Wideband fiber-optic Fabry-Perot acoustic sensing scheme using high-speed absolute cavity length demodulation

Yang Yang; Ya Wang; Ke Chen

doi:10.1364/OE.415750

1. Introduction

Fiber-optic acoustic sensors with a wide frequency range from 20 Hz to 20 kHz have been widely developed in many applications including sound source localization [1], anti-submarine surveillance [2], photoacoustic spectroscopy [3,4], and communications for magnetic resonance imaging (MRI) [5], etc. They have shown great advantages of high sensitivity, immunity to electromagnetic interference, intrinsic safety and remote sensing, in comparison with conventional electrical acoustic sensors. Due to the unique characteristics and the high performance, the wideband fiber-optic acoustic sensor is especially applicable as a speech-sound microphone for communication during the MRI procedure [6]. For voice communication, in order to achieve high fidelity sound signal detection, the sampling frequency is even up to 100kHz. Fiber-optic Fabry-Perot (F-P) acoustic sensor (FPAS) is one of the most popular fiber-optic acoustic sensors due to its high sensitivity and compact size. The F-P cavity of this type acoustic sensor generally consists of the fiber end face and the surface of the diaphragm. The FPAS transduces the acoustic wave by demodulating the F-P cavity length variation aroused by acoustic waves [7]. The demodulation rate determines the band width of the FPAS. Some applications such as photoacoustic spectroscopy or communications for MRI require robust wideband FPASs with low noise equivalent acoustic pressure. Therefore, a fast and robust F-P cavity length demodulation scheme with low noise level is very essential to the wideband FPAS.

For the wideband FPAS, the intensity based quadrature point (Q-point) demodulation method is the main demodulation technique due to its ultra-fast speed and low cost [8–11]. However, the Q-point demodulation method suffers from the light source power fluctuation, ambient temperature perturbation and optical fiber loss, which induce errors to the output signals [12]. Although, there were some studies to stabilize the Q-point with feedback control or other compensation method, the improvement of the output error is limited [13]. Moreover, the dynamic range of the output signal is limited and its equivalent F-P cavity length change range is less than λ/8 due to the narrow linear range [14]. The phase-generated carrier (PGC) demodulation technique induces a phase modulation through a laser-based frequency modulation or an optical path difference modulation [15,16]. The PGC demodulation technique is also widely used for wideband FPAS owing to its good merits of large dynamic range, high resolution, and good linearity [17]. However, the stability of PGC demodulation method is poor, and it is easy to be affected by the fluctuation of light source power, the amplitude drift of mixing signal and the phase modulation amplitude change. It also suffers from the signal fading and harmonic distortion problems. Phase-shifting interferometry can also measure the absolute optical path difference of a fiber-optic white light interferometry [18]. It utilizes a piezoelectric transducer to move the reference mirror to yield phase-shifted interference spectrums, which is more robust than PGC demodulation method. However, phase-shifting method suffers from the phase-difference error due to the imperfect properties of the 3 × 3 or 2 × 2 coupler. In addition, it is not suitable for an F-P interferometry sensor since a coupler must be employed as a beam splitter in the interferometer. Passive quadrature phase demodulations including two-wavelength and three-wavelength quadrature phase demodulation utilize quadrature phase relationship between wavelengths and trigonometric relationship to extract phase variable [19–23]. Compared to two-wavelength demodulation scheme, three-wavelength demodulation is more robust without calculating the DC component of the interferometric signals. The FPAS based on this type demodulation technique can perform a wide acoustic frequency range. However, the noise-limited minimum detectable sound pressure level (SPL) is poor. The FPASs based on two-wavelength and three-wavelength quadrature phase demodulations achieve minimum detectable acoustic pressures of ∼3.4 mPa/Hz¹^/² [20] and ∼1.06 mPa/Hz¹^/² [23], respectively. The three-wavelength demodulation employs three pairs of laser sources and photodetectors (PD) [22]. Different light paths might induce light power imbalances caused by the environmental temperature or mechanical perturbation, optical fiber losses or different responsivities between PDs [21]. Large amplitude of the F-P cavity length change will result in the quadrature phase deviations, which distorts the demodulation results [23]. Although the common-path three-wavelength demodulation scheme can solve above problems through wavelengths switching of a fast tunable Y-branch laser, the noise level is poor [23].

