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Abstract
In this work, we investigate the Fourier characteristics of wavelength-scanned optical spectrum of low-finesse Fabry-Pérot (FP) acoustic sensor both theoretically and experimentally. The wavelength scanning will transform the time-domain acoustic signal into phase modulation loaded on the FP sensor spectrum distributed along wavelength. Therefore the interference spectrum can be regarded as carrier signal in the wavelength domain. From this perspective, it is intelligible that the phase modulation loaded on the spectrum (carrier signal) will introduce sidebands in Fourier domain. The spatial frequency and phase of sideband components contain unique information of both acoustic signal and the corresponding sensor. These conclusions are experimentally proved by single sensor head as well as two parallel sensors. The Fourier characteristics of sideband components can be utilized to recognize and distinguish acoustic signals received by different sensors, indicating that it has potential applications in multiplexed FP sensor array and source localization, and so forth.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical fiber acoustic sensors based on low finesse Fabry-Pérot interferometer (FPI) have attracted great research interests in recent decades [1–6]. They have unique advantages of compact size and reflection-based working principle, which make these sensors easy to be packaged as sensing probes [7]. Demodulation techniques have been a key point for FPI type of sensors. The essence of existing methods is based on the measurement of the interference spectral pattern frame-by-frame. In other words, each frame of spectral data is regarded to be corresponding to a certain constant cavity length (corresponding to acoustic pressure at certain time). In different demodulation techniques, the sampling data amount for each spectral frame is diversely selected. For example, in Q-point based edge filtering method [1] or two-wavelength phase demodulation method [8,9], only one or two unique points are sampled to represent the whole spectral information of each frame, so they have simple processing algorithms and fast response speed. However, such small amount of raw data are not able to present intrinsic information of the sensor head in the output signal, hence they can only adapt to single-sensor application. For white light interferometry (WLI) technique, all spectral data within a certain wavelength range are sampled for signal demodulation in each frame [10–13], so the raw data amount is enough to express the sensor characteristics through spatial frequency and the corresponding Fourier phase. Benefiting from this, sensors can be multiplexed to array assisted by schemes like spatial frequency division multiplexing (SFDM) [14–17], but the cost is relative complicate calculation procedure.
According to our previous work, the wavelength scanning of fiber acoustic sensors can load the information of the sound wave onto the sensor spectrum in wavelength domain [18,19]. Under this process, the sensor spectrum can be regarded as a carrier signal, and it is modulated by the acoustic signal. Since acoustic waves are fast-varying signals in time-domain, a set of wavelength-scanned optical spectrum (WSOS) obtained by one round-trip scanning is not a frame that corresponds to a constant acoustic pressure at certain time, but is composed of a number of spectral frames, and each frame is sampled by a certain wavelength point. Therefore, the acoustic information at each moment is coded on only one sampling point at a certain wavelength, so the demodulation algorithms for both the intensity-modulation sensor [18] and phase-modulation sensor [19] are not complicated, while the WSOS still contains the intrinsic information (carrier signal) of the sensor head.
In our proposed phase interrogation algorithm to recover acoustic signal in wavelength domain from WSOS of interferometric acoustic sensors [19], two channels with certain phase difference are required. Since FP sensor can export only one channel of signal, the previously proposed method is not applicable to acoustic sensors based on FP cavity. In this article, we provide method from another point of view to obtain the acoustic signal in Fourier domain (spatial frequency domain) from the WSOS of the FP sensors. The WSOS can be considered as carrier signal (interferential pattern of FP sensors) that is phase-modulated by measured signals (acoustic waves). This modulation process will introduce sideband components in the Fourier spectrum of the WSOS. The intensity, spatial frequency, and phase of the sideband components in the Fourier domain can be utilized to obtain the acoustic pressure, frequency, and phase. Signals received by different sensors simultaneously can be distinguished through the carrier frequency and phase. The theory and mechanism is analyzed in detail, and is demonstrated by one sensor head as well as two parallel sensors in experiment. The results indicate potentials in applications such as sensor array multiplexing or source localization, etc.
