A Michelson interferometric fiber-optic acoustic sensor based on a large-area gold diaphragm is proposed in this paper. The Michelson interferometer (MI) based on 3×3 coupler is comprised of two beams that reflected from the gold diaphragm and a cleaved fiber end face. Thickness and diameter of the gold diaphragm are 300 nm and 2.5 mm, respectively. Based on the phase difference between each output port of the 3×3 fiber coupler, an ellipse fitting differential cross multiplication (EF-DCM) interrogation process is induced for phase demodulation, which can overcome the phase distortion caused by property degradation of 3×3 coupler. Experimental results show that the sensor has a phase sensitivity of about -130.6 dB re 1 rad/μPa@100 Hz. A flat response range between 0.8 to 250 Hz is realized with the sensitivity fluctuation below 0.7 dB. Besides, the signal-to-noise ratio (SNR) and minimal detectable pressure (MDP) of the sensor are 57.9 dB and 10.2 mPa/Hz1/2 at 5 Hz. The proposed sensor exhibits superiorities of compact size, high sensitivity, flat low-frequency response and ease of mass production, which gives the sensor great potential for low-frequency acoustic sensing and photo-acoustic spectroscopy.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Low-frequency acoustic waves detection research has attracted more and more attention in modern society. Due to the characteristics of low attenuation, strong diffraction capability and long propagation distance, low-frequency acoustic waves detection has high application values in many fields, such as natural disaster warning , medical treatment , oil pipeline detection , military monitoring  and photoacoustic spectroscopy . Nowadays, detection methods commonly used are based on electronic equipment such as capacitive and piezoelectric microphones [6,7]. However, there are still many restrictions of those methods including sensitive to electromagnetic interference, unsuitable for long distance sensing and complex system composition for signal readout.
Due to the unique superiorities of compact size, high sensitivity, ability of remote measurement, immunity to electromagnetic interference, and the feasibility of multiplexing, fiber-optic acoustic sensors have been extensively studied in the past decades [8–9]. Various kinds of fiber-optic acoustic sensing structures have been reported such as fiber gratings [10–12], fiber laser [13–16], and fiber interferometers [17–26], etc. Application of fiber gratings acoustic sensors is limited because sensing structure is sensitive to temperature change and large area transducer is required to achieve high sensitivity. In addition, the high level of low-frequency noise existing in fiber laser sensing system makes it not an effective scheme for low-frequency or even infrasound detection. Compared with the former two, diaphragm-based fiber interferometers are attractive candidates with the advantages of low noise level, high resolution and easy to fabricate. The most reported interferometers are Mach-Zehnder interferometers (MZIs) [18,22], Michelson interferometers (MIs) , Sagnac interferometers (SIs)  and Fabry-Perot interferometers (FPIs) [19–21].
For diaphragm-based fiber acoustic sensors, the sensing performance depends greatly on the characteristics of the deformable diaphragm. Various implementations of the diaphragm have been reported such as silicon [27,28], polymer (PET , UV adhesive , PDMS ), metal (silver , aluminum ), graphene [20,21] and so on. It can be concluded that there are still several limitations in the application of fiber low-frequency sensors. The reflectivity of most non-metallic material diaphragm is relatively low [25,27]. It results in additional attenuation and noise while the common solution is adding a layer of metal film on the surface to enhance the reflectivity, which also increases the thickness and fabrication complexity of the diaphragm. Besides, the thickness and radius of the diaphragm in [17,29] are restricted or cannot be precisely controlled due to the limit of fabricate method. Thus, the uniformity among different sensors of a same structure is difficult to maintain. At the same time, it is not feasible to specially improve the low-frequency performance by further optimizing the diaphragm size. On the other hand, the unstable chemical properties of the diaphragm material bring the risk of performance degradation as working in harsh environment. For example, the silver can be vulcanized in the air, which limits the life circle and application environment.
In this paper, we propose and demonstrate a Michelson interferometric fiber-optic acoustic sensor based on gold diaphragm. Compared to the reported diaphragm materials, gold has the advantages of stable chemical property and high reflectivity. The former provides the ability to adapt various environments while the latter ensures the intensity of reflected light. Besides, thinner and smaller diaphragm are designed to achieve high sensitivity and low noise level based on the analysis of diaphragm forced vibration. The gold diaphragm is fabricated by electron beam evaporation deposition method with 300 nm in thickness and 2.5 mm in diameter. The readout configuration is a MI based on 3×3 symmetric fiber coupler. The MI is comprised of the two beams of light reflected from the gold foil and a cleaved fiber end face. An ellipse fitting differential cross multiplication (EF-DCM) algorithm  is proposed to realize phase demodulation. The interrogation system proposed overcomes the drawbacks of traditional phase demodulation method based on 3×3 coupler that the splitting ratio must be strictly 1:1:1 and the phase difference of each port must be fixed at 120° [30–31]. Experimental results show that the sensor has a phase sensitivity of about -130.6 dB re 1 rad/μPa at 100 Hz. A flat response range between 0.8 to 250 Hz is realized with the sensitivity fluctuation below 0.7 dB. Minimal detectable pressure (MDP) of the sensor is about 10.2 mPa/Hz1/2@5 Hz. The proposed sensor exhibits great potential for low-frequency acoustic sensing and photo-acoustic spectroscopy.
