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Abstract
The applications of fiber-optic acoustic sensors are expanded to the high-temperature field, but it still faces challenges to realize the wide-band and high-sensitivity acoustic signal detection in high-temperature environments. Here, we propose a miniature membrane-free fiber-optic acoustic sensor based on a rigid Fabry–Pérot (F-P) cavity and construct an acoustic signal detection system. The system can achieve high-sensitivity acoustic detection while maintaining a wide frequency band in temperatures ranging from 20 °C to 200 °C. The prepared F-P cavity based on optical contact technology is the sensitive unit of the sensor, and has a high-quality factor of 8.8×105. Specifically, with the increasing of temperature, the sensitivity gradually increases, and the frequency response range does not change. A maximum sensitivity of 491.2 mV/Pa and a high signal-to-noise ratio of 60.9 dB are achieved at 200 °C. The sensor has an excellent acoustic signal response in the frequency range of 10 Hz-50 kHz with a flatness of ±2 dB. This study is important for the application of the fiber-optic acoustic sensor in high-temperature environments.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As the carrier of information and energy, acoustic signal detection has extensive applications in aerospace [1,2], energy industry [3,4] and environmental monitoring [5,6]. For instance, the working state of the zero-engine can be monitored through real-time acoustic signal detection to improve its performance and work efficiency. At first, acoustic signal detection is mainly based on electro-acoustic sensors. With the rapid development of optical fiber sensing technology, the research focus of acoustic signal detection has changed from electro-acoustic sensing technology to fiber-optic acoustic sensing technology.
In recent years, fiber-optic acoustic sensors based on Fabry-Pérot (F-P) interferometer have become a research hotspot due to their advantages of good stability, high sensitivity, and anti-electromagnetic interference [7–10]. Among them, the membrane-free F-P cavity acoustic sensor and the film fiber-optic Fabry-Pérot interferometric acoustic sensor are two important directions [11–13]. The former has a wider frequency response range and better environmental adaptability, and can also be used to detect a larger sound pressure [14]. The latter has higher sensitivity but it is easily affected by vibration, temperature and other factors [15,16]. The XARION Laser Acoustics Company proposed an optical microphone based on a F-P cavity structure, the maximum detectable sound pressure was 146 dB, but the sensitivity was only 10 mV/Pa [17]. In order to achieve higher sensitivity, Wu et al. proposed a fiber-optic acoustic sensor with a film as a sensitive unit [18], which had a high sensitivity of 690.1 mV/Pa and a flat frequency response from 100 Hz to 20 kHz, but its maximum detectable sound pressure was only 158.9 mPa. Unfortunately, the high-temperature characteristics of the sensors were not studied in the above reports.
With the continuous expansion of acoustic sensors’ applications [19,20], researchers have also carried out some researches on the performance of acoustic sensors in high-temperature environments. Hu et al. proposed a temperature self-compensated high-temperature fiber-optic acoustic sensor and tested its stability from −10 °C to 500 °C [21], which was able to operate briefly at high temperatures, but its frequency response range was only 1 kHz-5 kHz. Afterwards, Liu et al. proposed a membrane-free fiber-optic F-P sensor that can simultaneously measure sound and temperature, and studied its characteristics at 20 °C-120 °C [22]. Its signal-to-noise ratio was up to 53 dB, and the sensitivity of acoustic detection was only 4.65 mV/Pa. In short, there is currently a lack of fiber-optic acoustic sensors that can achieve high-sensitivity acoustic detection while maintaining a wide frequency band in high-temperature environments.
In the paper, we propose a fiber-optic acoustic sensor (FOAS) based on a rigid F-P cavity, which has the advantages of high sensitivity and wide frequency response range at high temperature. It is sensitive to acoustic signal through direct coupling of light and acoustic field. The F-P cavity is fabricated by the optical contact technology and has a high-quality (high-Q) factor of 8.8×105. In order to better explore the high-temperature characteristics of the sensor, we build an experimental system to test the acoustic performance of the sensor in high-temperature environments. The experimental results show that the sensor has a high sensitivity of 491.2 mV/Pa at 200 °C and a wide-band response of 10 Hz-50 kHz with a flatness of ±2 dB over the temperature range. Hence, the proposed sensor in the present study exhibits a significant meaning for applying in harsh environments.