2. Theoretical analysis
For low-finesse FPI structure, the reflected spectrum can be equalized to two-beam interference and can be expressed by a sinusoidal function in the wavelength region near the central wavelength λ0 [20]. Therefore, the WSOS of the low-finesse FPI acoustic sensor can be expressed by Eq. (1) according to the analysis in our previous work [19]. In the equation, R(λ) stands for the reflected spectrum of the FPI sensor, A and B are coefficients that determine the offset and contrast of the interference pattern, β is the angular spatial frequency of the interference spectrum, x(λ) is the acoustic signal (phase modulation item) loaded on the optical spectrum by wavelength scanning, and φ is the initial phase difference between the two beams. In the expression of x(λ), △Lm is the amplitude of sound induced cavity length variation, while ωa and αa stand for the angular frequency and phase of the acoustic wave. V (nm/s) represents the wavelength scanning speed. From the expressions we can see that the wavelength-domain acoustic frequency (WDAF) ω0 is related to the acoustic frequency and scanning speed, and we will prove this in the following experimental demonstration. The relationship shown in Eq. (1) is valid when the wavelength region of the sampled WSOS is not too wide.
Based on Eq. (1), the spatial frequency spectrum F(ω) of the WSOS R(λ) can be expressed by Eq. (2) according to the linear and convolution characteristics of Fourier transform. In the equation the asterisk is the convolution operator.In the analysis, we only consider harmonics of cos(x(λ)) and sin(x(λ)) lower than third order since higher order harmonics have very low intensities. According to the Bessel expansion rules given by ref [21], Bessel expansions of cos(x(λ)) and sin(x(λ)) are expressed by Eq. (3). J0(C) to J3(C) are Bessel functions of the first kind from zero to third order.Combining the Fourier characteristics of trigonometric functions and Bessel expansions shown in Eq. (3), each part of F(ω) can be respectively demonstrated in the following Eq. (4). In the expressions δ stands for unit impulse function.It can be concluded from the above expressions that item cos(x(λ)) presents the DC and second harmonic of the acoustic signal, while sin(x(λ)) contributes the fundamental frequency component and third order harmonic. With the assist of convolution characteristic of Fourier transform, the spatial frequency spectrum F(ω) of the WSOS of FPI sensor can be derived as Eq. (5). The result shows that the spatial frequency spectrum is consist of DC component FDC (at zero frequency), sensor spatial frequency (SSF) component FS (determined by the FP cavity length), left sideband FL and right sideband FR (determined by SSF, wavelength scanning speed, and acoustic frequency), and higher order harmonics F2nd and F3rd. Since we care more about the first order, the detailed expression of F2nd and F3rd is not given here.One noteworthy point is that the derived results in Eq. (4) are two-sided Fourier functions that contain symmetrical positive and negative frequency components, however in the final expression of F(ω) after convolution operation, only positive frequency components are retained since they have distinct physical meanings, while negative components are neglected. From the expressions of FL and FR in Eq. (5), sidebands are distributed on the two sides of the WDAF ω0 (ω0-β and ω0 + β). The sideband interval between the two sidebands is two times of the SSF β, while the central frequency is the WDAF.3. Single sensor verification
In order to verify the conclusions we have drawn in the theoretical analysis, we firstly conduct experiments using a single sensor head. The schematic diagram of the setup is demonstrated in Fig. 1. The FPI sensor is fabricated by inserting a lead-in fiber into a flange plate, and a piece of aluminum foil is fixed on the aperture of the flange plate by epoxy resin. The wavelength scanning of the sensor is realized by a conventional optical spectrum analyzer (OSA, Yokogawa AQ6370c). The results are plotted in Figs. 2(a) and 2(b).
Fig. 2 (a) WSOS of the sensor under exposure to 50 Hz acoustic wave; (b) Spatial frequency spectrum of the WSOS.