2. Diaphragm forced vibration theory
As illustrated previously, the vibration of diaphragm converts the acoustic signal into the length change of the MI sensing arm. Consequently, diaphragm is the key element of the sensor head, which determines the frequency response of the sensing system. The two models commonly used for diaphragm vibration analysis are plate model and membrane model. Based on the conclusion in , the membrane model is more suitable in our case because the calculated tensile parameter k is 276, which is much greater than 20. Therefore, when diaphragm deviates from equilibrium, the tension of the diaphragm is the main force making diaphragm return to the original equilibrium position. For application as a low-frequency microphone, the sensor must have a relatively flat frequency response. Under the assumption that the deformation is less than the thickness of diaphragm, the forced vibration amplitude and first-order resonant frequency of the diaphragm can be written as Eq. (1) and Eq. (2), respectively .
Properties of diaphragm are simulated to better design the parameters. In terms of gold diaphragm, when sound frequency, sound pressure, radius, thickness and tensile stress of the diaphragm are set to 100 Hz, 1 Pa, 1 mm, 500 nm and 2×107 N/m2, respectively, the deformation of diaphragm is shown in Fig. 1(a). It can be observed that deformation amplitude declines with the increasing radial distance to center. As for resonant frequency, as the bulk density of gold is 19300 kg/m3, relationship between radius, tensile stress and resonant frequency is performed as Fig. 1(b). As we know, maximum working frequency of the sensor should be controlled lower than one third of the resonant frequency of the diaphragm to ensure a flat frequency response , so the radius can’t be too large because it will lower resonant frequency and compress the available frequency band.
As the reflection of light usually occurs in center of diaphragm, the response sensitivity of the sensor is determined by the central deformation. For MI based sensors, the phase sensitivity Sφ (rad/Pa) is calculated as Eq. (3):
As the response curve can be regarded as flat in the low frequency band, so we can analyze the effect of diaphragm size on response sensitivity at 100 Hz which is illustrated as Fig. 2(a). When thickness is more than 500 nm, the sensitivity is very low. Even though larger radius helps to improve sensitivity, it will introduce more noise, reduce the flatness of diaphragm and limit flat region at the same time. Besides, lower tensile stress contributes to increase sensitivity but also brings lower resonant frequency as showed in Fig. 2(b).
Based on the discussion above, several aspects need be taken into consideration in the design of diaphragm. Although tensile stress is difficult to control precisely, it will not fluctuate dramatically as the process of fabrication is determined. Furthermore, in order to obtain lower noise level and wide flat response range, radius of diaphragm should be small and thickness of the diaphragm needs to be reduced to guarantee a relatively high sensitivity. As for material, gold is chosen because of its properties of good chemical stability, high reflectivity, relatively low Poisson’s ratio and Young’s modulus which enhance deformation sensitivity from the perspective of material mechanics . Given the above, the gold diaphragm is fabricated by electron beam evaporation deposition method. The thickness and radius are 300 nm and 1.25 mm, respectively. The detail procedure of preparing and transferring the diaphragm is mentioned in our previous work .
As shown in Fig. 3(a), The MI is comprised of two beams that reflected from the gold diaphragm and a cleaved fiber end face, respectively. The detail fabrication steps are described below. After the diaphragm is transferred to the outer metal sleeve, for the sensing arm, an 8° tilted fiber end face is polished to prevent Fresnel reflection. The fiber tip is inserted into the inner ceramic ferrule with the inner diameter of 125 μm. Then the inner ceramic ferrule together with the fiber tip is plugged into the outer ceramic ferrule whose inner diameter is 2.5 mm. The nested structure is inserted to the outer metal sleeve to make gold diaphragm as one reflective surface of MI. Another reflective surface is a cleaved fiber end face of the reference arm. The light reflected from the third face introduces additional noise. Therefore, the third face is intentionally damaged to prevent Fresnel reflection artificially. Aiming to enhance the interference fringe contrast, optical power reflected from the cleaved fiber end face and the gold film should be matched.
