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Abstract
An all-silica Fabry-Perot interferometer (FPI) based on a microbubble for high-pressure and high-temperature measurements is proposed and demonstrated. The microbubble-based air cavity is fabricated using a hollow silica tube and a single-mode optical fiber for pressure sensing. The suitable thickness between the two end faces of the microbubble enables the silica cavity to be used for temperature sensing. The wavelength shift of the reflection spectrum versus pressure is linear, and the sensitivity reaches −5.083 nm/MPa at room temperature (20 °C) within the range of 0 − 4 MPa. The temperature sensitivity reaches 12.715 pm/°C within the range of 20 − 700 °C. The very low temperature-pressure cross-sensitivity of the two cavities indicates that the proposed FPI sensor offers great potential for simultaneous high-pressure and high-temperature measurements in harsh environments.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber optic Fabry-Perot interferometers (FPIs) have many advantages, such as immunity to electromagnetic interference, corrosion resistance, and electrical insulation. Many methods have been proposed for fabricating FPIs, including arc discharge, film bonding, chemical and laser corrosion, and 3D printing [1–6]. These sensors have been widely used for strain, humidity, temperature, and pressure sensing [7–11]. In particular, FPI sensors deliver stable performance in harsh environments and are therefore suitable for application in the oil, aerospace, and steel industries [12–14]. FPI pressure sensors are mainly divided into two types based on the deformation of both the end face and sidewall of the F-P cavity [12,15–25]. Regardless of the type, narrowing the thickness is an effective way to improve the pressure sensitivity. The traditional fabrication methods, film bonding or welding is disadvantageous because of the manufacturing and technical complexities associated with these methods [2][6]. In recent years, microbubble-based devices have been widely studied because they obviate the need for bonding or welding processes and a very thin sensing area can be used, which can improve the pressure sensitivity and simplify the manufacturing process [26–29].
Ma et al. [26] used a fusion splicer to weld at the single-mode optical fiber (SMF) with a well-cut hollow silica tube (HST) at its end face, and then formed a microbubble with a thick wall by arc discharging at a specific position in the HST. However, the sensor has difficulties realizing high-sensitivity pressure sensing because of the thick wall of the microbubble. In a subsequent study [27], they produced a microbubble structure with a thickness of 4.3 µm by tapering the gas-pressured HST while arc discharging using the fusion splicer based on the steps in the previous study. Owing to the small size of the microbubble, the pressure sensitivity of the sensor was only 315 pm/MPa, and the low temperature sensitivity was approximately 1.55 pm/°C. Liao et al. [28] proposed a microbubble sensor by fusing two SMFs together by coating their end faces with oil with a similar refractive index. As the oil was vaporized and expanded to a microbubble owing to the high temperature, a thin-end microbubble could be formed at the end face of the fiber. Although the thickness of the end face of the microbubbles further decreased in Liao’s study, the thickness of the microbubble was uneven, and the thinnest area was limited to the top part of the microbubble. This resulted in a low-pressure sensitivity of 1.036 nm/MPa and a low-temperature sensitivity of 1 pm/°C. Li et al. [29] formed a microbubble structure by arc discharging on the end face of a pressurized HST, then inserted the SMF into the microbubble, and finally welded them together. The pressure sensitivity is approximately −6.382 nm/MPa whereas the temperature coefficient is lower at approximately 0.17 pm/°C. Li improved the uniformity of the microbubble thickness, but the mechanical strength of the sensor decreased as the sidewall of the microbubble was very thin (∼0.5 µm), which limited the measurement range. It should be noted that the temperature response of the FPI results from the thermal expansion and thermo-optic effect of the F-P cavity, and most of these sensors are based on a single air cavity; thus, the changes in the cavity length are mainly caused by the thermal expansion of the microbubbles. Therefore, the temperature response of an FPI based on a single air cavity is negligible [26].