2. Detection principle and system
2.1 Detection principle
The F-P cavity is an important application based on the principle of multi-beam interference. It uses a F-P cavity with an air cavity as sensitive unit to detect acoustic signal. When the external sound pressure signals act on the F-P cavity, it will change the molecular density in the air cavity, and the refractive index of air will be changed. The relationship between refractive index and the change of air density follows the Lorenz-Lorentz formula [23]
where n is the refractive index of air, $\rho $ is the density of the gas medium, and $\alpha $ is the average polarizability of isotropic molecules. At standard atmospheric pressure, Eq. (1) can be approximately simplified asTherefore, there is an approximate linear relationship between the refractive index of air and the density of the air medium. According to the ideal gas state equation, when the pressure of mass gas remains constant, the increase of temperature will result in a decrease in the density of air $\rho $, which in turn causes the decline in the air refractive index n.
From the Rüeger formula [24], we know that there is a linear relationship between the variation of the refractive index of air and the magnitude of the sound pressure. The refractive index of air under the action of sound pressure can be expressed as
In Fig. 1, the acoustic signal causes the change of the air density in the F-P cavity, resulting in a frequency shift $\varDelta f$ in the interference spectrum of the sensor. The relationship between $\varDelta f$ and the change of sound pressure can be expressed as [25]
where K is the linear coefficient of refractive index change corresponding to sound pressure change, c is the speed of light in a vacuum, $\varDelta p$ is the change in sound pressure. Through the phase modulation and lock-in amplification technology, $\varDelta f$ is converted into the variation of the demodulated signal to detect the acoustic signal.The transfer function of sensor output is denoted by T, which can be expressed by integrating the transmission function based on a multiple-beam interference of F-P cavity. We can further use Eq. (6) to solve its demodulated signal $S(n)$. Where ${R_1}$ and ${R_2}$ are the reflectivities of the two reflecting surfaces of the F-P cavity, and $BW$ is the bandwidth of the laser. ${\alpha _0}$ is a constant describing the optical loss, and $\eta $ is the round-trip loss in the air cavity, which is usually a constant.
According to Eqs. (5) and (6), the corresponding relationship between the peak value of the interference spectrum and the amplitude of the demodulated signal can be calculated by simulating. When the cavity length L and the laser center wavelength ${\lambda _0}$ are fixed, we can obtain the relationship between the spectral line and the demodulated signal with n. In Fig. 2(a), when the ${{nL} / {{\lambda _0}}}$ is smaller, the peak voltage of the spectral line and the amplitude of the demodulated signal gradually increase, and the slope of the demodulated signal is larger in Fig. 2(b). Here, the synchronous demodulated signal is used to observe and collect the acoustic signal, so the amplitude and slope of the demodulated signal have a direct impact on the performance of the sensor.
Fig. 2. (a) The relationship between the interference spectrum and demodulated signal with the refractive index of air; (b) The variation of the slope of the demodulated signal with the refractive index of air.
2.2 Preparation of FOAS
Here, we use fully rigid ultra-low-expansion glass (αl = 0 ± 0.02·10−6/K) from Corning Incorporated as the host material. It is prepared into F-P cavity with high-Q factor using optical contact technology (OCT). The OCT is an optical processing technology based on intermolecular attraction. When the smoothness of the surface exceeds a certain limit, the intermolecular distance between two adjacent surfaces is very small, and the molecules will attract each other due to electromagnetic interaction. Two smooth-surfaced components are held together by the intermolecular attraction. The OCT requires high surface smoothness and surface shape (surface roughness < 0.5nm, surface shape < 20/λ@632.8nm, parallelism < 1$^{\shortparallel}$).