Scattering attenuation resulting from the air gap between fiber tip and the diaphragm is a key point to be considered for optical power matching. Distance between the fiber end face and the gold film can be precisely adjusted with a five-axis precision aligner as shown in Fig. 3(b). To clarify, mathematic model of light scattering attenuation of the sensor head is shown in Fig. 4(a). Due to the high reflectivity, the gold film is regarded as an ideal mirror. Under this assumption, the transmission loss of light in the cavity can be equivalent to the splice loss of two optical fibers symmetrical about the gold film. Furthermore, mode field of step index single mode fiber can be simplified as Gaussian beam. Light propagation along the fiber at 1550 nm wavelength is illustrated in Fig. 4(b) with beam propagation method (BPM). We can see that light becomes divergent when it is injected into the air cavity. Because of the tilt end face, it shows that the distribution of light field is not symmetric about the fiber core. The simulation results of transmission efficiency with the change of air cavity length is showed in Fig. 4(c). Obviously, due to the angular attenuation, transmission loss of tilt end fiber is much larger than normal fiber. Even the cavity length is close to zero, the efficiency is below 0.4, which mainly results from the inevitable air gap and tilt inject angle. Considering the reflectivity of fiber end face and gold diaphragm, the air cavity length should be controlled about 200 μm level to balance the light intensities of two arms.
Cavity length adjustment procedure is described as follows. Firstly, the reflection spectrum of a cleaved fiber end face is acquired and fixed with an optical spectrum analyzer (YOKOGAWA, AQ6370c). Then, precisely adjusting the cavity length and monitoring the reflection spectrum of the sensor head. Optical power matching is realized when the two spectra overlap. Finally, fix the whole structure with epoxy glue. The fabricated sensor head is shown in Fig. 3(c). The diameter and length of the sensor are less than 5 mm and 2 cm, respectively. And experimental result illustrates that the optimal cavity length is slightly smaller than 100 μm. The wrinkle of the gold diaphragm is considered to be a reasonable explanation that the experimental result is lower than the expected result.
On the other hand, the optical path difference (OPD) between two arms should be small enough. Too large OPD will reduce the interference fringe contrast due to the limitation of the coherence length of light source. The length of reference arm is controlled with the help of a microscope and fiber cleaver (FUJIKURA, CT-32). Then the fiber tip is inserted into a silica capillary tube (SCT) with an inner diameter of 300 μm for protection. Just as the sensor head, the SCT is also sealed with epoxy glue. Interference spectrum of the MI sensor is shown in Fig. 5. Measured free spectrum range (FSR) is ∼0.3 nm and extinction ratio is about 15.5 dB.
3. Experimental results and discussions
The schematic of the sensing system is shown as Fig. 6. Light emitted from single frequency laser (NKT Photonics, X15) is injected into the input port 1 of the coupler. The wavelength is tuned to 1550 nm. The sensor head is connected with the output port 1 as one reflection mirror, and the end face of output port 2 is well cleaved as the other reflector. Interference occurs between the two lights reflected from the gold film and the well cleaved fiber end face at output port 1 and 2, respectively. In order to avoid Fabry-Perot interference at the sensing head, the fiber end face was polished with an angle of nearly 8° to reduce the Fresnel reflection. The sensor head is sealed into low frequency acoustic coupling cavity (B&K, WB-3570). The coupling cavity can generate single frequency acoustic wave with frequency range of 0.1∼251 Hz. The signal analyzer (B&K, LAN-XI 3160) receives control signal from computer and sends it to the wide band amplifier which drives acoustic coupling cavity. Simultaneously, a standard capacitive microphone (B&K, 4193-L-004) is sealed into cavity for calibration, whose output signal is collected by signal analyzer. In addition, pigtail at output port 3 is much shorter and the Fresnel reflection is artificially eliminated to reduce the influence of reflected light on the interference. Two identical photodetectors (New Focus, 1623) are connected with the input port 2 and 3, respectively to convert the light intensity into voltage. The signals of two PDs can be described as Eqs. (4)-(5):
A typical time domain signal acquired from the two PDs is shown in Fig. 7(a) for a 200 Hz acoustic signal. To obtain a relatively complete ellipse, the sound pressure is relatively high (about 108 dB re 20 μPa). An obvious phase difference can be observed between the two signals. The amplitudes of two channel signal have a relatively large difference due to the working wavelength does not lie in the dip or peak of the reflection spectrum. It proves there is no strict necessary requirement for working wavelength, which means the process of wavelength control can be omitted. Even though the reflection spectrum drifts slowly with the change of temperature or other disturbance, the EF-DCM algorithm can demodulate the signal without distortion . The scatter points can make up nearly half of an ellipse as shown in Fig. 7(b). The scatters fall on the fitting ellipse curve exactly and the phase change caused by acoustic wave is more than $\pi $. rad.
