) cantilever structure; (c) end view of the sensor.
Table 1. Geometric Parameters of the Designed designed Tri-FFPI Sensor
2.2 Design of the sensing method
The optical path diagram of the integrated sensor is shown in Fig. 3. When measuring vibration acceleration, the light intensity measurement method is used. The optical path ${K_1}$ in Fig. 3 is connected to ${S_1}.$ ${K_2}$ remains disconnected. The narrowband laser generated by the laser light source is amplified by the optical fiber power amplifier. Then coupled by the circulator before entering the designed compact Tri-FFPI sensor. Then, the light reflected by the sensor is converted into a voltage signal by the photodetector after being circulator coupled, and the signal is finally collected and recorded by the data acquisition card.
The reflected spectrum of the compact Tri-FFPI sensor contains the reflected spectra of FFPI-1, FFPI-2, and FFPI-3, as expressed by Eq. (1). However, the reflected light of FFPI-3 is too weak to be recognized in the spectrum. Therefore, the compact Tri-FFPI sensor can be seen as the series connection of FFPI-1 and FFPI-2, and the expression can be simplified as Eq. (2).
The spectrum of the compact Tri-FFPI sensor is calculated and shown in Fig. 4. The blue line represents the reflected light of the sensors to a broadband light source. The orange line represents the reflected light of the sensor to a laser light source. The reflected light of a laser light source can be seen as a slice of that of a broadband light source. The blue line is comprised of two cosine-like waves with different periods. According to Eq. (2), the cosine-like wave with a large period is generated by FFPI-1 interference.
There is an off-axis distance ${d_b}$ between the axis of the cantilever and the axis of the fine fiber, as shown in Fig. 2(b). The cantilever beam is forced to vibrate when there is a vibration in the direction of ${D_2}.$ The fiber mass produces a displacement $\Delta {L_{\textrm{FFPI - 1 - }V}}$ in the direction of the fiber axial direction, which changes the cavity length of FFPI-1, as shown in Fig. 5. $\Delta h$ represents the displacement of the fiber mass in the direction perpendicular to the fiber axis. In contrast, the cavity length of FFPI-2 will not change during the vibration measurement. Therefore, ${L_{\textrm{FFPI - 1}}}$ is the only variable in Eq. (2). By deriving Eq. (2), the relationship between $\Delta {R_V}(\lambda )$ and $\Delta {L_{\textrm{FFPI - 1}}}$ is obtained, as shown in Eq. (3).
Equation (3) represents the shift of the spectrum caused by $\Delta {L_{\textrm{FFPI - 1}}}.$ In addition, $\Delta {L_{\textrm{FFPI - 1}}}$ will also affect the light intensity of the reflected spectrum by the coefficient ${\delta _{\textrm{FFPI - 1}}}$ in Eq. (2). According to the Gaussian beam formula [16], ${\delta _{\textrm{FFPI - 1}}}$ can be expressed as Eq. (4):
According to Eq. (4), the relationship between ${\delta _{\textrm{FFPI - 1}}}$ and ${L_{\textrm{FFPI - 1}}}$ is obtained and shown as the blue curve in Fig. 6.
Equation (2) can be rewritten as Eq. (5). ${F_{\textrm{FFPI - 1}}}$ represents the shift of interference fringe.
To analyze the influence of ${\delta _{\textrm{FFPI - 1}}}$ and ${F_{\textrm{FFPI - 1}}}$ on ${R_V}(\lambda )$ respectively, Partial Differentials of ${R_V}(\lambda )$ are calculated as Eq. (6) and (7):
For the convenience of presentation, $\Delta {R_{V - \delta }}$ is used to represent the change of ${R_V}(\lambda )$ caused by $\Delta {\delta _{\textrm{FFPI - 1}}}$ and $\Delta {R_{V - F}}$ is used to represent the change of ${R_V}(\lambda )$ caused by $\Delta {F_{\textrm{FFPI - 1}}}.$ According to Eq. (6) and (7), $\Delta {R_{V - \delta }}/\Delta {R_{V - F}}$ is obtained as Eq. (8)
In order to ensure the linearity of vibration acceleration measurement, ${\varphi _{\textrm{FFPI - 1}}}$ is designed to be near $(n + \frac{1}{2})\mathrm{\pi ,\ }n = \textrm{0,1,2} \cdots .$ In this research, even if the temperature changes by 1000°C, the phase change caused by thermal expansion of FFPI-1 will not exceed 0.29π according to Eq. (9).