The spectrum-based white light interferometry (WLI) demodulation techniques, such as the cross-correlation demodulation, and total phase demodulation, are capable of stably demodulating the F-P cavity length against the light source power fluctuation, ambient temperature perturbation and optical fiber loss [24–26]. Because these impacts mainly influence the intensities of the optical interference spectrum while above demodulation techniques demodulate cavity length based on the phase information [24]. These spectrum-based WLI demodulation techniques can also achieve very high demodulation resolution of cavity length which directly determines the noise-limited minimum detectable SPL. However, the cross-correlation demodulation just runs a low maximum demodulation rate of hundreds of Hertz because of mass computation quantities and cannot be utilized on a wideband FPAS [24]. Compared to the cross-correlation demodulation, total phase demodulation not only realizes a high demodulation resolution of cavity length and robust demodulation results, but also a high demodulation rate and large dynamic range of the demodulated cavity length [26]. It is also utilized on dynamic tilt angle measurements for inclinometers [27,28]. A cantilever-based FPAS using a spectrum-based WLI demodulation technique achieves a 2-kHz acoustic frequency range and 5-μPa/Hz¹^/² minimum detectable SPL [29]. However, due to the limited bandwidth, this acoustic sensing scheme cannot be used in voice communication. Moreover, the previous reported improved Buneman frequency estimation and total phase demodulation has a potential of 300-kHz demodulation rate [30].

In this paper, we reported a spectrum based high-speed absolute cavity length demodulation scheme with a 70-kHz maximum line rate spectrometer for a wideband FPAS. An improved Buneman frequency estimation and total phase demodulation algorithm is utilized. The FPAS with a pre-stressed diaphragm achieves a wideband acoustic wave measurement by demodulating the real-time absolute F-P cavity lengths. In order to perform a high demodulation rate, the demodulation process is optimized by eliminating the normalization and envelope elimination processes. The interpolation process is also optimized by using matrix calculation of the linear interpolation. In addition, this scheme resists the intensity variation interference of the light source power perturbation, optical fiber loss and other environmental temperature perturbations. The bandwidth and the noise-limited minimum detectable SPL of the proposed acoustic sensing scheme are also measured.

2. Setup and principles

The schematic diagram of the demodulation scheme is shown in Fig. 1. The ultra-high speed spectrometer is designed with athermal optomechanics and the fastest camera for high resolution spectrum at more than 2-3x the speed of conventional spectrometers [31]. This type spectrometer can provide a 250-kHz maximum line rate and a spectrum range from 650 nm to 950 nm. In our scheme, the spectrometer (Cobra800, Wasatch Photonics) can provide a 70-kHz maximum line rate and a spectrum range from 780nm to 900 nm. A superluminescent light emitting diode (SLED) (850 nm SLED, Fiberer Global Tech Ltd.) with a 62-nm bandwidth at the center wavelength of 850 nm is utilized as the light source. The 62-nm bandwidth of the SLED can provide wide enough spectrum for the spectrum based demodulation method. All optical fibers in use of the demodulation scheme are single mode fiber (SMF) (HI780, Corning) at 850 nm as well as the optical fiber coupler. The broad band light emitted from the SLED transmits to the FPAS through the optical fiber coupler and the SMF. The two beams of reflected lights from the reflective diaphragm structure, between which the end surface of SMF and the surface of the diaphragm form a F-P interferometer, passes through the other output of the optical fiber coupler to reach the spectrometer. The fast demodulation algorithm is implemented by a computer to demodulate the absolute F-P cavity lengths from the interference spectrums sent from the spectrometer.

Fig. 1. The schematic diagram of the demodulation setup of the wideband diaphragm based FPAS using a 70-kHz line rate spectrometer.

