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A working-point trackable fiber-optic hydrophone with high acoustic resolution is proposed and experimentally demonstrated. The sensor is based on a polydimethylsiloxane (PDMS) cavity molded at the end of a single-mode fiber, acting as a low-finesse Fabry–Perot (FP) interferometer. The working point tracking is achieved by using a low cost white-light interferometric system with a simple tunable FP filter. By real-time adjusting the optical path difference of the FP filter, the sensor working point can be kept at its highest sensitivity point. This helps address the sensor working point drift due to hydrostatic pressure, water absorption, and/or temperature changes. It is demonstrated that the sensor system has a high resolution with a minimum detectable acoustic pressure of 148 Pa and superior stability compared to a system using a tunable laser.
© 2016 Optical Society of America
1. Introduction
Since the development of fiber-optic hydrophones in 1977 [1], many efforts have been made to develop different types of fiber-optic hydrophones with improved performance. Compared with piezoelectric hydrophones, fiber-optic hydrophones are inherently immune to electromagnetic interference, and they also have the advantages of small size, mechanical flexibility, and multiplexibility [2]. Current fiber optic hydrophones are mainly based on several techniques, including optical reflection at the fiber end [3–7], fiber Bragg gratings (FBGs) [8–15], distributed feedback fiber laser (DFBFL) [16–18], Mach–Zehnder interferometers (MZIs) [19], and Fabry–Perot interferometers (FPIs) [20–26].
Among the abovementioned techniques, the simplest design is based on the detection of pressure-induced changes of the Fresnel reflection coefficient at the tip of an optical fiber [4–6]. Hydrophones based on this technique have a small size and low cost, but suffer from low sensitivity [7]. These hydrophones have been demonstrated for shock wave detection in water [3,7]. Hydrophones based on FBGs, DFBFL, and MZI usually employ a pre-tensioned single-mode fiber inside a shell or cavity [8,10–12,17,19]. Sound can directly (or via a vibrating membrane) induce axial strain changes in the fiber, which modulate the wavelength or phase. These hydrophones have relatively high sensitivity, but have relatively large device sizes.
Hydrophones based on FPIs are often designed to detect sound pressure induced changes in the optical thickness of a solidified polymer Fabry-Perot (FP) cavity constructed at the tip of an optical fiber. This approach helps achieve a small sensor device that renders a high spatial resolution. The sensitivity can be easily enhanced by selecting a soft material as the FPI gap material or using multilayer reflectors to improve the finesse [22–24,26]. One inherent problem of FP hydrophones is that they inevitably suffer from the working point drift, because the cavity length may change due to hydrostatic pressure and/or temperature changes, or water absorption of the gap material. The working point drift can significantly reduce the pressure sensitivity of the hydrophone, or even make the sensor to fail. One possible approach to address the working point drift is to use a tunable laser as a light source and adjust the wavelength of the laser to compensate the drift of the working point. However, this approach will significantly increase the cost of the system. In addition, since an FPI illuminated with a tunable laser is extremely sensitive to the laser wavelength fluctuations, which can result in unstable interference signals, wavelength stabilization is usually required, increasing the complexity of the system.
In this paper, we report a low cost, white-light FPI based fiber-optic hydrophone system that consists of a polymer based FPI sensor head and another tunable FPI with a large cavity length tuning range. This system allows real-time tracking of the sensor working point as well as high resolution measurements. The fabrication of the hydrophone device entails a simple optical fiber based molding process, which enables high precision fabrication of polymer sensor heads with a large range of cavity lengths. It is experimentally demonstrated that the system can achieve a resolution of 148 Pa, and the performance of this system is superior to another system using an expensive tunable laser. This work is expected to impact many applications that require high performance miniature hydrophones [27,28].
2. Sensor operation principle, mechanics model, and fabrication
2.1 Operation principle
The schematic of the proposed fiber optic hydrophone system, which is based on white-light interferometry, is shown in Fig. 1. Light from a broad-band superluminescent diode (SLD) (Thorlabs, S5FC1018S) is sent to a Fabry-Perot tunable filter (FPTF) via a 1 × 2 coupler. The reflected light from the TF is then coupled into the FPI hydrophone device via another 1 × 2 coupler. The reflected light from the FPI sensor is collected by a photodetector (PD) (New Focus, Velocity 2011) and converted into an electric signal, which is the voltage output of the sensor. The PD is set to the AC-coupled mode.