Figure 2(a) shows the WSOS recorded by the OSA when the FPI sensor is exposed to acoustic wave of 50 Hz frequency. It should be noted that the spectrum data are firstly deduced from logarithmic scale to linear scale to obtain accurate Fourier transform result. Ripple waveform can be observed on the spectrum curve, and this is the manifestation that the acoustic signal is loaded on the sensor spectrum. The spatial frequency spectrum of the WSOS is acquired by taking the FFT algorithm, and the result can be seen in Fig. 2(b). As indicated in the figure, the peak in the low frequency (0.1998 nm−1) is the SSF which is determined by the free spectral range (FSR) of the interference pattern (the cavity length). Two obvious sideband peaks can be observed in the higher frequencies (f1 = 2.398 nm−1, f2 = 2.797 nm−1). In the test result, the frequency interval of the two sidebands is exactly two times of SSF. From the theoretical analysis in Section 2, the spatial frequencies of the two sidebands are ω0-β and ω0 + β respectively, while the SSF is β. Therefore the experimental result in Fig. 2 agrees well with the prediction of our theory. Although in the analysis of Eq. (5) the spatial frequencies are all in angular form (rad/nm), the conclusion is still suitable for spatial frequencies (nm−1) in the test result since spatial frequency has a constant multiple relationship of 2π with angular frequency. The 2nd and 3rd harmonics can be also observed, but the powers are more than 20 dB lower than the fundamental frequency component.
We then test the response of the spatial frequency spectrum of the WSOS to acoustic signals with different frequencies. In this test, the wavelength sampling interval, sweep speed, and sensitivity of the OSA are set fixed to be 0.01 nm, 2x speed, and middle sensitivity to guarantee a constant wavelength scanning speed. Test results are demonstrated in Figs. 3 and 4. Obvious frequency shift of the sidebands can be observed in Fig. 3(a) with the increasing acoustic frequency. Figure 3(b) shows that left sideband frequency, right sideband frequency, and their central frequency are all in linear relationship with the acoustic frequency with the same slope value of 0.052 s/nm. The central frequency means the middle value of left and right sideband frequencies and can be obtained easily from the relationship of ωC = 0.5(ωL + ωR), and it is exactly the WDAF. According to Eq. (1), the wavelength scanning speed can be computed to be 19.23 nm/s. Figure 4 demonstrates the SSF and the sideband interval in the test. The two values remain unchanged since the cavity length is fixed in this test, and the sideband interval keeps the two-time relationship with the SSF.
Fig. 3 (a) FFT spectra of the WSOSs when acoustic wave with different frequency is applied; (b) Relationship between the acoustic frequency and spatial frequency.
To further prove our analysis, we conduct another test, in which the acoustic frequency is fixed at 100 Hz, while the scanning speed is set to be different. It can be seen from Eq. (1) that the central frequency ω0 is determined by both the acoustic frequency ωa and wavelength scanning speed V. Once the acoustic frequency is fixed at a constant value, central frequency of the sidebands will be inversely proportional to the wavelength scanning speed. In our test, we keep the wavelength sampling interval and sensitivity of the OSA unchanged, while the sweep speed is switched from 2x speed to 1x speed, which can be adjusted through the OSA panel. The Fourier spectra of the WSOSs under the two scanning conditions are plotted in the following Fig. 5. We can see that the sideband components shift to higher spatial frequency when the scanning speed slows down. The central frequencies under 1x speed and 2x speed are 10.392 nm−1 and 5.196 nm−1, respectively. Combining the results from Figs. 3 to 5, we have experimentally proved the conclusions we have drawn in theoretical analysis that the central frequency of the sideband is proportional to the acoustic frequency and inversely proportional to the wavelength scanning speed, while the sideband interval is two times of the sensor spatial frequency which is determined by the FP cavity length.
Fig. 5 FFT spectra of the WSOSs with different scanning speed while the same 100 Hz acoustic signal is applied.
The following simple experiment demonstrates the evolution of the Fourier spectra under 200 Hz acoustic wave with sound pressure ranging from 71.7 dB to 86.1 dB (re 20 μPa). The Fourier spectra of the WSOSs of the sensor recorded by the OSA are plotted in Fig. 6(a). The peak powers of the both sidebands are becoming higher with the increasing of the sound pressure. The transition of the sideband powers is more clearly revealed by the inset of Fig. 6(a), while the relationship between sound pressure and the powers of the two sidebands and the SSF component is shown in Fig. 6(b). The powers of both sidebands are linearly increasing with sound pressure by nearly the same sensitivities approximate to 1 (0.97 and 0.98), and both have very high R2 value (goodness of fit), respectively are 0.997 and 0.998, as given by the linear fitting. Meanwhile, the SSF component power stays almost unchanged. The result indicates that the sideband intensities variation is equal to that of the sound pressure (in logarithmic scale). Hence the sideband intensities can be utilized to calibrate the sound pressure received by the FP sensor.