Therefore, $|{\cot ({\varphi_{\textrm{FFPI - 1}}})} |$ is in the range from 0 to 1.2. $\Delta {R_{V - \delta }}/\Delta {R_{V - F}}$ is in the range from 0 to 0.24%. This result shows that the change of light intensity has much less influence on the measurement results than the spectrum shift.
Temperature changes will also cause changes of ${L_{\textrm{FFPI - 1}}}$ and ${L_{\textrm{FFPI - 2}}}.$ Power fluctuations in the laser light source and the optical fiber power amplifier will also have an effect on the magnitude of ${R_V}(\lambda ).$ However, these changes are slow compared with the change caused by vibration, so the interference can be excluded by fast Fourier transform (FFT) to obtain the vibration signal, as shown in Fig. 7. When measuring the strain, it focuses on FFPI-3 and has no effect on the vibration acceleration measurement by FFPI-1.
When measuring the temperature and strain, the wavelength demodulation method is used to achieve accurate demodulation of the cavity lengths of FFPI-2 and FFPI-3. The optical path ${K_2}$ in Fig. 3 is connected to ${S_2}\textrm{.}$ ${K_1}$ remains disconnected. The broadband spectrum generated by the optical wavelength demodulator enters the compact Tri-FFPI sensor through the optical path ${I_2}.$ Then the reflected light re-enters the optical wavelength demodulator for recording. The spectrum of the Tri-FFPI sensor is shown in Fig. 8. The reflected light of FFPI-1 is so weak that it can be ignored in the spectrum. Each spectrum in Fig. 8 is comprised of two cosine-like waves with different periods. The cosine-like wave with a large period is generated by FFPI-3 interference. Both interference fringes of FFPI-2 and FFPI-3 change during the temperature measurement. By contrast, only the interference fringes of FFPI-3 change during the strain measurement.
Fig. 8. Reflection spectrum of the compact Tri-FFPI sensor during the temperature and strain measurements. (a) Spectra at different temperatures; (b) Spectra at different strains.
The adaptive high-precision demodulation method [17] is used to demodulate ${L_{\textrm{FFPI - 2}}}$ and ${L_{\textrm{FFPI - 3}}}.$ Because of thermal expansion, the cavity length of FFPI-2 and FFPI-3 increases with temperature. The change of ${L_{\textrm{FFPI - 2}}}$ can be expressed by Eq. (10):
FFPI-3 is an air cavity and it is supported by the support sleeve and encapsulation sleeve. The material of the support sleeve and encapsulation sleeve is quartz, which is the same as optical fibers used in this research. Their thermal expansion coefficient is ${\alpha _\textrm{q}}.$ When the temperature rises, the encapsulation sleeve will thermally expand and stretch the FFPIs through the support sleeve. The length change of the entire sensing region (${L_{\textrm{ent}}}$) can be expressed as Eq. (11):
When the temperature changes by $\Delta T,$ $\Delta {L_{\textrm{ent}}}$ can be also expressed as Eq. (12):
As $\Delta {L_{\textrm{FFPI - 1}}}\textrm{ = }{\alpha _\textrm{q}}{L_{\textrm{FFPI - 1}}}\Delta T$ and $\Delta {L_{\textrm{FFPI - 2}}}\textrm{ = }{\alpha _\textrm{q}}{L_{\textrm{FFPI - 2}}}\Delta T,$ the equation of $\Delta {L_{\textrm{FFPI - 3}}}$ is obtained by comparing Eq. (11) and (12):
