A. Optical Fiber Acoustic Sensors Based on FPI
A. 基于 FPI 的光纤声学传感器

Fabry-Perot interferometer (FPI), also known as etalon, mainly uses Fabry-Perot cavity as optical fiber sensing probe, which enables detection of external variables such as acoustic wave, strain, liquid level, pressure and so on [11]. The Fabry-Perot cavity is composed of two parallel reflectors divided by a certain distance [12], as illuminated in Figure 2. In addition, the air cavity backing the diaphragm plays a critical role in determining the sensor performance, particularly for miniature sensors with small air cavity. In practical applications, without compromising the optical sensitivity, the mechanical sensitivity can be increased by enlarging the air cavity, and then the sensitivity of FP sensor can be improved.
法布里-珀罗干涉仪（FPI），又称标准具，主要使用法布里-珀罗腔作为光纤传感探头，能够检测声波、应变、液位、压力等外部变量 [11] 。法布里-珀罗腔由两个平行的反射体组成，相隔一定距离 [12] ，如图所示 Figure 2 。此外，支持光圈的气腔在决定传感器性能方面起着关键作用，特别是对于具有小气腔的微型传感器。在实际应用中，在不影响光灵敏度的情况下，可以通过扩大气腔来提高机械灵敏度，从而提高 FP 传感器的灵敏度。

FIGURE 2.   图 2.

Optical fiber sensing system based on FPI.
基于 FPI 的光纤传感系统。

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FPI has been widely studied because of its high sensitivity, simple fabrication, small size and low cost. Acoustic and ultrasonic sensors based on FPI configuration have gradually attracted the attention of scholars. Wang et al. has combined micro-electromechanical system (MEMS) with optical fiber sensing technology to produce a small, highly sensitive underwater acoustic probe based on extrinsic Fabry-Perot interferometric (EFPI) [13]. The experimental results show that the signal detected by the sensor in standing wave tube is identical with the acoustic emission signal, and its response sensitivity is about −154.6 dB (re rad/μ Pa) Liu et al. introduced an optical fiber acoustic sensor based on pure silicon micro-cantilever beam [14]. The designed cantilever beam is fabricated by fs laser microfabrication at the end of the optical fiber, which acts as a built-in Fabry-Perot interferometer (FPI). Among them, the thickness and dimension of the micro-cantilever beam can be artificially defined to diversify the response frequency and measurement range, so as to adapt to different applications.
FPI 因其灵敏度高、制造简单、体积小、成本低而被广泛研究。基于 FPI 构型的声波和超声传感器逐渐引起了学者们的关注。Wang 等人将微机电系统 （MEMS） 与光纤传感技术相结合，生产了一种基于外源法布里-珀罗干涉测量 （EFPI） [13] 的小型、高灵敏度水声探头。实验结果表明，传感器在驻波管中检测到的信号与声发射信号相同，其响应灵敏度约为 −154.6 dB （re rad/μ Pa） Liu 等人介绍了一种基于纯硅微悬臂梁 [14] 的光纤声学传感器。设计的悬臂光束是通过光纤末端的 fs 激光微纳加工制成的，该微纳加工充当内置的法布里-珀罗干涉仪 （FPI）。其中，可以人工定义微悬臂梁的厚度和尺寸，使响应频率和测量范围多样化，以适应不同的应用。

In recent years, extrinsic Fabry-Perot interferometer (EFPI) based on diaphragm, as shown in Figure 2, has become a research hotspot, aiming at increasing the range of acoustic response. More importantly, the EFPI can be used for acoustic detection in air and underwater because of its enclosed air chamber.
近年来，基于振膜 Figure 2 的外源法布里-珀罗干涉仪 （EFPI） 已成为研究热点，旨在增加声学响应的范围。更重要的是，EFPI 具有封闭的气室，可用于空气和水下的声学检测。

Interference occurs due to the multiple superpositions of both reflected and transmitted beams on two parallel surfaces. After light comes through the F-P cavity, photo detector (PD) receives the interference signal and converts it. If the acoustic pressure is applied to the diaphragm, the phase change ΔΦ of the optical wave can be simply given as:

View Source\begin{equation*} \Delta \Phi =\frac {4\pi {n}\Delta {L}}{\lambda _{0} }\tag{1}\end{equation*}

由于反射光束和透射光束在两个平行表面上的多次叠加而发生干涉。光通过 F-P 腔后，光电探测器 （PD） 接收干涉信号并将其转换。如果对隔膜施加声压，则相变 ΔΦ 的光波可以简单地给出为：

ΔΦ=4πnΔLλ0(1)

View Source\begin{equation*} \Delta \Phi =\frac {4\pi {n}\Delta {L}}{\lambda _{0} }\tag{1}\end{equation*}

In Formula (1), n represents the refractive index of the medium filling the cavity. λ0 refers to the optical wavelength in vacuum. ΔL denotes the deflection of the diaphragm and can be expressed as:

View Source\begin{equation*} \Delta {L}=\frac {P\partial ^{4}\left ({{1-\upsilon ^{2}} }\right)}{4.2Eh^{3}}\tag{2}\end{equation*}

在公式 (1) 中，n 表示填充型腔的介质的折射率。λ 0 指真空中的光波长。ΔL 表示隔膜的挠度，可以表示为：

ΔL=P∂4(1−υ2)4.2Eh3(2)

View Source\begin{equation*} \Delta {L}=\frac {P\partial ^{4}\left ({{1-\upsilon ^{2}} }\right)}{4.2Eh^{3}}\tag{2}\end{equation*} 其中 P 表示与型腔压力相关的环境压力，∂ 表示半边长度 υ 是隔膜材料的泊松比 E 指杨氏模量和 h 是隔膜厚度。

In an FPI sensor, its sensitivity S at room temperature can be expressed as:

View Source\begin{equation*} S=\frac {3\partial ^{4}\left ({{1-\upsilon ^{2}} }\right)}{16Eh^{3}}\tag{3}\end{equation*}

在 FPI 传感器中，其灵敏度 S 在室温下可以表示为：

S=3∂4(1−υ2)16Eh3(3)

View Source\begin{equation*} S=\frac {3\partial ^{4}\left ({{1-\upsilon ^{2}} }\right)}{16Eh^{3}}\tag{3}\end{equation*}

According to Formula (3), it can be found that the sensitivity is in direct ratio to the fourth power of half-edge length and inversely proportional to the cube of diaphragm thickness. Therefore, in the FPI-based acoustic sensing system, the detection sensitivity can be improved from two aspects: the diaphragm thickness and the half-edge length. Thus, diaphragm material is crucial to for F-P sensors. Usually, the diaphragm materials of Fabry-Perot cavity mainly include micro-fabricated silicon film, metal film or diaphragm composed of single-mode/multi-mode fiber.
根据公式 (3) ，可以发现灵敏度与半边长的四次方成正比，与隔膜厚度的立方成反比。因此，在基于 FPI 的声学传感系统中，可以从振膜厚度和半边长两个方面提高检测灵敏度。因此，隔膜材料对于 F-P 传感器至关重要。通常，法布里-珀罗腔的隔膜材料主要包括微加工硅膜、金属膜或由单模/多模光纤组成的隔膜。