Fig. 6 (a) FFT spectra of the WSOS under 200 Hz signal with different sound pressure; (b) Relationship between sound pressure with the intensities of spatial frequency component and sideband components.
4. Two parallel sensors demonstration
Based on previous analysis, the phase modulation loaded on the WSOS will lead to sideband components in the Fourier domain, and the sideband interval is related to the sensor spatial frequency. Therefore it is reasonable to think that the Fourier characteristics of the WSOS can be applied to multiple sensors with different cavity length. In order to verify this idea, we take an experiment using two parallel sensors with the assist of a symmetric 2 × 2 fiber coupler. The experimental setup is demonstrated by Fig. 7. The two sensors have the same configuration as shown in Fig. 1, while the cavity lengths are different so that they have unique spatial frequencies, which are helpful to recognize sideband components of different sensors.
The experimental results are given in Fig. 8. The optical spectra of the two sensors without acoustic wave applied are respectively plotted in Fig. 8(a), in which we can see obvious FSR difference caused by distinct cavity length. The composite spectrum of the two parallel sensors is demonstrated by Fig. 8(b).
Fig. 8 (a) Optical spectra of the two individual sensors with different cavity length. (b) Composite spectrum of the two sensors. (c) FFT spectrum when 50 Hz signal is applied to both sensors. (d) FFT vectors at spatial frequencies corresponding to the 2 sensors. (e)FFT vectors of the sideband components. (f) Phase map for sideband 1 recognition. (g) Phase map for sideband 2 recognition.
Later, we expose both sensors to 50Hz acoustic wave, as shown in Fig. 7. The distances from the two sensors to the loudspeaker are not intentionally controlled. The Fourier spectrum of the composite WSOS recorded by the OSA is obtained in Fig. 8(c), and the composite WSOS is shown in the inset. It is obvious that recognizing the signals received by the two sensors directly from the WSOS can be hardly realized, but the Fourier spectrum makes it possible. In lower frequency range, two SSFs (0.12092 nm−1 and 0.3023 nm−1) can be observed, corresponding to the two sensors (shorter cavity sensor 1 and longer cavity sensor 2). When our sight moves to higher spatial frequencies, there are four obvious peaks, which are two groups of sideband components corresponding to the acoustic signals received by the two sensors. However, there will be uncertainty if we try to recognize sideband groups only through spatial frequency characteristics. For example, in Fig. 8(c), sideband 1 (sb1) is a left sideband of a certain sensor, and sb2, sb3 and sb4 are all possible to be the right sideband of sb1, which causes confusion. Therefore, we need extra information in the sideband recognition process. Analysis shows that the phase information of the sideband is related to the phase of the corresponding sensor. The detailed explanation is given below.
From Eq. (5), the Fourier phase at the sensor spatial frequency φS, left sideband θL, and right sideband θR are related to the symbol of different order of Bessel function of C (determined by the sensor sensitivity and the sound pressure). In order to explain this, we give an example here when J0(C) and J1(C) are both positive. Under this circumstance, the vectors of sensor spatial frequency VS, left sideband VL, and right sideband VR can be expressed by the following Eq. (6) according to Eq. (5).
According to the real and imaginary items of the Fourier vectors in Eq. (6), the corresponding phases of these vectors are derived in Eq. (7).From the derived results in Eq. (7), phase conditions when J0(C) and J1(C) are both positive can be easily listed out, as demonstrated by the first row of Table 1. Phase conditions in other circumstances are also listed in Table 1 in the same way.
Table 1. Phase Condition Related to the Symbol of Bessel Function of C
From Table 1, it can be summarized that in all conditions, the Fourier phase of the SSF vector and corresponding sideband vectors should match the relationship shown by Eq. (8) below.
