Phase Demodulation of Short-Cavity Fabry–Perot Interferometric Acoustic Sensors With Two Wavelengths

A phase interrogation method for a fiber-optic acoustic sensor based on a short-cavity extrinsic Fabry-Perot interferometer (EFPI) is proposed with two wavelengths. A multichannel tunable optical filter is employed, which selects out two monochromatic beams from the broadband interference spectrum of EFPI with fixed wavelength interval. The influence of the wavelength interval on the recovery of the phase signal has been theoretically and experimentally analyzed. To get the best sensitivity, the wavelength interval is fixed at one quarter of the period of sensor interference fringes. An optimized differential cross multiplication algorithm is utilized to demodulate the acoustic signal, which can eliminate the impact of optical power imbalance between the two light paths. This system may be a universal phase demodulation unit for short-cavity EFPI acoustic sensors. The EFPI acoustic sensing head is formed by an aluminum-attached polyethylene terephthalate membrane and a cleaved fiber tip. The sensor interrogated by the proposed demodulation system demonstrated large dynamic range in low-frequency domain under high sound pressure. A signal-to-noise ratio (SNR) of ~53 dB is obtained at 80 Hz. These features make the sensor especially suitable for noise detection.

SECTION 1. Introduction

Fiber-optic acoustic sensors have attracted increasing attention owing to their advantages of compact size, high sensitivity, immunity to electromagnetic interference, and ease of multiplexing to large arrays [1], [2]. Based on these advantages, fiber-optic acoustic sensors have been extensively studied in many fields such as health monitoring of large structures [3], early warning of major natural disasters (earthquake [4], debris flow [5]), and leakage detection of pipelines [6] and military fields (underwater surveillance [7], and atmospheric nuclear explosion monitoring [8]). According to the operation mechanism, fiber-optic acoustic sensors can be classified as follows [9]: intrinsic sensors [10], [11], interferometric sensors (Sagnac [12], Mach-Zehnder [13], [14], Michelson [15], and Fabry-Perot [16]–​[20]), fiber laser sensors [21], fiber grating based sensors [22], and other kinds of sensors based on special optical structures [23].

Among these sensors, miniature extrinsic Fabry–Perot interferometers (EFPI) composed of fiber tip and deflectable diaphragm are the most commonly studied because of their characteristics of small size, high sensitivity and good stability. The working principle of EFPI based acoustic sensor is that, when acoustic wave applies on the diaphragm, it vibrates with the applied sound pressure, which modulates the cavity length of the EFPI and results in the intensity or phase change of the output interferential light.

Extracting acoustic signal from the output interferential light is the key point to be studied. For the traditional interferometric fiber-optic acoustic sensors utilizing intensity-based quadrature point (Q-point) demodulation [17]–​[20], the interferometer must be fixed at Q-point to insure the maximum sensitivity and linearity. However, Q-point always suffers from random drift caused by thermal induced optical path difference (OPD) fluctuation and static background pressure change [24], [25]. To compensate the drift of Q-point, complicated feedback regulation configurations are needed, which increases the system cost immensely [26]. Many phase interrogation methods such as homodyne and heterodyne demodulation have been proposed to address the drawbacks of Q-point demodulation. Among these, passive homodyne methods such as phase generated carrier (PGC) algorithm [27], [28] and symmetric 3 × 3 coupler algorithm [28] are the mostly applied. However, the two methods also have their shortcomings. PGC algorithm needs complicated carrier modulation system. Moreover, the dynamic range and frequency response range is limited [25], [28] , [29]. Symmetric 3 × 3 coupler algorithm requires the 3 × 3 coupler to be absolutely symmetric to insure that the splitting ratio of each channel is equal and the phase difference between them is 120° [15]. Furthermore, these two methods have poor effect when applied to short-cavity EFPI sensors [29].

Phase demodulation has been applied to diaphragm-based short-cavity acoustic sensors by Ma [25] and Xu [27], but the reflection from fiber end face is artificially minimized to eliminate the FP interference. In addition, the demodulation method proposed by Jun Ma has small dynamic range and the output signal is frequency-dependent. A two-wavelengths quadrature passive homodyne demodulation scheme has also been proposed by utilizing two lasers [30]. It should be noted that additional tunable lasers and WDM devices are needed. Moreover, output wavelength of the two lasers must be corresponded with the free space range (FSR) of the EFPI interference spectrum, which means that the EFPI cavity length is confined by the two operating wavelengths.

