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In this article, we propose an interrogation method of fiber acoustic sensor to recover the time-domain signal from the sensor spectrum. The optical spectrum of the sensor will show a ripple waveform when responding to acoustic signal due to the scanning process in a certain wavelength range. The reason behind this phenomenon is the dynamic variation of the sensor spectrum while the intensity of different wavelength is acquired at different time in a scanning period. The frequency components can be extracted from the ripple spectrum assisted by the wavelength scanning speed. The signal is able to be recovered by differential between the ripple spectrum and its self-fitted curve. The differential process can eliminate the interference caused by environmental perturbations such as temperature or refractive index (RI), etc. The proposed method is appropriate for fiber acoustic sensors based on gratings or interferometers. A long period grating (LPG) is adopted as an acoustic sensor head to prove the feasibility of the interrogation method in experiment. The ability to compensate the environmental fluctuations is also demonstrated.
© 2017 Optical Society of America
1. Introduction
Acoustic sensing is of great significance in many applications such as medical diagnosis, earthquake monitoring, oil pipeline leakage detection and sonar systems, etc. Traditional method for acoustic sensing is based on electrical and mechanical technologies such as MEMS, electromagnetic induction and PZT. Compared with these methods, fiber sensing technology is exhibiting a great deal of advantages such as small size, light weight, high sensitivity and resistance to electro-magnetic interference (EMI), etc. The most common types of fiber acoustic sensor are fiber gratings and fiber interferometers, including long period grating (LPG) [1], fiber Bragg grating (FBG) [2–5], phase-shifted fiber Bragg grating (PS-FBG) [6,7], Mach-Zehnder interferometers (MZI) [8,9], Michelson interferometers (MI) [10], Sagnac interferometers (SI) [11], and Fabry-Perot interferometers (FPI) [12–19].
A key point in the fiber acoustic sensing is the signal recover technique. For a majority of fiber acoustic sensors, the sensing mechanism is based on optical spectrum modulation, such as resonant peak intensity change, wavelength shift or phase variation. Therefore, interrogation methods such as edge filtering [20] and phase demodulation techniques [21–24] have been widely used. These methods are effective in recovering the time-domain signal but some strict requirements are also put forward. In edge filtering technique, the laser wavelength should be controlled at the quadrature point (Q point) of the spectrum hypotenuse [14]. As for phase interrogation, extra phase modulator or frequency shifter is usually indispensable [21]. Another vital problem is that the environmental factors such as temperature or pressure may also have impact on the sensor head, leading to a cross-effect or signal distorsion.
In our work, a spectrum interrogation method for fiber acoustic sensor is proposed. Owing to the dynamic spectrum variation in accordance with the acoustic signal, a ripple waveform will appear since the intensity of different wavelength is monitored at different time in the scanning process. The frequency components of the acoustic signal can be analyzed from the ripple spectrum through the wavelength scanning speed. By taking the differential between the ripple waveform and its self-fitted curve, the time domain signal can be obtained. The illumination for this spectrum demodulation method is broadband source (BBS), so the complicated Q point tracking and stabilization [14] is not needed. If environmental factors change, the self-fitted curve experiences the same variation with the ripple spectrum, thus the differential process can eliminate the surrounding factors interference. Experiments are conducted by employing a LPG as the sensor head to prove our scheme.
2. Theoretical analysis and simulation
For a certain fiber acoustic sensor, we can assume the initial optical spectrum at static condition to be S0(λ). When acoustic wave is applied on the sensor, the spectrum will be varying with time in synchronize with the acoustic signal. In other words, the spectrum under acoustic wave is the function of both wavelength and time. This can be expressed by Eq. (1). Since the optical spectrum is acquired by scanning in a certain wavelength range to monitor the optical intensity at different wavelengths, the time can be expressed by the wavelength and scanning speed, as demonstrated in Eq. (2). In the equations, λ is the wavelength, λ1 is the start wavelength of the scanning range, △S(λ) is the spectrum variation function, and V(nm/s) is the scanning speed.
