Open Access
Add to BibSonomy
Abstract
This paper demonstrates, for the first time, a novel demodulation technique that can be applied for interrogating a shortest cavity in multi-cavity Fabry–Pérot (F–P) sensors. In this demodulation technique, using an amplified spontaneous emission (ASE) light source and two optical fiber broadband filters, the interference only occurs in a shortest F–P cavity that is shorter than the half of the coherence length. Using a signal calibration algorithm, two low-coherence interference optical signals with similar coherence lengths were calibrated to obtain two quadrature signals. Then, the change in the cavity length of the shortest F–P cavity was interrogated by the two quadrature signals and the arctangent algorithm. The experimental results show that the demodulation technique successfully extracted 1 kHz and 500 Hz vibration signals with 39.28 µm and 64.84 µm initial cavity lengths, respectively, in a multi-cavity F–P interferometer. The demodulation speed is up to 500 kHz, and the demodulation technique makes it possible for multi-cavity F–P sensors to measure dynamic and static parameters simultaneously. The results show that the demodulation technique has wide application potential in the dynamic measurement of multi-cavity F–P sensors.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber-optic Fabry–Pérot (F–P) sensors have broad application prospects in various fields, such as aerospace, large-scale construction, and oil collection; this is because they have high sensitivity, anti-electromagnetic interference, a small size, and high thermal resistance [1–4]. In these fields, multiple parameters such as temperature, pressure, acceleration, acoustics, and ultrasonic affect each other, which makes it difficult to measure a single parameter. Therefore, multi-parameter F–P sensors are designed to measure multiple parameters simultaneously. Almost all fiber-optic F–P sensors used for multi-parameter measurement are fiber-optic F–P sensors with multiple cavities [5–10]. However, these multi-parameter sensors cannot measure dynamic signals, such as acceleration, ultrasonic and acoustics, because of there is no high-speed demodulation technique that can be used to interrogate multi-cavity F–P sensors. In some fields, the frequency of these parameters is as high as 40 kHz [11]. Therefore, the demodulation frequency is often required to be greater than 80 kHz. Moreover, in the field of aerospace testing, dynamic pressure is a key parameter during aerospace engine testing. Micro-electro-mechanical system (MEMS) pressure sensors with multiple F–P cavities are often produced for pressure testing because of their airtightness and consistency [12–14]. However, the existing high-speed demodulation technique cannot be used on multi-cavity F–P sensors. Therefore, the demodulation technique in high speed becomes intractable when the F–P sensor has multiple cavities.
The interrogation methods that can be applied to multi-cavity F–P sensors mainly include peak tracking, Fourier transform, cross-correlation, and non-scanning cross-correlation methods. The peak tracking method has a slow speed and small range, and it is difficult to use to demodulate dynamic signals [5–7]. Because the spectrum of the multi-cavity F–P sensor is composed of signals of different frequencies, the Fourier transform method is a commonly used interrogation method [8–10,15,16]. The cross-correlation method finds the maximum value by cross-correlating the sensor spectrum with another ideal spectrum [17–19]. Although the demodulation methods based on spectral analysis have high accuracy, the demodulation speed is difficult to exceed 1 kHz [18]. With the development of spectrometers, high-speed spectrometers have become a potential dynamic demodulation instrument. However, the price of such high-speed spectrometers is their main limiting factor. The non-scanning cross-correlation method uses the principle of low-coherence interference. When the optical path difference (OPD) between the F–P sensor and another interferometer are equal, the maximum intensity is obtained [12,20–23]. Although the demodulation methods have high accuracy, the demodulation speed is still difficult to exceed 3 kHz [22]. Therefore, the speeds of the above methods do not meet dynamic demodulation requirements.
To meet the requirements of dynamic signal demodulation, many demodulation techniques have been proposed. The intensity of optical signals with different wavelengths were used to demodulate the phase change of sensors. On this basis, several dual-wavelength or three-wavelength demodulation methods have been proposed [24–31]. However, none of these dynamic demodulation techniques can be used for multi-cavity F–P sensors.
In this paper, for the first time, we propose a demodulation technique that can be applied for a shortest cavity in multi-cavity F–P sensors. In this demodulation technique, using an ASE light source and two optical fiber broadband filters, the interference only occurs in a shortest F–P cavity that is shorter than the half of the coherence length. The quadrature signals are obtained from two filtered optical intensity signals and the initial cavity length, and then the change in the cavity length of the sensor is extracted. This demodulation technique has fast demodulation speed and a simple system as advantages, and it has wide application potential in the dynamic measurement of multi-cavity F–P sensors.