In this letter, we have demonstrated a phase demodulation method for short-cavity EFPI with two wavelengths via a tunable optical filter. Q-point drift problem of traditional intensity-based EFPI sensor can be solved. Two signals are acquired by filtering out two monochromatic beams from the broadband interference spectrum with a fixed wavelength interval. Influence of △λ on the sensitivity of demodulation system has been theoretically and experimentally demonstrated. In addition, an optimized differential cross multiplication (DCM) algorithm is proposed to eliminate the impact of optical power imbalance between the two light paths. Experimental results show that, as long as △λ is fixed, wavelengths of the two monochromatic beams have little impact on the demodulated signal. Moreover, large dynamic range and good linearity can also be reached.

The EFPI acoustic sensor head is based on the fiber tip end face and an aluminum-attached polyethylene terephthalate (PET) diaphragm. The thickness and radius of the PET diaphragm are 50 μm and 9.6 mm, respectively. Experimental results show that the proposed sensor has a good performance in low-frequency domain under high sound pressure. A signal-to-noise ratio (SNR) of ∼53 dB is obtained at 80 Hz and the minimum detectable pressure (MDPs) is∼3.4 mPa/Hz^1/2. Sound pressure of more than 112 dB can be detected. Recently, considerable attention has been paid to noise pollution detection which exists widely in airports, road traffic, industrial and many harsh environmental conditions [32]. Due to that fact, serious noise pollution mainly derives from low-frequency (20–200 Hz) sound waves with relative high sound pressure [32]. Therefore, the sensor proposed is suitable for the detection of environmental noise pollution. In addition, the demodulation system may be a good candidate for the phase interrogation of EFPI acoustic sensors with short cavity length.

SECTION 2. Basic Configuration and Operation Principles

2.1 Configuration

Schematic configuration of the EFPI acoustic sensor system is shown in Fig. 1 . The output light from Er-doped amplified spontaneous emission (ASE) broadband light source is pre-amplified by an EDFA. The power amplified light will then launch into the EFPI sensor head. First, the reflection spectrum of EFPI sensor is measured directly by an optical spectrum analyzer (OSA AQ6370C) to calculate the FSR. Then, acoustic wave generated by the speaker applies on the diaphragm. Cavity length of the EFPI is modulated by the sound pressure and, consequently, the phase of the output interferential light. The reflected broadband light, which carries the acoustic wave signal, launches into the tunable filter (WaveShaper-4000s). Adjusting working parameter of the filter, two monochromatic beams with fixed wavelength interval are filtered out from the EFPI interference spectrum. The 3 dB width of each beam is 0.2 nm. The two beam output from the filter are converted into electrical signal by two PDs (New Focus 1623). These two signals are then collected and processed by a data acquisition (DAQ) and process system with a sampling rate of 50 kHz. A sound level meter is placed beside the sensor head for the calibration of sound pressure.

Fig. 1.

Schematic configuration of the EFPI acoustic sensor system.

Fig. 2 shows the configuration of the EFPI sensor head [20]. An aluminum-attached polyethylene terephthalate (PET) diaphragm is used as the sensing diaphragm. A small piece of 3 μm-thickness aluminum foil is pasted on the PET diaphragm to enhance the reflectivity. A ceramic ferrule and a metal sleeve are used for the support and alignment of the fiber. The EFPI cavity is formed by the cleaved end face of the SMF and inner surface of the PET diaphragm. Cavity length of the EFPI sensor can be roughly adjusted by rotating the thread sleeve or precisely controlled by a five-axis aligner to get proper FSR and high fringe contrast. The whole structure is sealed by UV glue.

Fig. 2.

Configuration of the EFPI acoustic sensor head.

Compared with the PET film, the influence of aluminum foil on fundamental resonance frequency $f_{0}$ is negligible. So $f_{0}$ of the diaphragm can be calculated as [20]

$$\begin{align} {f_0} = \frac{{10.33\,h}}{{2\,\pi {r^2}}}\sqrt {\frac{E}{{12\rho (1 - {\mu ^2})}}}. \end{align}$$

The radius, thickness, Poisson ratio, Young's modulus and density of the diaphragm are ${\rm{r\,= \,9.6 mm}}$, ${\rm{h\,= \,50\,\mu m}}$, $\mu \,= \,0.39$, ${\rm{E\,= \,2.5\,GPa}}$, and ${\rm{1.38\,\times \,103\,kg/ m}}^{3}$, respectively. Then, the calculated fundamental resonance frequency is 378 Hz.