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The schematic diagram of the wideband FPAS is shown as the enlarged view of Fig. 1. The FPAS consists of the 850-nm SMF with a ceramic ferrule, metal shell and the diaphragm. The ceramic ferrule is inserted into the shell and fixed with the epoxy glue. A stainless-steel diaphragm (304) with the thickness of 5 μm and the diameter of 10.9 mm is pre-stress and bonded onto the metal shell with epoxy, which build a FPAS with a wideband range from 10 Hz to 20 kHz. Then, the endface of the optical fiber tip and the surface of the diaphragm form a F-P cavity. The two beams of reflected lights, from the endface of the fiber tip and the surface of the diaphragm, interfere with each other, as shown in the enlarged view of the sensor head in Fig. 1. The acoustic wave acts on the diaphragm and renders the vibration of the diaphragm, which leads to the variation of the F-P cavity length. The acoustic wave can be measured through demodulation of the real-time absolute F-P cavity lengths. Thus, the 70-kHz maximum line rate of the spectrometer corresponds to 70-kHz sampling rate used to measure the acoustic signal, which covers the human sound frequency range from 20 Hz to 20 kHz. The relationship between the acoustic pressure and the deflection of the diaphragm can be written as [8]

(1)$$P = \frac{{Ast\Delta d}}{{{r^2}}} + \frac{{BEt\Delta {d^3}}}{{(1 - \upsilon ){r^4}}}$$

where P is the applied acoustic pressure, A and B are dimensionless coefficients, s is the pre-stress, t is the thickness of the diaphragm, Δd is the F-P cavity length change which is also the deflection of the diaphragm, r is the radius of the diaphragm, E and υ are the Young’s modulus and Poisson’s ratio of the material of the diaphragm, respectively. From Eq. (1), the pressure is proportional to the deflection of the diaphragm when the applied pressure is small while the relationship between them changes into non-linear with increasing pressure [8]. The sensitivity of the FPAS is

(2)$$S = \frac{{\Delta d}}{{\Delta P}}$$

The two-beam interferometric-light intensity using a broadband light source can be written as

(3)$$I(\lambda )= 2{I_0}(\lambda )\left[ {1 + \gamma \cos \left( {\frac{{4\pi d}}{\lambda } + {\varphi_0}} \right)} \right]$$

where I₀(λ) is the intensity of the output light of the light source, λ is the wavelength of the output light, γ is the fringe visibility, d is the F-P cavity length and φ₀ is the initial phase of the interferometric light. The spectrum based fast F-P cavity demodulation employs an improved Buneman frequency and total phase demodulation algorithm, which has been reported in the previous published paper [30]. The calculation errors induced by the Buneman frequency estimation was suppressed by re-calculating the peak index and phase from the amplitude and phase frequency spectrum when the peak index approximates an integer value. The demodulated F-P cavity length can be expressed as [30]

(4)$$\left\{ \begin{array}{l} d = \frac{1}{{2{k_0}}}({{\varphi_{\xi p}} - {\varphi_0} + 2\pi [{\tilde{a}} ]} )\\ {\varphi_{\xi p}} = {{\tilde{\varphi }}_m} - ({{{\tilde{\varphi }}_{m + 1}} - {{\tilde{\varphi }}_m}} )({{{\tilde{\xi }}_p} - m} )\\ \tilde{a} = \frac{{{k_0}{{\tilde{\xi }}_p}}}{{{k_1} - {k_0}}} + \frac{{{\varphi_0}}}{{2\pi }} - \frac{{{\varphi_{\xi p}}}}{{2\pi }} \end{array} \right.$$

where k₀ and k₁ are the beginning and the end wavenumbers of the wavenumber domain optical spectrum, φ_ξp is the wrapped phase at the real peak ${\tilde{\xi }_p}$ which is the location index of the real peak in the amplitude spectrum of the wavenumber domain spectrum, $\tilde{a}$ is the estimated parameter which is an integer theoretically, ${\tilde{\varphi }_m}$ and ${\tilde{\varphi }_{m + 1}}$ are the phases obtained from the phase spectrum corresponding to m and m+1, respectively.