The FPI device (i.e., sensor head) [inset of Fig. 1] consists of a Polydimethylsiloxane (PDMS) based FP cavity formed between a single-mode optical fiber endface and a silver reflective mirror coated on the PDMS. The acoustic pressure can induce a change to the FP cavity length, which is detected by the optical measurement system. The FPTF is used to facilitate the sensor interrogation as well as track the drift of the sensor working point. It is constructed by using a single-mode fiber end face as a fixed mirror and another moving mirror attached to a piezoelectric actuator (Thorlabs, PK2JUP2). The control signal to the actuator is sent by using the digital to analog (D/A) output of a data acquisition card (DAQ) (National Instruments, USB-6259) connected to a personal computer (PC).
For the low coherence optical system with two FPIs shown in Fig. 1, the output voltage of the photodetector is [30]
where I0 is the input light source power, λ is the wavelength, δ1 and δ2 are the optical path differences (OPDs) of the FPI sensor and the tunable FPI, respectively, σ is the spectra width of the source, R is the responsivity of the photodetector in the unit of volts per watt, and γ is the total loss factor that is due to the reflectivity of the FPIs, the light propagation loss in the FP cavities and along fiber links, and the splitting loss of the couplers. Note that the output is a function of the differential OPD (i.e., δ1-δ2).To track and adjust the sensor working point, a control voltage signal is sent to the FPTF from the PC via the DAQ, which has a sinusoidal AC component (AC1) and a DC bias. The DC bias is used to change the OPD δ2 of the FPTF, while the AC signal is used to generate a single-frequency modulation (AC2) to the differential OPD in the absence of an acoustic input. Due to the AC2, an output voltage signal (AC3) with the same frequency can be obtained from the PD. To achieve real-time tuning of the sensor working point, the DC bias is swept to change the cavity length of the FPTF over its entire range, which will induce a change in the amplitude of AC3. When the amplitude of AC3 reaches its maximum, the differential OPD will be at a quadrature point; that is,
In this case, the maximum sensitivity is achieved, indicating the success of the working point tracking. In order for the sensor to work properly, the sensor operation point should be kept as close to the zero order quadrature point (m = 0) as possible. In this case, the sensor output can be considered to be linearly proportional to the input acoustic pressure.To characterize the fiber optic hydrophone device, a commercial underwater transducer (International Transducers Corporation, ITC-1042) is used as an acoustic source as well as a reference sensor, which has an optimal working frequency of 80 kHz according to the manufacture provided specifications. To produce the sound stimulus signal, an arbitrary waveform generator pre-amplified with an audio receiver (SONY, STR-DH130) is used to generate an electric input applied to the transducer.
2.2 Sensor design and mechanics model
For proof-of-concept, the frequency range of the fiber optic hydrophone device was designed to be from 40 kHz to 140 kHz with a bandwidth of 100 kHz, which was chosen to match with that of the reference transducer. To better predict the sensor performance, the sensor structure was modeled by using COMSOL simulations. The model is shown in the inset of Fig. 2(a). The dynamic pressure is applied to the top and side of the sensor head.
Fig. 2 Mechanics modeling of the sensor head: (a) mechanical sensitivity and fundamental natural frequency versus the PDMS cavity length and (b) sensitivity frequency responses of the PDMS cavity for different viscous damping coefficients η (small damping: η = 1 × 10−5 Ns/m, medium damping: η = 1 × 10−4 Ns/m, and large damping: η = 2 × 10−4 Ns/m). The inset in (a) shows the model of the sensor head (a cylinder under dynamic pressure from the top and side). In (a), the eigenfrequency module of COMSOL was used to obtain the natural frequencies by searching the longitudinal resonance modes from several oscillation modes of the PDMS cylinder. In (b), the water drag effect on the surface of the sensor head was included as the spring foundation sub-model in COMSOL with a viscous damping coefficient η.