Many researchers use different diaphragm materials for acoustic detection, which has potential application prospects in structural health monitoring and medical ultrasound. Guo et al. introduced an EFPI optical sensor based on ultra-thin silver film for ultrasonic detection in 2012 [15]. Wang et al. demonstrated an infrasound sensor based on polymer diaphragm in 2016 [16]. External infrasound disturbance will cause vibration of the diaphragm, change the length of F-P cavity, and finally lead to the shift of interference spectrum. Through theoretical simulation and experimental verification, the sensor can effectively detect low-frequency infrasound signals of 1–20 Hz. At the same time, an optical fiber infrasound sensor based on ultraviolet adhesive diaphragm is introduced in Wuhan National Laboratory, which shows good acoustic response between 1 Hz and 20 kHz [17]. Subsequently, an acoustic sensor was proposed [18], in which a tapered optical fiber was attached to a nitrile-butadiene diaphragm. Under the action of acoustic pressure, tapered optical fibers bend with the deformation of diaphragm, and finally show a calculable change in transmission power. An ultra-wideband optical fiber acoustic sensor based on graphene film is proposed [19]. The sensor head assembly is based on EFPI structure of graphene film. The experimental results show that the proposed acoustic sensor can achieve ultra-wideband frequency response from 5 Hz to 0.8 MHz.
许多研究人员使用不同的隔膜材料进行声学检测，这在结构健康监测和医学超声方面具有潜在的应用前景。Guo 等人于 2012 年推出了一种基于超薄银膜的 EFPI 光学传感器，用于超声波检测 [15] 。Wang 等人在 2016 年演示了一种基于聚合物振膜的次声传感器 [16] 。外部次声干扰会引起振膜振动，改变 F-P 腔的长度，最终导致干扰谱的偏移。通过理论仿真和实验验证，该传感器可以有效检测 1–20 Hz 的低频次声信号。同时，武汉国家实验室引入了一种基于紫外胶膜片的光纤次声传感器，该传感器在 1 Hz 和 20 kHz [17] 之间表现出良好的声学响应。随后，提出了 [18] 一种声学传感器，其中锥形光纤连接到丁腈隔膜上。在声压作用下，锥形光纤随着隔膜的变形而弯曲，最终表现出可计算的传输功率变化。提出了 [19] 一种基于石墨烯薄膜的超宽带光纤声学传感器。传感器头组件基于石墨烯薄膜的 EFPI 结构。实验结果表明，所提出的声学传感器可以实现从 5 Hz 到 0.8 MHz 的超宽带频率响应。

However, because it involves micro-fabrication or chemical corrosion, the fabrication process of diaphragms is complex and expensive. In addition, the most critical point is that the air intercepted from outside will enter the Fabry-Perot cavity in an unpredictable way, which will greatly affect the measurement performance of the acoustic sensors based on FPI.
然而，由于涉及微加工或化学腐蚀，隔膜的制造过程复杂且昂贵。此外，最关键的一点是，从外部截获的空气会以不可预测的方式进入法布里-珀罗腔，这将极大地影响基于 FPI 的声学传感器的测量性能。

B. Optical Fiber Acoustic Sensors Based on FBG
B. 基于 FBG 的光纤声学传感器

Fiber Bragg grating (FBG) is an optical passive device, which is a sensor made by periodically modulating the axial refractive index of the fiber core. It has the advantages of good stability, high sensitivity and easy connection with other optical fiber devices, so it obtains extensive application. Hill et al. first involved fiber Bragg grating (FBG) in 1978 [20]. As Meltz et al. [21] developed the method of transverse holographic fabrication, FBG gradually formed. And then ultrasound measurement based on FBG has also developed rapidly [22]. They studied a hydrophone based on FBG, which can detect 950 kHz acoustic signal.
光纤布拉格光栅 （FBG） 是一种光学无源器件，是通过周期性调制纤芯的轴向折射率制成的传感器。它具有稳定性好、灵敏度高、易于与其他光纤器件连接等优点，因此获得了广泛的应用。Hill 等人于 1978 [20] 年首次涉及光纤布拉格光栅 （FBG）。随着 Meltz 等人 [21] 开发了横向全息制造方法，FBG 逐渐形成。然后基于 FBG 的超声测量也得到了迅速 [22] 发展。他们研究了一种基于 FBG 的水听器，它可以检测 950 kHz 的声信号。

At present, fiber Bragg grating (FBG) has become a research hotspot of underwater acoustic signal detection. When the acoustic signal acts on the optical fiber, the effective refractive index and other parameters of the optical fiber will change, which will cause the reflection wavelength of the FBG to move and realize the sensing of the acoustic signal.
目前，光纤布拉格光栅 （FBG） 已成为水声信号检测的研究热点。当声信号作用在光纤上时，光纤的有效折射率等参数会发生变化，这会导致 FBG 的反射波长移动，实现对声信号的传感。

When the incident light enters the fiber Bragg grating (FBG), the relationship between the central wavelength of the reflection λB and the effective refractive index neff and the grating period Λ is as follows [23]:

View Source\begin{equation*} \lambda _{\textrm {B}} =2n_{\textrm {eff}} \Lambda\tag{4}\end{equation*}

当入射光进入光纤布拉格光栅 （FBG） 时，反射 λ 的中心波长 λ B 和有效折射率 n 伊芙 和光栅周期 Λ 如下 [23] ：

λB=2neffΛ(4)

View Source\begin{equation*} \lambda _{\textrm {B}} =2n_{\textrm {eff}} \Lambda\tag{4}\end{equation*}

When the FBG is acted by acoustic signal, the effective refractive index and grating period will change, which will lead to the shift of the central wavelength of reflected light. The offset changes caused by acoustic signals can be calculated as [24]:

View Source\begin{equation*} \Delta \lambda _{\textrm {B}} =2n_{\textrm {eff}} \Delta \Lambda +2\Lambda \Delta n_{\textrm {eff}}\tag{5}\end{equation*}

当 FBG 受声信号作用时，有效折射率和光栅周期会发生变化，这将导致反射光的中心波长发生变化。由声学信号引起的偏移变化可以计算为 [24] ：

ΔλB=2neffΔΛ+2ΛΔneff(5)

View Source\begin{equation*} \Delta \lambda _{\textrm {B}} =2n_{\textrm {eff}} \Delta \Lambda +2\Lambda \Delta n_{\textrm {eff}}\tag{5}\end{equation*}

The intensity of the output light, which is theoretically proportional to the acoustic signal, can be obtained by demodulating the Bragg wavelength offset.
输出光的强度理论上与声信号成正比，可以通过解调布拉格波长偏移来获得。