We grind and polish the quartz glass as the flat plate on both sides and select the better side as the internal reflection surface. The other side is treated with a small wedge angle to prevent unwanted interference, and the internal surface is coated highly reflective films (99%@1550 nm), and the wedge angle surface coated with anti-reflection films (0.2%@1550 nm). Then we also grind and polish the quartz glass as connecting pieces on both sides, and cut it in an appropriate size to contact with the flat plate after cleaning by the OCT. We design chamfer treatment on the inner side of the connecting piece to achieve better contact. Figure 3(a) is the flow chart of F-P cavity preparation. A flat plate and two connecting pieces are first bonded by the OCT, and then the second flat plate is bonded with the connecting pieces. After ensuring that the surface of the OCT is qualified, the F-P cavity is deeply bonded at high temperature and then is cleaned and cut to prepare an integrated F-P cavity product. Figure 3(b) is an actual image of the F-P cavity, an air cavity with the dimensions of 2 mm × 2 mm is used to detect the acoustic signal. Next, we align the fiber collimator with the F-P cavity, adjust the interference spectrum to the best position, and then couple them with the optical glue curing agent to prepare an integrated FOAS.
Fig. 3. (a) The flow chart of the preparation of the F-P cavity structure by OCT; (b) An actual image of the F-P cavity; (c) The bonding interface of the F-P cavity at 13X magnification; (d) The bonding interface of the F-P cavity at 1.24KX magnification; (e) The bonding interface of the F-P cavity at 4.6KX magnification.
We test the bonding interface of the F-P cavity by the scanning electron microscopy (SEM). As shown in Fig. 3(c), when magnify at 13X, it can be clearly observed that FPE is a good integrated structure. Figure 3(d) is the image after magnifying the part of the F-P cavity to 1.24KX times. It can be seen that the bonding surface is tightly combined. After enlarging it to 4.6KX times, as shown in Fig. 3(e), the bonding interface is smooth and neat without any holes and voids. Such results show that the OCT has high bonding strength and good quality, and can be used to prepare the F-P cavity in batches. Furthermore, the F-P cavity is bonded in high-temperature conditions, so it has a certain high-temperature resistance.
2.3 Experimental setup
Figure 4 shows the experimental test system for high-temperature characteristics of FOAS. The light source is a continuous-tunable single-frequency narrow-linewidth laser with a maximum optical power output of 40 mW and a center wavelength of 1550 nm from NKT photonics. The laser is modulated by a phase modulator (PM) containing LiNbO3 crystal, which is driven by a sine wave of 6 MHz. The laser frequency is scanned by using a 6.1 Hz triangular wave signal. The modulated signal incidence into the F-P cavity through the fiber collimator, and the multi-beam interference occur between the two parallel mirrors. The optical signal of the sensor output is converted into an electrical signal by a photodetector (PD). The electrical signal is demodulated by a lock-in amplifier (LIA) to obtain two different demodulated signals, which are called as demodulated signal 1 and demodulated signal 2, respectively. It is noteworthy that the reference signal input by LIA is the synchronous signal of the modulated signal. The two demodulated signals output by LIA are used alternately. One of the demodulated signals is used as an error signal to feedback and adjust the laser through the lock-frequency controller (LFC). This error signal makes LFC module's control function always exist, and finally makes the error to zero. At this point, the laser frequency is locked at the resonant point of the F-P cavity. The other demodulated signal is used to sense the acoustic signal after frequency locking. When the acoustic signal causes a slight change in the refractive index of the air, the demodulated signal produces a shift relative to the zero point, so that the acoustic signal can be intuitively observed. In this experimental system, the FOAS is placed in a high-temperature tube furnace with openings on both sides, and acoustic signal is applied at the openings for calibration and test.
Fig. 4. The experimental test system of the FOAS. PM, phase modulator; SG, signal generator; PD, photodetector; LIA, lock-in amplifier; OSC, oscilloscope; LFC, lock-frequency controller; HVA, high voltage amplifier. Here, red lines are optical path, black lines are electrical path.
3. Experimental results and discussion
In order to further verify the high-temperature characteristics of the FOAS, we first study the interference spectra of the sensor at different temperatures. We conduct it in the range of 20–220 °C and study the characteristics of sensor such as sensitivity, frequency response, flatness and signal-to-noise ratio (SNR). When the temperature reaches the preset value, the acoustic signal test is performed after stabilizing for 10 minutes.