To investigate the effect of the sensor cavity length on the performance, the mechanical sensitivity (cavity length change with respect to pressure change; i.e., dL/dp) and fundamental natural frequency (f0) as a function of the PDMS cavity length (10 μm to 100 μm) were obtained, as shown in Fig. 2(a). As the PDMS cavity length increases, the fundamental natural frequency decreases, while the mechanical sensitivity increases. This results in a tradeoff between sensor bandwidth and sensitivity. If one would like to obtain a flat acoustic response from the fiber optic hydrophone, the fundamental natural frequency should be designed to be far away from the operation frequency range, which however, will compromise the sensitivity. On the other hand, since the optical detection system is a low coherence system, the optical difference of the FPI needs to be much longer than the coherence length of the SLD source, which requires a relative long PDMS cavity. However, when the PDMS cavity becomes too long, due to the diffraction, the intensity coupled back to the optical fiber will be too weak, and thus significantly reducing the visibility of the interference. Considering these tradeoffs, the sensor cavity length was chosen to be ~46 μm, which renders an OPD of 128.8 μm (refractive index of PDMS is 1.4). This OPD is more than three times of the coherence length of the light source (~38.1 μm), which is also short enough to ensure a good visibility of interference. For this cavity length, the fundamental natural frequency was obtained as 195 kHz, which is larger than the designed maximum operation frequency of 140 kHz. At the same time, a relatively high mechanical sensitivity of 1.2 × 10−4 nm/Pa can be achieved.
Another factor that affects the bandwidth of the sensor is the damping. In Fig. 2(b), the sensitivity frequency responses of the sensor (i.e., mechanical sensitivity versus frequency) for different damping scenarios (small, medium, and large) are shown. Larger damping results in a flatter sensitivity frequency response, which could help increase the sensor bandwidth. The damping considered here is the viscous damping from the surrounding water, which however, can hardly be tailored in the design of the sensor head.
For the sensor material selection, PDMS was chosen to ensure a high mechanical sensitivity due to its low Young’s modulus, as well as its excellent acoustic impedance match with water. In Table 1, the mechanical sensitivity dL/dp, fundamental natural frequency f0, acoustic impedance Z of a sensor made of PDMS with a fixed cavity length of 46 μm was compared with two other materials (Polyethylene terephthalate (PET) and Parylene-C) that were used to make Fabry-Perot hydrophones [21,25], at 80 kHz (the optimal working frequency of the reference transducer). As expected, since PDMS is much softer than the other two materials, the mechanical sensitivity is much higher than those of two other materials. Although the fundamental natural frequency is lower for the PDMS cavity, it is still acceptable for the designed working range of 40 kHz to 140 kHz. Furthermore, compared to the other two materials, PDMS also has better impedance match with water, rendering it a better material choice for hydrophones.
Table 1. Comparison of acoustic impedance, mechanical sensitivity, and fundamental natural frequency obtained with different materialsa. v, E, ρ, c, are the Poisson’s ratio, Young’s modulus, density, and speed of sound, respectively.
2.3 Sensor fabrication
The fabrication process of the FPI hydrophone is illustrated in Fig. 3. First, a batch of single mode optical fibers (Corning, SMF-28e) are prepared by cleaving and cleaning on one ends followed by titanium dioxide optical coating (thickness: λ/4 at 1310nm) [Fig. 3(a)]. The optical coating acts as a partial mirror at the interface between the optical fiber core and PDMS material. Without the optical coating, the reflection at the interface is too small due to the small difference of refractive indices of the optical fiber core and PDMS. A single fiber is then treated with triethoxysilane silane (Gelest, Tridecafluoro-1,1,2,2-etrahydrooctyl) in order to help increase the adhesion of PDMS to the fiber end face. Another fiber, which is used as a mold, is treated with anti-adhesion silane (Gelest, Methacryloxypropyltrimethoxysilane) for easy releasing after the PDMS molding process [Fig. 3(b)]. The chemical treatment is performed by dipping and baking processes in a fume hood. The geometric and optical property changes due to the chemical treatment are minimal since the coating is applied by adding a few layers of functional molecules via covalent bonding to the substrate. Then, the optical fiber with the adhesion coating and the fiber mold are coarsely aligned by using two 5-axis manual stages under two microscopes positioned with 90 degree angle of separation [Fig. 3(c)]. After the initial alignment, a drop of uncured PDMS is applied to the fiber with adhesion coating. Next, the fiber mold is moved to approach the deposited PDMS drop until the fiber touches the drop. The fiber with adhesion coating is connected to an optical interrogation system (Micron Optics, SM130) for precisely obtaining a gap distance between the two fibers [Fig. 3(d)]. The optical cavity length is calculated by using pairs of two adjacent peaks of the interference spectrum generated by the Fabry-Perot cavity between the two optical coating interfaces [29], which is monitored in real time during the fabrication process. By using this optical fiber based molding process, large range and high precision gap adjustment can be achieved without using an external optical measurement system. Our experimental results suggest that the achievable resolution of the cavity length fabrication is ~100 nm and the cavity length range can be from ~17 μm to 1 mm. Once the desired gap distance is achieved, the PDMS is cured on the stages at room temperature for 24 hours [Fig. 3(e)]. Finally, the fiber mold with the anti-adhesion layer is removed from the cured PDMS and the top surface of the PDMS structure is coated with a thin silver layer by using sputtering process (thickness: ~100 nm) [Fig. 3(f)]. The diameter of the fabricated PDMS sensor head are around 130 µm.
