Study on the Sensitization Effect of Flywheel-Like Diaphragm on Fiber-Optic Fabry-Perot Acoustic Sensor

A flywheel-like sensitive diaphragm, which breaks the sensitivity limitations imposed by the increased thickness and the decreased radius in edge-clamped circular structure, has been proposed and analyzed in fiber Fabry-Perot (FP) acoustic sensor. A new model is built around the effect of diaphragm’s structure parameters on sensitivity of a fiber FP acoustic sensor with common ductile material. The proposed sensor based on flywheel-like stainless diaphragm in 5mm diameter and 0.035mm thickness has been fabricated and its acoustic performances were tested. The test results show that our acoustic sensor can realize acoustic measurement from 0.1 kHz to 19 kHz. The sensor exhibits an acoustic pressure sensitivity of 1.525nm/Pa at the frequency of 4.5 kHz. The noise-limited minimum detectable pressure (MDP) level of $\sim 13.06~\mu Pa/\sqrt {Hz} \text{@} 4.5\textrm {kHz}$ and the acoustic pressure signal-to-noise ratio (SNR) of 70.42 dB@4.5kHz are achieved, respectively. And the mean SNR of cavity length variation of 62.43dB can be acquired over the entire frequency range. Comparing with the edge-clamped circular structure, the flywheel-like structure endows the common ductile sheet material the ability to response to acoustic pressure. Cost-effective and compact size give the proposed acoustic sensor a competitive edge, something of crucial importance to commercial applications.


I. INTRODUCTION
Fiber optic acoustic sensor has shown its great potential in recent decades [1]- [12] because of their unique advantages such as immunity to electromagnetic interference, high resolution, fast response, and compact size. Fiber-tip Fabry-Perot (FP) interferometers (FPI) between a cleaved fiber end and a sensitive diaphragm have demonstrated high sensitivity without the need for a long length of optical fiber compared with Mach-Zehnder interferometers [1] and Michelson interferometers [2]. The sensitivity of the diaphragm in the FP acoustic sensor is defined as the ratio of the length variation of the FP cavity to the acoustic pressure. So various kinds of diaphragm materials have been studied for FPI acoustic sensors, such as silicon [3], silica [4], chitosan [5], silk fibroin [6], UV adhesive [7], silver [8], graphene [9], The associate editor coordinating the review of this manuscript and approving it for publication was Sukhdev Roy. aluminum [10] and Parylene-C [11]. The abovementioned sensing diaphragms are usually edge-clamped circular structure. The sensor's acoustic pressure sensitivity is proportional to a 4 h 3 , where a is the radius and h is the thickness of the diaphragm [8]. Therefore, the diaphragms are typically oriented toward larger radius and smaller thickness to improve the sensor's sensitivity. Gong et al. demonstrated an acoustic sensor based on a Parylene-C diaphragm of 9 mm in diameter and 2.4 nm in thickness, with a sensitivity of 2239 nm/Pa at the frequency of 20 Hz [11]. Ni et al. demonstrated a FPI acoustic sensor based on an ultrathin graphene diaphragm with a thickness of 10nm, and the noise-limited minimum detectable pressure (MDP) level of 0.77Pa/ √ Hz@5Hz and 33.97µPa/