Because the vibration and strain will not change the length of FFPI-2, the change of ${L_{\textrm{FFPI - 2}}}$ obtained by the adaptive high-precision demodulation method [17] is $\Delta {L_{\textrm{FFPI - 2 - }T}}.$ According to Eq. (10), the temperature can be obtained. The change of ${L_{\textrm{FFPI - 3}}}$ obtained by the demodulation method contains $\Delta {L_{\textrm{FFPI - 3 - }T}},$ $\Delta {L_{\textrm{FFPI - 3 - }S}},$ and $\Delta {L_{\textrm{FFPI - 3 - }V}}.$ As $\Delta {L_{\textrm{FFPI - 3 - }V}}$ caused by vibration acceleration is much faster than $\Delta {L_{\textrm{FFPI - 3 - }T}}$ caused by temperature and $\Delta {L_{\textrm{FFPI - 3 - }S}}$ caused by strain, it can be removed from the signal by low-pass filtering. The obtained signal is recorded as $\Delta {L_{\textrm{FFPI - 3 - low}}}.$ Then the demodulated $\Delta {L_{\textrm{FFPI - 2 - }T}}$ is used to remove $\Delta {L_{\textrm{FFPI - 3 - }T}},$ as shown in Fig. 7 and Eq. (14).
When the strain is applied in the ${D_1}$ direction, as shown in Fig. 1, the encapsulation sleeve pulls the fiber on both sides through the support sleeve to move in the ${D_1}$ direction. Since FFPI-1 and FFPI-2 are free from the applied strain, the strain is focused on FFPI-3. The $\Delta {L_{\textrm{FPI - 3 - }S}}$ can be expressed as Eq. (15). Compared with Eq. (14), the applied strain $\varepsilon$ can be expressed as Eq. (16):
The optical paths ${I_1}$ and ${I_2}$ in Fig. 3 cannot be used for sensing at the same time, because light can pass through the three FFPIs and affect with each other, making measurements inaccurate. A 2×2 optical switch (MOS1: D2×2B) is used to automatically and quickly switch between ${S_1}$ and ${S_2}$ to enable the simultaneous measurement of vibration acceleration, temperature, and strain in time division multiplexing, as show in Fig. 9. The entire sensing system has a sampling frequency of ${f_{\textrm{sam}}}.$ For each sample, the sampling time is $\Delta {t_{\textrm{sam}}} = 1/{f_{\textrm{sam}}}.$ The switch between ${S_1}$ and ${S_2}$ by the optical switch during $\Delta {t_{\textrm{sam}}}$ enables the sequential measurement of vibration, temperature, and strain. $\Delta {t_V}$ represents vibration measurement time and $\Delta {t_{T,S}}$ represents temperature and strain measurement time. The sampling time is set as 1s in this research, so the the interval between each switch needs to be 0.5s. In a sampling time of 1s, the optical path ${S_1}$ is connected to ${K_1}$ during the first 0.5s to measure vibration. Then the optical path ${S_2}$ is connected to ${K_2}$ to measure temperature and strain. Therefore, vibration, temperature, and strain can be measured in one sampling.
2.3 Sensor development
Before the compact Tri-FFPI sensor is developed, its structural parameters need to be determined. The length of the cantilever (${L_{\textrm{FFPI - 1}}}$), the length of the fiber mass (${L_{\textrm{FFPI - 2}}}$), the diameter of the cantilever (${d_\textrm{c}}$), and the distance between the cantilever and fiber mass (${d_{\textrm{axis}}}$) are the key dimensions of the designed Tri-FFPI sensor for vibration acceleration measurements. The vibration measurement sensitivity and resonant frequency of the Tri-FFPI sensor are related to these dimensions. To analyze their relationship, ANSYS Workbench was used to build the finite element model, as shown in Fig. 10. The material is set as quartz. Its density, Young’s modulus, and Poisson’s ratio are set as 2200 kg/m3, 72 GPa, and 0.15, respectively. The encapsulation sleeve was set as “fixed support”. The support sleeve is fixed in the encapsulation sleeve and the optical fiber is fixed in the support sleeve. A coordinate system is established with the left end of the fiber as the origin.