The interference spectra of FOAS at different temperatures are shown in Fig. 5(a). With the increasing of temperature, the interference spectra have a significant frequency shift. To achieve accurate measurement of acoustic signals at different temperatures and improve the accuracy of frequency locking, we match the resonant frequencies by adjusting the temperature of the laser. Figure 5(b) shows the variation of the interference spectra’s peak voltage at different temperatures. When the temperature is changed from 20 °C to 200 °C, the peak voltage of the interference spectra gradually increase from 0.6 V to 2.9 V. This result is due to the decrease in the density of the medium in the air cavity, which reduces the refractive index of the air. With the further increase of temperature to 220 °C, the value decreases to 2.8 V. The 220 °C is close to the high-temperature limitation of the sensor, and the weak deformation of the FOAS leads to the weakening of the interference effect.
Fig. 5. (a) The interference spectra at different temperatures; (b) The variations of the interferometric spectra’s peak voltage at different temperatures; (c) The FWHM of sensor corresponding to different temperatures.
The quality factor ($Q = {{{\lambda _{\textrm{laser}}}} / {FWHM}}$) is the most important parameter of the F-P cavity, which can be calculated from the center frequency of the laser and the full width at half maximum (FWHM) of the interference spectrum. Here, the center frequency of the laser remains unchange, and the FWHM directly determines the size of the Q factor. Figure 5(c) is the FWHM of the interference spectra at different temperatures. During the temperature change, the FWHM remains within a relatively stable range, with an average of 364 MHz and a maximum change of 27 MHz. The Q factor is calculated to be $8.8 \times {10^5}$, and it doesn’t change significantly with the increasing of temperature. It shows that the change of sensor’s performance in the high-temperature environments is independent of the Q factor of the F-P cavity, which is mainly affected by external conditions.
Sensitivity is a pivotal performance index of the sensor, which is characterized by the ratio of the output voltage to the input sound pressure when the sensor is working stably. The two output demodulated signals are used to test the sensitivity, respectively. Since the amplitudes and slopes of the two demodulated signals are quite different, the demodulated signal 1 is defined as a low-sensitivity test channel, and the demodulated signal 2 is defined as a high-sensitivity test channel. The amplitude of the demodulated signal 2 is 22 V, and the amplitude of the demodulated signal 1 gradually increase from 9.5 V to 22 V and then remains unchange, as shown in Fig. 6(a). In Fig. 6(b), the slopes of the two demodulated signals gradually increase with the temperature from 20 °C to 200 °C; when the temperature is increased to 220 °C, they have a significant drop. The changing trends of the two demodulated signals’ slopes are basically the same. This result corresponds to the changing trend of the interference spectra, which further verify the results of simulation.
Fig. 6. (a) The amplitude change of demodulated signals; (b) The slope change of the demodulated signals; (c) The sensitivity change of the FOAS; (d) The detectable maximum sound pressure of the FOAS.
The change of sensitivity is proportional to the amplitude and slope of the demodulated signals. Figure 6(c) is the curve of the FOAS sensitivity at different temperatures. When the temperature is changed from 20 °C to 200 °C, the sensitivity of the sensor gradually increase with temperature. At 200 °C, the sensitivities of the two signals reach the maximum of 91.1 mV/Pa and 491.2 mV/Pa, respectively. When the temperature is increased to 220 °C, the sensitivity decline to 48.5 mV/Pa and 355.2 mV/Pa. The change of sensitivity is consistent with the change of demodulated signal’s slope, the decrease of demodulated signal’s slope lead to the decline of sensitivity. The sensitivities of the two demodulated signals have a large difference in value, but their changing trends are same. Therefore, when the amplitude of the demodulated signal is jarless, the sensitivities change with the slope. In addition, Fig. 6(d) shows the maximum detectable sound pressure, which is determined by the amplitude of the demodulated signal and the sensitivity of the sensor. The maximum detectable sound pressure of the FOAS is 93.7 dB at different temperatures. The experimental results of maximum detectable sound pressure are consistent with the corresponding relationship of sensitivity, which shows a decreasing trend.