2.2 Operation Principles

Because of the low reflectivity of the fiber end face. The EFPI can be regarded as a low-finesse two-beam interferometer. The intensity of reflected interferential light can be expressed as

$$\begin{align} I(t,\lambda) = A + B\;{\rm{cos}}\left[ {\frac{{4\pi }}{\lambda }nL + {\varphi _0}} \right] \end{align}$$ where A is the constant voltage, which depends on the optical power and the gain in the detection electronics. B is the fringe visibility. L and $\varphi _{{0}}$ is the cavity length and initial phase of the FPI, respectively. And n is the refractive index of air (n ≍ 1). FSR of the EFPI can be express as $$\begin{align} FSR = \frac{{{\lambda ^2}}}{{2\,nL}}. \end{align}$$ When the cavity length is modulated by the applied acoustic wave, the reflected interferential light becomes $$\begin{align} I(t,\lambda) = A + B\;{\rm{cos}}\left[ {\frac{{4\pi }}{\lambda }nL + \theta (t) + {\varphi _0}} \right]. \end{align}$$

Here, θ is the phase variation caused by the sound pressure. To get two signals with fixed phase bias, two wavelengths are filtered out from the broadband interferential light. The phase difference between them is

$$\begin{align} \Delta \varphi = 4\pi nL\left({\frac{1}{{{\lambda _1}}} - \frac{1}{{{\lambda _2}}}} \right) = 4\pi nL\frac{{{\lambda _2} - {\lambda _1}}}{{{\lambda _1}{\lambda _2}}} \approx 2\,\pi \frac{{\Delta \lambda }}{{FSR}}. \end{align}$$

Two signals corresponding to λ₁ and λ₂ can be approximated as

$$\begin{align} {I_1}(t) &= {A_{1}} + {B_{1}}{\rm{cos}}\left[ {\theta (t) + {\varphi _1}} \right] \nonumber\\ {I_2}(t) &= {A_{2}} + {B_{2}}{\rm{cos}}\left[ {\theta (t) + {\varphi _1} + \Delta \varphi } \right] \end{align}$$ where $\varphi _{{0}}\,= \,{\rm{4\pi nL/ \lambda }}_{{1}}+ \varphi _{{0}}$. For the traditional dual-wavelength methods, dual light sources or two photoelectric detectors are inevitable, which result in two light paths. Stability, accuracy, and SNR of the system may be influenced by the imbalance of optical power between the two light paths [33]. In our scheme, the imbalance of optical power derives from optical source fluctuations, insertion loss of the filter, responses of the two photoelectric detectors, and spectrum drift caused by fluctuation of environmental temperature and pressure. In a traditional DCM scheme, the amplitude of output signal depends directly on ${\rm{B}}_{{1}}$ and ${\rm{B}}_{{2}}$ [31], which should be affected by the imbalance of optical power. To solve this problem, a normalization calculation is conducted before the traditional DCM process. Providing that the sound pressure is high enough, the normalized signal can be calculated as $$\begin{align} {I^{\prime}_{1;2}}(t) = \frac{{{I_{1;2}}(t) - ({A_{1;2}} - {B_{1;2}})}}{{({A_{1;2}} + {B_{1;2}}) + ({A_{1;2}} - {B_{1;2}})}}. \end{align}$$

After normalizing, the direct current (DC) component is eliminated and the alternative current (AC) component is given by

$$\begin{align} {I_1}_{,AC} &= {{B}^{\prime}_1}{\rm{cos}}\left[ {\theta (t) + {\varphi _1}} \right] \nonumber \\ {I_{2,}}_{AC} &= {{B}^{\prime}_2}{\rm{cos}}\left[ {\theta (t) + {\varphi _1} + \Delta \varphi } \right] \end{align}$$ where ${\rm{B}}_{{1}}{^{\prime}}$ and ${\rm{B}}_{{2}}{^{\prime}}$ is the normalized intensity constant ( ${\rm{B}}_{{1}}^{{\prime}}{\rm{\approx B}}_{{2}}^{{\prime}}\approx 0.5$). As a result, the AC component is independent on optical power.