In all of the above microbubble manufacturing processes, the F-P cavity was fabricated to have a thinner end face. Few studies have attempted to improve the pressure sensitivity of sensors by thinning the side of the F-P cavity when fabricating the microbubble. In this paper, a novel microbubble-based FPI sensor is proposed and demonstrated. In contrast to the above reports, the sensor mainly realizes pressure sensing by deformation of the thin sidewall of the microbubble (air cavity). Despite the thin sidewall, the cross-sensitivity of the air cavity is very low. Moreover, the sensor realizes a compound cavity with the function of temperature sensing by exploiting the thermal expansion and thermo-optic effects of the thick part at the end of the microbubble (silica cavity). Compared to traditional sensors based on sidewall deformation [14][25], the proposed sensor has a compact structure and offers improved pressure sensitivity owing the significantly reduced thickness of the sidewall. Apart from this, no additional structures and processes are required for temperature sensing [30], which greatly improves the manufacturing efficiency. In addition, the sensor can operate stably in high-temperature environments owing to its all-silica structure. The results show that the pressure sensitivity of the sensor reaches −5.083 nm/MPa and the temperature sensitivity reaches 12.715 pm/°C. This means that the proposed sensor has great application prospects in harsh environments for high-temperature and high-pressure sensing.
2. Operating principle and fabrication
Figure 1(a) shows a structural diagram of the microbubble-based FPI sensor with an ellipsoidal shape, where d and L3 are the diameters of the short and long axes, respectively. L1 and L2 are the lengths of the air and the silica cavities, respectively. t represents the thickness of the sidewall of the microbubble. L is the distance between the fusion point and outer end face (r3) of the sensor. The air cavity is formed by the end face of the SMF (r1) and the inner end face of the microbubble (r2), whereas the silica cavity is formed by the inner (r2) and outer (r3) end faces of the microbubble. The fusion point between the SMF and HST creates space in the microbubble hermetic. Therefore, when the surrounding gas pressure changes, the sidewall of the microbubble is deformed owing to the difference between the internal and external pressure of the sensor, resulting in a change of the air cavity length of the sensor. The finite element analysis (COMSOL multiphysics) was used to qualitatively simulate the deformation of the microbubble structure (d = 470 µm, L3 = 550 µm, t = 10 µm, L2 = 180 µm, and L = 1 cm) under a pressure of 4 MPa. The deformation scale factor of the sensor is set as 500 in COMSOL software to show the deformation clear. As expected, the deformation of the sensor is mainly concentrated in the microbubble of the head of the sensor, and it’s mainly caused by the deformation of the sidewall of the microbubble, as shown in Fig. 1(b).
Fig. 1. Diagram of the (a) structure of the sensor and (b) deformation of the microbubble at 4 MPa simulated by COMSOL software.
Figure 2 shows the reflected electric fields of the three reflective interfaces of the sensor (r1, r2, and r3). Only the first-order reflected fields of the three interfaces were considered because of the low reflectivity of the silica/air surface. The total reflected electric field (Er) can be regarded as the sum of the three reflected electric fields and can be expressed as
The relationship between the wavelength shift $(\Delta {\lambda _P})$ of the air cavity of the FPI sensor and the variation in $\Delta OP{D_P}$ is written as
According to Eq. (5), the wavelength shift $(\Delta {\lambda _P})$ of the FPI sensor is directly proportional to the change in $\Delta OP{D_P}$. The $\Delta \lambda _P$ is linearly related to the variation in air cavity length $(\Delta L)$, as the change in the air refractive index $({n_a})$ can be ignored owning to the weak deformation of the air cavity. Similarly, the relationship between the temperature and wavelength shift of the silica cavity is given by:
The wavelength shift $(\Delta {\lambda _T})$ at high-temperature is mainly affected by the thermal expansion $(\beta )$ and thermo-optic $(\partial )$ coefficients.
