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A stable phase demodulation system for diaphragm-based acoustic sensors is reported. The system is based on a modified fiber-optic Sagnac interferometer with a stable quadrature phase bias, which is independent of the parameters of the sensor head. The phase bias is achieved passively by introducing a nonreciprocal frequency shift between the counter-propagating waves, avoiding the use of complicated active servo-control. A 100 nm-thick graphite diaphragm-based acoustic sensor interrogated by the proposed demodulation system demonstrated a minimum detectable pressure level of ~450 µPa/Hz1/2 and an output signal stability of less than 0.35 dB over an 8-hour period. The system may be useful as a universal phase demodulation unit for diaphragm-based acoustic sensors as well as other sensors operating in a reflection mode.
© 2015 Optical Society of America
1. Introduction
Since Bucaro et al. firstly reported acoustic detection by using a fiber optic Mach-Zehnder interferometer (MZI) in 1977 [1], fiber-optic interferometric sensors have emerged as an important sensing technology for acoustic measurement [2–8]. Cole et al. demonstrated ultrasound detection with a similar MZI setup in water with no significant variation of the sensitivity in the frequency range of 10-100 kHz, which compares well with the theory [2]. Hocker et al. later improved the sensitivity by two orders of magnitude through embedding the sensing arm of the MZI into a composite structure which has a lower elastic modulus compared with silica [3]. Other configurations such as Michelson interferometer [4], Sagnac interferometer [5] and Fabry-Perot interferometer (FPI) [6–8] have also been developed for acoustic/ultrasonic detection.
Compared with the MZI, the FPI is a reflection-mode point sensor suitable for space-limited applications, and the short gauge length also reduces the cross-sensitivity to other measurands [6, 7]. Alcoz et al. demonstrated an ultrasonic sensor with a short intrinsic FPI formed by dielectric mirrors embedded in the fiber [6], and an incident ultrasonic wave modifies optical path length of the Fabry-Perot (FP) cavity through the strain-optic effect. Murphy et al. reported an acoustic sensor based on an extrinsic FPI of which the air cavity is formed by inserting two cleaved fiber ends into a hollow core fiber [7]. Beard et al. built a FP cavity at the fiber end with a thin layer of transparent polymer, which varies in thickness when subjected to ultrasonic waves [8]. Another kind of fiber-optic FPIs called diaphragm based FPIs, with a hollow-cavity covered by a deflectable diaphragm, have also been studied extensively for acoustic detection due to their high sensitivity and compact size [9–13].
For practical applications of these acoustic sensors, the interferometers should be stabilized to a quadrature point (Q-point) where the phase to intensity conversion is linear and has a maximum slope. The Q-point may drift due to fluctuation in ambient temperature and background pressure, causing instability of the sensor output. Various techniques such as active homodyne and heterodyne demodulation have been employed to address this problem [14, 15]. For the active homodyne demodulation, one of the simplest and earliest techniques is to use a piezoelectric fiber stretcher in the reference arm to actively compensate phase in the MZI [16]. However, this technique is ineffective when applied to short-cavity FPI sensors because the two arms of the FPI share the same single-mode fiber and there is no access to the reference arm for active phase compensation. Active tuning of the frequency of a narrow-band laser is used instead as an alternate demodulation scheme for the stabilization of the FPIs. Electrical feedback [17] and diffractive grating control [18] are used to tune the laser frequency and maintain the Q-point in real time. However it requires active control of the laser wavelength and increases the complexity of the system. A passive two-wavelength demodulation scheme has also been developed for effectively stabilizing the phase-bias drift whereas additional optical filters and electronic switching unit are needed to separate the two wavelengths [19].
On the other hand, Sagnac interferometers have proven to be insensitive to slow environmental disturbance and been used in gyroscopes [20], hydrophones [21], surface acoustic wave detectors [22] and optical switches [23]. Stable operation of the interferometer around the quadrature phase bias has been achieved by using a 3 × 3 directional coupler [24] or by placing a frequency shifter [25] or phase modulator [26] in the Sagnac loop. Compared to the active homodyne for MZIs or active tuning of laser frequency for FPIs, the Sagnac interferometer is interrogated passively and all-optically without the need for electric feedback to individual sensor.