For fiber acoustic sensors with favorable performance, the spectrum variation (wavelength or intensity) should have a linear relationship with the acoustic pressure. Thus, the time can be separated from the spectrum variation function △S(λ). Assuming that a pure tone signal is applied on the sensor head and the optical spectrum is varying in a sinusoidal form, the spectrum function can be written as Eq. (3). It can be learned from Eq. (3) that a periodic waveform will appear on the spectrum after a round of wavelength scanning, and the period of this ripple curve is determined by both the acoustic frequency and the scanning speed. By taking the differential between the ripple spectrum S(λ,t) with the initial spectrum curve S0(λ), and transforming the result from wavelength domain to time domain by Eq. (2), the ripple wave can be extracted as shown in Eq. (4). The recovered time-domain signal may be modulated by an envelope since the intensity variation caused by spectrum fluctuation has different values at different wavelength. This can be removed by a division with the spectrum variation function △S(λ).
There are two methods to determine the initial spectrum curve S0(λ). One is to record the data of the spectrum under static condition for the reference. But this method is easily affected by surrounding factors such as temperature and RI. When the environmental parameters change, the interrogated result will suffer from signal fading or even distorsion. Another technique is to fit the ripple spectrum with a proper function. Since the reference curve S0(λ) is fitted from the ripple spectrum itself, they will have the same response to the environmental perturbations. After differential process, the perturbations can be eliminated to a great extent.
As for the envelope function △S(λ), it can be determined by fitting the upper edge curve S1(λ) and the lower edge curve S2(λ) with the same type function. It is derived from the substraction between these two curves, as expressed in Eq. (5). The schematic diagram of the ripple mechanism is shown in Fig. 1. When the sensor is exposed to acoustic wave, the spectrum varies between S1(λ) and S2(λ). Therefore the intensities of different wavelength locate on different spectrum due to the time-dependent scanning process, as indicated by the red points in Fig. 1. Hence, the ripple curve is produced.
In our work, we employ a LPG as the acoustic sensing element to verify the proposed interrogation method. The LPG is glued on a polyethylene terephthalate (PET) film and kept straight, as shown in Fig. 2. The acoustic wave will generate the vibration of the film and thus introducing a dynamic curvature modulation to the LPG [25].
A simulation is conducted to investigate the spectrum response to acoustic vibration. Previous research has explained that when the LPG is bent, the intensity of the resonant dip is modulated while the wavelength stays almost unchanged [26]. Since the PET film causes dynamic curvature modulation to the LPG when exposed to acoustic wave, we can assume the alternating current (AC) coupling coefficient η to be a time-varying parameter, which mainly changes the resonant dip intensity. When a sinusoidal acoustic signal is applied on the sensor, the spectrum function of the LPG can be written as Eq. (6) and (7).
In the simulation, the parameters are set to these values: the length and grating pitch of the LPG are 7cm and 500μm. The AC coupling coefficient η0 and its acoustic induced change △η are 2 × 10−8 and 5 × 10−10. The start wavelength of the scanning process and the LPG resonant wavelength are 1545nm and 1550nm. The wavelength scanning speed and the acoustic frequency are 50nm/s and 200Hz. The simulated spectrum is exhibited in Fig. 3. The inset of Fig. 3 is the recovered time-domain signal by differential between the ripple curve and the initial spectrum. An obvious envelope can be observed in the recovered signal, which is brought by the different value of the spectrum variation function △S(λ) at different wavelengths. According to the analysis in the previous discussions, the envelope can be eliminated by a division method as Eq. (4). The edge curves and the signal after envelope elimination are demonstrated in Figs. 4(a) and 4(b). After the division method, the envelope is almost removed, indicating the feasibility of the proposed scheme.
Fig. 4 (a) Edge curves of the ripple spectrum and (b) Recovered time-domain signal before and after envelope elimination in the simulation.
