Flexible and stable demodulation techniques of large-scale fiber-optic Fabry–Perot (FP) acoustic sensors are highly desirable for accelerating their industrial applications. In this paper, we report a novel self-calibrating wavelength shifting interferometry (WSI) technique that enables simultaneous multi-point acoustic detection using diaphragm based fiber-optic FP acoustic sensors. A widely tunable modulated grating Y-branch (MG-Y) laser (1527∼1567 nm) performs high-speed wavelength switching, introducing phase-shifts in the wavelength domain for real-time phase retrieval. The proposed self-calibrating WSI is easily extended for multiplexing FP acoustic sensors by calibrating the corresponding phase-shift step of each sensor probe. Based on a modified Hariharan 5-step phase shifting algorithm, the phase-shift step for each channel can be calibrated in real-time, making the system robust in applications involving large environmental perturbations. An all-optical multi-point acoustic detection system based on WSI is proposed and experimentally demonstrated for the first time. Sound source localization experiments show that the multi-point acoustic detection system works stably and the positioning accuracy is about 2.42 cm.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Optical fiber acoustic sensors have been widely used in various fields, such as sound source localization , leakage detection [2,3], non-contact imaging , and photoacoustic spectroscopy , etc. Compared with conventional electrical acoustic sensors, they have the unique advantages of compact size, high sensitivity, anti-electromagnetic interference and remote sensing ability . With the advancement of fiber-optic acoustic sensors and high-performance demodulation techniques, all-optical acoustic sensors have the potential to replace traditional electrical acoustic sensors in various areas, especially in the field of medical imaging requiring miniature sensor probes , or acoustic emission (AE) monitoring in harsh environments . Diaphragm-based fiber-optic Fabry–Perot (FP) acoustic sensor is one of the most sensitive fiber-optic acoustic sensors reported to date . The diaphragm vibrates with applied acoustic signal, resulting in length changes of the FP cavity . Fiber-optic FP acoustic sensors have been applied in partial discharge detection , remote monitoring of gas micro-leakage  and non-contact ultrasonic detection in low-pressure carbon dioxide medium . However, most of these applications are single-point acoustic detection. Since the quadrature points (Q-points) of multiple FP acoustic sensors are difficult to maintain consistent due to background temperature or pressure fluctuations, the most widely used Q-point intensity demodulation scheme [13,14] is invalid for multi-point acoustic detection. Phase interrogation schemes such as dual-wavelength or three-wavelength quadrature phase demodulation methods [12,15,16] have the advantages of large dynamic range and high-resolution, but they are also schemes for single-point acoustic interrogation. In practical applications, it is difficult for different FP sensors to maintain quadrature phase conditions at the same time. Fiber-optic FP sensors can be multiplexed in parallel assisted by cepstrum-division multiplexing (CDM) [17,18]. In that case, each FP sensor needs to have a different cavity length and the reflection spectrum is a combination of all FP interferometer contributions, which results in limited multiplexing channels and complex sensor fabrications. In addition, due to the limited acquisition speed of the spectrometer and the complex demodulation algorithm, the CDM method can only be used for relatively low frequency acoustic measurements. In 2018, Wang, et al. proposed a time division multiplexing (TDM) assisted coherent phase detection scheme, which is an optional phase demodulation technique for multiplexing diaphragm-based optical fiber acoustic sensors . A 1*n coupler connects all the sensors in parallel with single mode fiber (SMF) delay line in different lengths for TDM. The optical sampling rate is about 60 kHz. However, the SMF delay line for each sensor probes is easily affected by irrelevant environmental vibrations, introducing phase demodulation errors. Flexible and high-resolution demodulation techniques for multiplexing fiber-optic FP acoustic sensors may greatly accelerate their industrial application, and, therefore, are highly desirable.