In this paper, we proposed a passive demodulation scheme for diaphragm-based reflection-type acoustic sensors via a modified Sagnac interferometer. The stable quadrature phase bias is achieved by inducing a nonreciprocal frequency shift between the two counter-propagating waves in the interferometer. Due to the inherent property of the Sagnac loop, this phase bias is insensitive to the slow environmental disturbance.
The acoustic sensor head to be used in conjunction with the demodulation system is similar to that of diaphragm-based fiber-end FPIs [9–13] but the reflection from the fiber/air interface is intentionally minimized to ensure that no Fabry-Perot fringes could be generated. Only the reflections from the diaphragm form useful signals and a constant quadrature phase bias between the reflected waves counter-propagating in the Sagnac loop is guaranteed, avoiding the use of any active feedback control as has been employed for the previous FPI based acoustic sensors. It is well know that the Q-point of a FPI is cavity-length-dependent, the fact that it is difficult to fabricate fiber FPIs with exactly the same cavity length means that, for different sensors, the laser wavelength needs to be tuned to different values to ensure optimal phase to intensity conversion. In our system, the phase bias is neither affected by the separation between the fiber-end and the diaphragm (equivalent to the cavity length of FPI) nor the length of the lead in/out fiber (same as the FPI). Consequently the system may be used to demodulate diaphragm-based acoustic sensors with different structural parameters. A multilayer graphite (MLG) diaphragm based acoustic sensor is interrogated by the proposed demodulation system and demonstrates stable operation over an 8-hour-long period and a minimum detectable acoustic pressure level of ~450 µPa/Hz1/2at the frequency of 5 kHz.
2. Basic configuration of the demodulation system
Figure 1(a) shows the schematic configuration of the proposed demodulation system. It is a Sagnac interferometer with an additional directional coupler (DC2) to allow light waves to be delivered to the acoustic sensor head. Light from a superluminescent diode (SLD) is split, by the directional coupler (DC1), equally into the clockwise (CW) and counterclockwise (CCW) waves. The center wavelength, spectrum width and output power of the SLD are respectively 1545 nm, ~40 nm and ~10 mW. The CW wave follows the path a-c-1-4 and passes through the frequency shifter, depolarizer, piezoelectric transducer (PZT) and the lead in/out fiber to the sensor head. It is then reflected at the diaphragm and returns to DC2 and further to the photodetector (PD) via path 4-2-d-b. Similarly, the CCW wave follows the path a-d-2-4 to the sensor head and returns the PD through the path 4-1-c-b. The CW and CCW waves are signal waves, and they experience the same optical path (opposite in directions) and interfere with each other at the input of the PD even if the source coherence is low.
Fig. 1 (a) Schematic configuration of the modified Sagnac interferometer-based demodulation system. APC: angle polished connector; inset: schematic of the sensor head. Optical frequencies at different locations for (b) CW and (c) CCW waves.
In addition to the above described CW and CCW waves, two other optical paths exist in the modified Sagnac interferometer and they are unwanted waves. They are respectively a-c-1-4-1-c-b and a-d-2-4-2-d-b, which we called them “short” and “long” waves respectively. Since a SLD source instead of a narrow band laser is used here, the short and long waves would neither interfere coherently with the signal waves (CW and CCW waves) nor with each other because of the larger optical path differences as compared with the coherence length of the light source, which is ~60 μm in our current experiment. However, additional noise may still be induced due to the beating of the Fourier components within the wide spectra of the signal and the unwanted waves [27]. This problem may be overcome by using a pulsed light source to separate the signal waves and the unwanted short and long waves in the time domain [24].