To miniaturize the sensor, both ${L_{\textrm{FFPI - 1}}}$ and ${L_{\textrm{FFPI - 2}}}$ should be as small as possible. During the process of sensor fabrication, a fiber cutter is used to fabricate the fiber mass. When ${L_{\textrm{FFPI - 2}}}$ is approximately 2 mm or longer, flat end faces can be obtained. Otherwise, the flatness of the end face is hard to guarantee. Therefore, ${L_{\textrm{FFPI - 2}}}$ is set as 2000 µm in the FEM simulation. The direction of the applied acceleration is shown in Fig. 10. Different values of ${L_{\textrm{FFPI - 1}}},$ ${d_\textrm{c}},$ and ${d_{\textrm{axis}}}$ have been analyzed, and the simulation results are described in Fig. 11. Figure 11(a) shows that the acceleration measurement sensitivity increases with ${L_{\textrm{FFPI - 1}}}$ and decreases with ${d_\textrm{c}}.$ In contrast, the resonant frequency decreases with ${L_{\textrm{FFPI - 1}}}$ and increases with ${d_\textrm{c}},$ as shown in Fig. 11(b). To optimize the size of the cantilever beam, the comprehensive coefficient Q [18] is used to comprehensively evaluate the sensor resonant frequency and vibration acceleration measurement sensitivity performance. The designed sensor is desired to have a higher resonance frequency and sensitivity, so the sigmoid function is added to the expression of $Q,$ as shown in Eq. (17). A larger Q represents better comprehensive performance.
Fig. 11. Sensor size optimization. (a). The relationship between sensitivity and the sensor size; (b). The relationship between resonant frequency and sensor size; (c). The comprehensive performance.
As shown in Fig. 12, the sensor has good sensitivity linearity in the range of 0–6000 Hz when the resonant frequency is larger than 7400 Hz. Therefore, $R^{\prime}$ is set as 7400 Hz in this study. Normalized Q with different ${L_{\textrm{FFPI - 1}}}$ and ${d_\textrm{c}}$ are shown in Fig. 11(c). The smaller the value of ${d_\textrm{c}}$ is, the more difficult it is to manufacture the sensor. Meanwhile, the cantilever beam should not block the fiber core of the fiber. In this research, ${d_\textrm{c}}$ is set as ${d_\textrm{c}}\textrm{ = }60\mathrm{\mu m}\textrm{.}$ Then, when the ${L_{\textrm{FFPI - 1}}}\textrm{ = }200\mathrm{\mu m,}$ Q takes the optimal value.
The effect of ${d_{\textrm{axis}}}$ on the resonant frequency and sensitivity of the sensor is shown in Fig. 13. The sensitivity increases with ${d_{\textrm{axis}}},$ but the resonant frequency decreases with ${d_{\textrm{axis}}}.$ To ensure that the cantilever beam of FFPI-1 does not block the fiber core, ${d_{\textrm{axis}}}$ should be larger than 35 µm. As the designed sensor is expected to have a good linearity in the measurement frequency range of 0-6000 Hz. According to the analysis in Fig. 12, the resonance frequency needs to be higher than 7400 Hz. The analysis in Fig. 13 shows that the resonant frequency decreases with ${d_{\textrm{axis}}}$ and the sensitivity increase with ${d_{\textrm{axis}}}.$ When ${d_{\textrm{axis}}}$ is larger than 40µm, the resonance frequency will be less than 7400 Hz. Therefore, ${d_{\textrm{axis}}}$ is set as 40 µm to ensure that the sensor has a resonant frequency of not less than 7400 Hz.