FBG has the advantages of short standard distance, versatility and easy of multiplexing. In particular, FBG has the ability to be sensitive to many tested objects while multiplexing [25]. FBG acoustic sensors can also be used in acoustic hydrophones, non-destructive assessment, biomedical sensing and structural health monitoring [26]. Over the past decade, a variety of laser and FBG combination technologies have been studied by academia and industry. Tan et al. designed and validated a sensing system based on bipolar fiber Bragg grating laser which can simultaneously measure static pressure, temperature and acoustic signals [27]. In 2016, FAZ Technologies Ltd. developed a quasi-distributed optical sensing system [28] for measuring temperature, pressure, acoustic and acceleration by combining fiber Bragg grating (FBG) sensing technology with tunable laser technology. The system has the advantages of high speed and high precision. Siska et al. introduced an acoustic vibration sensing system which combines distributed feedback laser diode and FBG technology [29]. It can be used to detect temperature, strain, vibration or pressure.
FBG 具有标准距离短、用途广泛、易于多路复用等优点。特别是，FBG 能够在多路复用 [25] 时对许多测试对象敏感。FBG 声学传感器还可用于声学水听器、无损评估、生物医学传感和结构健康监测 [26] 。在过去的十年中，学术界和工业界研究了各种激光和 FBG 组合技术。Tan 等人设计并验证了一种基于双极光纤布拉格光栅激光器的传感系统，该系统可以同时测量静压、温度和声信号 [27] 。2016 年，FAZ Technologies Ltd. 通过将光纤布拉格光栅 （FBG） 传感技术与可调谐激光技术相结合，开发了一种准分布式光学传感系统 [28] ，用于测量温度、压力、声学和加速度。该系统具有高速、高精度等优点。Siska 等人介绍了一种结合了分布式反馈半导体激光管和 FBG 技术的 [29] 声学振动传感系统。它可用于检测温度、应变、振动或压力。

Meanwhile, multiplexing technology and FBG array have also been studied in FBG sensing. In 2007, a fiber optic underwater acoustic sensor was described [30], as depicted in Figure 3. The main innovation is that the sensor probe is composed of two fiber Bragg gratings (FBG). The sensing system can realize self-demodulation through a pair of matched FBGs, which effectively improves the detection sensitivity. In the experimental test, the sensitivity of underwater acoustic pressure measurement can reach 0.78 nm/MPa in the range of 100-200 dB (re rad/μ Pa).
同时，多路复用技术和 FBG 阵列在 FBG 传感中也得到了研究。2007 年，描述了 [30] 一种光纤水声传感器，如 Figure 3 所示。主要创新是传感器探头由两个光纤布拉格光栅 （FBG） 组成。该传感系统可以通过一对匹配的 FBG 实现自解调，有效提高了检测灵敏度。在实验测试中，水声压力测量的灵敏度在 100-200 dB （re rad/ μ Pa） 范围内可以达到 0.78 nm/MPa。

FIGURE 3.   图 3.

Fiber optic underwater acoustic sensor.
光纤水声传感器。

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In 2015, Wang et al. studied a distributed acoustic sensor with a weak FBG (WFBG) array with an optical erasure interval of 2 m in an Φ -OTDR system with a balanced Michelson interferometer [31]. Subsequently, in order to achieve greater temperature tolerance, they used broadband weak fiber Bragg grating (BWFBG) array instead of ordinary WFBG array to better achieve seismic monitoring [32]. Furthermore, a distributed acoustic sensing system based on weak-FBG array proposed by Sheng Liu [33] was described in Figure 4. The main structure of the system is a balanced Michelson interferometer configuration consisting of a weak FBG array, a 3×3 coupler and two faraday rotator mirrors (FRM). Among them, the weak FBG array is composed of 661 FBGs with a distance of 2.5 m between adjacent FBGs. The spatial resolution of the system is 2.5 m. Acoustic vibration of up to 1000 Hz can be measured accurately in 1.6 km of optical fiber length.
2015 年，Wang 等人研究了一种具有弱 FBG （WFBG） 阵列的分布式声学传感器，其光学擦除间隔为 2 m，Φ -带有平衡迈克尔逊干涉仪 [31] 的 OTDR 系统。随后，为了实现更大的耐温性，他们使用宽带弱光纤布拉格光栅 （BWFBG） 阵列代替普通的 WFBG 阵列，以更好地实现地震监测 [32] 。此外，文中还介绍了 Sheng Liu [33] 提出的一种基于弱 FBG 阵列的分布式声学传感系统 Figure 4 。该系统的主要结构是一个平衡的迈克尔逊干涉仪配置，由一个弱 FBG 阵列、一个 3×3 耦合器和两个法拉第旋转镜 （FRM） 组成。其中，弱 FBG 阵列由 661 个 FBG 组成，相邻 FBG 之间的距离为 2.5 m。该系统的空间分辨率为 2.5 m。在 1.6 km 的光纤长度内可以精确测量高达 1000 Hz 的声学振动。

FIGURE 4.   图 4.

A DAS system based on weak-FBG array.
基于弱 FBG 阵列的 DAS 系统。

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A. Interferometric Optical Fiber Acoustic Sensors
A. 干涉光纤声学传感器

Under the action of external sound waves, the refractive index and core diameter of the phase-modulated fiber-optic sensor will change, thereby changing the propagation path of the optical signal in the fiber, and finally the variation of phase occurs. However, because of the high frequency of light, the phase change of light wave cannot be directly detected via the existing detection technology. But in terms of the change in the intensity of light, it can be easily detected. Therefore, the phase change is usually transformed into light intensity change in experiment, and then the acoustic signal is obtained by demodulation technology [37].
在外界声波的作用下，调相光纤传感器的折射率和纤芯直径会发生变化，从而改变光信号在光纤中的传播路径，最终发生相位的变化。然而，由于光的频率很高，现有的检测技术无法直接检测光波的相位变化。但就光强度的变化而言，它很容易被检测到。因此，通常在实验中将相位变化转化为光强变化，然后通过解调技术 [37] 获得声信号。

It is assumed that the amplitudes of the two beams are E1 and E2 , respectively. If the phase of one light is modulated by external acoustic disturbances, the other light is isolated from external disturbances so that it is not affected. Then the intensity of interference light can be expressed as:

View Source\begin{equation*} E^{2}=E_{1} +E_{2} +2E_{1} E_{2} cos \left ({{\Delta \phi +\phi _{0}} }\right)\tag{6}\end{equation*}

假设两个光束的振幅为 E 1 和 E 2 分别。如果一个灯的相位受到外部声学干扰的调制，则另一个灯与外部干扰隔离，因此不会受到影响。那么干涉光的强度可以表示为：

E2=E1+E2+2E1E2cos(Δϕ+ϕ0)(6)

View Source\begin{equation*} E^{2}=E_{1} +E_{2} +2E_{1} E_{2} cos \left ({{\Delta \phi +\phi _{0}} }\right)\tag{6}\end{equation*} 其中 φ 0 是两个相干光束之间的初始相位差。Δϕ 是相位调制引起的相位差，直接对应干涉光的强度。通过检测干涉信号的强度，可以确定两束光之间的相位变化，并可以解调测得的物理参数。干涉传感技术因其在应变、振动、磁场和声学测量方面的广泛应用前景而受到广泛的关注和研究。目前，调相光纤声学传感器主要基于三种干涉原理：马赫-曾德尔干涉 （MZI）、迈克尔逊干涉 （MI） 和萨格纳克干涉 （SI）。 [38]

1) Mach-Zehnder Interferometer
1） 马赫-曾德尔干涉仪

Bucaro et al. firstly proposed the structure of Mach-Zehnder interferometer (MZI) in the field of optical fiber acoustic sensing, as described in Figure 5 [39].
Bucaro 等人首先在光纤声学传感领域提出了马赫-曾德尔干涉仪 （MZI） 的结构，如 Figure 5 [39] 中所述。

FIGURE 5.   图 5.