It should be noted that the sensors can be batch fabricated by using a similar method described in [35], which can help further reduce the fabrication cost. The sensor batch fabrication is beyond the scope of this work.
3. Sensor characterization
The performance of fiber optic hydrophone was characterized in a water tank (size: 450 mm × 300 mm × 300 mm) from 40 kHz to 140 kHz. The commercial ultrasound transducer was placed at a distance of 65 mm from the sensor, which was used as both an acoustic source and a reference sensor. By using the transmission response of the commercial transducer, the absolute acoustic pressure at the sensor location (with a distance of 65 mm) was obtained and used in the sensor performance characterization.
3.1 Sensitivity, resolution, and directivity
The sensitivity of the sensor was obtained by generating a pure tone signal at 80 kHz with the commercial transducer and by changing its output sound pressure. The results are shown in Fig. 4(a). It can be seen that over the tested pressure range of 100 kPa, the sensor exhibits an excellent linearity. Based on a linear fitting of the calibration curve, the sensitivity of the sensor was obtained to be 13.2 mV/kPa. Due to the limited emission power of the commercial transducer, we were not able to obtain the dynamic range of the sensor, which is expected to be much larger than 100 kPa. In order to be able to compare the sensitivity of our sensor with a previously reported FPI hydrophone made of multilayer films of SiO2 and TiO2 [26], the sensitivity was divided by the DC component of the photodetector output UDC. A sensitivity of 3.38 × 10−3 V/kPa/V at 80 kHz was obtained, which is 4 orders of magnitude higher than that of the hydrophone reported in [26] (3.43 × 10−7 V/kPa/V at 1.56MHz).
Fig. 4 Sensor characterization results: (a) Sensor sensitivity calibration curve. (b) Directivity obtained at 80 kHz. The directivity curve was obtained by normalizing the voltage output of the sensor at different incident sound angle to that at zero incident angle. (c) Temporal response of the sensor at 80 kHz. The inset shows the output sound pressure pulse from the transducer. (d) Sensitivity frequency response of the sensor. The distance to the acoustic source is 65 mm and the input acoustic azimuth angle is θ = 0 °. The experimental results were overlaid with the simulation curve shown in Fig. 2(b) for η = 1 × 10−4 Ns/m.
The high sensitivity of the sensor leads to a high resolution. The RMS noise floor of the sensor system without any acoustic input was found to be 1.95 mV, which was determined by the total noise level of the photodetector and the thermal-mechanical noise of the PDMS cavity. Based on the obtained sensitivity and noise floor, the resolution of the sensor in terms of noise equivalent pressure (NEP) was obtained as 148 Pa. This resolution was found to be much better than that of the thin polymer film FPI hydrophone (2.3 kPa) [20] and that of the fiber Bragg grating hydrophone (440 Pa) [15]. Given the tested bandwidth of 100 kHz, normalized NEP was calculated to be 0.47.
To characterize the directivity of the sensor, the dependence of the sensor response amplitude with respect to the input sound azimuth angle θ [illustrated in Fig. 1] was obtained. In the experiment, the sensor was initially aligned with the vertical axis and then rotated with an increment of 10°. The measured response as a functional of the angle θ is shown in Fig. 4(b). A directional response of the sensor can be clearly observed. This indicates that the sensor head is mostly sensitive to the acoustic pressure component in the axial direction.