Fig. 13. The effect of ${d_{\textrm{axis}}}$ on the resonant frequency and sensitivity of the sensor.
The resonant frequency and sensitivity of the designed sensor with ${d_{\textrm{axis}}} = 40\mathrm{\mu m}$ are verified using Ansys workbench. The modules of “Modal” of Ansys workbench is used and the result shows that the designed sensor has a resonant frequency of 7351.5 Hz. As analyzed in Fig. 5, RS-2 will have displacements in both x-axis and y-axis directions in vibration acceleration measurement. It can be seen from Fig. 14 that the displacement in x-axis is smaller than that in y-axis direction. The displacement of RS-2 in x-axis direction is used to measure vibration acceleration.
Fig. 14. The displacements of RS-2 when measuring vibration acceleration. (a) The displacements of RS-2 in x-direction. (b) The displacements of RS-2 in y-direction.
The development process of the designed sensor is shown in Fig. 15. In this study, 10% HF solutions were used to etch the fiber, as shown in Fig. 15(a). The cantilever beam with a diameter of 60 µm was obtained by etching for 2.5 h, as shown in Fig. 15(b). One end of the cantilever beam was fused to the end-flat fiber, as shown in Fig. 15(c). The fused cantilever beam was cut using a femtosecond laser to obtain the cantilever beam, as shown in Fig. 15(d) and (e). The free end of the cantilever beam was fused to another end-flat fiber to obtain FFPI-1, as shown in Fig. 15(f). The fiber mass was cut out of the fiber using a fiber cutter, and an end-flat fiber was used to form FFPI-3, as shown in Fig. 15(g) and (h). The sensor was protected and encapsulated using a support sleeve and encapsulation sleeve, as shown in Fig. 15(i).
Fig. 15. The fabrication process of the designed sensor. (a) Optical fiber etching; (b) Etched optical fiber with a diameter of 60 µm; (c) Fine optical fiber fused to the end-flat fiber; (d) Cutting fine optical fiber using a femtosecond laser; (e) The obtained cantilever beam; (f) FFPI-1 containing cantilever beam; (g) Obtained fiber mass cutting by the fiber cutter; (h) Three FFPIs in series; (i) Sensor packaging.
3. Experiments and performance analysis
3.1 Temperature measurement
To test the high-temperature performance of the designed sensor, a high-temperature furnace and a thermostat were used, as shown in Fig. 16. The high-temperature furnace is used to test the thermal characterization of the designed sensor in the range of 400–1000°C. The thermostat is used to test the thermal characterization of the designed sensor in the range of 30–300°C. As mentioned in Section 2.1, the FFPI-2 is used to measure temperature. The optical path ${K_2}$ in Fig. 3 is connected to ${S_2}.$ ${K_1}$ remains disconnected. The reflected spectrum is recorded by an FBG demodulator (MOI si155). The adaptive high-precision method based on wavelength demodulation [17] is used to demodulate the cavity length of FFPI-2. The demodulation results are shown in Fig. 17. The temperature measurement sensitivity, linearity, and error are 1.55 nm/°C, 99.99%, and 0.59% F.S., respectively.
Fig. 16. The setup of the thermal characterization experiment. (a) Thermal characterization experiment in the range of 400–1000°C. (b) Thermal characterization experiment in the range of 30–300°C.