2. Principle of demodulation algorithm
Multi-cavity F–P sensors are designed to measure multiple parameters simultaneously. The typical structure of a fiber-optic multi-cavity F–P sensor is shown in Fig. 1. The reflective surfaces constitute two F–P interferometers with different cavity lengths. The cavity lengths of each cavity cannot be the same; otherwise, the interference signals will interfere with each other and cannot be interrogated. Different F–P cavities are sensitive to different external parameters. For multi-cavity F–P sensors, the interference equation is so complicated that the current dynamic demodulation method cannot be used. However, when a broadband light source is used in combination with appropriate filters, the interference phenomenon can only occur in an F–P cavity with a short cavity length.
A schematic of the dual-wavelength dynamic demodulation technique for the interrogation of a shortest cavity in multi-cavity fiber-optic F–P interferometer is shown in Fig. 2. A flat-topped beam with a wavelength range of 1527–1601 nm was emitted by the ASE light source (OPEAK, LSM-ASE-CL). The light emitted by the ASE light source reached the multi-cavity F–P interferometer through the single-mode fiber and the 3 dB optical fiber coupler. A multi-cavity F–P interferometer consists of a gradient-index (GRIN) lens and a 300-µm-thick double-polished quartz glass sheet. A quartz glass piece was fixed on a piezoelectric transducer (PZT). The reflectivity of the interface between the quartz glass and air was approximately 0.04. The short F–P cavity was consisted of the GRIN lens and the upper surface of the quartz glass sheet. The long F–P cavity was consisted of the lower surface and the upper surface of the quartz glass sheet. The coupler splits the beam into two paths that pass through two optical fiber broadband filters with center wavelengths of 1548.14 nm and 1552.744 nm. The bandwidth of both filters was 15 nm. Two interferometric signals at each center wavelength were obtained using two photodiodes (PDs), PD1 and PD2 (New Focus, 2503-FC-M). The detectable wavelength range of the PDs is 900–1700nm. The voltage signals were collected by analog-to-digital conversion (ADC) and transmitted to a personal computer (PC). The demodulation speed was 500 kHz.
Fig. 2. Schematic of the dual-wavelength dynamic demodulation technology for the interrogation of a short cavity in multi-cavity fiber F–P interferometer.
The coherence length of the optical signal received by the photodetectors is
The low-reflectivity F-P interferometer can be approximated as a two-beam interferometer. For low-reflectivity multi-cavity F–P sensors, regardless of the loss during propagation, the light intensity received by the photodetector is
When the coherence length C is greater than $2{n_1}{L_{FP1}}$ and C is much less than $2{n_2}{L_{FP2}}$, interference only occurs in the short cavity. The optical signal received by the photodetector can be approximated as
As shown in Fig. 3, Eq. (3) was used for simulation with 1548.14 nm and 1552.744 nm center wavelengths, and both bandwidths are 15 nm. The coherent lengths of light received by the photodetectors are 159.882 µm and 160.73 µm, respectively. Therefore, the short F–P cavity length should be less than half the coherence length, approximately 80 µm. The OPD introduced by the long F–P cavity length should be five times longer than the coherent length, approximately 800 µm. In experiments, the OPD introduced by the long F–P cavity was $2{n_2}{L_{FP2}}$, about 864 µm, which is much longer than the coherent length. Therefore, interference only occurs in the short F–P cavity. In a short cavity length range, such as 30 µm to 40 µm, we can approximate the Eq. (3) as