3. Experimental results and discussion
In the experiment, the scanning speed of the optical spectrum analyzer (OSA, Yokogawa AQ6370c) is set to be double speed, about 128nm/s. When a 200Hz sinusoidal acoustic signal is applied on the LPG sensor head shown in Fig. 2, the spectrum data is recorded by the OSA and plotted in Fig. 5(a). As expected, a ripple waveform can be observed. The LPG's resonant dip is approximately fitted by the Lorentz fitting. By taking a differential with the Lorentz fitting curve and transform the result from wavelength to time through the scanning speed, the interrogated time-domain signal is plotted as the black curve in Fig. 5(b). As predicted in the analysis and simulations, the differential result is modulated by an envelope which causes nonuniformity of the signal amplitude when exposed to the same acoustic signal. The envelope is promising to be removed by division with the substraction of the two edge curves (upper edge and lower edge). In this work, we adopted an extremum fitting method to obtain the edge curves. Specifically, the upper edge and lower edge curves can be fitted from maximum values and minimum values respectively. In order to search the extremum points from the spectrum data, a peak search function is proposed. All the maximum values should satisfy Eq. (8) while minimum values meet Eq. (9). The search result of the maximum and minimum values are plotted in Fig. 5(c). The two edge curves fitted from the maximum values and minimum values are plotted in Fig. 5(a), demonstrated as the red and blue curves respectively, together with the ripple spectrum plotted as the black curve. The acoustic induced spectrum variation tendency can be inferred from the two edge curves. The spectrum variation at longer wavelength side of the resonant dip is very weak so that may cause a fuzzy result of the interrogation. Therefore, the shorter wavelength side is selected to recover the acoustic signal. Based on the two fitted edge curves, the envelope of the recovered signal can be removed, as shown by the red curve in Fig. 5(b). Compared with the signal before the division method, the envelope is eliminated to a large extent. The frequency spectrum is acquired by taking the Fast Fourier Transform (FFT), as plotted in Fig. 5(d). The signal to noise ratio (SNR) is 21.4dB, and the harmonic component is 18.5dB lower than the main frequency components at 200Hz. The results prove the effectiveness of our proposed spectrum interrogation method.
Fig. 5 (a) Fitted edge curves of the ripple spectrum. (b) Time-domain signals before and after envelope elimination. (c) Extremum values found by the peak search function. (d) FFT spectrum of the recovered signal.
The Eq. (3) in the theoretical analysis indicates that the ripple in the wavelength domain is dependent on both the scanning speed and the acoustic frequency. In order to seek a confirmation, another two experiments are conducted. Firstly, the scanning speed of the OSA is switched to ordinary speed (64nm/s) and double speed (128nm/s) respectively, and the same acoustic signal of 200Hz sinusoidal waveform is applied on the sensor. The spectra under different speed are recorded, as shown in Fig. 6(a). It is obvious that the wavelength spacing between the adjacent peaks in the ripple spectrum under double speed is twice as that of ordinary speed. From Eq. (3), when the acoustic frequency is kept as a constant, the frequency reflected on the spectrum in wavelength domain is inverse proportional to the scanning speed. When the scanning speed is faster, the time for scanning a certain wavelength range is shorter. So for a fixed acoustic frequency, the number of acoustic signal period recorded by the spectrum is less. The demodulated time-domain signals recovered by the proposed method based on the scanning speed are exhibited in Fig. 6(b), which show a consistent frequency.
Fig. 6 (a) Spectra and (b) Recovered signals of 200Hz acoustic wave under ordinary speed and double speed.
Another experiment is carried out by applying acoustic signals of different frequency (200Hz and 1000Hz sinusoidal signal) to the sensor head while the spectra is recorded under a fixed scanning speed (double speed). The spectra and recovered time-domain signals are plotted in Figs. 7(a) and 7(b), respectively. In the ripple spectra, the wavelength interval of 200Hz is five times as that of 1000Hz, clearly shown in the inset of Fig. 7(a). This is in consistent with the interrogated time-domain signal in Fig. 7(b), and matches well with Eq. (3).
For the recovered signal of 1000Hz, the signal-to-noise ratio (SNR) is 30dB at 1000Hz with acoustic pressure of 73.5dB, and the 3dB bandwidth is 24.5Hz. The minimum detectable pressure (MDP) is calculated to be 604.6μPa/Hz1/2. For the 200Hz signal, the MDP can be also calculated to be 3.05mPa/Hz1/2. The lower frequency signal suffers a higher noise level due to the 1/f noise, thus a higher MDP is reasonable.