3.2 Vibration acceleration measurement
The vibration acceleration test was set up as shown in Fig. 18. The optical path ${K_1}$ in Fig. 3 is connected to ${S_1},$ and ${K_2}$ remains disconnected. The power of the laser (KG-DFB-15-M-10-S-FA) used in this research was up to 10 dBm. The sampling frequency of the used photodetector (KG-PR-200M-FC) is up to 200 MHz, so that the high-frequency vibration can be measured. The power of the optical fiber power amplifier (KG-EDFA-HP-33-D-FA) used was up to 33 dBm. When the designed sensor is used to sense vibration acceleration, the fiber mass generates displacement in the direction of the fiber axis, as shown in Fig. 5. The intensity of the reflected light changes accordingly. These changes are recorded by the photodetector and data acquisition card. The measurement results show that the designed sensor can perform effective measurements at frequencies up to 6 kHz, as shown in Fig. 19. The performances of the sensor at 2 kHz, 4 kHz, and 6 kHz with a range of 0–100 g are shown in Fig. 19(a). The measurement sensitivity of the sensor increases with vibration frequency, which is consistent with the trend in Fig. 12. Different sensitivities result in different voltages output by the light intensity demodulation system when measuring the same acceleration at different frequencies. This makes it inconvenient to read the measured acceleration from the demodulation system. Therefore, to output the same results when measuring the same vibration acceleration, the measurement results at different frequencies need to be calibrated. The calibration is to convert the voltage output of the light intensity demodulation system into acceleration output.
Fig. 19. The tested vibration acceleration performance. (a). Vibration acceleration measurement performance at different frequencies; (b). Calibrated sensor performance.
The least square method is used to fit the voltage output. As the amplitude of the output voltage is zero when no vibration is applied, the fitted lines should pass through the origin, as shown in Fig. 19(a). Their equations can be expressed as Eq. (18), (19), and (20), respectively.
where $\overline {A_{2\textrm{kHz}}^U} ,$ $\overline {A_{\textrm{4kHz}}^U} ,$ and $\overline {A_{\textrm{6kHz}}^U}$ represent the voltage amplitude on the fitted lines at 2 kHz, 4 kHz, and 6 kHz, respectively; ${a_{\textrm{real}}}$ represents the applied vibration acceleration; ${k_{\textrm{2kHz}}},$ ${k_{\textrm{4kHz}}},$ and ${k_{\textrm{6kHz}}}$ represents the slopes of fitted lines, which are also the measurement sensitivity at different frequencies. ${k_{\textrm{2kHz}}},$ ${k_{\textrm{4kHz}}},$ and ${k_{\textrm{6kHz}}}$ are calculated to be 0.77 mV/g, 0.99 mV/g, and 1.87 mV/g, respectively. Then, the voltage outputs in Fig. 19(a) at different frequencies are divided by the corresponding sensitivities accordingly to obtain the calibrated acceleration outputs, as shown in Fig. 19(b). When the vibration frequency is 6 kHz, the designed sensor has the highest the measurement sensitivity of 1.87 mV/g. Its linearity and measurement errors are 99.98% and 1.44% F.S., respectively.3.3 Strain measurement
As shown in Fig. 20, a tensile machine was used to calibrate the strain measurement performance of the developed compact Tri-FFPI sensor. The sensor was clamped by the tensile machine. The strain applied to the sensor was adjusted by linearly adjusting the stretch of the tensile machine. As mentioned in Section 2.1, the applied strain was focused on FFPI-3. The cavity length of FFPI-1 was not affected by the applied strain. The adaptive high-precision method was used to demodulate the cavity length of FFPI-2. The demodulation results are shown in Fig. 21. A strain measurement range of 0–2500 µɛ was tested. The strain measurement sensitivity, linearity, and error of the developed sensor are 9.52 nm/µɛ, 99.99%, and 1.03% F.S., respectively.
3.4 Analysis of the cross interference
In the acceleration measurement, the vibration will cause changes of ${L_{\textrm{FFPI - 1}}}$ and ${L_{\textrm{FFPI - 3}}}.$ However, the change of ${L_{\textrm{FFPI - 3}}}$ can be filtered out by low-pass filtering, as shown in Fig. 7. ${L_{\textrm{FFPI - 2}}}$ will not change in response to vibration. Therefore, the measurement of acceleration will not interfere with the temperature and strain measurements.
In the strain measurement, the designed structure of the compact Tri-FFPI sensor makes the applied strain focused at FFPI-3. The cavity lengths of FFPI-1 and FFPI-2 will not be affected. Therefore, the measurement of the strain will not interfere with the temperature and acceleration measurements.