Taking a derivative of the two AC signals and a cross multiplication process is induced. The two signals after cross multiplication process are expressed as follows:

$$\begin{align} {I_{1,C}} &= - {{B}}^{\prime}_{1}{{B}}^{\prime}_{2}{\rm{sin}}\left[ {{\varphi _1} + \theta \left(t \right)} \right]{\rm{cos}}\left[ {{\varphi _1} + \Delta \varphi + \theta \left(t \right)} \right]\theta ^{\prime}\left(t \right) \nonumber \\ {I_{2,C}} &= - {{B}}^{\prime}_{1}{{B}}^{\prime}_{2}{\rm{sin}}\left[ {{\varphi _1} + \Delta \varphi + \theta \left(t \right)} \right]{\rm{cos}}\left[ {{\varphi _1} + \theta \left(t \right)} \right]\theta ^{\prime}\left(t \right) \end{align}$$ where ${\rm{\theta ^{\prime}(t)\,= \,}}\,d\theta / d{\rm{t}}$. Therefore, the differential signal can be expressed as $$\begin{align} {V_D} = {B^{\prime}_1}{B^{\prime}_2}\sin (\Delta \varphi)\theta ^{\prime}(t). \end{align}$$

Then, the differential signal is integrated to get the acoustic information

$$\begin{align} {V_{out}} = C\;{\rm{sin}}\;(\Delta \varphi)\theta (t) \end{align}$$ where C is a normalized constant. For the traditional dual-wavelength demodulation schemes, the two wavelengths must be separated by a quarter of the FSR to get two quadrature signals [30], which means that the length of the EFPI cavity is restricted. We can see from (11) that, in our scheme, wavelength interval only influences the system's sensitivity. As a result, the interrogation system may not be restricted by the cavity length of EFPI acoustic sensors. However, when the wavelength interval ${\rm{\bigtriangleup \lambda \,= \,(2k+ 1)}}$. FSR/4 (k is integer), the phase difference ${\rm{\bigtriangleup \varphi \,= \,(2k+ 1). \ \pi / 2}}$ , the demodulated signal has maximum phase to intensity conversion.

SECTION 3. Experimental Characteristics

Fig. 3 shows the interference spectrum of the EFPI and the two beams filtered out by tunable filter. Fringe contrast of the EFPI ∼14 dB and FSR is ∼16 nm indicating that the cavity length L≈75 um. Center wavelengths of the two beams output from tunable filter are 193.2875 THz (1552.092 nm) and 193.7875 THz (1548.087 nm), respectively. Extinction ration of each channel is more than 45 dB. The 3 dB bandwidth of the two beams is 0.025 THz (0.2 nm). From the spectrum we can see that the two beams are distributed symmetrically beside one peak wavelength (≈1550 nm) of the EFPI interference spectrum.

Fig. 3.

Interference spectrum of the EFPI and the two monochromatic beams output from the tunable filter.

To exam the phase difference of two signals, an acoustic wave with the frequency of 200 Hz and sound pressure of 101 dB is applied on the EFPI sensor head. Output time-domain voltages of the two PDs are shown in Fig. 4. A phase difference of approximately π/2 can be observed. Due to the high sound pressure applied, a distortion of the waveform is observed.

Fig. 4.

Output signal of the two PDs.

Different wavelength interval is tested to investigate the influence of △λ on the demodulation result. As shown in Fig. 5, △λ changes from 2 nm to 4 nm with an increment of 0.4 nm with $(\lambda _{{1}}+ \lambda _{{2}})/ 2$ fixed at 1550 nm. DC components of the time domain waveforms of demodulated 200 Hz acoustic signal with different △λ are shown in Fig. 5 (a) . The corresponding peak-to-peak values are depicted in Fig. 5(b). It can be seen that as △λ increases from 2 nm to 4 nm (△ϕ varies from 45° to 90°), amplitude of the output signal increases identically, which fits perfectly with (8). When ${\rm{\bigtriangleup \lambda = 8 nm}}$, the minimum sensitivity is achieved. In the experiment, the wavelength interval is fixed at 4 nm to get the maximum sensitivity. However, there is no need to settle △λ at 4 nm rigidly because a small error can only cause a little dampening of the sensitivity.

Fig. 5.

(a) Demodulated time domain waveforms of 200 Hz acoustic signal with different △λ. (b) Amplitude of the demodulated signal with different △λ.