Mach-zehnder interference structure.
Mach-zehnder 干涉结构。

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The basic principle of the general Mach-Zehnder fiber-optic interferometer is shown in Figure 5. The coherent light emitted by the laser source is divided into two separate beams by a 1×2 optical coupler. After passing through the coupler, the beams are transmitted in two paths which are named as the signal arm and the reference arm respectively. When the external acoustic pressure exerts on the signal arm, the fiber size of the sensing arm is stretched or contracted, and the refractive index of the sensing arm is changed, causing the phase modulation of optical signal. However, the reference arm is isolated by some substance so that it is not affected by external acoustic pressure. The modulated light and the reference light are coupled by the 2×1 coupler and then they interfere with each other. The interference signal is received by the photodetector, and then the acoustic signal is obtained though the subsequent process of signal demodulation. According to the principle of interference, it suggests that when two beams with the same frequency and the same vibration direction interfere with each other, the interference intensity of the light can be expressed as:

I=I1+I2+2I1I2−−−−√cos(Δφ)(7)

View Source\begin{equation*} I=I_{1} +I_{2} +2\sqrt {I_{1} I_{2}} cos \left ({{\Delta \varphi } }\right)\tag{7}\end{equation*} where I1 and I2 are the initial intensities of the two beams, and Δφ is the initial phase difference between the two beams.
通用马赫-曾德尔光纤干涉仪的基本原理如 所示 Figure 5 。激光源发射的相干光被 1×2 分成两束单独的光束 光耦合器。光束通过耦合器后，沿两条路径传输，分别称为信号臂和参考臂。当外部声压施加在信号臂上时，传感臂的光纤尺寸被拉伸或收缩，传感臂的折射率发生变化，从而引起光信号的相位调制。但是，参考臂被某些物质隔离，因此不受外部声压的影响。调制光和参考光由 2×1 耦合 耦合器，然后它们相互干扰。干扰信号由光电探测器接收，然后通过随后的信号解调过程获得声信号。根据干涉原理，它表明当相同频率和相同振动方向的两束光束相互干涉时，光的干涉强度可以表示为：

I=I1+I2+2I1I2−−−−√cos(Δφ)(7)

View Source\begin{equation*} I=I_{1} +I_{2} +2\sqrt {I_{1} I_{2}} cos \left ({{\Delta \varphi } }\right)\tag{7}\end{equation*} 其中 I 1 和我 2 是两个光束的初始强度，Δφ 是两个光束之间的初始相位差。

At this time, the phase difference Δφ of the two beams which interfere with each other can be seen as the addition of the following three factors: the initial phase difference φ0 owing to the asymmetry of the two optical paths themselves, the phase difference φs due to the external pressure, and the phase difference φε resulting from the change of fiber length caused by strain, which can be expressed as:

Δφ=φ0+φs+φε(8)

View Source\begin{equation*} \Delta \varphi =\varphi _{0} +\varphi _{\textrm {s}} +\varphi _{\varepsilon }\tag{8}\end{equation*}
此时，相位差 Δφ 在相互干扰的两束光束中，可以看作是以下三个因素的相加：初始相位差 φ 0 由于两条光路本身的不对称性，相位差φ s 由于外部压力，以及相差φ ε 由应变引起的纤维长度变化所致，可表示为：

Δφ=φ0+φs+φε(8)

View Source\begin{equation*} \Delta \varphi =\varphi _{0} +\varphi _{\textrm {s}} +\varphi _{\varepsilon }\tag{8}\end{equation*}

The initial phase difference φ0 is a constant value, so the change in light intensity detected by photodetector is only related to the changes in the phase differences φs and φε mentioned above. Thus, it is possible to calculate the corresponding change in the phase difference Δφ of the two beams after obtaining the intensity change. The acoustic vibration acting on the signal arm can be acquired through the analysis of the phase difference.
初始相位差φ 0 是一个常数值，因此光电探测器检测到的光强度变化仅与相位差的变化有关 φ s 和 φ ε 上述。因此，可以计算相位差 Δφ 的相应变化 获得强度变化后的两个光束。作用在信号臂上的声学振动可以通过相位差分析来获得。

This single Mach-Zehnder interferometer can easily detect acoustic signals. Subsequently, in order to locate the acoustic source further, a distributed optical fiber sensing system with dual Mach-Zehnder structure is gradually investigated [40], as illustrated in Figure 6.
这种单马赫-曾德尔干涉仪可以轻松检测声学信号。随后，为了进一步定位声源，逐渐研究了具有双马赫-曾德尔结构的分布式光纤传感系统 [40] ，如图所示 Figure 6 。

FIGURE 6.   图 6.

A DAS system with dual mach-zehnder structure.
具有双马赫-曾德尔结构的 DAS 系统。

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After amplification and modulation, the light emitted by the laser is divided into clockwise and counterclockwise beams by a 1×2 coupler. The two light signals pass through coupler 2 and coupler 3, interfere at the end of the paths, and then are received by photodetectors respectively. In Figure 6, if the length of the reference arm is set to l and the distance between the coupler 2 and the acoustic source is set to x , the time delay of the two light paths can be expressed as [41], [42]:

d=2l−xc/n−xc/n=2nc(l−x)(9)

View Source\begin{equation*} d=\frac {2l-x}{c / n}-\frac {x}{c / n}=\frac {2n}{c}\left ({{l-x} }\right)\tag{9}\end{equation*} where c represents the speed of light in vacuum and n represents the refractive index of the fiber core. By estimating the time delay, the location of acoustic source can be realized.
经过放大和调制后，激光器发出的光被 1×2 分成顺时针和逆时针光束 耦合。两个光信号通过耦合器 2 和耦合器 3，在路径末端发生干涉，然后分别被光电探测器接收。在 Figure 6 中，如果参考臂的长度设置为 l 耦合器 2 与声源之间的距离设置为 x ，两条光路的时间延迟可以表示为 [41] ： [42]

d=2l−xc/n−xc/n=2nc(l−x)(9)

View Source\begin{equation*} d=\frac {2l-x}{c / n}-\frac {x}{c / n}=\frac {2n}{c}\left ({{l-x} }\right)\tag{9}\end{equation*} ，其中 c 表示光在真空中的速度，n 表示纤维纤芯的折射率。通过估计时延，可以实现声源的位置。