Phase-shifting interferometry (PSI) is a well-established high-precision, rapid and quantitative phase retrieval technique that has been widely used in surface profile testing, 3D shape measurement and live cell imaging [20–23]. It requires typically 3 to 8 phase-shifted frames for accurate digital phase demodulation, most commonly realized by a piezoelectric transducer (PZT). However, due to a series of problems such as hysteresis, nonlinearity and temperature drift, PZT may distort and cause phase shift errors. In addition, the mechanical phase shift frequency of PZT is limited, which hinders its application in high frequency acoustic sensing. Jiang et al. proposed a novel phase demodulation method for FP acoustic sensors based on phase shifting technique and birefringence crystals . Four birefringence crystals with different thickness were used to obtain quadrature phase-shifted signals. Sinusoidal sonic signals of 21 kHz and 40 kHz can be successfully monitored by a four-step phase-shifting algorithm (PSA). Another potential solution is wavelength shifting interferometry (WSI), which generates the phase-shift by wavelength change of the light source. For a fixed wavelength-shift and an FP sensor with known initial cavity length, the corresponding phase-shift value can be accurately calculated based on the theoretical model of two-beam interference. For another FP sensor with a different cavity length, the phase-shift value can also be calculated, enabling simultaneous demodulation of multiple FP sensors. It should be noted that the cavity lengths of the multiple FP sensors are not required to be completely different or consistent, so that the manufacturing difficulty and the cost can be greatly reduced, which is essential for industrial applications. To date, WSI techniques are mainly applied in surface profile and thickness measurements [25,26], as well as relatively low-frequency quantitative phase imaging . The development of fast-switching, high-quality tunable lasers makes WSI an attractive alternative of multiplexing fiber-optic FP acoustic sensors.
In this work, we propose a high-resolution cavity length demodulation technique for fiber-optic FP acoustic sensor array based on WSI. A monolithically integrated modulated grating Y-branch (MG-Y) laser was used for high-speed wavelength shifting. Cavity lengths of FP acoustic sensors can be simultaneously demodulated by a novel self-calibrating five-step PSA at a rate of 100 kHz. To the best of our knowledge, this is the first time to achieve multiplexing of fiber-optic FP acoustic sensors using WSI technique. Simultaneous acoustic detection of a four polyethylene terephthalate (PET) diaphragm based FP acoustic sensor array demonstrates its multiplexing performance. Moreover, we realize sound source location using the all-optical acoustic sensor array.
For WSI-based acoustic demodulation systems, the core component is the high-speed, stable and widely tunable light source. In this work, we utilize a MG-Y laser (ATLS 7500, AOC), a kind of vernier tuned distributed Bragg reflector (VT-DBR) laser, for high-speed wavelength switching to introduce phase shifts in the wavelength domain. It has high wavelength stability and repeatability due to precise electronic tuning without mechanical movement [15,28]. The output wavelength of the MG-Y laser is determined by the injection currents of the right reflector section, the left reflector section and the phase section, and the output intensities are adjusted by fine-tuning the injection current of the semiconductor optical amplifier (SOA) section . Herein, we realize high precision wavelength control in the range of 1527 ∼ 1567 nm utilizing a field-programmable gate array (FPGA), and adjust the output intensity at each wavelength to be consistent (10.5 dBm) . Considering that the output intensity at each wavelength has been adjusted in real time, there is no need to normalize the interference fringe or subtract the direct current (DC) term in WSI, which greatly reduces the complexity of demodulation and improves the robustness of the system.
In standard PSI, a sequence of N phase-shifting interferograms with constant phase shifts are required for phase retrieval. Usually a minimum of three phase-shifting interferograms are needed. To date, numerous PSAs have been proposed or extended [20,29], such as 3-step, 4-step, 5-step and least-square algorithm, etc. In general, more phase shift steps result in higher phase extraction accuracy and larger phase-shift error tolerance. However, it also comes with slower demodulation speed and increased complexity. In order to strike a balance between the demodulation speed and the phase retrieval accuracy, we used a modified 5-step Hariharan PSA  in this work, which is one of the most widely used PSAs with high phase retrieval accuracy. Further, the phase-shift step θ is calibrated in real time to enhance its robustness for applications in harsh environments.
2.1 Self-calibrating 5-step PSA for single-point demodulation
The WSI system for the interrogation of a single fiber-optic FP acoustic sensor is shown in Fig. 1. Figure 1(a) illustrates the schematic diagram. A MG-Y tunable laser is used as the light source. Synchronized wavelength switching and data acquisition are implemented by an FPGA. The inset shows the diagram of the FP acoustic sensor. Polyethylene terephthalate (PET) diaphragms with thickness of 6 µm are used to fabricate the FP acoustic sensors. A low-finesse FP cavity is formed between the cleaved end face of the fiber and the inner surface of the PET diaphragm. We used capillaries to support and align the fiber. The capillary used for PET diaphragm attachment has an inner diameter of 3.4 mm. As shown in Fig. 1(b), the five operating wavelengths are sequentially switched. The intensities corresponding to each wavelengths are uploaded to a computer for real-time phase retrieval. Figure 1(c) presents the flow chart of the demodulation process, the principles and details will be described below.