As for the maximum acoustic pressure that can be detected by our experimental setup, it can be theoretically analyzed. As we have discussed, the curvature of the LPG is dynamically modulated by the diaphragm vibration, and the intensity of the LPG's resonant dip is also changed. In order to guarantee the sensor performance, the LPG should work in the linear region. Based on this premise, the maximum acoustic pressure can be theoretically analyzed by the elastic mechanics. An experiment is conducted to test the LPG's static response to curvature so as to confirm the dynamic range. The relationship between the resonant dip intensity with the curvature variation is plotted in the Fig. 8. The sensitivity is falling off slowly with the increasing curvature. According to the trend of the sensitivity curve, we set the maximum curvature to be 1.2m−1 in our experiment to maintain the linearity. The inset of Fig. 8 reveals the spectrum variation with the curvature. Little red shift of the resonant wavelength can be also observed except for the dominant intensity variation, which agrees with the previous experimental results that the ripple waveform is very weak in the longer wavelength side. The little wavelength shift results from the axial strain of the LPG produced by the curvature variation.
According to the elastic mechanics, the deformation of a thin diaphragm caused by the applied pressure is expressed as the Eq. (10). In the expression, r is the diaphragm radius and a is the distance from the center of the film. E and μ stands for the Young's modulus and Poisson's ratio of the diaphragm material, while h is the thickness. Obviously, the deformation at the center can be represented by the d0 in Eq. (11).
The relationship between the curvature and center deformation is exhibited in the inset of Fig. 8. According to the maximum curvature of 1.2m−1, the corresponding pressure can be calculated to be 1.27Pa. Thus the equivalent maximum acoustic pressure is 96.1dB with 20μPa as reference. It should be emphasized that the dynamic range (detectable maximum acoustic pressure and MDP) is also dependent on the sensor structure and diaphragm characteristics. For different sensor head or films, the dynamic range can also be analyzed by this method.
For the purpose of investigating the ability of environmental interferences elimination, we tested the sensor response with different environmental factors. Previous research has manifested that the LPG is easily affected by the surrounding RI and temperature [27,28]. These surrounding parameters fluctuation will cause a spectrum variation. Thus, in experiment, the surroundings are changed by dropping ethyl alcohol solution and hot water respectively on the grating region. The ethyl alcohol solution changes the surrounding RI of the sensor head, while the hot water (about 80°C) affects both the RI and temperature. When the sensor is exposed to the same acoustic signal under these environmental factors, the spectra recorded by the OSA are plotted in Fig. 9(a). An obvious variation of the spectrum in both wavelength and intensity can be observed. The interrogated signals using the proposed spectrum fitting and differential method are demonstrated in Fig. 9(b). The recovered signals show a uniformity and thus confirming the competence to remove environmental interferences.
4. Conclusion
In summary, an interrogation technique assisted by ripple spectrum self-fitting and differential method for fiber acoustic sensor is proposed. Theoretical analysis and experimental results indicate the effectiveness of the proposed method. The optical spectrum of the sensor will show a ripple waveform due to the wavelength scanning process. The fringes on the spectrum is determined by both the acoustic frequency and the wavelength scanning speed. The ripple spectrum can be fitted by a proper function. The time-domain signal is able to be recovered through differential between the ripple spectrum and its self-fitted curve and transforming the result from wavelength domain to time domain using the scanning speed. Since the interrogation method is based on the ripple spectrum differential with its self-fitted curve, the environmental perturbations such as temperature and RI can be eliminated to a great extent. Experiment is conducted by employing a LPG sensor to prove this ability. This method also benefits from the BBS illumination so that the complicated Q point tracking is left out. Owing to these advantages, the proposed method can be applied on low-frequency applications and hydrostatic insensitive hydrophones, etc.
Funding
National Natural Science Foundation of China (NSFC) under Grant 61275083 and Grant 61290315; Fundamental Research Funds for the Central Universities (HUST: No. 2014CG002).
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