The sine and cosine values of these angles can be easily obtained from the Fourier vectors (real and imaginary) at the corresponding spatial frequencies according to the Euler’s formula and the process is exampled by Eq. (7). As shown in Figs. 8(d) and 8(e), the Fourier vectors of the two SSF components and four sidebands are demonstrated respectively. The conclusion of phase characteristic drawn from Table 1 and Eq. (8) can contribute to sideband group recognition together with the spatial frequency characteristic to enhance the confidence of the result. Take sb1 for example, the Fourier phase differences with sb2 (θ2-θ1), sb3 (θ3-θ1) and sb4 (θ4-θ1) are presented in the phase map shown by Fig. 8(f). Meanwhile, 2φ1 + π and 2φ2 + π are also demonstrated on the phase circle (φ1 and φ2 are the Fourier phase of the SSF of sensor 1 and sensor 2). It can be seen in the figure that θ4-θ1 and 2φ2 + π are very close to the conclusion of Eq. (8), while other results on the phase circle are far away from that relationship. The recognition result for sb1 through phase characteristic indicates that sb1 and sb4 are of the same sideband group, and they are corresponding to sensor 2. In other words, sb1 and sb4 are the left and right sidebands of sensor 2 exposed to a certain acoustic signal. Therefore, the sb2 and sb3 are sidebands of sensor 1. If we survey these sideband components further from spatial frequency, it can be found that the frequencies of sb1 to sb4 are 2.29746 nm−1, 2.47884 nm−1, 2.72068 nm−1, and 2.90206 nm−1. Obviously, the frequency interval between sb4 and sb1 is twice of SSF2 (0.3023 nm−1), while the interval from sb2 to sb3 is two times as that of SSF1 (0.12092 nm−1). Therefore recognition results from phase characteristic demonstrated by Eq. (8) can be further enhanced by the spatial frequency characteristic shown by Eq. (5). Under this conclusion, it can be seen that the central frequency of sb1 and sb4 is equal to that of sb2 and sb3 (2.59976 nm−1), indicating that the two sensors receive acoustic signals of the same frequency (computed to be 49.99 Hz using the wavelength scanning speed of 19.23 nm/s obtained in Fig. 2. The result agrees with the experimental condition shown in Fig. 7. In addition, from Table 1, the phase difference of the acoustic signals received by different sensors can be also computed through the phase characteristic, which has potential in source localization or distance measurement [22], and so forth.
5. Summary
To summarize, we investigate the Fourier characteristics of the wavelength-scanned optical spectrum of low-finesse FP acoustic sensor, including spatial frequency characteristics and phase characteristics. Wavelength scanning will introduce sound induced phase modulation to the interference spectrum (carrier signal), leading to sideband components in the Fourier domain. The sideband frequency interval is two times of the sensor spatial frequency, while the central frequency is determined by both acoustic frequency and wavelength scanning speed. Fourier phase of the sidebands are also related to the phase at the SSF and acoustic signal. Utilizing the Fourier characteristics, the acoustic frequency and pressure can be obtained from the WSOS, and signals received by multiple sensors can be recognized and distinguished, which has great potential in acoustic sensor array or source localization, etc.
Funding
National Natural Science Foundation of China (No. 61775070, 61275083, 61505239); Fundamental Research Funds for the Central Universities, HUST: No. 2017KFYXJJ032, 2017KFXKJC002
References
1. Z. Gong, K. Chen, X. Zhou, Y. Yang, Z. Zhao, H. Zou, and Q. Yu, “High-sensitivity Fabry-Perot interferometric acoustic sensor for low-frequency acoustic pressure detections,” J. Lightwave Technol. 35(24), 5276–5279 (2017). [CrossRef]
2. W. Jo, O. Kilic, and J. F. Michel, “Highly sensitive phase-front-modulation fiber acoustic sensor,” J. Lightwave Technol. 33(20), 4377–4383 (2015). [CrossRef]
3. F. Xu, J. Shi, K. Gong, H. Li, R. Hui, and B. Yu, “Fiber-optic acoustic pressure sensor based on large-area nanolayer silver diaghragm,” Opt. Lett. 39(10), 2838–2840 (2014). [CrossRef] [PubMed]
4. X. Mao, S. Yuan, P. Zheng, and X. Wang, “Stabilized Fiber-Optic Fabry–Perot Acoustic Sensor Based on Improved Wavelength Tuning Technique,” J. Lightwave Technol. 35(11), 2311–2314 (2017). [CrossRef]
5. J. Ma, H. Xuan, H. Ho, W. Jin, Y. Yang, and S. Fan, “Fiber-optic Fabry–Pérot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013). [CrossRef]
6. C. Jan, W. Jo, M. Digonnet, and O. Solgaard, “Photonic-crystal-based fiber hydrophone with sub-100 μPa/√Hz pressure resolution,” IEEE Photonics Technol. Lett. 28(2), 123–126 (2016). [CrossRef]
7. F. Wang, Z. Shao, J. Xie, Z. Hu, H. Luo, and Y. Hu, “Extrinsic Fabry–Pérot underwater acoustic sensor based on micromachined center-embossed diaphragm,” J. Lightwave Technol. 32(23), 4026–4034 (2014).