The FP acoustic sensor used here can be regarded as a low-finesse two-beam interferometer. Intensity of the reflected interferential light at a specific wavelength λ can be expressed as
For convenience, we set λ3 at the center wavelength of the tunable range, 1547 nm, the five operating wavelengths for WSI can be determined based on θ and L0. Herein, for single-point demodulation, the preset phase-shift step θ is determined as π/2 radians to achieve the best sensitivity and make it insensitive to phase-shift errors . Equation (4) can be converted to32]. Based on Eqs. (1)–(3), the intensities at the five operating wavelengths can be expressed as
2.2 Simultaneous demodulation of fiber-optic FP acoustic sensor array
If we know the phase-shift step corresponding to each sensing channel, the 5-step WSI technique using a single MG-Y laser can be easily extended for multiplexing fiber-optic FP acoustic sensors. Fortunately, the phase-shift step can be calculated by Eq. (3) for a known cavity length and a fixed wavelength-shift. The schematic of the WSI-based multiplexing system is illustrated in Fig. 2. A 1*N coupler is used to achieve spatial-division-multiplexing (SDM) of multiple sensors. The signals reflected from each sensor are detected by multiple PDs and then uploaded to a computer for data processing. Herein, we use the average cavity length Lavg for the determination of the five operating wavelengths. Equation (5) for generating π/2 phase-shift can be converted to
Figure 3 exhibits the flowchart of the self-calibrating 5-step WSI for simultaneous demodulation of an N-channel sensor array. As the single-sensor demodulation process, full-spectrum scanning is required to obtain the initial cavity length of each sensor at the beginning. Next, five operating wavelengths are determined based on Lavg. Phase-shift step of each channel is calculated based on the corresponding initial cavity length and is calibrated in real-time based on the LDC. The proposed WSI technique can realize simultaneous cavity length demodulation of large-scale fiber-optic acoustic sensor array with high precision and large dynamic range.
3. Experimental results and discussion
We established a four-channel acoustic sensing system to demonstrate the validity and performance of the proposed WSI demodulation scheme. Four sensor probes are put in an anechoic test box for simultaneous acoustic sensing. A speaker connected to the signal generator is used to generate acoustic signals of different frequencies. Linear wavelength scanning from 1567 nm to 1527 nm at an interval of 8 pm was first performed to obtain the initial cavity length of each channel. Figure 4 shows the interference spectrums of the four sensors. It can be seen that the fringe visibility and DC component of the interference spectrums are different owing to the influences of different insertion loss of couplers, different gains and responsivities of the PDs and different sensor cavity lengths, etc. Since the PD used in channel-3 (Thorlabs, USA) is inconsistent with the PDs (Keyang Photonics, China) used in the other three channels, the amplitudes of Channel-3 is quite different from the other three channels. It will not influence the effectiveness of the proposed WSI demodulation methods. Based on a white light interference absolute cavity length demodulation method [32,33], the initial cavity lengths of the four sensors are calculated as 152.845 µm, 147.205 µm, 126.481 µm and 136.766 µm, respectively. The average cavity length is 140.824 µm. In order to introduce five-step π/2 phase-shifts corresponding to the average cavity length, the five operating wavelengths are determined as 1551.256 nm, 1549.128 nm, 1547.000 nm, 1544.872 nm and 1542.744 nm. Corresponding actual initial phase-shift steps for the four channels are calculated as 0.542π, 0.523π, 0.449π and 0.485π (97.7°, 94.1°, 80.8°, and 87.4°). The phase-shift steps are all in the range of [π/3, 2π/3], ensuring the demodulation accuracy.
Subsequently, five operating wavelengths are sequentially switched. Corresponding light intensities at different wavelengths are detected and then separated in the time domain for cavity length demodulation. All the four channels are demodulated simultaneously. In particular, demodulation results of Sensor-1 are extracted to demonstrate the system performance. Figure 5 displays the time domain responses and demodulation results of Sensor-1. When no acoustic signal is applied, the intensity waveforms corresponding to λ1 ∼ λ5 are shown in Fig. 5(a). Cavity length variations are then calculated based on the self-calibrating 5-step PSA. The standard deviation of demodulated cavity length variations is about 0.3 nm, demonstrating the stability of demodulation results. Figures 5(b) and 5(c) display the original intensity waveforms and demodulated cavity length variations at 4 kHz, 1.0 Pa acoustic signals. Corresponding power spectrum is presented in Fig. 5(d) with a signal to noise ratio (SNR) of about 70.2 dB. It can be found that the demodulation result is consistent with the applied acoustic signal. The minimum detectable pressure (MDP) is calculated to be 68.9 µPa/Hz1/2.