In order to increase the demodulation computation rate and efficiency, the normalization and the envelope elimination processes are omitted. The improved Buneman frequency and total phase demodulation algorithm directly obtains the peak location index and corresponding phase from the amplitude and phase spectrums when the number of cycles approximates an integer, which can reduce the impact of the error incurred from Buneman frequency estimation. This improvement can also reduce the impact of the envelope and DC component of the optical interference spectrum, since the number of the envelope cycle or the DC component is small (less than 3) and the tail of the envelope peak in amplitude spectrum has little impact on the peak of the interference signal.

In the demodulation process, the linear in wavenumber of the interference spectrum before the fast Fourier transform (FFT) is indispensable, since the optical spectrum along the scanning wavelength is a chirp signal [26]. An interpolation process is needed for resampling the interference signal in wavenumber domain. Besides the FFT, the computation quantity of the wavenumber interpolation process also needs to be considered. The typical interpolation methods include linear interpolation, polynomial interpolation and spline interpolation. Compared to linear interpolation method, polynomial interpolation and spline interpolation have the advantage of smoother interpolation curve but more complicated calculation and more computation quantity. By using the linear interpolation, the interpolated point can be expressed as

(5)$$I({{k^n}} )= \frac{{{k^n} - {k_{m + 1}}}}{{{k_m} - {k_{m + 1}}}}I({{k_m}} )+ \frac{{{k^n} - {k_m}}}{{{k_{m + 1}} - {k_m}}}I({{k_{m + 1}}} )$$

where I(kⁿ) is the interpolated intensity at the interpolated wavenumber kⁿ, k is the wavenumber which is k = 2π/λ, I(k_m) and I(k_m+1) are the captured intensity at two adjacent wavenumbers k_m and k_m+1, respectively. From Eq. (3), the coefficients of the two terms are only related to the interpolated wavenumber and its two adjacent wavenumbers. Generally, for a specific spectrometer, the wavelengths of the captured optical spectrum are invariable. The interval of the interpolated wavenumbers can be obtained as Δk = 2π(λ₁-λ₀)/λ₁λ₀N from the beginning wavelength λ₀, the end wavelength λ₁ and the number N of the sampling points of the optical spectrum. Thus, the coefficients of the linear interpolation can be pre-calculated before the interpolation procedure. The linear interpolation calculation of the resampling spectrum can be written in matrix multiplication as

(6)$$\begin{aligned}&[{I({{k^0}} ),I({{k^1}} ),\ldots ,I({{k^{N - 1}}} )} ]\\ &\quad = [{I({{k_0}} ),I({{k_{^1}}} ),\ldots ,I({{k_{N - 1}}} )} ]\left[ {\begin{array}{ccccccccc} 0&0&0&.&.&.&0&0&1\\ .&.&.&{}&{}&{}&0&{{\alpha_{N - 2,N - 2}}}&0\\ .&.&.&{}&{}&{}&{{\alpha_{N - 3,N - 3}}}&{{\alpha_{N - 3,N - 2}}}&0\\ .&.&.&{}&{}&.&{{\alpha_{N - 4,N - 3}}}&0&0\\ 0&0&0&{}&.&.&0&0&0\\ 0&0&0&.&.&{}&.&.&.\\ 0&0&{{\alpha_{2,2}}}&.&{}&{}&.&.&.\\ 0&{{\alpha_{1,1}}}&{{\alpha_{1,2}}}&{}&{}&{}&.&.&.\\ 1&{{\alpha_{0,1}}}&0&.&.&.&0&0&0 \end{array}} \right]\end{aligned}$$

where [I(k⁰), I(k¹),…, I(k^N-1)] is the interpolated intensity vector of the interference spectrum, [I(k₀), I(k₁),…, I(k_N-1)] is the captured intensity vector by the spectrometer, α_m,n and α_m-1,n are the two coefficients of the linear interpolation equation in Eq. (5), the subscript n of which represents the nth interpolated data. From Eq. (6), an interpolation matrix is pre-constructed before interpolation calculation and the coefficients are only determined by the wavelengths of the spectrometer. In addition, as can be seen from the interpolation matrix, it is a sparse matrix. A sparse matrix-vector multiplication is utilized to calculate the Eq. (6), which significantly reduces the computation quantity [32].