where $A\textrm{ = }6{I_0}\Delta k$ is the DC term and $B(L)\textrm{ = } - 2{I_0}\Delta k\frac{{\sin (\Delta k{n_1}{L_{FP1}})}}{{\Delta k{n_1}{L_{FP1}}}}$ is the amplitude function of the interference term. $B(L)$ can be regarded as a linear function within a small length variation range. When the $\Delta k$ values of the two filters are close and the initial light power ${I_0}$ is the same in the two-filter passband range, A and $B(L)$ can be regarded as approximately equal. The light intensity received by PD1 and PD2 can be approximated as where ${I_1}$ and ${I_2}$ are the voltage signals received by PD1 and PD2, respectively; ${\theta _1}\textrm{ = }\frac{{4\pi {n_1}{L_0}}}{{{\lambda _1}}}$ and ${\theta _2}\textrm{ = }\frac{{4\pi {n_1}{L_0}}}{{{\lambda _2}}}$ are the initial phases of the signals received by PD1 and PD2, respectively; and ${\lambda _1}$ and ${\lambda _2}$ are the center wavelengths of the two filters, respectively. In this paper, ${\lambda _1}\textrm{ = }1548.14nm$ and ${\lambda _2}\textrm{ = }1552.744nm$. ${L_0}$ is the initial length of the short cavity. When the short cavity length starts to change, the voltage signals received by PD1 and PD2 are where $\Delta {\theta _1}\textrm{ = }\frac{{4\pi {n_1}\Delta L}}{{{\lambda _1}}}$ and $\Delta {\theta _2}\textrm{ = }\frac{{4\pi {n_1}\Delta L}}{{{\lambda _2}}}$ are the phase changes caused by the vibration signal generated by the PZT, and $\Delta L$ is the cavity length change driven by the vibration signal. When $\Delta L \ll {L_0}$ and ${\lambda _1} \approx {\lambda _2}$, $\Delta {\theta _1}$ can be considered equal to $\Delta {\theta _2}$. Thus, Eq. (7) and Eq. (8) can be approximated asThe initial cavity length ${L_0}$ is obtained using the white light interferometry (WLI) technique [15] and the high-order harmonic frequency cross-correlation technique [18]; ${\theta _1}$ and ${\theta _2}$ can be obtained. The signals that eliminate the DC voltage are calibrated as follows:
Fig. 3. Diagram of interference signals simulation with 1548.14 nm and 1552.744 nm center wavelengths.
The phase value $\Delta \theta ^{\prime}$ in the range $- {\pi / 2}$ to ${\pi / 2}$ was calculated. Deviations occur when $\Delta \theta $ approaches ${\pm} {\pi / 2}$, which caused fringes of ${\pm} \pi $. By combining the original quadrature phase-shifted signals to determine whether the phase jump is $\pi $ or $- \pi $, the recovered phase value $\Delta \theta$ is obtained. Then, the signal $\Delta L$ can be extracted:
3. Analysis and simulation
The demodulation technique was simulated using Eq. (3). The center wavelengths ${\lambda _1}$ and ${\lambda _2}$ of the two filters were set to 1548.14 nm and 1552.744 nm, respectively. Both bandwidths were set at 15 nm. The coherent length of the filtered optical signal was approximately 160 µm, and thus the initial cavity length ${L_0}$ was set to 35 µm, and the refractive index ${n_1}$ was set to 1. A sinusoidal vibration signal with an amplitude of 1.5 µm was used in the simulation. The change in the cavity length $\Delta L$ was set to ±1.5 µm. The simulation signal is added with a noise signal with a signal-to-noise ratio (SNR) of approximately 32.18 dB. The simulation parameters as shown in Table 1. Simulation results show that the demodulation technique for multi-cavity F–P sensors is feasible.
Table 1. Simulation parameters
The demodulation processes and results of the interference signals are shown in Fig. 4, and the demodulation error is shown in Fig. 5. Figure 4(a) shows two signals that filter out the DC component. The calibrated signals are shown in Fig. 4(b), and the Lissajous figure is shown in Fig. 4(c). Figure 4(d) demonstrates the demodulated waveform. As shown in Fig. 4(d), a sinusoidal signal with an amplitude of 1.5 µm was successfully extracted. The absolute error of the demodulation technique is less than 0.01 µm without adding noise. When noise was added, the absolute error of the demodulation technique was still less than 0.035 µm. The simulation demonstrates that the demodulation technique can accurately extract the applied signal.
Fig. 4. (a) ${I_1}$ and ${I_2}$ without a DC voltage. (b) Calibrated signals, ${F_1}$ and ${F_2}$ (c) Lissajous figure for ${F_1}$ and ${F_2}$. (d) Waveform of demodulation results.
4. Experiments
A schematic of the experiment is shown in Fig. 2. To evaluate the properties of the demodulation technique, a multi-cavity F–P interferometer with different short cavity lengths was tested, and a 1 kHz signal and 500 Hz signal were used to drive the PZT. The two experiments were set to different initial cavity lengths. The spectra of the multi-cavity F–P interferometer consisting of a GRIN lens and quartz glass are shown in Fig. 6. The initial short cavity length, ${L_0}$, was measured as 39.28 µm and 64.84 µm, respectively.