Distributed acoustic sensors based on Mach-Zehnder interferometer have the characteristics of low cost, simple structure and long sensing range. It can be used for distributed acoustic sensing and positioning of large-scale structural health monitoring. At present, the research based on optimized demodulation algorithm has been widely concerned by academia. Sun et al. introduced the algorithm of time delay estimation in the experiment of Mach Zehnder interferometric sensing [43], and realized signal homodyne demodulation by using 3×3 optical fiber coupler. The resolution of the system is less than 100 m on a 6.8 km long optical fiber. Zhan Chun et al. validated the working principle of distributed optical fiber sensing system based on Mach-Zehnder interferometer on the testing optical fiber of 8 km [44]. Vibration detection at frequencies of 100 Hz-20 kHz was realized. The spatial resolution of 100 m was obtained by combining optical delay effect with cross-correlation algorithm. Then, they proposed a phase demodulation algorithm of 3×3 coupler for vibration and acoustic detection [45]. Experiments show that the sensitivity and resolution of the system are improved. The optical fiber perturbation positioning sensor developed by Zhang Chunxi’s research group [40] has been tested on 18.46 km long-distance optical fiber cable, which can display the perturbation position in real time. However, the average positioning error is about 390 m. They deduced a multi-disturbances localization algorithm based on correlation theory and frequency-domain analysis [46]. The theory proves the feasibility of the algorithm in distributed sensing system based on Mach-Zehnder interferometer, and it is suitable for structural health monitoring, intrusion detection and oil and gas leakage detection. Subsequently, they designed an intrinsically distributed acoustic emission sensor based on the system [47]. By measuring the time delay of two optical signals, the position of acoustic emission can be deduced. It is found that the average positioning error is about 206 m in the range of 20 km. In 2014, Chen et al. validated a distributed optical fiber vibration sensing configuration based on Mach-Zehnder interferometer [48]. The vibration source was located by the dispersion effect between the sensing signal and the reference signal, and the delay error was estimated by a cross-correlator. The pencil break signal with a frequency of 9 MHz can be detected on the sensing fiber of 320 km, and the spatial resolution of 31 m can be achieved. In 2016, Zboril et al. used Mach-Zehnder optical fiber sensing system to detect acoustic vibrations caused by touching on the window panes [49]. Finally, the results have shown that the system can measure the very weak acoustic vibration generated on the surface of plastic windows, and has high sensitivity, which can be applied to the field of safety protection. Yang et al. used the quadratic cross-correlation algorithm to estimate the time delay based on the dual Mach-Zehnder interferometric distributed optical fiber sensing system [50], which effectively reduced the noise error and improved the location accuracy of the disturbance signal.
基于马赫-曾德尔干涉仪的分布式声学传感器具有成本低、结构简单、感应距离长等特点。它可用于分布式声学传感和大规模结构健康监测的定位。目前，基于优化解调算法的研究已受到学术界的广泛关注。Sun 等人在马赫曾德尔干涉传感 [43] 实验中引入了时延估计算法，并使用 3×3 实现了信号零差解调 光纤耦合器。该系统在 6.8 公里长的光纤上的分辨率小于 100 米。詹春等在 8 km [44] 的光纤测试上验证了基于马赫-曾德尔干涉仪的分布式光纤传感系统的工作原理。实现了 100 Hz-20 kHz 频率的振动检测。将光学延迟效应与互相关算法相结合，获得了 100 m 的空间分辨率。然后，他们提出了一种 3×3 的相位解调算法 用于振动和声学检测 [45] 的耦合器。实验表明，系统的灵敏度和分辨率都有所提高。张春曦课题组 [40] 研发的光纤扰动定位传感器已在 18.46 km 长距离光缆上进行了测试，可实时显示扰动位置。然而，平均定位误差约为 390 m。他们基于相关理论和频域分析 [46] 推导出了一种多扰动定位算法。该理论证明了该算法在基于马赫-曾德尔干涉仪的分布式传感系统中的可行性，适用于结构健康监测、入侵检测和油气泄漏检测。随后，他们基于该系统 [47] 设计了一种本征分布式声发射传感器。通过测量两个光信号的时间延迟，可以推断出声发射的位置。发现在 206 km 范围内，平均定位误差约为 20 m。2014 年，Chen 等人验证了一种基于马赫-曾德尔干涉仪 [48] 的分布式光纤振动传感配置。通过传感信号与参考信号之间的色散效应定位振动源，并通过互相关器估计延迟误差。在 320 km 的传感光纤上可以检测到频率为 9 MHz 的铅笔断裂信号，并且可以实现 31 m 的空间分辨率。2016 年，Zboril 等人使用 Mach-Zehnder 光纤传感系统来检测因触摸窗玻璃而引起的声学振动 [49] 。 最后，结果表明，该系统可以测量塑料窗表面产生的非常微弱的声学振动，并且具有很高的灵敏度，可以应用于安全防护领域。Yang 等基于双马赫-曾德尔干涉分布式光纤传感系统 [50] ，采用二次互相关算法估计时延，有效降低了噪声误差，提高了扰动信号的定位精度。

In recent years, acoustic sensing technology has been gradually applied in partial discharge detection. Because partial discharge cannot be measured directly, it is usually monitored by optical fiber ultrasonic detection because of its strong anti-electromagnetic interference ability and insulation performance [51]–​[53]. Posada Roman et al. [54] used a multi-channel Mach-Sender interferometer system to detect the acoustic emission signal caused by partial discharge in the transformer model, and tested it at 150 kHz, and obtained a higher resolution than 10 Pa.
近年来，声学传感技术逐渐应用于局部放电检测。由于局部放电不能直接测量，由于其具有很强的抗电磁干扰能力和绝缘性能 [51] ，通常采用光纤超声波检测进行监测。 [53] Posada Roman 等人 [54] 在变压器模型中使用多通道 Mach-Sender 干涉仪系统检测局部放电引起的声发射信号，并在 150 kHz 下进行测试，获得了高于 10 Pa 的分辨率。

2) Michelson Interferometer
2） 迈克尔逊干涉仪

The sensing optical path diagram based on Michelson optical fiber interferometer is shown in Figure 7.
基于迈克尔逊光纤干涉仪的传感光路图如 Figure 7 所示。

FIGURE 7.   图 7.

The structural chart of michelson interferometer.
迈克尔逊干涉仪的结构图。

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Among them, the reflective end of the reference and sensing fibers is an important component of the optical fiber interferometer. After passing through the coupler, the light signal emitted by the light source is divided into two channels, one through the reference fiber arm, the other through the signal arm, which is disturbed by external sound. When reaching the mirror, the two beams of light are reflected back to the coupler and interfere with each other. The interference light carries sound information. After being detected by photoelectric detectors, it assumes the change of light intensity, and eventually converts it into electrical signal. Then it can demodulate the sound signal through signal processing. The intensity of light received by the photodetector can be expressed as:

P=P0(1+cos(Δϕ))(10)

View Source\begin{equation*} P=P_{0} \left ({{1+cos \left ({{\Delta \phi } }\right)} }\right)\tag{10}\end{equation*} where Δϕ is the phase difference caused by the acoustic pressure between the reference light and the signal light. Compared with Mach-Zehnder interferometer, the structure of Michelson interferometer uses less fiber couplers and reduces the optical loss. But its main disadvantage is that the interference signal reflected to the photodetector will also be reflected to the laser source, which will have a negative impact on the normal operation of the laser and form the noise. Therefore, in order to eliminate this kind of noise, it is necessary to increase the application of optical isolator.
其中，参考和传感光纤的反射端是光纤干涉仪的重要组成部分。光源发出的光信号通过耦合器后，分为两个通道，一个通过参考光纤臂，另一个通过信号臂，受到外界声音的干扰。当到达镜子时，两束光被反射回耦合器并相互干扰。干扰灯携带声音信息。在被光电探测器检测到后，它假设光强的变化，并最终将其转换为电信号。然后它可以通过信号处理对声音信号进行解调。光电探测器接收到的光强度可以表示为：

P=P0(1+cos(Δϕ))(10)

View Source\begin{equation*} P=P_{0} \left ({{1+cos \left ({{\Delta \phi } }\right)} }\right)\tag{10}\end{equation*} 其中 Δφ 是由参考光和信号光之间的声压引起的相位差。与马赫-曾德尔干涉仪相比，迈克尔逊干涉仪的结构使用更少的光纤耦合器，降低了光损耗。但其主要缺点是反射到光电探测器的干涉信号也会反射到激光源，这会对激光器的正常工作产生负面影响，形成噪声。因此，为了消除这种噪声，有必要增加光隔离器的应用。