Figure 2 shows the flow chart of the spectrum based fast F-P cavity demodulation procedure. The optical interferometric spectrums captured by the fast spectrometer are sent to the computer. The demodulation algorithm is performed by a LabVIEW program. By using the optimized linear interpolation calculation, the spectrum data is resampled in wavenumber domain. The length N of the spectrum data is the power of 2 and the FFT can be utilized to obtain the amplitude spectrum and phase spectrum. From the amplitude spectrum, the peak location index is roughly estimated by using the Buneman frequency estimation formula. Then, the wrapped phase is calculated from the rough peak index and linear phase characteristic according to the Eq. (4). Once the rough peak index and the wrapped phase are obtained, the parameter a can be calculated. After above calculations, the cavity length can be demodulated from Eq. (4).

Fig. 2. The flow chart of the spectrum based fast F-P cavity demodulation.

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3. Experimental setup

The schematic diagram of the experimental setup for the test of the wideband FPAS using the spectrum-based fast F-P cavity demodulation is shown in Fig. 3. The demodulation setup of the wideband FPAS has been illustrated above. The spectrometer performs the maximum line rate of 72 kHz with 2048 pixels and a 12-bit sampling resolution. In our experiment, the spectrum is configured at a 50-kHz line rate, since the spectrum distortion at a higher line rate will deteriorate the demodulated F-P cavity length results. In order to evaluate the performance of the wideband FPAS scheme, the FPAS, a condenser microphone (B&K 4189, Brüel & Kjær) and a loud speaker are placed in an acoustic isolation box to isolate the environment vibration and acoustic noise perturbations. The output voltage signal of the microphone is measured by a 16-bit data acquisition (DAQ) module (ENET-9163, National Instruments) with a 50-kHz sampling rate. The microphone is placed near the FPAS for acoustic pressure calibration. The more accurate amplitude of the output signal of the microphone is measured by a lock-in amplifier (SR830, Stanford Research Systems), which is utilized to calibrate the demodulated signal of the FPAS with the sensitivity of 45.7 mV/Pa of the microphone. Meanwhile, the loud speaker is also driven by the lock-in amplifier to be a sound source.

Fig. 3. Schematic diagram of the experimental setup for the wideband FPAS using the spectrum-based fast F-P cavity demodulation.

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4. Experimental results and discussions

Figure 4 shows the interference spectrum captured by the spectrometer without applying the acoustic pressure to the FPAS. Considering the trade-off between the signal-to-noise ratio (SNR) and the line rate, the exposure time of the spectrometer is set to 20 μs, which renders the spectrometer running at 50 kHz line rate. In order to obtain the highest SNR, the interference spectrum was truncated from 820 nm to 880 nm with 1024 sampling points to be utilized to demodulate the F-P cavity length. Consequently, the demodulated F-P cavity length was 175.83 μm.

Fig. 4. The interference spectrums of the FPAS without applying acoustic pressure.

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The frequency response of the FPAS from 20 Hz to 20 kHz was measured as shown in Fig. 5. The acoustic pressures are calibrated from the B&K 4189 microphone through the lock-in amplifier. From Fig. 5, the resonance frequency of the FPAS is ∼14.2 kHz. The frequency response curve from 20 Hz to 10 kHz is relatively flat. The sensitivities at the typical frequencies of 500 Hz and 10 kHz within the flat frequency response range are 9.63 nm/Pa and 13.38 nm/Pa, respectively. Therefore, the FPAS is capable of measuring a wideband acoustic wave from 20 Hz to 10 kHz, which almost covering the human voice frequency range. Since the spectrometer used in our wideband FPAS demodulation scheme has a maximum line rate of 72 kHz, the maximum bandwidth of the acoustic frequency is 31 kHz based on Nyquist criterion. The bandwidth of the FPAS can be extended to 20 kHz by optimizing the size of the diaphragm such as reducing the radius or increasing the thick-ness to increase the resonance frequency of the FPAS according to Eq. (1). In this way, the human voice frequency range from 20 Hz to 20 kHz can be covered completely.