The key element to achieve stable phase bias is the frequency shifter, which introduces an optical frequency shift δf when light passes through it. The use of the frequency shifter results in different optical frequencies at different locations of the interferometer paths, as indicated in Figs. 1(b) and 1(c).The optical frequency of CW/CCW is shifted from f0 to f0 ± δf after passing through the frequency shifter for the first time and the frequencies of both waves are f0 ± δf at the sensor head. The frequencies of the reflective waves are further shifted from f0 ± δf to f0 ± 2δf after passing through the frequency shifter again, and the optical frequencies of the two signal waves are f0 ± 2δf at the PD. Under the assumption of ideal 50/50 fiber couplers, the phase difference between the CW and CCW, i.e., the phase bias φs, may be related to the frequency shift δf by,
where ΔL is the path length difference between the path d-2 and the path c-1, which are two paths connecting the two couplers DC1 and DC2. c is the speed of light in vacuum, and n is the refractive index of the optical fiber. The factor of 2 in the bracket of Eq. (1) is due to the facts that both the CW and CCW waves travel forth and back through the frequency shifter.A variable optical attenuator (VOA) is placed in the Sagnac loop. Different samples of sensor heads (see the inset of Fig. 1(a)) could have different reflectivities and the use of the VOA would ensure that the intensities of the interfering CW and CCW waves being more or less the same at the PD. A depolarizer, which is fabricated by splicing two sections of highly birefringence fibers with a length ratio of 1:2 and their axes being offset by 45 degrees, is used to minimize the system instability due to polarization state fluctuation [26]. A PZT based phase modulator is used for system calibration purpose and will be described in detail in Section 4. The sensor head used in this study comprises a MLG diaphragm and a single mode fiber (SMF) with its end-face cleaved at an angle of ~8 degree. The angled end-face significantly reduces back-reflection into the fiber, and hence the FP cavity between the fiber end-face and the diaphragm would not be formed. This differentiates the current sensor from the conventional FP based ones [9–13]. The detailed fabrication process of the sensor head will be described in Section 5. It should be mentioned that the MLG diaphragm-based acoustic sensor used here is for demonstration purpose only and the demodulation system could be applied to other types of reflection-type phase modulation sensors.
3. Principle of operation
In the MZI, the incident light is split into two beams by a fiber directional coupler and the two beams, with one acting as the sensing arm the other as the reference arm, travel in two different optical paths. The two beams are combined and interfere at the second directional coupler [15]. In the Sagnac interferometer, the incident light beam is also split into two by a fiber directional coupler. However, the two spilt beams travel in the same optical path in opposite directions (i.e., CW and CCW) and the two beams are combined by the same directional coupler. The basic theories of fiber optic Sagnac interferometer-based acoustic sensor have been described previously [20, 21]. Our work in this paper concerns the demodulation of diaphragm-based reflection-type acoustic sensors, and a second coupler is used to connect the sensor head to the Sagnac loop, as shown in Fig. 1(c). This configuration is different from the standard Sagnac configuration and we name it here a modified Sagnac interferometer. The modified Sagnac interferometer has some similarity with the standard Sagnac interferometer in that the CW and CCW beams in both interferometers travel in the same fiber (but opposite directions) and hence they are insensitive to low frequency disturbance. However, in the modified Sagnac Interferometer, the CW and CCW beams need to leave the loop to reach the sensor head. They are reflected by the diaphragm (at different times) and then re-enter into the loop via the second coupler. In this sense, the optical paths of the CW and CCW beams are different from those of a standard Sagnac interferometer.