√
Hz@10kHz can be achieved [9]. However, the larger radius and smaller thickness of diaphragm increases the cost and difficulty of the manufacture process, and reduces the sensor's mechanical strength. Recently, the researchers have proposed and demonstrated a novel diaphragm structure based on cantilever used in FPI acoustic sensor. Liu et al. proposed a FPI acoustic sensor based on a silica micro-cantilever beam fabricated by femtosecond (fs) laser micromachining, and the acoustic pressure sensitivity of 9.75µm/MPa is achieved at the resonant frequency of 0.74 MHz [3]. Chen et al. proposed a stainless cantilever beam based FPI acoustic sensor and achieved a pressure responsivity of 211.2 nm/Pa at the frequency of 1 kHz [12]. However, cantilever based diaphragm structure has bred new challenges, that is operation only in the frequency region below the resonance frequency [13] and nonlinear response [14].
In this paper, a cost-effective stainless flywheel-like diaphragm is proposed and its sensitization effect induced by structure parameter is discussed. The FPI acoustic sensor with flywheel-like diaphragm has shown three merits: (1) the flywheel structure breaks the sensitivity limitations imposed by the increased thickness and the decreased radius in edge-clamped circular structure, (2) the flywheel-like structure endows the common ductile sheet material (such as stainless, copper, and aluminum) the ability to response to acoustic pressure, (3) cost-effective (in materials and crafts) and compact size give the FPI acoustic sensor a competitive advantage in commercial applications. The experimental results indicate that the proposed sensor has a sensitivity of 1.525nm/Pa @ 4.5 kHz and a noise-limited MDP of Hz@4.5kHz. A mean SNR of 62.43dB can be achieved in the frequency response range of 0.1 kHz ∼19 kHz. The proposed flywheel-like sensitive diaphragm is believed to have a bright application prospect. Fig. 1(a) is the schematic of our acoustic sensing head that comprises of a fiber, a metal handle, a ceramic ferrule, a glass tube, and a flywheel-like diaphragm. First, the flywheellike diaphragm was fixed on one end of a glass tube using epoxy adhesive. Then, a fiber cladded with metal handle and ceramic ferrule have been inserted from the another end of the glass tube, as shown in the Fig.1 (b). Finally, the sensing head is enclosed in an aluminum housing, as shown in the Fig.1 (c). Throughout the process, the epoxy adhesive plays a role in pre-fixation, and all the components are connected and fastened, via a screw-thread on the metal shell. As the Fig.1 shows, there are many hollowed-outs on the diaphragm that endow to keep the balance of internal and external pressure. The flywheel-like diaphragm was produced in bulk using the laser engraving technology. Hence, the flywheel-like structure apply to all common ductile sheet material such as stainless, copper, and aluminum. Compared with ultra-thin novel materials and circular structure [3]- [11], inexpensive materials and simple crafts give a competitive advantage to the proposed sensor in commercial applications. In addition, the proposed sensing head only has a boundary size of 5mm × 11mm (diameter × length), which makes is more convenient in encapsulation for meeting various application scenarios.

A. DYNAMIC PROPERTIES OF FLYWHEEL-LIKE DIAPHRAGM
As a dynamic signal, the acoustic wave needs to be transformed into detectable physical parameter by the sensitive diaphragm. Thus the diaphragm is a critical component to the acoustic sensor based on FPI structure. The diaphragm will have a deformation when the acoustic waves are loaded. Therefore, the acoustic waves is finally converted to the synchronous variation of cavity length of FPI and the two frequencies are consistency. As illustrated in Fig. 2, the diaphragm was carved into flywheel shape in stainless sheet. The flywheel-like diaphragm consists of three components: circle ring (CR), spoke, and central diaphragm (CD). The diaphragm was fixed on the glass tube via the CR. So the vibration model of flywheel-like diaphragm can be analyzed according to the leaf-spring hinge [15]. According to the dynamic principles, the deflection l(t) of a flywheel-like diaphragm must meet with the motion equation, that is where m = ρπr 2 h is weight of proof mass, ρ, h and r are the material density, diaphragm's thickness and CD's radius, respectively. β is the damping coefficient of acoustic wave in air, k is spring constant of the flywheel-like diaphragm, P(t) (in Pa) is the acoustic pressure acting on the diaphragm, t is a time parameter. The pressure response of flywheel-like diaphragm, which is the solution of Eq. (1), can be expressed as where l(ω, t) is the maximum deformation of the flywheellike diaphragm at the angular frequency ω, P(t) is the time domain acoustic pressure under the frequency ω/2π. ω 0 is the natural angular frequency, which can be calculated by the Eq. (3) and Eq. (4) [15].
where in Eqs. (3) and (4) k is spring constant, E is the Young's modulus of the diaphragm, w and 2a are the spoke's width and the CR's inner diameter, respectively. Based on the Eq. (3) and (4), the varying curves of natural frequency of flywheel-like stainless diaphragm with its structural parameters can be calculated. Fig.3 (a) has described the numerical simulation results of the natural frequency variation with the diaphragm's thickness (h) and spoke's width (w). As we can see that our sensor's theoretical natural frequency can be tailored by changing the diaphragm's structure parameters. In our sensor configuration, a flywheel diaphragm fabricated by a structure parameters combination [4, 2, 0.5, 0.035] (in mm) (corresponding to CR's inner diameter 2a, CD's diameter 2r, spoke's width w, and diaphragm's thickness h) has been used to assemble the fiber FP acoustic sensor. In this case, a theoretical natural frequency of the proposed sensor is 7.975 kHz. And the diaphragm's theoretical response curve simulated by ANSYS soft is shown in the Fig.3 (b). And we can see that the diaphragm has a flat frequency responsivity and the fluctuating range is 1.75dB.
The acoustic pressure response sensitivity S a (ω, t) of the proposed sensor is defined as the ratio of the deflection l(ω, t) of a flywheel-like diaphragm to the acoustic pressure P(t) at the frequency of ω, which is written as: The Eqs. (2) ∼ (5) reveal that the acoustic pressure response sensitivity S a (ω, t) of the proposed sensor is closely related to the structure parameters of a flywheel-like diaphragm.