The experimental results with an initial cavity length of 39.28 µm and 1 kHz sinusoidal signal are shown in Figs. 7 and 8. The peak-to-peak amplitude of PZT was approximately 2.6 µm. After obtaining two voltage signals, we first calibrate the optical power imbalance caused by the flatness of the light source, different gain of photodetectors, and different filter transmittances. In this experiment, ${I_2}$ was amplified 1.42 times. Figure 7(a) shows the adjusted voltage signals. Figure 7(b) shows the calibration signals, and the Lissajous figure is shown in Fig. 7(c). Figure 7(d) demonstrates the demodulated waveform. The peak-to-peak amplitude of demodulated signal was 2.62 µm. The peak-to-peak amplitude error of the demodulation results is 0.02 µm. A power density spectrum diagram of the demodulated signal is shown in Fig. 8.
Fig. 7. (a) ${I_1}$ and ${I_2}$ driven using a 1 kHz sinusoidal signal. (b) Calibrated signals ${F_1}$ and ${F_2}$. (c) Lissajous figure for ${F_1}$ and ${F_2}$. (d) Waveform of demodulation results.
The experimental results with an initial cavity length of 64.84 µm and 500 Hz sinusoidal signals are shown in Fig. 9 and 10. The peak-to-peak amplitude of PZT was approximately 1.4 µm. ${I_2}$ was still amplified by 1.42 times. Figure 9(a) shows the adjusted voltage signals. Figure 9(b) shows the calibration signals, and the Lissajous figure is shown in Fig. 9(c). Figure 9(d) demonstrates the demodulated waveform. The peak-to-peak amplitude of demodulated signal was 1.39 µm. The peak-to-peak amplitude error of the demodulation results is 0.01 µm. A power density spectrum diagram of the demodulated signal is shown in Fig. 10. As shown in Fig. 4, Fig. 7 and Fig. 9, the simulation results are almost the same as the demodulation results. The Fig. 4(d), Fig. 7(d) and Fig. 9(d) show that the sinusoidal vibration signals with different amplitude were successfully extracted.
Fig. 9. (a) ${I_1}$ and ${I_2}$ driven by a 500 Hz sinusoidal signal (b) calibrated signals ${F_1}$ and ${F_2}$. (c) Lissajous figure of ${F_1}$ and ${F_2}$. (d) Waveform of the demodulation results.
5. Conclusion
In conclusion, a dual-wavelength dynamic demodulation technique for the interrogation of a shortest cavity in multi-cavity fiber-optic F–P sensors has been demonstrated. In this paper, for the first time, a demodulation technique that can be used for multi-cavity F–P sensors in high speed was proposed. In the demodulation technique, the ASE light source and the two optical fiber broadband filters were used for extract the interference pattern contributed by the shortest cavity in multi-cavity fiber-optic F–P sensors. The calibration algorithm was proposed to obtain the two quadrature signals, and the arctangent algorithm was used to interrogate the change of shortest F–P cavity length. The results show that the drive signals of different frequencies with different initial cavity lengths are successfully demodulated by a shortest cavity in the multi-cavity F–P interferometer. Compared with other demodulation techniques that can be used for multi-cavity F–P sensors, the demodulation technique has the advantage of fast demodulation speed. The demodulation technique makes it possible to extract dynamic parameters in multi-cavity F–P sensors. Experimental results demonstrate the potential of this technique for the measurement of dynamic signals in multi-cavity F–P sensors.
Funding
Innovative Research Group Project of the National Natural Science Foundation of China (51821003); National Natural Science Foundation of China (51935011, 52075505).
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.