In contrast to the heating mode of the traditional arc discharge fusion splicer, laser welding has the advantages of accurate power input with a high energy density, deep penetration, good directivity, and an accurate heating position [31–33]. Therefore, a CO2 laser processing system (LZM-100, Fujikura, Tokyo, Japan) was used to prepare the sensor. This laser enables different positions of the microbubble to be accurately heated, and the fiber to be rotated during welding, which makes it possible to obtain a symmetric microbubble with a unique structure. Figure 3 illustrates the fabrication process of the sensor. First, an end-cut HST with outer and inner diameters of 320 µm and 130 µm, respectively, was affixed to the one side of the fiber clamp (EV 400, Fujikura, Tokyo, Japan) of the CO2 laser processing system. Then, its position was adjusted to ensure that the end of the HST was located in the laser heating zone, as shown in Fig. 3(a). Second, the end of the HST was manually welded to form a hermetic structure. Because the fiber could be rotated at a uniform speed during the welding process, a symmetrical sealed structure was formed when the laser power was 400 bit, the welding time was 30 s, and the rotating speed was 0.075 °/ms, as shown in Fig. 3(b). Third, a syringe was used to pump air into the HST to form and expand the microbubble while it was being continuously heated under the same laser power and rotating speed with the welding time of 20 s, as shown in Fig. 3(c). Fourth, the entire structure was moved such that the sidewall of the microbubble was positioned in the center of the heating zone. Thus, the microbubble was not uniformly heated when the laser power was 320 bit, the welding time was 20 s, and the rotating speed was 0.075 °/ms. The temperature of the action area of the CO2 laser decreased gradually from the center to the outside of the bubble. At the point at which the energy absorbed by the end face of the microbubble is equal to the energy emitted, the temperature in this area ceases to rise. This prevents the end face of the microbubble from transforming into a molten state to become thinner. As a result, the sidewall closer to the area being heated expands faster than the end of the microbubble. Consequently, a microbubble structure with a thin sidewall and thick end face is obtained, as shown in Fig. 3(d). The microbubbles with different sizes and sidewall thicknesses can be obtained by adjusting the welding time and laser power. Finally, the cleaved SMF was manually controlled for insertion into the HST at a specific location, whereupon the HST and fiber were welded together at a fixed position away from the fiber tip with the laser power of 305 bit, and the welding time of 35 s, as shown in Fig. 3(e) and 3(f). This procedure enabled an FPI sensor with a specified air cavity length to be obtained.
Fig. 3. Fabrication procedure of the sensor: (a) end-cut HST in the CO2 laser; (b) fusing one end of the HST; (c) attaching the gas-filled capillary; (d) adjusting the position to fuse the sidewall of microbubble; (e) fusing the SMF with the HST; (f) complete structure of the sensor.
Microscope (BX53M Olympus, Tokyo, Japan) images of the three fabricated devices with the sidewall thicknesses (t) of 9.8, 12.6, and 35.9 µm, respectively, are shown in Fig. 4(a). The diameter of the short axis (d) was 528.4, 546.3, and 642.6 µm, respectively. The diameter of the long axis (L3) was 604.1, 632.3, and 726.6 µm, respectively. Because the length of the sensor (L) is 2.0 cm, the microbubbles and fusion points cannot be observed at the same time in the field of view of the microscope as the maximum field of view is 0.26 cm×0.33 cm. Therefore, we observed the state of the microbubbles and fusion points under the same magnification, respectively, and then stitched them together. Figure. 4(b) shows the corresponding FPI reflection spectra. Because of the compound cavity structure, a large envelope exists in the interference spectrum. Fast Fourier transform (FFT) was used to obtain the corresponding frequency components of the two cavities.
Fig. 4. (a) Microscope images of the three fabricated devices and (b) corresponding reflection spectra of the three fabricated samples, respectively.
Sample 2 was used as an example. First, the power unit of the interference spectra was converted to “mW,” as shown in Fig. 5(a). This spectrum was then converted to the spatial frequency spectrum by FFT. The latter spectrum contains three distinct peaks, which represent the air, silica, and the air-silica cavities, respectively, as shown in Fig. 5(b). The interference spectrum of the air and silica cavities can be derived using the narrow-band filtering method. Because the two reflecting interfaces of the silica cavity (r2 and r3) are curved, it is difficult to keep the two interfaces strictly parallel; hence, the interference spectrum of the silica cavity is relatively weak, as shown in Fig. 5(c) and (d). Based on the results in Fig. 5, and using Eq. (3), we can calculate the length of the two cavities of these sensors. The calculated air cavity lengths (L1) of samples 1, 2, and 3 are 60.1, 71.3, and 75.1 µm, respectively, with the corresponding silica cavity lengths (L2) demodulated as 227.8, 196.8, and 196.7 µm respectively.