B. OPTICAL PRINCIPLES OF ACOUSTIC SENSOR
As illustrated in Fig. 4, the proposed acoustic sensor is comprised of two mirrors. The first one is the fiber endface and the second one is flywheel-like diaphragm. The incident beam was divided two beams at the fiber end-face. The first beam reflected by fiber end-face is referred to as reference beam. Another beam propagates along the FP cavity and reflected back by the diaphragm as modulated beam. The returning light beams merge together at fiber end-face and create an interference signal. Due to the smaller reflectivity of R 1 and R 2 of the fiber end-face and the flywheel-like diaphragm, the propagation model of the proposed acoustic sensor can be analyzed according to the two-beam interference. So the interference intensity I r in the FP cavity can be approximated as [16]: where ξ is the loss coefficient of FP cavity; ϕ = 4π nl 0 λ is the phase difference, where n, l 0 , and λ are the refractive index, the initial cavity length, and the operating wavelength, 99288 VOLUME 8, 2020 respectively; I i is the intensity of incident beam. According to the analysis of FP cavity length loss [17], ξ can be determined by: where ω 0 is the mode field radius. For a single-mode fiber and an air medium, ω 0 and n are set as 4.9µm and 1, respectively. Thus, ξ is a function of λ and l 0 . During the interference intensity demodulation, the variation of light intensity I caused by the cavity length fluctuation l can be expressed as follows: where I r is the interference intensity modulated by acoustic pressure, I r is the interference intensity in absence of acoustic pressure. According to the Eq. (8), we can see that the variation of light intensity received by the photo-detector (PD) is proportional to the cavity length fluctuation caused by acoustic pressure. A similar conclusion has been reached in Ref. [16], [19]. Because our acoustic sensor's initial cavity length is available to be tuned to the operating point of an interference fringe to maximize the optical sensitivity during the interference intensity demodulation, the phase difference ϕ = 4π nl 0 λ may be adjusted to be (k + 1 2)π , where k is a nature number. In the intensity demodulation system, the interference intensity I r is finally converted to the output voltage of the PD. Assuming that the output voltage V r from the PD is defined as: where η is the responsivity of the InGaAs photo-detector, ∼1.07 A/W at 1550 nm [20]. Then, in combination with Eqs (8) and (9), the cavity length fluctuation l caused by acoustic pressure is derived as where V 0 is the output voltage from the PD in absence of acoustic pressure. Thus, the pressure deflection behavior of the proposed acoustic sensor can be measured to analyze its acoustic pressure sensitivity. In our sensor configuration, the interference spectrum measured by a broadband source in combination with the AQ6370C having a wavelength resolution of 0.02nm, as shown in Fig. 5. According to the interference spectrum, a double-peak phase demodulation method was performed to set the initial cavity length as 85.3768µm. Moreover, the reflectivity R 1 of the fiber end-face was calculated as 3.37% by using the Fresnel reflection and the effective reflectivity R 2 of the stainless diaphragm was calculated as 0.5992% from the visibility of interference fringes in Fig. 5. Then, ξ in the Eq. (8) and Eq. (10) was calculated as 0.2 by using the Eq. (7).