Then the FP acoustic sensors were used to detect 8 kHz and 12 kHz acoustic signals. The corresponding time domain cavity length variations and power spectrums are shown in Figs. 6(a) and 6(b). Experimental results prove its ability to demodulate acoustic signals of different frequencies. Figure 6(c) plots the frequency response of Sensor-1. Limited by the performance of the loud speaker, the tested frequency range is 1 kHz to 16 kHz. Theoretically, considering the demodulation frequency of 100 kHz and the Nyquist sampling theorem, the maximum frequency that can be demodulated is approximately 50 kHz.
Taking advantages of the cavity length demodulation scheme, a large dynamic range of acoustic pressure can be detected. Figure 7(a) shows the acoustic pressure response of the Sensor-1 at 4 kHz. Larger acoustic pressure results in a larger cavity length amplitude. The relationships between the amplitude of cavity length variations and the applied acoustic pressure have been fitted and plotted in Fig. 7(b). The applied sound pressure varies between 0 Pa and 2.86 Pa by adjusting the output voltage of the signal generator. It can be found that the responses of all the four channels have a good linearity (R2 ≥ 0.999 for all channels) and similar sensitivity. The sensitivity of Sensor-1 is calculated to be 102.8 nm/Pa, and the sensitivity of the other three sensors is calculated as 134.4 nm/Pa, 108.7 nm/Pa and 122.9 nm/Pa, respectively. The minor differences in sensitivity may be due to differences in the adhesion of diaphragms , the position or orientation of the sensor, and so on.
Sound source localization is a typical application for multipoint acoustic sensing. All-optical acoustic sensor array exhibits significant superiority for sound source localization in harsh environments, and has attracted much research interests in recent years [1,34]. Fiber-optic FP acoustic sensors are suitable for sound source localization for their probe-type structure and high sensitivity. We used the WSI-based four channel acoustic demodulation system to realize two-dimensional (2D) sound source localization. As shown in Fig. 8, the four fiber-optic sensor probes are placed at four points on the XY coordinate axis. Each sensor is 45 cm away from the origin point O. Coordinates of the four sensors are Sensor-1 (45, 0), Sensor-2 (0, 45), Sensor-3 (−45, 0) and Sensor-4 (0, −45), respectively. A hyperbolic localization algorithm is utilized to locate the sound source . The time differences of arrival (TDOA) measured by two pairs of sensors along the orthogonal axes are used to determine two hyperbolic curves. For Sensor-1 and Sensor-3 on the horizontal axis, the sound source location (x, y) should satisfy:
Figure 9 plots the time-domain waveforms detected by the four-sensor array when the actual sound source position is (30, 15). Herein, three times the noise value is set as the threshold, and the arrival time is determined when the first peak or valley occurs. The TDOA between Sensor-1 and Sensor-3 was calculated as 1.66 ms, and that for Sensor-2 and Sensor-4 was 0.68 ms. The estimated coordinate of the sound source position is (30.42, 14.11), which is in good agreement with the actual position (30, 15).
Considering of the 100 kHz optical sampling frequency, the theoretical spatial resolution of the sound source localization is about 0.34 cm. In order to evaluate the positioning accuracy of the proposed sound source localization system, we conducted localization tests at 25 different positions. Localization results of 6 repeated measurements are shown in Fig. 10. The estimated sound source positions are marked as red crosses, and the actual sound source positions are presented as black circles. Positioning errors of all measurements are no larger than 2.42 cm, demonstrating its accuracy. The positioning results show that effective 2D sound source localizations can be realized based on the all-optical four-sensor system.
In this paper, we propose a WSI-based cavity length demodulation technique and demonstrate its application in multiplexing fiber-optic FP acoustic sensors. A widely tunable monolithic MG-Y laser is used for high-speed wavelength shifting, introducing known phase-shifts for large-scale acoustic sensor array. To maintain high sensitivity and good stability in all the sensing channels, the phase-shift steps are controlled in the range of [π/3, 2π/3], which corresponds to an acceptable cavity length difference of approximately ± 1/3 Lavg. It greatly reduces the difficulty of sensor fabrication and mass production. Based on a self-calibrating 5-step PSA, a 100 kHz cavity length sampling frequency is obtained. We experimentally demonstrated an all-optical four-sensor acoustic demodulation system based on this WSI technique, and used it for 2D sound source localization. Experimental results show that the positioning accuracy is about 2.42 cm. Considering its all-optical structure, compact size, high precision and good stability, this WSI-based multi-point acoustic detection system has great potentials in industrial applications.
National Natural Science Foundation of China (61520106013, 61727816); Fundamental Research Funds for the Central Universities (DUT18ZD215).
The authors declare no conflicts of interest.
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