8. J. Xia, S. Xiong, F. Wang, and H. Luo, “Wavelength-switched phase interrogator for extrinsic Fabry-Perot interferometric sensors,” Opt. Lett. 41(13), 3082–3085 (2016). [CrossRef] [PubMed]
9. H. Liao, P. Lu, L. Liu, S. Wang, W. Ni, X. Fu, D. Liu, and J. Zhang, “Phase demodulation of short-cavity Fabry–Perot interferometric acoustic sensors with two wavelengths,” IEEE Photonics J. 9(2), 1–9 (2017). [CrossRef]
10. C. Ma and A. Wang, “Signal processing of white-light interferometric low-finesse fiber-optic Fabry-Perot sensors,” Appl. Opt. 52(2), 127–138 (2013). [CrossRef] [PubMed]
11. Z. Yu and A. Wang, “Fast white light interferometry demodulation algorithm for low-finesse Fabry–Pérot sensors,” IEEE Photonics Technol. Lett. 27(8), 817–820 (2015). [CrossRef]
12. 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] [PubMed]
13. Y. Jiang, “Fourier‐transform phase comparator for the measurement of extrinsic Fabry-Perot interferometric sensors,” Microw. Opt. Technol. Lett. 50(10), 2621–2625 (2008). [CrossRef]
14. D. Tosi, “Simultaneous detection of multiple fiber-optic Fabry–Perot interferometry sensors with cepstrum-division multiplexing,” J. Lightwave Technol. 34(15), 3622–3627 (2016). [CrossRef]
15. Z. Yu and A. Wang, “Fast demodulation algorithm for multiplexed low-finesse Fabry-Pérot interferometers,” J. Lightwave Technol. 34(3), 1015–1019 (2016). [CrossRef]
16. Y. Jiang and C. Tang, “Fourier transform white-light interferometry based spatial frequency-division multiplexing of extrinsic Fabry-Pérot interferometric sensors,” Rev. Sci. Instrum. 79(10), 106105 (2008). [CrossRef] [PubMed]
17. J. Xie, F. Wang, Y. Pan, Z. Hu, and Y. Hu, “Optical fiber acoustic sensing multiplexing system based on TDM/SFDM,” Chin. Opt. Lett. 13(1), 010401 (2015). [CrossRef]
18. X. Fu, P. Lu, W. Ni, H. Liao, S. Wang, D. Liu, and J. Zhang, “Spectrum interrogation of fiber acoustic sensor based on self-fitting and differential method,” Opt. Express 25(4), 4429–4437 (2017). [CrossRef] [PubMed]
19. X. Fu, P. Lu, W. Ni, H. Liao, X. Jiang, D. Liu, and J. Zhang, “Phase interrogation of diaphragm-based optical fiber acoustic sensor assisted by wavelength-scanned spectral coding,” IEEE Photonics J. 10(3), 1–11 (2018).
20. S. Hu, B. Dong, K. Yu, J. Zhou, and L. Wang, “A hydrophone based on high-birefringence fiber loop mirror,” 5th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Smart Structures and Materials in Manufacturing and Testing (International Society for Optics and Photonics, 2010), paper 76590W. [CrossRef]
21. A. Dandridge, A. Tveten, and T. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE J. Quantum Electron. 18(10), 1647–1653 (1982). [CrossRef]
22. A. Sun, Z. Wu, D. Fang, J. Zhang, and W. Wang, “Multimode interference-based fiber-optic ultrasonic sensor for non-contact displacement measurement,” IEEE Sens. J. 16(14), 5632–5635 (2016). [CrossRef]
