Objective Fiber-optic acoustic sensors play an important role in various fields owing to their unique features such as miniature size, antielectromagnetic interference, wide frequency response, and good performance in harsh environments. Diaphragm-based extrinsic Fabry-Perot interferometric (EFPI) acoustic sensors have attracted considerable interest owing to their high sensitivity and reflective-type sensor structure. Quadrature-point (Q-point)-based intensity detection is one of the most widely used demodulation techniques for EFPI acoustic sensors. However, the dynamic range of sound pressure detected by intensity is limited. Signal distortion occurs when detecting strong acoustic signals. Besides, the Q-points of different sensors are susceptible to external environmental fluctuations, thereby eliminating the possibility of multiplexing and multipoint detection. Phase-generated carrier (PGC) demodulation methods typically require a piezoelectric transducer (PZT) to generate the phase carrier; hence, such systems are bulky. In addition, the mechanical characteristics of the PZT will result in a limited frequency response range. Frequency- or wavelength-modulated phase-shifting interferometry (PSI) is a promising alternative for high-speed phase retrieval. The target quadrature phase shift is introduced by the frequency-or wavelength-tuning of a tunable laser, thereby avoiding the nonlinear errors caused by the phase shifters such as PZTs. For EFPI sensors with different cavity lengths, the phase shift can be calculated separately to achieve simultaneous demodulation. This creates the possibility of multiplexing and multipoint detection. Two-dimensional (2D) sound source localization is one of the most typical applications of multipoint acoustic detection. Compared with fiber Bragg grating (FBG) acoustic sensor, which suffers from the problem of low sensitivity, the fiber-optic EFPI acoustic sensor is more suitable for sound source localization and has the advantages of a probe-type structure and high sensitivity imparted by the high-performance and flexible multipoint demodulation techniques.
Methods Frequency-modulated quasicontinuous phase-shift interferometry (FMQC-PSI) was employed to construct a phase-demodulation system. An all-semiconductor programmable modulated grating Y-branch (MG-Y) tunable laser was used as the phase shifter. This laser has a frequency sweep range of 191.316--196.328 THz with a flat intensity output. Fast and stable frequency tuning was performed using a field-programmable gate array (FPGA) to introduce phase shifts. Four optical frequencies with π/2 phase bias were sequentially switched to generate quasicontinuous quadrature phase-shifted signals. Based on a stable 5-step phase-shifting algorithm, any five adjacent intensity signals were used to recover the time-varying phase signal modulated by the applied sound pressure. Thus, a phase sampling rate of 600 kHz was achieved during continuous frequency modulation. EFPI acoustic sensors with a wide cavity length range can be effectively demodulated by adjusting the four operating frequencies. Because of the absence of mechanical moving parts, high-speed and stable phase demodulation was realized.
Results and Discussions The FMQC-PSI system demodulated an EFPI fiber-optic microphone with a cavity length of 279.502 μm based on a PET diaphragm. It correctly recovered the phase signal of the applied acoustic signal at different sound pressures at a frequency of 3 kHz (Fig.3). The demodulated phase signal had a good sinusoidal waveform, indicating the advantage of the system in detecting strong sound signals. At 3 kHz and 2.43 Pa, the signal-to-noise ratio (SNR) of the sensor output signal was calculated as 76.8 dB, with a background noise of 25.4 dB (Fig.4). The sensitivity of the sensor is 0.63 rad/Pa when the applied sound pressure amplitude varied between 0.75 Pa and 2.43 Pa, good linearity is observed in this range. The frequency response characteristic curve of the sensor in the frequency range of 1--10 kHz was obtained (Fig.5). Moreover, the system can correctly demodulate EFPI sensors with different cavity lengths and frequencies (Fig.6). In the 2D sound source localization experiment, a four-sensor sound source localization system was constructed. The hyperbolic positioning algorithm is used to estimate the sound source position. The time difference of arrival (TDOA) measured by the two pairs of sensors along the orthogonal axis is used to determine the two hyperbolas. When the point sound source was placed at the coordinates of (30 cm, -15 cm), the localization result of the sound source position was estimated as (30.01 cm, -15.82 cm), which is in good agreement with the actual position. Six repeated measurements at 25 different positions were performed to test its positioning accuracy. The positioning results at the same sound source position were found to be highly consistent, and the positioning errors of all measurements were not larger than 1.98 cm (Fig.9).
Conclusions In this study, a frequency-modulated quadrature phase-shifted demodulation technique was used to demodulate the phase of diaphragm EFPI optical fiber microphone, and its application for sound source localization was demonstrated. Quasicontinuous phase-shifted signals were generated by the sequential modulation of four laser frequencies with π/2 phase differences. The phase sampling rate depends on the frequency tuning rate of the laser up to 600 kHz. Owing to the wide frequency tuning range (191.316--196.328 THz), EFPI acoustic sensors with different cavity lengths (33.518--745.504 μm) can be demodulated by adjusting the specific values of the four laser frequencies. In addition, the simultaneous demodulation of multiple acoustic sensors can be easily achieved by space division multiplexing. We built a compact four-sensor FMQC-PSI system for 2D sound source localization. The experimental results demonstrated the effectiveness of this method.