As mentioned above, the influence of optical power imbalance on output signal can be eliminated by the optimized DCM scheme. Experiments are carried out to test the impact of interference spectrum drift on signal recovery. During the experiments, wavelength interval is 4 nm. To simulate the drift of interference spectrum, the value of $\lambda _{{2}}\,(\lambda _{{2}}\,> \,\lambda _{{1}})$ changes from 1546.1 nm to 1556.1 nm with an increment of 2 nm. The frequency of applied acoustic wave is 200 Hz. Experimental results are shown in Fig. 6. Fig. 6 (a) shows the demodulated DC time domain waveforms with different $\lambda _{{2}}$, and their peak-to-peak values are shown in Fig. 6 (b). We can see that asλ₂ changes, the amplitude of the output signal keeps almost constant.

Fig. 6.

(a) Demodulated time domain waveforms of 200 Hz acoustic signal with different $\lambda _{{2}}$. (b) Amplitude of the demodulated signal with different $\lambda _{{2}}$.

The linearity of our sensor is tested by applying sound pressure from 0.2 Pa to 7.96 Pa (80 dB to 112 dB) at 200 Hz on the EFPI sensor head. The maximum sound pressure that our loudspeaker can produce is ∼110 dB. It should be noted that, higher sound pressure can be detected. Relationship between sound pressure and amplitude of the demodulation signal is depicted in Fig. 7. The result indicates that large dynamic range (up to more than 112 dB) and good linearity (R-square value of 0.99032) can be obtained.

Fig. 7.

Amplitude of output signal with different sound pressure at 200 Hz.

Fig. 8 depicts the time domain waveform and corresponding frequency spectrum with the frequency of acoustical signal at 80 Hz and 5000 Hz, respectively. The signal to noise ratio (SNR) at 80 Hz is ∼52 dB, indicating a minimum detectable phase (MDP) of ∼3.4 mPa/Hz^1/2 . Due to the frequency limit of our speaker  >40 Hz), the experiment is carried out from 50 Hz to 5000 Hz. A flat frequency response is obtained from 50 Hz to 200 Hz. From the experimental result, we can see that the sensor works better at the low frequency domain. This is because that the radius of the sensor is relatively large (9.6 mm) and therefore the calculated resonance frequency response is 378 Hz. For a specific diaphragm based transducer, lower resonance frequency and higher sensitivity can be achieved by enlarging the radius of diaphragm. However, the noise will also increase at the same time. For the acoustic sensor working at low-frequency domain, the major problem is the elimination of low-frequency noise [21]. The noises of acoustic sensor can be mainly divided into several types listed as follows: detector noise (noise equivalent power), intensity and phase noise of the light source, optical and electrical short noise and thermo-mechanical noise. Among these, for the EFPI acoustic sensor, thermo-mechanical noise is dominant [24]. Thermo-mechanical noise is considerable and unavoidable for the EFPI sensor with large size. To design a low-frequency acoustic sensor with good low-frequency response and low noise equivalent pressure level, the radius of the diaphragm should be designed to get a balance between them. The sensor is special designed for low-frequency environmental noise pollution detection.

Fig. 8.

Frequency spectrum of the demodulated acoustic signal. (Inset) Time domain waveform signal. (a) 80 Hz. (b) 5000 Hz.

SECTION 4. Conclusion

In this paper, a phase demodulation scheme for short-cavity EFPI utilizing two wavelengths is proposed. The Q-point drift problem of traditional intensity-based EFPI sensor can be solved. Two monochromatic beams are acquired by filtering out two individual wavelengths through a tunable filter from the broadband interference spectrum with 3 dB width of 0.2 nm. To get the best sensitivity, the wavelength interval between the two beams is fixed at   nm, which equals one quarter of the FSR of EFPI interference spectrum. Impact of △λ on demodulation result has been theoretically and experimentally analyzed. A normalization process is induced into the traditional DCM scheme, which can reduce the influence of optical power imbalance. This scheme is a good candidate for the phase demodulation of widely used short-cavity EPFI acoustic sensor.

The EFPI acoustic sensor is formed by an aluminum-attached PET diaphragm. FSR of EFPI is ∼16 nm and the calculated cavity length is ∼75um. The radius of the diaphragm is 9.6 mm, and the corresponding fundamental resonance frequency $f_{0}$ is 378 Hz. Flat frequency response can be obtained at low-frequency domain. A SNR of 52 dB is obtained at 80Hz with the corresponding MDPs of ∼3.4 mPa/Hz^1/2. The sensor has large dynamic range (up to 112 dB) at low frequency domain. These features verify that our sensor is performable for the detection of environmental noise pollution.