In the temperature measurements, a change of temperature will also cause changes of ${L_{\textrm{FFPI - 1}}}$ and ${L_{\textrm{FFPI - 3}}}.$ The change of ${L_{\textrm{FFPI - 1}}}$ caused by temperature varies much slower than that caused by vibration. In this research, FFT is used to eliminate the temperature interference from the acceleration measurements. Therefore, the measurement of temperature will not interfere with the acceleration measurement. As mentioned in Section 2.1, the temperature interfering with ${L_{\textrm{FFPI - 3}}}$ can be compensated by FFPI-2, as shown in Figs. 7 and 16.
However, to a certain extent, the error of strain measurement will be influenced by the error of temperature measurement. These influences can be expressed by measurement linearity and error, as shown by Eq. (21) and (22). By substituting the measured data into Eq. (21) and (22), the measurement linearity and error of the designed sensor in a temperature-changing environment are calculated to be 99.98% and 1.40% F.S., respectively.
where ${\delta _{syn}}$ and ${\sigma _{sym}}$ represent the synthetic linearity and error of strain measurement in the environment with temperature changing; ${\delta _\varepsilon }$ and ${\sigma _\varepsilon }$ represent the strain measurement linearity and error when the temperature changes are ignored; and ${\delta _T}$ and ${\sigma _T}$ represent the temperature measurement linearity and error of the Tri-FFPI sensor.To verify the quasi-simultaneous measurement of vibration, temperature, and strain experimentally, experimental devices were set up as shown in Fig. 22. According to the signal demodulation process in the section 2.2, the verification experiment was divided into two steps. Firstly, an experimental device which can apply temperature and vibration was set up to verify the quasi-simultaneous measurement of temperature and vibration, as shown in Fig. 22(a). The experimental device included a vibrator and a high temperature furnace. A rod connected with the vibrator was used to transmit vibration to the designed sensor in the furnace. The connecting rod is extended in the furnace through a vent hole on the top of the furnace. Secondly, an experimental device which can apply temperature and strain was set up to verify the quasi-simultaneous measurement of temperature and strain, as shown in Fig. 22(b). The experimental device included a tensile machine and a high temperature furnace. A rod connected with the tensile machine was used to transmit tension to the designed sensor in the furnace. The connecting rod is extended in the furnace through a vent hole on the top of the furnace.
Fig. 22. Analysis of the cross interference. (a). Temperature and vibration measurement test. (b). Temperature and strain measurement test.
Due to the limitation of our experimental equipment, the applied temperature range, vibration range, and strain range were 30–300°C, 0–10 g, and 0–1000 µɛ, respectively. In the first measurement step shown in Fig. 22(a), the temperature was set to 30°C, 100°C, 200°C, and 300°C successively. At each temperature, the vibration acceleration was set to 2 g, 4 g, 6 g, 8 g, and 10 g successively at 500 Hz. The measurement time of each experiment was longer than 1s to ensure that at least one sampling time was included. The output of the designed sensor was measured by the photodetector and the optical wavelength demodulator in Fig. 3. According to the demodulation method mentioned in the section 2.2, the demodulation results were obtained and shown in Fig. 23. Figure 23(a) shows the measured temperature at different vibration accelerations and the maximum measurement error is 1.62%F.S.. Figure 23(b) shows the measured vibration at different temperatures and the maximum measurement error is 2.7%F.S.. In the second measurement step shown in Fig. 22(b), the temperature was set to 30°C, 100°C, 200°C, and 300°C successively. At each temperature, the strain was set to 200 µɛ, 400 µɛ, 600 µɛ, 800 µɛ, and 1000 µɛ, successively. The output of the designed sensor was measured using the optical wavelength demodulator in Fig. 3. According to the demodulation method mentioned in the section 2.2, the demodulation results were obtained and shown in Fig. 24. Figure 24(a) shows the measured temperature at different strain and the maximum measurement error is 1.45%F.S. Figure 24(b) shows the measured strain at different temperatures and the maximum measurement error is 1.84%F.S.