III. EXPERIMENT AND ANALYSIS
According to the analysis of section II, an experimental setup based on an intensity demodulation method has been built to test the proposed sensor response to acoustic wave, as shown in Fig. 6. The experimental apparatus mainly includes 1550nm ultra-narrow linewidth laser (UNLL, power stability ≤ ±0.05dB in 8hour, wavelength stability ≤ ±1pm) [18], circulator, acoustic sensor, InGaAs photo-detector (PD), loud-speaker, signal generator (SG), reference acoustic sensor (Type 4190, Brüel & Kjaer) [21], data acquisition (DAQ) card. The laser beam emitting from UNLL is launched into a circulator, and then propagates into the acoustic sensor. The acoustic wave emitted by the loud-speaker deforms the diaphragm, leading to changes of the FP cavity length. A PD is used to detect the interferometric signal. Then the cavity length variation can be demodulated from the changes of the output signal intensity by the interferometric intensity demodulation mechanism based on the Eq. (10). Furthermore, the acoustic field evoked by the loud-speaker can be modulated by the SG. And the acoustic field characteristics (such as frequency and intensity) can be calibrated by the reference sensor. In order to ensure synchronous measurement, our acoustic sensor and the reference sensor are located side by side and they are placed opposite to the loud-speaker, and the distance is about 25cm. When no acoustic pressure is imposed on the diaphragm, the output voltage from the PD is defined as the system noise levels V 0 and the mean values of the repeated measures is 0.016mV. VOLUME 8, 2020

A. ACOUSTIC PRESSURE RESPONSE
To test the sensor's acoustic pressure response, the amplitude of a sinusoidal excitation signal sent by the SG with the frequency of 4.5 kHz changes from 0.5V to 5.0V. So we achieved a varying acoustic field modulated by the excitation signal. In this case, the output signal of the acoustic sensor changes with different amplitudes of the excitation signal as shown in Fig. 7. And a similar tendency of output signal has been found in the reference sensor (BK4190). The output signal amplitude of our acoustic sensor and BK4190 were respectively depicted by the blue dotted curve and red solid curve in Fig. 8(a).
Obviously, our sensor and BK4190 have a similar output response to the modulated acoustic field. The reason for nonlinear region is that loud-speaker's output is no longer linear in 4V ∼ 5V. And the red solid curve in the Fig.8 (b) has described the acoustic pressure changes in different excitation signal's voltage. Based on the Eq. (10), the variation of FP cavity length can be calculated as the blue dotted curve in Fig.8 (b). We can clearly see that the variation of FP cavity length was consistent with the acoustic pressure. Hence, the pressure sensitivity of our acoustic sensor can be calculated as 1.525nm/Pa by the slope ratio of two fitting curves in Fig.8 (b). For an edge-clamped circular stainless diaphragm, the pressure sensitivity can be calculated by the formula of S = 3(1 − σ 2 )(2a) 4 256Eh 3 [19], where 2a = 5mm and h = 0.035mm are respectively the diameter and the thickness, and σ = 0.247 and E = 201GPa are respectively the Poisson ratio and Young's modulus of the stainless diaphragm. The theoretical pressure sensitivity in terms of acoustic pressureinduced deflection is calculated to be 2.79 × 10 −3 nm/Pa. So there is good reason to believe that the flywheel-like structure endows diaphragm with excellent acoustic pressure response performance under the same conditions (such as material and structure parameter). Moreover, Fig. 8(a) has also indicated that the output signal's pressure sensitivity is 1.39 times higher than that revealed by the reference sensor (BK4190) in the same acoustic field.   Fig. 9 shows power spectral density (PSD) of our sensor's output signal when a sinusoidal excitation signal's amplitude of 3V at 4.5 kHz is applied. We can see that our sensor's floor-noise is as low as −95.93dB and the signal to noise ratio (SNR) is 70.42dB at the frequency of 4.5 kHz. According to previous research results [22], [23], Hz) is by definition the incident acoustic pressure that induces an output signal equal to the noise. It is equal to the noise spectral density of the sensor (in V /

√
Hz) divided by the calibrated sensor response sensitivity (in V /Pa). In our experimental configuration, the sensor's output voltage in absence of acoustic pressure is recorded and calculated its noise spectral density. Then our sensor's MDP is ∼13.06µPa/ √ Hz at 4.5kHz.