For the current modified Sagnac configuration with a reflective diaphragm-based sensor head, the basic principle of operation is outlined briefly as follows. When the diaphragm is subjected to a harmonic acoustic pressure of P(t) = P0cos(wst), the deflection of the diaphragm may be described by u(t) = u0cos(wst), where P0 and u0 are the amplitude of the acoustic pressure and the pressure-induced diaphragm deflection, and ws is the angular frequency of acoustic pressure wave. Due to the existence of the fiber delay line, the CW and CCW waves arriving at the reflective diaphragm have a time difference of τ. The phase difference Δφ between the CW and CCW waves may be expressed as,
where φs is the phase bias given by Eq. (1), and k = 2π/λ is the wavenumber.The light intensity I(t) at the PD may be expressed as
where Il, Is, Icw, Iccw are respectively the light intensities of the long, short, CW and CCW waves at the PD and, for simplicity, they are assumed to have the same intensity of I0/4. According to Eq. (1), by selecting the frequency shift δf and the path length difference ΔL in a coordinated manner, the phase bias can be set to φs = 2mπ + π/2 (m is an integer), i.e., operating at the Q-point.At the Q-point and for a small phase modulation amplitude of ku0<<π/2, the ws-frequency component from the Sagnac interferometer may be approximated by,
Iac is maximized when the frequency of the acoustic signal fs ( = ws/2π) is equal to fp = 1/2τ, which is the proper frequency of the Sagnac loop. For a fiber delay line with the length of ~2 km, the proper frequency of the Sagnac loop fp is ~50 kHz. The frequency-dependent output of the Sagnac interferometer indicates that the proper frequency should be set near the frequency range of acoustic signal in order to achieve optimal sensitivity. This property makes the system ideally suited for narrow-band acoustic signal measurement such as sinusoidally modulated continuous-wave photo-acoustic gas detection. For acoustic detection with a broad frequency range, the frequency dependence of system may be compensated according to Eq. (4) to acquire the exact signal [24].4. Characterization of the demodulation system
The performance of the demodulation system was firstly calibrated by using a phase modulator formed by coiling a section of optical fiber around a PZT (see Fig. 1). The PZT is driven by an electrical signal generator and the amplitude of the phase modulation is proportional to the voltage applied to the PZT. The diaphragm-based sensor head is now replaced by a piece of SMF with a cleaved end, which provides a fixed optical reflectivity of ~3.5%. Such an arrangement avoids any possible influence on the reflected light signal from the MLG diaphragm, which would be very sensitive to environmental acoustic disturbance. The frequency shift of the frequency shifter is fixed to 70 MHz and the quadrature phase bias is achieved by adjusting the length of the fiber delay line. To ensure a π/2 phase bias is achieved, a sinusoidal voltage at the frequency of 20 kHz is applied to the PZT phase modulator and the peak to peak amplitude of the phase modulation is adjusted to 2π. Figure 2 shows the oscillator trace of the output signal for a fiber delay line of approximately 2 km. Figure 2(a) is an arbitrary trace with a phase bias deviated from the desirable π/2. According to Eq. (1), a change of ΔL by ~0.37 m would theoretically change the phase bias by π/2. The path length difference ΔL is then carefully adjusted by cleaving the fiber delay line until the waveform of the signal shows peaks and dips with equal amplitudes, as shown in Fig. 2(b), which indicates the phase bias φs = 2mπ + π/2 is achieved.
Fig. 2 Oscilloscope traces of the PD output for fiber delay lines with different lengths around 2 km. Upper trace: φs deviated from 2mπ + π/2; lower trace: φs equals to 2mπ + π/2.
After the π/2 phase bias is achieved, the performance of the demodulation system for detecting dynamic phase modulation was tested with a sinusoidal phase modulation applied by the PZT at the frequency of 5 kHz. The measured output voltage has a linear response to the applied phase modulation, as shown in Fig. 3(a). It should be pointed out that the PZT modulator provides a simulated phase modulation signal, which is used to confirm that the π/2 phase bias obtained and to evaluate the performance of the demodulation in detecting dynamic phase modulation. It is not used or needed in the system for diaphragm-based sensors.
Fig. 3 (a) Output voltage of the demodulation system as a function of applied phase modulation at the frequency of 5 kHz; (b) MDP as a function of phase modulation frequency from 1 to 20 kHz; inset: output frequency spectrum measured with an electrical spectrum analyzer for a phase modulation amplitude of ~1 rad at the frequency of 5 kHz.
The inset in Fig. 3(b) shows the spectrum of the system output measured with electrical spectrum analyzer (ESA) with a bandwidth of 100 Hz. The applied phase modulation is at 5 kHz with the amplitude of ~1 rad. The signal to noise ratio (SNR) at 5 kHz is ~61.7 dB, giving a minimum detectable phase (MDP) of ~80 μrad/Hz1/2. As shown in Fig. 3(b), the MDP decreases with increasing modulation frequency and a minimum value of ~24 μrad/Hz1/2 is achieved at ~18 kHz. The frequency dependence of the MDP is an intrinsic characteristic of the Sagnac interferometer [24]. As shown in Eq. (4), the output signal is expected to increase with the increasing modulation frequency and reaches to a maximum value at the frequency of 1/2τ, which is ~50 kHz for a ~2 km long path difference ΔL. However, the noise in the output is also frequency dependent, and increases with the frequency in the range of 0 to 50 kHz until reaching a maximum value around 50 kHz, as shown in Fig. 4. The interplay of the signal and the noise factors results in a minimum MDP at ~18 kHz.