To acquire the frequency response of the sensor, acoustic waves with frequency from 0.8 to 250 Hz are applied. As the sound signal applied is single frequency sinusoidal signal, sinusoidal fitting is used to obtain the amplitude of demodulated waveform. Compared with the common methods such as calculating the maximum or minimum and doing subtraction, sinusoidal fitting is a more targeted method and possesses ronger noise resistance ability due to finding the global optimization solution. Figures 8(a)–8(c) demonstrate the demodulated signal and sinusoidal fitting curves at 1 Hz, 5 Hz and 200 Hz, respectively. Besides, the linearity of sensing at 5 Hz is implemented. As performed in Fig. 8(d), (a) good linearity with R2 value of 0.998 and large dynamic range reaching up to 111.4 dB are achieved.
Further, the noise level of the sensor is analyzed by calculating signal noise ratio (SNR) and noise equal pressure (NEP). The corresponding frequency spectrum can be obtained from fast Fourier transform (FFT) of the time domain signal as shown in Fig. 9. When the applied sound pressure is about 107 dB, the SNR of 20 Hz and 250 Hz are 55.6 dB, and 54.9 dB, respectively. And there is no obvious harmonic component in the spectrum. For more detail, SNR and NEP of 0.8∼250 Hz are calculated. As can be seen in Fig. 10, the SNR of the acoustic wave under 1 Hz is much lower than that of higher frequencies due to the severe impact of 1/f noise which is the dominant noise for low-frequency signal. On the other hand, suppose we intend to sample the equal periods for signals of different frequencies to ensure enough data. The lower the frequency, the longer the sampling time we need. This inevitably increases the instability and the chance to be disturbed. Accordingly, relatively stable and high level of SNR (∼50 dB) can be observed when frequency is larger than 5 Hz. The noise level is limited to below 58dB from 5 Hz to 250 Hz. The minimum detectable pressure (MDP) calculated at 5 Hz is about 10.2 mPa/Hz1/2.
Another important characteristic of acoustic sensor is frequency response. Measured frequency response of our sensor with the frequency range of 0.8-250 Hz is shown in Fig. 11. The blue dots in the graph are measured results while the red curve is the simulation curve based on the discussion in section 2. It is clear that the sensor performs a flat sensitivity within the measured frequency range. The sensitivity fluctuation is less than 0.7 dB while the average sensitivity is about -131.3 dB re 1 rad/μPa. In addition, the first-order resonant frequency is about 13.6 kHz, which leaves great space in frequency domain for acoustic detection. The application areas of the sensor are broadened because it can be applied not only to low-frequency detection but also audible band acoustic sensing. Restricted by the maximum available frequency of sound source, experiments for higher frequencies are not proposed.
The comparisons of the low-frequency acoustic sensing performances between our work and other reported schemes are listed in Table 1. It can be observed that our sensor has a relatively high sensitivity and flat response in the range of low frequency. At the same time, a lower MDP is achieved indicating the noise is well controlled. To summarize, good performance at low-frequency domain indicates that the proposed sensor can be a favorable candidate for low-frequency acoustic detection such as environmental noise pollution monitors in harsh environments.
In summary, a Michelson interferometric fiber low-frequency acoustic sensor based on gold diaphragm has been proposed in this paper. Lights reflected from the gold film and cleaved fiber end facet at two output ports of the 3×3 fiber coupler interfere with each other. The gold film with 300 nm in thickness and 2.5 mm in diameter is fabricated with the electron beam evaporation deposition method. An ellipse fitting differential cross multiplication algorithm is proposed for phase demodulation, which provides enhanced tolerance to the property of 3×3 couplers and responsibility of photoelectric detectors. Experimental results show that the sensor has a phase sensitivity of -130.6 dB re 1 rad/μPa@100 Hz. A flat response range between 0.8 to 250 Hz is realized with the sensitivity fluctuation of 0.7 dB. SNR and MDP of the sensor are 57.9 dB and 10.2 mPa/Hz1/2 at 5 Hz. Stable, compact size, high sensitivity and easy for mass production makes the sensor performable for low-frequency acoustic sensing, photo-acoustic spectroscopy and noise pollution monitoring.
National Key Research and Development Program of China (2018YFF01011800); National Natural Science Foundation of China (61775070); Fundamental Research Funds for the Central Universities (2017KFYXJJ032, 2019kfyXMBZ052).
The authors declare no conflicts of interest.
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