Fig. 23. Quasi-simultaneous measurement of temperature and vibration acceleration. (a). Temperature measured by FFPI-2. (b). Vibration acceleration measured by FFPI-1.
Fig. 24. Quasi-simultaneous measurement of temperature and strain. (a). Temperature measured by FFPI-2. (b). Strain measured by FFPI-3.
In the experiment of quasi-simultaneous measurement, the measurement errors of vibration acceleration, temperature, and strain are slightly larger than that of individual measurement experiments. This is because the measurement ranges were narrowed. The calculation of the full-scale measurement error is shown as Eq. (23).
where ${\delta _{\textrm{FS}}}$ represents the full-scale measurement error; x and $\bar{x}$ represent the measured value and true value of the measured parameter; M represents the measurement range. It can be seen from Eq. (23) that ${\delta _{\textrm{FS}}}$ will increase when the measurement range M is narrowed.4. Discussion
In this paper, a compact Tri-FFPI sensor consisting of three FFPIs in series is designed for the sensing of high temperature, acceleration, and strain. The total length and diameter of the sensing part are only 2558.9 µm and 250 µm, respectively. Compared with the recent FBG-based multi-parameter measurement sensor [18], the designed sensor in this research has a smaller size and wider measurement ranges. The FFPI-1 of the designed sensor contains a cantilever and is used to measure vibration acceleration. The light intensity demodulation method is used in the demodulation of vibration. The maximum vibration acceleration measurement sensitivity of the designed sensor is 1.87 mV/g, which is lower than that of the recent FFPI-based vibration sensors (17 mV/g and 11.1 mV/g) [19,20]. However, the designed sensor has a much wider measurement range of 0–100 g than the ranges of the sensors in Ref. [19] (0.02–0.5 g) and [20] (0.5–5 g). The vibration measurement linearity and error of the designed sensor were tested to be 99.98% and 1.44% F.S., respectively. The FFPI-2 of the designed sensor is used to measure temperature and its measurement range is 0–1000°C, which is the same as the recent FFPI-based temperature sensor [21]. By contrast, the measurement sensitivity of the designed sensor (1.55 nm/°C) is higher than that in Ref. [21] (0.01226 nm/°C). The temperature measurement linearity and error were tested to be 99.99% and 0.59% F.S., respectively. FFPI-3 is used to measure strain. Its measurement sensitivity is 9.52 nm/µɛ in the measurement range of 0-2500 µɛ, which is much wider than the ranges of recent FFPI-based strain sensors [22,23]. When the temperature changes were ignored, the measurement sensitivity, linearity, and error of the designed sensor are tested to be 9.52 nm/µɛ, 99.99%, and 1.03% F.S., respectively. FFT method and different FFPIs are used to eliminate interference between temperature and vibration acceleration measurement. The effect of vibration on the strain measurements can be eliminated by low-pass filtering. The effect of temperature on the strain measurements can be compensated by the FFPI-2 signal. The strain applied on the designed sensor focuses on FFPI-3, and the cavity length of FFPI-1 and FFPI-2 will not be affected. Therefore, the applied strain does not affect the measurement of temperature and vibration. The equation for error transmission in the temperature compensation of the strain measurement is given in this article. In a temperature-changing environment, the linearity and error of the strain measurement were calculated to be 99.98% and 1.40% F.S., respectively. The signal demodulation method has been verified by quasi-simultaneous measurement experiments in this research.
Funding
National Natural Science Foundation of China (51720105016, 51890884, 51805421, 52105560).
Acknowledgments
We thank the funding from National Natural Science Foundation of China (Nos. 51720105016, 51890884, 51805421) and National Natural Science Foundation of China Youth Science Fund Project (No. 52105560). We also thank the support from the International Joint Laboratory for Micro/Nano Manufacturing and Measurement Technologies.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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