Fig. 5. (a) Reflection spectrum of sample 2; (b) FFT of reflection spectrum of sample 2; frequency component of the (c) air cavity and (d) silica cavity.
3. Experiments and results
The setup for the high-temperature pressure measurements is shown in Fig. 6. A nitrogen gas cylinder with a pressure regulator (QY-C1-10-Y, resolution ±0.02 MPa, Festo (China), Shanghai, China) and a digital pressure meter (700G08, Fluke, WA, USA) were used for pressure measurement. A tube furnace was used for temperature measurements, and an optical fiber sensing interrogator (SM125, Micron Optics Inc., Atlanta, GA, USA) with a wavelength range of 1510–1590 nm and a resolution of 5 pm was used for signal demodulation. The sensor head was placed in a sealed alumina ceramic tube located in the central area of the heating zone of the tube furnace heating, and the reflection of the sensor was monitored in real time.
Fig. 6. Schematic diagram of the system to measure the high-temperature-pressure performance of the FPI sensor.
The results of the pressure test of the air cavity of the three samples, measured in the range from 0 − 4 MPa in increments of 0.5 MPa at 20 °C, are shown in Fig. 7. The maximum pressure sensitivity reaches −5.083 nm/MPa of the three samples. As the length of the air cavity decreases with an increase in the gas pressure, the wavelength becomes shorter. According to a previous report [29], the pressure sensitivity of a sensor is related to the diameter and thickness of the microbubble in that the pressure sensitivity of the sensor increases as the diameter of the microbubble increases. Compared with their study, in our study the pressure sensitivity of the sensor with the thinnest sidewall thickness and the shortest microbubble axis was the highest. Therefore, the pressure sensitivity of the sensor can be inferred to increase as the thickness of the sidewall of the microbubble decreases.
A detailed analysis of the performance of Sample 2 was warranted. The test results of a one-round pressure rise and fall experiment of the two cavities of the sensor for the pressure range 0 − 4 MPa are shown in Fig. 8(a). The pressure sensitivity of the air cavity was −4.776 nm/MPa and shows a good linear relationship. As expected, the relative shift of wavelength for the silica cavity was hardly dependent on the pressure change, and the maximum wavelength shift was less than −0.615 nm, as shown in Fig. 8(b).
Fig. 8. Wavelength shifts for the (a) air cavity and (b) silica cavity of sample 2 in the range 0 − 4 MPa at 20 °C, respectively; wavelength shifts for the (c) air cavity and (d) silica cavity of sample 2 from 20 − 700 °C in atmospheric pressure, respectively.
The high-temperature performance of the sensor is shown in Fig. 8(c) and 8(d). The sensor was tested in the temperature range of 20 − 700 °C in steps of 50 °C, and the temperature at each measurement point was maintained for 10 min to allow the temperature in the ceramic tube to stabilize. In terms of the air cavity, the change in the refractive index at high temperatures can be ignored, and thus thermal expansion plays a major role in the temperature sensitivity. For the silica cavity, the temperature sensitivity is mainly attributable to the change in the thermally induced refractive index at the thick silica end [34]. Because the thermal expansion coefficient of the SMF is slightly larger than that of the HST, the fiber extends beyond the HST when the temperature increases, resulting in a shorter air cavity length [29]. This explains the wavelength shift to shorter wavelengths. For the air cavity, the linearity of the wavelength shift of the reflection spectrum versus temperature is poor, and the process of increasing and decreasing the temperature is characterized by obvious hysteresis, as shown in Fig. 8(c). Considering the small difference in the thermal expansion coefficient between the SMF and HST, the wavelength shift corresponding to the air cavity should not be greater than 6 nm. Moreover, the temperature response of the air cavity in the range from 20 − 700 °C has poor linearity and obvious hysteresis. This phenomenon is similar to the high-temperature annealing behavior of long-period gratings in pure silica microstructure fibers which was previously reported [35]. We consider this to have been caused by the residual stress in the welding of the SMF and HST during the fast heating and cooling steps of the laser fusion process [36]. Figure 8(d) shows that the reflection spectrum of the silica cavity shifted to longer wavelengths owing to the thermo-optic effect of silica at high temperatures. The temperature sensitivity of the silica cavity was 12.715 pm/°C, and the wavelength shift had a good linear relationship with the temperature.