Fig. 4 Output noise spectrum in the frequency range from 0 to 100 kHz. Inset: enlarged noise spectrum in the frequency range from 0 to 20 kHz.
It is interesting to discuss the fundamental noise limit of the demodulation system. For the PD received power level in microwatts region, the electrical noise may be ignored [20] and the optical noise in the system (σo) may be described by the following relationship [28],
where I0 is the mean photocurrent from the PD, e is the elementary charge, B is the frequency bandwidth of the detection, and Δv is the bandwidth of the optical source. The first and second terms in the right hand side of Eq. (5) refer to the shot noise σs and excess photon noise σe, respectively. For our experimental system, Δv is ~6 THz, the optical power level at the PD is ~3 μW and the responsivity of PD is 0.9 A/W. The signal to noise ratio (SNR) for the power of the output signal and noise of the system under a phase modulation of 1 rad might be expressed as,According to Eq. (6), the MDP at the frequency of ~18 kHz is calculated to be ~0.7 μrad/Hz1/2, with the shot noise σs of ~0.45μrad/Hz1/2 and the excess photon noise of ~0.54 μrad/Hz1/2. This value is lower than the experimental result of ~24 μrad/Hz1/2 at the frequency of ~18 kHz, indicating the system performance is limited by additional noise sources such as from the unwanted short and long waves and other reflected/scattered lights in the Sagnac loop [24, 27].5. A diaphragm based acoustic sensor with stable performance
A 100-nm thick MLG diaphragm based acoustic sensor is then tested by connecting it to the demodulation system, as shown in Fig. 1. The diaphragm-based sensor is fabricated by following the procedure described as follows: firstly, a piece of MLG/Nickel (Ni)/MLG film (Graphene Supermarket) is flattened by pressurizing it between two glass slides (Fig. 5(a)). In the meaning time, a thin layer of ultraviolet (UV) curable liquid gel is placed at the end of a hollow ceramic sleeve with an inner bore diameter of ~2.5 mm, as shown in Fig. 5(b). The gel-coated sleeve is then pressed onto the flat MLG/Ni/MLG film, and the liquid gel between the sleeve and MLG/Ni/MLG film is then cured under the exposure of UV light for 6 hours (Fig. 5(c)). This process ensures that the MLG/Ni/MLG film is firmly stuck to the end of the sleeve. The hollow-sleeve covered with the MLG/Ni/MLG film is then immersed into a ferricchloride (FeCl3) and hydrochloric acid (HCl) mixture solution to etch away the Ni layer (Fig. 5(d)). The combination of FeCl3 and HCl solution also contributes to the removal of etching residuals [29]. By flushing the sleeve end in fresh de-ionized water, the upper MLG film that is attached to the sleeve is separated from the lower MLG film. The sleeve covered with the MLG film is then dried at 90 °C for ~1 hour to remove the residual water. Finally, a SMF cable with a standard angle polished connector (APC) is inserted into the sleeve and they are fixed together with epoxy to form the sensor head. The APC consists of a ceramic ferrule with the outer diameter of 2.5 mm and the SMF is fixed at the central bore of the ferrule. The end facet of the SMF in the APC has a tilted angle of 8°, which reduces the back-reflection light from the fiber end. The length of the air-cavity (the spacing between the fiber end and the diaphragm) is controlled through a translation stage under the monitoring of an optical microscope. Microscope images of the ferrule sleeve covered with the MLG film and the final sensor head are shown in Figs. 5(f) and 5(g), respectively.