References
1. J. Wang, B. Dong, E. Lally, J. Gong, M. Han, and A. Wang, “Multiplexed high temperature sensing with sapphire fiber air gap-based extrinsic Fabry-Perot interferometers,” Opt. Lett. 35(5), 619–621 (2010). [CrossRef]
2. C. Gouveia, M. Zibaiic, H. Latific, M. J. B. Marques, J. M. Baptista, and P. A. S. Jorge, “High resolution temperature independent refractive index measurement using differential white light interferometry,” Sens. Actuators, B 188, 1212–1217 (2013). [CrossRef]
3. J. Liu, P. Jia, H. Zhang, X. Tian, H. Liang, Y. Hong, T. Liang, W. Liu, and J. Xiong, “Fiber-optic Fabry–Perot pressure sensor based on low-temperature co-fired ceramic technology for high-temperature applications,” Appl. Opt. 57(15), 4211–4215 (2018). [CrossRef]
4. P. Jia, G. Fang, T. Liang, Y. Hong, Q. Tan, X. Chen, W. Liu, C. Xue, J. Liu, W. Zhang, and J. Xiong, “Temperature-compensated fiber-optic Fabry–Perot interferometric gas refractive-index sensor based on hollow silica tube for high-temperature application,” Sensors and Actuators B B-Chem 244, 226–232 (2017). [CrossRef]
5. X. Wang, S. Wang, J. Jiang, K. Liu, P. Zhang, W. Wu, and T. Liu, “High-accuracy hybrid fiber-optic Fabry-Pérot sensor based on MEMS for simultaneous gas refractive-index and temperature sensing,” Opt. Express 27(4), 4204–4215 (2019). [CrossRef]
6. J. Yin, T. Liu, J. Jiang, K. Liu, S. Wang, Z. Qin, and S. Zou, “Batch-producible fiber-optic Fabry–Pérot sensor for simultaneous pressure and temperature sensing,” IEEE Photonics Technol. Lett. 26(20), 2070–2073 (2014). [CrossRef]
7. R. Wang and X. Qiao, “Hybrid optical fiber Fabry–Perot interferometer for simultaneous measurement of gas refractive index and temperature,” Appl. Opt. 53(32), 7724–7728 (2014). [CrossRef]
8. Y. Liu, T. Zhang, Y. Wang, D. Yang, X. Liu, H. Fu, and Z. Jia, “Simultaneous measurement of gas pressure and temperature with integrated optical fiber FPI sensor based on in-fiber micro-cavity and fiber-tip,” Opt. Fiber Technol. 46, 77–82 (2018). [CrossRef]
9. H. Gao, Y. Jiang, Y. Cui, L. Zhang, J. Jia, and J. Hu, “Dual-cavity Fabry–Perot interferometric sensors for the simultaneous measurement of high temperature and high pressure,” IEEE Sens. J. 18(24), 10028–10033 (2018). [CrossRef]
10. S. Pevec and D. Donlagic, “Miniature fiber-optic sensor for simultaneous measurement of pressure and refractive index,” Opt. Lett. 39(21), 6221–6224 (2014). [CrossRef]
11. J. Jiang, T. Zhang, S. Wang, K. Liu, C. Li, Z. Zhao, and T. Liu, “Noncontact Ultrasonic Detection in Low-Pressure Carbon Dioxide Medium Using High Sensitivity Fiber-Optic Fabry–Perot Sensor System,” J. Lightwave Technol. 35(23), 5079–5085 (2017). [CrossRef]
12. J. Liu, P. Jia, F. Feng, G. An, T. Liang, Y. Hong, and J. Xiong, “MgO single crystals MEMS-based fiber-optic Fabry–Perot pressure sensor for harsh monitoring,” IEEE Sens. J. 21(4), 4272–4279 (2021). [CrossRef]
13. X. Wang, J. Jiang, S. Wang, K. Liu, and T. Liu, “All-silicon dual-cavity fiber-optic pressure sensor with ultralow pressure-temperature cross-sensitivity and wide working temperature range,” Photonics Res. 9(4), 521–529 (2021). [CrossRef]
14. Z. Shao, Y. Wu, S. Wang, C. Zhang, Z. Sun, M. Yan, Y. Shang, E. Song, and Z. Liu, “All-sapphire-based fiber-optic pressure sensor for high-temperature applications based on wet etching,” Opt. Express 29(3), 4139–4146 (2021). [CrossRef]
15. S. Pevec and D. Donlagic, “MultiParameter fiber-optic sensor for simultaneous measurement of thermal conductivity, pressure, refractive index, and temperature,” IEEE Photonics J. 9(1), 1–14 (2017). [CrossRef]
16. Y. Jiang, “Fourier transform white-light interferometry for the measurement of fiber-optic extrinsic Fabry–Pérot interferometric sensors,” IEEE Photonics Technol. Lett. 20(2), 75–77 (2008). [CrossRef]
17. Z. Wang, Y. Jiang, W. Ding, and R. Gao, “A cross-correlation based fiber optic white-light interferometry with wavelet transform denoising,” Proceedings of the SPIE8924 (2013).