Fig. 5. Frequency response of the wideband FPAS from the frequency range of 10 Hz ∼ 20 kHz.

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By using the spectrum-based fast F-P cavity length demodulation method, the real-time absolute F-P cavity length can be demodulated. Thus, the deformation of the diaphragm of the FPAS caused by the acoustic wave can be obtained. The AC component of the real-time F-P cavity length signal describes the measured acoustic waveform. In order to test the real-time acoustic wave measurement, the real-time absolute F-P cavity lengths of the FPAS were measured under the acoustic frequencies of 500 Hz, 1000 Hz, 5000 Hz and 10000 Hz with the acoustic pressure of 200 mPa, respectively. Figures 6(a)-(d) show the real-time cavity lengths (blue curves) and the output voltage signals (red curves) measured by the microphone in time domain while Figs. 6(e)-(h) describe the frequency spectrums of the time-domain cavity lengths. The measured cavity lengths data are in agreement with the voltage signals of the microphone. From their frequency spectrums, the peaks at 500 Hz, 1000 Hz, 5000 Hz and 10000 Hz can be observed, which are corresponding to the acoustic frequencies.

Fig. 6. The measured real-time absolute F-P cavity lengths of the wideband FPAS and their corresponding frequency spectrums after FFT at the acoustic frequency of 500 Hz, 1000 Hz, 5000 Hz and 10000 Hz with the acoustic pressure of 200 mPa, respectively.

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The SPL and the sound pressure measured by the FPAS were calibrated through the condenser microphone. The frequency spectrums calibrated in SPL of the time-domain responses of the FPAS in Figs. 6(a)–(d) are shown in Figs. 7(a)-(d), respectively. For the sound pressure of 200 mPa, the frequency spectrums show SNRs of 58.2 dB, 47.3 dB, 60 dB and 61.2 dB at the acoustic frequencies of 500 Hz, 1000 Hz, 5000 Hz, and 10000 Hz, respectively. The noise-limited minimum detectable SPLs are 21.8 dB, 32.7 dB, 20 dB, and 18.8 dB, respectively. Consequently, the minimum detectable sound pressures are deduced to be 0.24 mPa/Hz¹^/², 0.86 mPa/Hz¹^/², 0.2 mPa/Hz¹^/², and 0.17 mPa/Hz¹^/² with the frequency resolution of 1 Hz based on the relationship between the SPL and the sound pressure. These results show the proposed wideband acoustic sensing scheme is sensitive enough for communications of human voice since human beings can hardly hear sound clearly under 20 dB.

Fig. 7. Frequency spectrums calibrated in SPL of the time-domain response of the FPAS in Fig. 6 (a)-(d) at the acoustic frequencies of (a) 500 Hz, (b) 1000 Hz, (c) 5000 Hz and (d) 10000 Hz, respectively.

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The noise-limited minimum detectable SPL is a very important parameter for an acoustic sensor, which is determined by the SNR of the interference spectrum in our scheme since the real-time cavity length signals are demodulated from the interference spectrums. The interferometric signal is optimized to reach the dynamic range of the spectrometer by adjusting the output power of the laser source. The contributions to the noise of the interference spectrum include electrical noise from the detector noise and circuit noise, ambient vibration noise, and thermos-mechanical noise of the diaphragm. The ambient vibration noise was suppressed to the minimum by using an isolation box, which was not the dominant. The electrical noise is related to the spectrometer. In our scheme, the dynamic range of the spectrometer is also limited because of the 12-bits analog-to-digital (AD) converter. Using a spectrometer with lower electrical noise and higher bits AD converter can significantly improve SNR of the interference spectrum. Thermo-mechanical noise stems from the stochastic vibrations of the diaphragm because of the air damping [33]. For the acoustic sensors, the air is dispensable to transmit sound wave. Although, the air damping cannot be avoided, thermal-mechanical noise caused by stochastic vibrations is also proportional to the mechanical susceptibility of the diaphragm. The pre-stress diaphragm degrades the mechanical susceptibility and then reduces the stochastic vibrations. Therefore, the thermos-mechanical noise is reduced.