Fig. 5 Fabrication process of the 100 nm-thick MLG-diaphragm-based acoustic sensor. (a) Flattening the MLG/Ni/MLG film by pressurizing it between two glass slides; (b) coating the periphery of the hollow ceramic sleeve with UV curable liquid gel; (c) curing the gel between the MLG/Ni/MLG film and sleeve; (d) etching away the Ni layer in the MLG/Ni/MLG sample; (e) inserting a ferrule with a SMF fixed at its center into the sleeve to form an air cavity; microscope image of (f) the ferrule sleeve covered with MLG film and (g) the finished sensor head.
Figure 6(a) shows the output spectrum measured with the ESA for an applied acoustic pressure level of ~800 mPa at 5 kHz. The acoustic signal is emitted from a loudspeaker driven by a signal generator [13]. The SNR is ~45 dB, corresponding to a minimum detectable pressure of ~450 μPa/Hz1/2. The signal power at 5 kHz is monitored continuously for ~8 hours and the results are shown in Fig. 6(b). The signal fluctuation is less than 0.35 dB, showing that the system has good long term stability that is difficult to achieve with conventional fiber Fabry-Perot based demodulation approach.
Fig. 6 (a) Measured output spectrum of a diaphragm based sensor for applied acoustic signal amplitude of 800 mPa at the frequency of 5 kHz; (b) output signal fluctuation over duration of ~8 hours.
It should be pointed out that the phase bias (φs) between the CW and CCW waves reflected from the diaphragm is independent of the length of the lead in/out fiber as well as the length of the air-gap between the fiber end-face and the diaphragm. This is because that the frequencies of the CW and CCW waves in the optical path between the frequency shifter and the diaphragm are the same and equal to f ± δf, as shown in Figs. 1(b) and 1(c). Any change in the lengths of the lead fiber and/or air-cavity should affect the CW and CCW waves equally and the phase difference should remain the same. For the same reason, the operating point of the current system is also insensitive to slow environmental disturbances. This is in contrast to the previous Fabry-Perot based demodulation systems [9–13], in which the Q point varies from sensor to sensor due to the different lengths of air-cavity and environmental perturbations, and the laser wavelength needs to be tuned or controlled through a servo-loop.
For the conventional MZI demodulated by active homodyne or PGC techniques [16, 30], the MDP achieved is in the range of 1-10 μrad/Hz1/2, which is better than that in our system. However, the system we demonstrated here needs neither complex PGC processing electronics nor active control of the phase bias during measurement. In addition, the use of diaphragm-based sensors in a modified Sagnac configuration ensures high sensitivity without the need for long length of sensing fiber as used in the MZI based acoustic sensors [1–3].
6. Summary
In summary, a demodulation system for diaphragm-based reflective-type acoustic sensors is demonstrated. The system uses a modified fiber Sagnac interferometer incorporating a frequency shifter to achieve a stable π/2 phase bias between the reflected CW and CCW waves. Applied acoustic pressure deflects the diaphragm and results in dynamic modulation of the phase difference between the counter-propagating waves, which is faithfully converted into light intensity modulation at the interferometer. The phase bias or operating point is independent on the structural parameters of the sensor head as well as the length of the lead in/out fiber, and hence may be used as a universal demodulator for reflective diaphragm–based sensors with different types and parameters. System tests with a PZT-based phase modulator and a MLG diaphragm-based acoustic sensor showed that the system provides a MDP of ~24 µrad/Hz1/2 and a minimum detectable pressure of ~450 µPa/Hz1/2. The output of the sensor demodulated by this system exhibits an output fluctuation of less than 0.35 dB over an 8 hour period. It should be mentioned that the MDP of ~0.05 µrad/Hz1/2 at the frequency of 5 MHz has been achieved by a FPI ultrasonic sensor [31]. Our focus here is the stability issue, and we have achieved good longer term stable operation without the need of active servo-control or complex electronic signal processing, which are used in previous systems. In combination with the sensitive diaphragm based acoustic sensor we developed, this system also provides a good minimum detectable pressure for acoustic measurement [9–13]. This work demonstrates the feasibility of demodulating diaphragm-based acoustic sensors without active control of the phase bias or complex electronic signal processing.
Acknowledgment
This work was supported by the National Natural Science Foundation of China (NSFC) through Grant no. 61290313 and the Hong Kong Polytechnic University through the project G-YM16.
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