18. Z. Jing and Q. Yu, “White light fiberoptic EFPI sensor based on cross-correlation signal processing method,” Proceedings of ISTM, 3509–3511 (2005).
19. H. Chen, J. Liu, X. Zhang, W. Wang, Z. Ma, W. Lv, and Z. Guo, “High-order harmonic-frequency cross-correlation algorithm for absolute cavity length interrogation of white-light fiber-optic Fabry–Perot sensors,” J. Lightwave Technol. 38(4), 953–960 (2020). [CrossRef]
20. S. Wang, J. Zhang, J. Jiang, K. Liu, X. Wang, X. Zhang, Z. Wu, J. Zhou, H. Xiao, and T. Liu, “Position-deviation-compensation demodulation method for multi-channel polarized low-coherence interferometry,” Opt. Express 26(13), 17407–17417 (2018). [CrossRef]
21. J. Yin, T. Liu, J. Jiang, K. Liu, S. Wang, F. Wu, and Z. Ding, “Wavelength-division-multiplexing method of polarized low-coherence interferometry for fiber Fabry–Perot interferometric sensors,” Opt. Lett. 38(19), 3751–3753 (2013). [CrossRef]
22. S. Wang, T. Liu, J. Jiang, K. Liu, J. Yin, Z. Qin, and S. Zou, “Zero-fringe demodulation method based on location-dependent birefringence dispersion in polarized low-coherence interferometry,” Opt. Lett. 39(7), 1827–1830 (2014). [CrossRef]
23. W. Daihua, L. Shuxin, Y. Gang, J. Pinggang, and Z. Yan, “Study on parallel multiplexed Fabry–Pérot fiber optic accelerometers and the signal demodulation method,” Acta Opt. Sin. 30(6), 1776–1782 (2010). [CrossRef]
24. K. A. Murphy, M. F. Gunther, A. M. Vengsarkar, and R. O. Claus, “Quadrature phase-shifted, extrinsic Fabry–Perot optical fiber sensors,” Opt. Lett. 16(4), 273–275 (1991). [CrossRef]
25. M. Schmidt and N. Fürstenau, “Fiber-optic extrinsic Fabry–Perot interferometer sensors with three-wavelength digital phase demodulation,” Opt. Lett. 24(9), 599–601 (1999). [CrossRef]
26. J. Jia, Y. Jiang, L. Zhang, H. Gao, S. Wang, and L. Jiang, “Dual-wavelength DC compensation technique for the demodulation of EFPI fiber sensors,” IEEE Photonics Technol. Lett. 30(15), 1380–1383 (2018). [CrossRef]
27. J. Jia, Y. Jiang, H. Gao, L. Zhang, and Y. Jiang, “Three-wavelength passive demodulation technique for the interrogation of EFPI sensors with arbitrary cavity length,” Opt. Express 27(6), 8890–8899 (2019). [CrossRef]
28. J. Jia, Y. Jiang, J. Huang, J. Hu, and L. Jiang, “Symmetrical demodulation method for the phase recovery of extrinsic Fabry–Perot interferometric sensors,” Opt. Express 28(7), 9149–9157 (2020). [CrossRef]
29. J. Jia, Y. Jiang, and Y. Cui, “Phase demodulator for the measurement of extrinsic Fabry–Perot interferometric sensors with arbitrary initial cavity length,” IEEE Sens. J. 20(7), 3621–3626 (2020). [CrossRef]
30. Q. Liu, Z. Jing, A. Li, Y. Liu, Z. Huang, Y. Zhang, and W. Peng, “Common-path dual-wavelength quadrature phase demodulation of EFPI sensors using a broadly tunable MG-Y laser,” Opt. Express 27(20), 27873–27881 (2019). [CrossRef]
31. Q. Liu, Z. Jing, Y. Liu, A. Li, Y. Zhang, Z. Huang, M. Han, and W. Peng, “Quadrature phase-stabilized three-wavelength interrogation of a fiber-optic Fabry–Perot acoustic sensor,” Opt. Lett. 44(22), 5402–5405 (2019). [CrossRef]