In addition to the noises mentioned above, the F-P cavity length demodulation algorithm is also very important to the improvement of the noise-limited minimum detectable SPL. The noise level of the frequency spectrum comes from time-domain SPL signal, the noise of which derives from the noise of the real-time cavity length signal. The variance of the real-time cavity length signal can be utilized to describe the noise level, which can be expressed as

(7)$${\mathop{\rm var}} (d) = \frac{1}{{4k_0^2}}{\mathop{\rm var}} ({\varphi _{\xi p}})$$

from Eq. (4) according to the variance estimation theory. It comes from the noise of the interference spectrums. The measured cavity length resolutions are close to the cavity length standard deviations calculated from Cramer-Rao bound in our previous work [30]. Thus, the proposed scheme has a good minimum detectable SPL.

Temperature has an impact on the stainless-steel diaphragm, which might influence the response of the diaphragm to the acoustic wave. The proposed spectrum-based F-P cavity length demodulation method can demodulate the real-time and absolute cavity lengths. The AC component of the real-time signals represents the acoustic signal and the DC component illuminates the mean cavity length which is the static F-P cavity length. The variation of the DC component can be utilized to measure temperature based on the thermal expansion of the F-P cavity [34]. Therefore, since the temperature can be measured in real time, the temperature compensation of the sensor head can be performed.

5. Conclusion

In summary, this paper demonstrates a wideband fiber-optic FPAS scheme by utilizing an improved Buneman frequency estimation and total phase demodulation algorithm with a 70-kHz maximum line rate spectrometer. The setup consists of a wideband SLED with a center wavelength of 850 nm and a high-speed spectrometer with a maximum line rate of 70 kHz, which is utilized to obtain the interference spectrum of the acoustic sensor head. The FPAS is made by a pre-stress stainless steel diaphragm based on F-P interferometer. The interpolation process of the cavity length demodulation is optimized through matrix calculation of the linear interpolation. In this way, the demodulation algorithm efficiency is increased. The real time F-P cavity lengths can be steadily demodulated at 50 kHz. The experimental results show that the sensitivities of the sensor head at typical frequencies of 500 Hz and 10 kHz are 9.63 nm/Pa and 13.38 nm/Pa, respectively, and the resonance frequency is ∼14.2 kHz. The bandwidth range of the acoustic sensor head is from 20 Hz to 10 kHz. The noise-limited minimum detectable SPL is 18.8 dB corresponding to the sound pressure of 0.17 mPa/Hz¹^/², which is predominantly limited by the noise of spectrometer. The spectrum-based cavity length demodulation also contributes to the improvement of minimum detectable SPL. Compared to the intensity demodulation method, this wideband FPAS scheme has the advantages of immunity to light source power perturbation, optical fiber loss and other environmental temperature or vibration perturbations. For the communication in MRI, a silica diaphragm of the acoustic sensor head fabricated by the MEMS technique is more preferable due to its MRI comparable. In terms of the merits mentioned above and the wideband covering the human sound frequency, this wideband acoustic sensing scheme is very promising for communications during MRI. In our future work, the acoustic sensor head with a silica diaphragm will be developed.

Funding

National Natural Science Foundation of China (61905034); Natural Science Foundation of Liaoning Province (2019-MS-054).

Disclosures

The authors declare no conflicts of interest.

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Wideband fiber-optic Fabry-Perot acoustic sensing scheme using high-speed absolute cavity length demodulation

Abstract

1. Introduction

2. Setup and principles

3. Experimental setup

4. Experimental results and discussions

5. Conclusion

Funding

Disclosures

References

Cited By

Figures (7)

Equations (7)

Optics Express