Michelson optical fiber sensing system has clear principle, simple structure and high theoretical value. Many researchers try different demodulation algorithms to further optimize the performance of the system. Chojnack proposed a distributed sensing system based on unbalanced Michelson interferometer in 2002 [55], and used digital processing technology and 3×3 coupler for signal processing and phase demodulation respectively. Dual-Michelson interferometer systems are used to locate the acoustic disturbance in 4012 m sensing optical fiber in Beijing University of Posts and Telecommunications [56]. The location accuracy is 51 m, which can be used for perimeter safety detection. Wang et al. obtained a sensitivity of about −150 dB (re rad/μ Pa) by 3×3 coupler demodulation in a sensing system combined with a Φ -OTDR and a Michelson interferometer [57]. Experiments show that the system can simultaneously locate and restore external acoustic disturbances. Liu et al. used the system to detect external acoustic disturbances [58]. The sensitivity of −148 dB (re rad/μ Pa) is successfully obtained by using the phase carrier demodulation algorithm on the system.
迈克尔逊光纤传感系统原理明确，结构简单，理论价值高。许多研究人员尝试不同的解调算法，以进一步优化系统的性能。Chojnack 于 2002 年提出了一种基于非平衡迈克尔逊干涉仪的分布式传感系统 [55] ，并采用了数字处理技术和 3×3 耦合器分别用于信号处理和相位解调。双迈克尔逊干涉仪系统用于定位北京邮电大学 4012 m 传感光纤中的声扰 [56] 。定位精度为 51 m，可用于周界安全检测。Wang 等人获得了约 −150 dB （re rad/μ Pa） 的 3×3 传感系统中的耦合器解调与 Φ 相结合 -OTDR 和迈克尔逊干涉仪 [57] 。实验表明，该系统可以同时定位和恢复外部声学干扰。Liu 等人使用该系统来检测外部声学干扰 [58] 。灵敏度为 −148 dB（re rad/μ Pa） 通过在系统上使用相位载波解调算法成功获得。

3) Sagnac Interferometer  3） 萨格纳克干涉仪

Angeline et al. [59] have further developed Sagnac technology in the field of distributed optical fiber sensing based on fiber optic gyroscope (FOG) technology. Figure 8 describes the principle of distributed acoustic sensing based on Sagnac interference. The incident light is divided into two clockwise (CW) and counterclockwise (CCW) pulses propagating along the optical fiber loop by a 50:50 coupler. After a week of cycle, they interfere at the coupler. When the external sound acts on the optical fiber, the refractive index of the core changes, and finally the phase changes. After demodulation by the photodetector (PD), it transforms into the change of light intensity.
Angeline 等 [59] 人在基于光纤陀螺仪 （FOG） 技术的分布式光纤传感领域进一步开发了 Sagnac 技术。 Figure 8 描述了基于 Sagnac 干扰的分布式声学传感原理。入射光分为顺时针 （CW） 和逆时针 （CCW） 两个脉冲，通过 50：50 耦合器沿光纤回路传播。一周的循环后，它们会干扰耦合器。当外部声音作用在光纤上时，纤芯的折射率发生变化，最后相位发生变化。经光电探测器 （PD） 解调后，转化为光强的变化。

FIGURE 8.   图 8.

Principle diagram of sagnac interferometer.
萨格纳克干涉仪原理图。

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When a beam of light passes through an optical fiber of length l , the phase delay ΔΦ produced by the acoustic signal is as follows:

ΔΦ==β(Δl)+l(Δβ)β(Δl)+l∂β∂n(Δn)+l∂β∂d(Δd)(11)

View Source\begin{align*} \Delta \Phi=&\beta (\Delta l)+l(\Delta \beta) \\=&\beta (\Delta l)+l \frac {\partial \beta }{\partial n}(\Delta n)+l \frac {\partial \beta }{\partial d}(\Delta d)\tag{11}\end{align*}
当光束穿过长度为 l 的光纤时 ，相位延迟 ΔΦ 产生的声信号如下：

ΔΦ==β(Δl)+l(Δβ)β(Δl)+l∂β∂n(Δn)+l∂β∂d(Δd)(11)

View Source\begin{align*} \Delta \Phi=&\beta (\Delta l)+l(\Delta \beta) \\=&\beta (\Delta l)+l \frac {\partial \beta }{\partial n}(\Delta n)+l \frac {\partial \beta }{\partial d}(\Delta d)\tag{11}\end{align*}

In Formula (11), d denotes the diameter of the sensing fiber core and β is the propagation constant of light wave in optical fibers, β=nk0 . Where n is the refractive index of the core, k0 is the wave number of light in vacuum, k0=2π/λ0 , and λ0 is the wavelength of light in vacuum.
在公式中 (11) ，d 表示传感纤芯的直径和β 是光波在光纤中的传播常数，β=n k 0 .其中 n 是纤芯的折射率 k 0 是光在真空中的波数，k 0 =2π/ λ 0 和 λ 0 是真空中光的波长。

The first item in Formula (11) represents the phase difference Δϕ1 (Strain effect) caused by the change of the length of the sensing fiber; the second item is the phase difference Δϕn (Elastic light effect) caused by the change of the refractive index of the sensing fiber; and the third item is the phase difference (Poisson effect) caused by the change of the diameter of the sensing fiber core, which can be generally
公式 (11) 中的第一项表示相位差 Δ φ 1 （应变效应）由传感光纤长度的变化引起;第二项是相位差 Δ φ n （弹性光效应）由传感光纤的折射率变化引起;而第三项是传感纤芯直径变化引起的相位差（泊松效应），一般可以

neglected because of its relatively small value.

Δϕ=β(Δl)+l∂β∂n(Δn)=Δϕ1+Δϕn(12)

View Source\begin{equation*} \Delta \phi =\beta \left ({{\Delta l} }\right)+l\frac {\partial \beta }{\partial n}\left ({{\Delta n} }\right)=\Delta \phi _{1} +\Delta \phi _{\textrm {n}}\tag{12}\end{equation*}
由于其价值相对较小而被忽略。

Δϕ=β(Δl)+l∂β∂n(Δn)=Δϕ1+Δϕn(12)

View Source\begin{equation*} \Delta \phi =\beta \left ({{\Delta l} }\right)+l\frac {\partial \beta }{\partial n}\left ({{\Delta n} }\right)=\Delta \phi _{1} +\Delta \phi _{\textrm {n}}\tag{12}\end{equation*}

Clockwise and counterclockwise light interfere at the coupler, and the output interference signal carries the phase difference caused by the acoustic signal. The relationship between the external acoustic signal and the output light intensity can be expressed as follows:

I=I0(1+cos(Δϕ))=4I0 cos2(Δϕ2)(13)

View Source\begin{equation*} I=I_{0} \left ({{1+cos \left ({{\Delta \phi } }\right)} }\right)=4I_{0}~cos^{2}\left ({{\frac {\Delta \phi }{2}} }\right)\tag{13}\end{equation*}
顺时针和逆时针方向的光在耦合器处发生干扰，输出的干扰信号携带声信号引起的相位差。外部声信号与输出光强之间的关系可以表示如下：

I=I0(1+cos(Δϕ))=4I0 cos2(Δϕ2)(13)