B. ACOUSTIC FREQUENCY RESPONSE
To test the sensor's acoustic frequency response, a broadband frequency sweep experiment has been performed. In this case, the frequency of a sinusoidal excitation signal sent by the SG with the amplitude of 3V changes from 0.1 kHz to 19 kHz. The PD is used to record the sensor's output signal at different frequencies. And then the variation of sensor's cavity length calculated by the Eq. (10) is regarded as the frequency response. Fig.10 has depicted the sensor's output signal, when the frequency of an excitation signal with the amplitude of 3V are 0.1 kHz, 10 kHz and 19 kHz, respectively. Over the entire test frequency range, our sensor has a good acoustic fidelity, as indicated by the output waveform showing good agreement with excitation signal. In these conditions, our sensor's cavity length variation can be achieved 11.4915nm, 4.1797nm and 6.7218nm, respectively. Moreover, Fig. 11(a) shows the output signal's amplitude of the reference sensor (BK4190). Based on that curve, we can calibrate the acoustic pressure curve [see Fig. 11(b)] generated by loud-speaker under the excitation signal's frequency changes from 0.1 kHz to 19 kHz at amplitude of 3V. Our sensor's cavity length variation in the action of acoustic pressure shows in the Fig. 11(c). By comparing the response curves of reference sensor (BK4190) and acoustic sensor in Fig. 11, we can see that our sensor's cavity length variation is consistent with acoustic pressure changes measured by reference sensor. Therefore, we consider that our acoustic sensor and reference sensor (BK4190) have a similar frequency response in the range of 0.1 ∼ 19 kHz.  To further test the sensor's characteristic in frequency domain, the power density spectrum of the cavity length variation is carried out, as the color-curves shown in Fig 12. The red dotted line indicates the SNR of sensor's cavity length variation in frequency domain. And we can see that the peak of sensor's cavity length variation occurs at ∼8 kHz, which is very near the natural frequency of 7.975 kHz. Moreover, the mean SNR of cavity length variation of 62.4305dB can be achieved in the frequency range of 0.1 kHz ∼ 19 kHz.
As shown in Table 1, our acoustic sensor have demonstrated a low MDP (∼13.06µPa/ √ Hz) at 4.5 kHz, a high average SNR (62.43dB) over a fairly broad response range (0.1 kHz to 19 kHz). All these are due to the flywheel-like structure can improve diaphragm's responsiveness to acoustic pressure in fiber FP acoustic sensor. Moreover, low-price diaphragm material (stainless) and simple craft (laser engraving) make the proposed acoustic sensor more attractive in commercial applications. VOLUME 8, 2020

IV. CONCLUSION
In summary, we proposed a novel flywheel-like structure diaphragm used in fiber FPI acoustic sensor. The flywheel-like structure breaks the sensitivity limitations imposed by the increased thickness and the decreased radius of a circular diaphragm used in traditional fiber FPI acoustic sensors. The sensor exhibits an acoustic pressure sensitivity of 1.525nm/Pa at the frequency of 4.5 kHz. The noise-limited MDP of ∼13.06µPa √ Hz@4.5kHz and the acoustic pressure SNR of 70.42dB@4.5kHz are achieved, respectively. And the mean SNR of cavity length variation of 62.43dB can be acquired in the frequency range of 0.1 kHz ∼ 19 kHz. Other merits of the proposed sensor are its compact size (diameter × length: 5mm × 11mm) and cost-effective (in materials and crafts). The flywheel-like diaphragm based fiber FP acoustic sensor is believed to have a bright application prospect.