3.2 Temporal and frequency responses
To characterize the temporal responses of the sensor, the commercial transducer was used to generate ultrasound pulses. In order to avoid the reverberation interferences in the water tank, pulses defined in the form of s(t) = (1-cos(2πft/n))/2 × sin(2πft) × (t<(n/f)), where f is the center frequency of the emission sound, t is time, and n = 10 is the cycle number in each pulse, were used to trigger the transducer, as shown in the inset of Fig. 4(c). The temporal responses of the hydrophone at various input sound frequencies were measured and representative results at 80 kHz are shown in Fig. 4(c). Clearly, the sensor was able to capture the pulses without much distortion. There appears to be another pulse following the first one with a time difference of ~220 μs between the two pulses. This was believed to be due to the echo from the closest tank wall which was ~15 cm away from the transducer and sensor head.
To study the sensor frequency response, single frequency sweeping of the input sound from 40 kHz to 140 kHz was carried out with an incident azimuth angle of θ = 0 °. The sensitivity frequency response of the fiber optic hydrophone is shown in Fig. 4(d), which was obtained by normalizing the output of the fiber optic hydrophone to that of the reference transducer at the same frequency. The frequency response curve of the reference transducer was provided in the data sheet by the manufacture, which was assumed to be accurate. The sensitivity gradually increases as the frequency increases and is approaching the fundamental frequency (195 kHz). The sensitivity frequency response is found to compare well the simulated mechanical sensitivity frequency response shown in Fig. 2(b) for the medium damping case.
4. Tracking of the sensor working point
To demonstrate the tracking of the sensor working point, two scenarios were tested, as illustrated in Fig. 5. In the first scenario [Fig. 5(a)], a constant single tone sound was generated by using the underwater transducer in the water tank, and a DC bias voltage was sent to the tunable FPI from −10 V to 10 V, in order to sweep its cavity length; i.e., sweeping the working point of the sensor. The amplitude of the photodetector output signal was recorded during the sweeping process. Obtaining the maximum signal amplitude would indicate the successful tracking of the sensor operation point. The second scenario [Fig. 5(b)] can be used in the case when the acoustic source is not always present. When the sensor is placed in water, the cavity length of the sensor can change due to the temperature difference, the water absorption of the material, and more importantly, the hydrostatic pressure in water, which may result in a large cavity length change. To demonstrate the tracking of the sensor working point for this scenario, a 100 kHz sinusoidal AC signal with a peak-to-peak amplitude of 1 V, together with a sweeping DC bias from −9.5 V to 9.5 V were applied to the tunable FPI. The sensor was placed in the same location in the water tank, but there was no acoustic input from the transducer. Similar to the first scenario, when the maximum signal amplitude of the photodetector was obtained, the system was tuned to work at its maximum sensitivity.
Fig. 5 Tracking of sensor working point. (a) Scenario 1 when the acoustic source is present. (b) Scenario 2 when the acoustic source is absent. (c) Output of the photodetector as a function of the DC bias voltage applied to the tunable FPI obtained for the two scenarios.
To compare the effectiveness of sensor working point tracking in both scenarios, the obtained signal amplitude as a function of the applied DC bias voltage for both scenarios are plotted in Fig. 5(c). It can be seen that in both cases, three peaks can be identified over the sweeping voltage range of −10 V to 10V. Since the sensor cavity length was considered to be the same for the two tracking scenarios, the peak positions should be identical for the two cases. The experimental results exhibit small variations of peak positions for the two cases, which were believed to be due to the distortion of the acoustic signal produced by the transducer as well as the slightly nonlinear response of the piezo-actuator used in the tunable FPI. The largest variation of positions was between Peak 1 and Peak 4, which will only result in a sensitivity difference of less than 6.5%. It should be noted that although Peak 1 obtained in the second scenario and Peak 4 obtained in the first scenario are shown to have the maximum values, any of the other two peaks can also be used as the sensor working points. These peaks are corresponding to the higher order quadrature points, at which the sensitivities of the sensor would be only slightly lower (< 8% for Scenario 1 and <15% for Scenario 2) than that obtained at the zero order quadrature point.