The frequency response range of the FOAS is directly observed and collected by the acoustic signal response data of a certain frequency point through the frequency analyzer. In the testing of frequency response, the output amplitude of the SG remains 5 V. After the signal is stabilized, the frequency response data are collected, and then the data are normalized to study its response flatness. Figure 7 shows that during the process of the temperature change the FOAS has a good acoustic signal response in the range of 10 Hz-50 kHz with a flatness of ±2 dB at 20 °C-220 °C, but the flatness has a small change at 220 °C. The results show that the change of temperature has little effect on the frequency response and flatness of the FOAS. The inconsistency of the response at 220 °C is due to the sensor reachs the limit of temperature tolerance, and the coupling optical path of the sensor changes at this time. Figure 8 shows the frequency response and the SNR of the sensor at 200 °C. Figure 8(a) is the response of the FOAS at 10 Hz, which is the minimum response frequency of the sensor, with an SNR of 10.3 dB. Figure 8(b) shows the response of the FOAS at 1 kHz, which is the best response frequency point of the sensor with a maximum SNR of 60.9 dB. Figure 8(c) shows the response of the FOAS at 50 kHz with an SNR of 9.2 dB. The comparison of the FOAS’s response at 200 °C and 220 °C is shown in Fig. 8(d). The SNR are 29.1 dB at 200 °C and 17.2 dB at 220 °C, respectively, which show a significant decline. The drop of the SNR indicates that the performance of the FOAS at 220 °C has significantly descended.
Fig. 8. The frequency response and SNR characteristics of the sensor at 200 °C; (a) Frequency response of the FOAS at 10 Hz; (b) Frequency response of the FOAS at 1 kHz; (c) Frequency response of the FOAS at 50 kHz; (d) The comparison of the FOAS’s response at 200 °C and 220 °C.
The sensitivity, frequency response and flatness of the FOAS appear overall consistency over temperatures. The variation of its performance at 20–200 °C can be attributed to the influence of temperature on the interference effect in the air cavity, and the results are consistent with the simulation. The characteristics of the FOAS show inconsistency at 220 °C, which is caused by the temperature resistance limit of the FOAS. At the extreme temperature, the optical glue curing agent of the FOAS has been slightly scorched, and the optical path of the collimator gradually shifts. When the temperature is further increased, coupling failures cause the damage of the FOAS. Figure 9 shows the demodulated signals of the FOAS at 220 °C and 230 °C. In Fig. 9(b), the demodulated signals have a splitting phenomenon, where the frequency locking and sensing test at this temperature is difficult to perform. The inability of couplant to withstand high temperature is the main problem in the current research about FOAS, which also restricts the application of the sensor in the higher temperature environments. The next step is to increase the temperature tolerance of the sensor by changing the coupling medium or coupling method. Starting from the coupling method, the integration of the sensor is realized by laser welding, and its resistance temperature will be expected to increase to more than 1000 °C. This will further expand the application of the sensor in the harsh environments such as higher temperatures.
4. Conclusion
A high-sensitivity miniature FOAS is fabricated by coupling a rigid F-P cavity with two fiber collimators. Through theoretical simulation and comparative experiments, the change of the sensor's interference spectra and demodulated signals are studied in the temperature range of 20–220 °C. Meanwhile, its characteristics such as sensitivity, frequency response range, flatness and SNR under different temperatures are verified. In the process of temperature ranging from 20 to 200 °C, the FOAS has high sensitivity of 491.2 mV/Pa, good frequency response in 10 Hz-50 kHz with the flatness of ±2 dB, and the latter two are not affected by temperature. The acoustic performance of the FOAS shows that it can achieve high-sensitivity acoustic detection while maintaining a broad frequency band at high temperature. In this experiment, the FOAS shows good temperature adaptability below 200 °C, which has the potential and feasibility of application in high-temperature and harsh environments. By further exploring the coupling method of the high-temperature resistance, it is expected to increase its application temperature. Furthermore, we hope to broaden the frequency response range by improving the demodulation system and coupling accuracy. The results of this study have important guiding significance for the application of fiber-optic acoustic sensors in high-temperature environments.
Funding
National Natural Science Foundation of China (12104417, 62131018); Shanxi “1331 Project” Key Subject Construction (1331KSC); the Fundamental Research Program of Shanxi Province (202103021222012, 20210302124161); Shanxi Province Postgraduate Innovation Project (2021Y620).
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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