View Source\begin{equation*} I=I_{0} \left ({{1+cos \left ({{\Delta \phi } }\right)} }\right)=4I_{0}~cos^{2}\left ({{\frac {\Delta \phi }{2}} }\right)\tag{13}\end{equation*}

After photoelectric conversion, acoustic signal can be restored by audio processing system.
光电转换后，声音信号可以通过音频处理系统恢复。

The sensing system based on Sagnac interferometer has the advantages of small size, light weight, easy laying, high sensitivity, anti-electromagnetic interference, intrinsic safety, etc. It has been widely used in offshore oil exploration, intelligent oil wells, anti-submarine warfare, port traffic monitoring, seismic monitoring, aging monitoring of civil buildings and other practical scenarios [60]. In practical applications, there is often a need to monitor multiple pipelines at the same time, so distributed optical fiber sensor array based on Sagnac interferometer comes into being. It can not only detect the occurrence of disturbance events, but also determine the location of sound source in real time. At present, many scholars are studying optical fiber acoustic sensor array. In a 2002’s report, the experimenter installed a triaxial hydrophone array 145 m off the coast of South Florida [61].
基于萨格纳克干涉仪的传感系统具有体积小、重量轻、易敷设、灵敏度高、抗电磁干扰、本质安全等优点。已广泛应用于海上石油勘探、智能油井、反潜战、港通监测、地震监测、民用建筑老化监测等实际场景 [60] 。在实际应用中，往往需要同时监测多条管道，因此基于萨格纳克干涉仪的分布式光纤传感器阵列应运而生。它不仅可以检测干扰事件的发生，还可以实时确定声源的位置。目前，许多学者都在研究光纤声学传感器阵列。在 2002 年的一份报告中，实验者在南佛罗里达州海岸 145 m 处安装了一个三轴水听器阵列 [61] 。

A two-sensors fold Sagnac sensing array (FSSA) was proposed by Vakoc [62], as illustrated in Figure 9. The light pulses are split into clockwise pulses (CW) through port a of the 3×3 coupler and counterclockwise pulses (CCW) through port e of the 3×3 coupler, one port of which is unused. The CW pulses are transmitted from port a to port b of the 2×2 coupler 2 and are reflected to port c of the coupler1 by the reflector after traveling up the delay coil. A part of the CW pulses enters each sensing rung through the 2×2 coupler 3, and the resulting pulse sequence returns to the port d of the 3×3 coupler. The PZT wrapped around the optical fiber is placed in the second sensing fiber, which allows us to modulate the phase by applying a voltage to simulate the acoustic signal. The CCW pulses travel the same path in the opposite direction, and the interference between the CW pulses and the CCW pulses occurs in the 3×3 coupler. The FSSA showed a phase sensitivity of approximately 0.8 μrad/Hz−−−√ when a balanced detector was used, and the desensitization of the delay coil, which was detected in the system, was agree with the theory.
Vakoc [62] 提出了一种双传感器折叠 Sagnac 传感阵列 （FSSA），如图所示 Figure 9 。光脉冲通过 3×3 的端口 a 分成顺时针脉冲 （CW） 耦合器和逆时针脉冲 （CCW） 通过 3×3 的端口 E 耦合器，其中一个端口未使用。CW 脉冲从 2×2 的端口 a 传输到端口 b 耦合器 2 的 2 端口，并在延迟线圈上行后被反射器反射到耦合器 1 的端口 C。一部分 CW 脉冲通过 2×2 进入每个传感梯级 耦合器 3，得到的脉冲序列返回到 3×3 的端口 d 耦合。缠绕在光纤上的 PZT 放置在第二根传感光纤中，这使我们能够通过施加电压来模拟声学信号来调制相位。CCW 脉冲沿相反方向传播同一路径，CW 脉冲和 CCW 脉冲之间的干扰发生在 3×3 耦合。FSSA 显示，当使用平衡探测器时，相位敏感度约为 0.8 μrad/Hz−−−√ FSSA，并且在系统中检测到的延迟线圈的灵敏度降低与理论一致。

FIGURE 9.   图 9.

Acoustic sensing system based on folded sagnac array.
基于折叠萨格纳克阵列的声学传感系统。

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Figure 9 illustrates the working principle of the optical fiber sensor. The incident light is divided into two light paths along clockwise (CW) direction and counterclockwise (CCW) direction by coupler 1. When clockwise pulses pass through the sensing arm and counterclockwise pulses pass through the reference arm, they will firstly meet at 2×2 coupler 2. Some of them continue to move in the direction opposite to the original propagation direction, and interfere in coupler 1. The other part of the light passes through coupler 3 and interferes. The interference signals are received by photodetectors respectively.
Figure 9 说明了光纤传感器的工作原理。入射光通过耦合器 1 沿顺时针 （CW） 方向和逆时针 （CCW） 方向分为两条光路。当顺时针脉冲通过传感臂和逆时针脉冲通过参考臂时，它们将首先在 2×2 处相遇 耦合器 2.其中一些继续沿与原始传播方向相反的方向移动，并干扰耦合器 1。光的另一部分穿过耦合器 3 并产生干扰。干涉信号分别由光电探测器接收。

In the aspect of optimizing demodulation algorithm, many research works have also been done. In 2008, Hang et al. proposed a distributed optical fiber acoustic sensor based on Sagnac array [63], which can be used for real-time monitoring and location of multiple pipeline leakage incidents at the same time. Experiments show that the location error is less than 0.54%. Qian et al. [64] introduced a kind of optical fiber acoustic sensor based on Sagnac ring. It uses four sensing coils on the sensing arm to restore and locate the acoustic signal. Researchers at Fudan University have innovatively proposed a cepstrum method for long-distance time-domain positioning in a sensing system combined with Mach-Zehnder and Sagnac interferometers, and achieved better location accuracy [65]. In the research of distributed optical fiber vibration sensor system based on dual-interference, Wang et al. preprocessed the dual-interference signal by combining the minimum control recursive averaging algorithm with generalized cross-correlation algorithm, so as to reduce the error of time delay estimation and locate and restore the disturbance signal more accurately [66].
在优化解调算法方面，也做了大量的研究工作。2008 年，Hang 等人提出了一种基于 Sagnac 阵列 [63] 的分布式光纤声学传感器，可用于同时对多个管道泄漏事件进行实时监测和定位。实验表明，位置误差小于 0.54%。Qian 等 [64] 介绍了一种基于 Sagnac 环的光纤声学传感器。它使用传感臂上的四个传感线圈来恢复和定位声学信号。复旦大学的研究人员创新性地提出了一种在传感系统结合马赫-曾德尔和萨格纳克干涉仪进行长距离时域定位的倒谱方法，并取得了更好的定位精度 [65] 。在基于双干扰的分布式光纤振动传感器系统研究中，Wang 等通过将最小控制递归平均算法与广义互相关算法相结合，对双干扰信号进行预处理，以减少时延估计的误差，更准确地 [66] 定位和恢复干扰信号。