With a DC bias voltage swept between −10V and 10V, the cavity length change of the tunable FPI was 2.99 μm, which renders a tracking range for the sensor cavity length of 2.14 μm (the refractive index of PDMS is 1.4). According to the calculated mechanical sensitivity of the sensor (1.2 × 10−4 nm/Pa) shown in Table 1, the cavity length change due to the hydrostatic pressure of 1 meter depth of water (9.8 kPa) should be less than 1.2 nm, as the static sensitivity of the sensor is usually smaller than the dynamic pressure sensitivity. Therefore, it is expected that the tracking of the sensor working point tracking can be achieved under the hydrostatic pressure of over 1600 m (1 mile) depth of water, which will result in a cavity length change of less than 2 μm (smaller than the demonstrated sensor cavity tracking range of 2.14 μm). Note that the maximum tuning range of the tunable FPI is 11.2 μm when applying a 75 V DC bias (i.e., maximum voltage range of the piezo actuator). Therefore, the maximum tracking range of the sensor working point is 8 μm for the current system, which indicates that the sensor working point could be trackable under deep water of 6400 m depth.
5. Discussion
When a tunable laser is used as a light source to illuminate the same FP hydrophone, as shown in Fig. 6(a), the working point of the sensor can also be tracked by sweeping the laser wavelength. Here, we compared the performance of the white-light interferometric system shown in Fig. 5 with this tunable laser based system. In the experiment, the FP hydrophone was kept in the water tank and the optical systems were simply switched at point A [see Figs. 5 and 6(a)] when a single frequency continuous sound was played with the transducer. The sensor output obtained with the tunable laser system exhibited significant drift, while the white-light system was demonstrated to be remarkably stable, as shown in Figs. 6(b) and 6(c).
Fig. 6 Comparison of the white-light interferometric system and a tunable laser based interferometric system. (a) Schematic of the tunable laser based system with the same FP hydrophone. (b) Time domain output of the sensor in response to a harmonic sound input at 80 kHz. (c) Zoom-in time response in the highlighted time window of (b).
These results show that without wavelength stabilization, the hydrophone system with a tunable laser can greatly suffer from the wavelength instability induced phase noise. The associated phase noise, δΦλ, due to the source wavelength fluctuations is given by [30]
In comparison, assuming the same source wavelength fluctuations , the associated phase fluctuation for the white-light system isFor the white light system, (~0.33μm), which is significantly smaller than δ1 ≈46 μm × 2 × 1.4 = 128.8 μm. This explains the superior stability of the white light system, which is another advantage of the proposed hydrophone system.6. Conclusion
A white-light, working-point trackable fiber-optic hydrophone system is demonstrated. This system consists of two FPIs: one being the FP sensor head and the other being a homemade tunable FP filter. A mechanics model is developed to facilitate the design of the geometric parameters of the sensor head. The fabrication of the FP sensor entails a simple, low cost, polymer molding process by using an optical fiber based mold. This process enables high-resolution sensor cavity length control with a large range. The tunable FPI is constructed by using two fiber mirrors, with one controlled to move by using a piezoelectric actuator. It can be used to facilitate the tracking of sensor working point, so that the sensor can always work at its maximum sensitivity point. In the experiments, the fiber optic hydrophone is shown to have a good linear response for up to 100 kPa, with a high sensitivity of 13.2 mV/kPa and a high acoustic pressure resolution of 148 Pa. Tracking of the sensor working point is also successfully demonstrated with such a system. In addition, the white-light hydrophone system is shown to have superior performance to another much more expensive tunable laser based system. This white-light hydrophone system can help address the sensor working point drift of a FP hydrophone, due to hydrostatic pressure and/or temperature changes, or water absorption of the sensor cavity material. With the demonstrated sensor cavity length tracking range of 2.14 μm, it is estimated that the sensor working point can be trackable even when the sensor is placed in deep water of over 1600 m. Therefore, this system renders the capability of detecting weak acoustic signals in deep water, which may open up new applications of using fiber optic hydrophones for deep ocean exploration.
Funding
National Science Foundation (NSF) (ECCS1509504); Special Project of National Key Scientific Equipment Development of China (2013YQ03091503).
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