Figure 9 shows the temperature response of the air cavity when the sensor was heated to 900 °C and maintained at this temperature for 3 hours, after which the temperature was gradually returned to room temperature. The temperature response of the air cavity of the sensor was significantly improved. The wavelength exhibits a very slight shift of less than −0.550 nm, as shown in Fig. 9. Therefore, the annealing experiment at 900 °C is considered to eliminate the residual stress at the fusion point, which largely cancels the hysteresis and the excessive wavelength shift of the air cavity.
The stability of the sensor was assessed by carrying out three rounds of pressure tests by increasing the temperature from 20 − 700 °C in the steps of 100 °C. As shown in Fig. 10, three indicators were used to measure the working stability of the sensor: the repeatability error, hysteresis, and linear error [37]. The sensor operates stably in the range 20 − 600 °C with small repeatability and linear errors, and minimal hysteresis (≤ 4%). The sensor maintains good linearity at 700 °C, but the hysteresis and repeatability worsen (> 4%), as shown in Fig. 10(h). Moreover, the pressure sensitivity of the sensor decreases with increasing temperature, as shown in Fig. 10(i). This is due to the temperature dependence of the Young's modulus of the HST. The Young's modulus of silica increases as the temperature increases, such that the microbubble is difficult to deform at high temperatures, resulting in a decrease in pressure sensitivity [38][39]. The decrease in the pressure sensitivity caused by the increased temperature would lead to an increase in the testing error, which would limit the measurement range [25].
Fig. 10. Results of three rounds of pressure tests of sample 2 in the range (a)−(h) 20 − 700 °C in increments of 100 °C; (i) pressure sensitivities of sample 2 in the range 20 − 700 °C.
The working performance of the sensor after exposure to high temperatures was verified by conducting three rounds of pressure tests on the three sensors at 20 °C. As shown in Fig. 11, the sensors operate stably and normally, and the pressure sensitivities of samples 1 and 2 are almost equal to those before high-temperature treatment. Therefore, the sensors can be inferred to continue to exhibit good working performance at high temperatures.
Fig. 11. Results of three rounds of pressure tests of the three samples in the range 0 − 4 MPa at room temperature after high-temperature treatment at 700 °C.
The experimental results presented above indicate that the sensor developed in this study can be used for simultaneous pressure and temperature measurements. The temperature-pressure cross-sensitivity is an important indicator of the pressure characteristics of the sensor at high temperatures, and the cross-sensitivity of the two cavities of the sensor can be inferred from the following matrix [40]:
Because the air and silica cavities are insensitive to changes in the temperature and pressure, the temperature sensitivity of the air cavity and the pressure sensitivity of the silica cavity, K1T and K2P, respectively, both approximated 0. Taking the experimental results of the sensor at 600 °C as an example, the cross-sensitivity matrix of the sensor can be expressed as:
According to Eq. (8), the temperature-pressure cross-sensitivities of the air and silica cavities are almost 0, which ensures the accuracy of the pressure and temperature measurements of the sensor at high temperatures and pressures. The accuracy of the sensor could be further improved by increasing the pressure sensitivity of the sensor by further thinning the sidewall of the microbubble or by increasing the distance between the fusion point and the microbubble to reduce the cross-influence of the temperature and pressure of the sensor.
4. Conclusion
We proposed and experimentally demonstrated a novel FPI sensor. The sensor has a microbubble structure with a thin sidewall and thick end face for high-pressure and high-temperature monitoring. The experimental results showed that the pressure sensitivity of the sensor can reach −5.083 nm/MPa, and the temperature sensitivity can attain 12.715 pm/°C with a very low temperature-pressure cross-sensitivity. Compared with previous microbubble-based FPIs, the temperature sensitivity of the proposed device was greatly improved, and the pressure sensitivity was relatively high. Additionally, the mechanical strength of the proposed FPI sensor is enhanced owing to its compact size and the relatively thick sidewall of the microbubble, which makes subsequent packaging convenient and suitable for higher-pressure environments.
Funding
National Natural Science Foundation of China (61735009, 61975108, 62005153).
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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