B. Optical Fiber Acoustic Sensors Based on Backscattering
B. 基于背向散射的光纤声学传感器

For a sensor based on interference technology, only a single vibration can be located at the same time, that is to say, multiple sound disturbances cannot simultaneously be located independently. Another technology under study is based on optical backscattering sensors, mainly referred to the phase-sensitive optical time-domain reflectometer (Φ -OTDR). At present, distributed optical fiber acoustic sensor based on Φ -OTDR primarily is composed of optical fiber interferometer and sensor based on optical fiber backscattering. Φ -OTDR is caused by the interference of backscattered light from different parts of the optical fiber. Phase change is perceived by subtracting the output time-varying light power trajectory from the previously stored reference light power trajectory, and the position of the disturbance is proportional to the time when the trajectory changes. Φ -OTDR system is fundamentally based on the interference of reference light and Rayleigh scattering light coming back from the inside of the optical fiber. The phase of Rayleigh scattering light is disturbed by perturbation events, which makes the amplitude of Rayleigh scattering light change. Distributed acoustic sensors based on Φ -OTDR provide information of position, frequency or amplitude of sound disturbance by measuring intensity changes.
对于基于干扰技术的传感器，只能同时定位单个振动，也就是说，不能同时独立定位多个声音干扰。另一种正在研究的技术是基于光学背向散射传感器，主要是指相位敏感光学时域反射仪 （Φ -OTDR 的 OTDR 中）。目前，基于 Φ 的分布式光纤声学传感器 -OTDR 主要由光纤干涉仪和基于光纤背向散射的传感器组成。Φ -OTDR 是由来自光纤不同部分的背向散射光的干扰引起的。通过从先前存储的参考光功率轨迹中减去输出时变光功率轨迹来感知相位变化，扰动的位置与轨迹变化的时间成正比。Φ -OTDR 系统从根本上基于参考光和从光纤内部返回的瑞利散射光的干涉。瑞利散射光的相位受到扰动事件的干扰，这使得瑞利散射光的振幅发生变化。基于 Φ 的分布式声学传感器 -OTDR 通过测量强度变化来提供声音干扰的位置、频率或幅度信息。

In recent years, the technology of combining other interferometer with Φ -OTDR system has been formed and popularized. Researchers at Chongqing University have successively studied a distributed optical fiber sensing system which combines Mach-Zehnder interferometer (MZI) with phase-sensitive optical time-domain reflector (Φ -OTDR) [67], [68]. The system is used to measure the acoustic perturbation caused by the abrupt break of pencil near the optical fiber ring. The spatial resolution of 5 m and the frequency response of 6.3 MHz are obtained under the 1150 m sensing optical fiber [69]. Then Shandong Key Laboratory of Optical Fiber Sensing Technology combined Michelson interferometer (MI) with Φ -OTDR in distributed optical fiber acoustic measurement, and innovatively adopted 3×3 coupler demodulation technology [70]. The basic principle diagram is shown in Figure 10. A Michelson interferometer structure consisting of a coupler and two Faraday rotating mirrors with half arm length z is added to the output of the conventional Φ -OTDR configuration.
近年来，其他干涉仪与 Φ -OTDR 系统已经形成并普及。重庆大学的研究人员先后研究了一种将马赫-曾德尔干涉仪 （MZI） 与相位敏感光时域反射镜 （Φ -OTDR） [67] ， [68] .该系统用于测量光纤环附近铅笔突然断裂引起的声学扰动。在 1150 m 传感光纤 [69] 下获得了 5 m 的空间分辨率和 6.3 MHz 的频率响应。然后，山东省光纤传感技术重点实验室将迈克尔逊干涉仪 （MI） 与 Φ -OTDR 在分布式光纤声学测量中创新性地采用了 3×3 耦合器解调技术 [70] .基本原理图如 所示 Figure 10 。一种迈克尔逊干涉仪结构，由一个耦合器和两个半臂长的法拉第旋转镜组成 被添加到传统 Φ -OTDR 配置的输出中。

FIGURE 10.   图 10.

Configuration of interferometer based on Φ -OTDR.
基于 Φ 的干涉仪配置 -OTDR 的 OTDR 中。

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The Rayleigh scattering signal is injected into the Michelson interferometer. Suppose that the incident coherent optical signal is a rectangular monochrome pulse with frequency f and pulse width ω . When t=0 , the optical pulse is emitted into the optical fiber, and the backward Rayleigh scattering light propagates in the optical fiber. The backward Rayleigh scattering light obtained is as follows:

View Source\begin{align*}&\hspace{-2.8pc}e_{\mathrm {r}}(t)=\sum _{i=1}^{N} A_{i} cos \left [{2 \pi f\left ({t-\tau _{\mathrm {i}}}\right)}\right] \\&\qquad \qquad \qquad exp \left ({-\alpha \frac {C \tau _{\mathrm {i}}}{n_{\mathrm {f}}}}\right) {rect}\left ({\frac {t-\tau _{\mathrm {i}}}{\omega }}\right)\tag{14}\end{align*}

瑞利散射信号被注入迈克尔逊干涉仪。假设入射相干光信号是频率为 f 的矩形单色脉冲 和脉冲宽度 ω .当 t=0 时 ，光脉冲发射到光纤中，后向瑞利散射光在光纤中传播。获得的反向瑞利散射光如下：

er(t)=∑i=1NAicos[2πf(t−τi)]exp(−αCτinf)rect(t−τiω)(14)

View Source\begin{align*}&\hspace{-2.8pc}e_{\mathrm {r}}(t)=\sum _{i=1}^{N} A_{i} cos \left [{2 \pi f\left ({t-\tau _{\mathrm {i}}}\right)}\right] \\&\qquad \qquad \qquad exp \left ({-\alpha \frac {C \tau _{\mathrm {i}}}{n_{\mathrm {f}}}}\right) {rect}\left ({\frac {t-\tau _{\mathrm {i}}}{\omega }}\right)\tag{14}\end{align*} 其中 A i 是 i 的振幅 -第 个散射波，τ i 是散射波的时间延迟，N 是散射波的总数，α 代表衰减常数。当 （t− τ i /ω) 介于 0 和 1 之间，则矩形函数 rect（t− τ i /ω) 的值为 1，否则为零。其中，τ i =((2 n f l i ）/c） 、 l i 表示输入端与 i 之间的距离 -th 散射体 C 是真空中的光速，n f 是核心的折射率。

The delayed wave generated by optical signal passing through Michelson interferometer can be expressed as:

View Source\begin{align*}&\hspace{-2.8pc}e_{\mathrm {d}}(t)=\sum _{\mathrm {j}=1}^{\mathrm {N}} A_{\mathrm {j}} cos \left [{2 \pi f\left ({t-\tau _{\mathrm {j}}-\tau _{\mathrm {z}}}\right)}\right] \\&\qquad \qquad exp \left ({-\alpha \frac {C \tau _{\text {j}}}{n_{\mathrm {f}}}}\right) {rect}\left ({\frac {t-\tau _{\mathrm {j}}-\tau _{z}}{\omega }}\right)\tag{15}\end{align*}

光信号通过迈克尔逊干涉仪产生的延迟波可以表示为：

ed(t)=∑j=1NAjcos[2πf(t−τj−τz)]exp(−αCτjnf)rect(t−τj−τzω)(15)

View Source\begin{align*}&\hspace{-2.8pc}e_{\mathrm {d}}(t)=\sum _{\mathrm {j}=1}^{\mathrm {N}} A_{\mathrm {j}} cos \left [{2 \pi f\left ({t-\tau _{\mathrm {j}}-\tau _{\mathrm {z}}}\right)}\right] \\&\qquad \qquad exp \left ({-\alpha \frac {C \tau _{\text {j}}}{n_{\mathrm {f}}}}\right) {rect}\left ({\frac {t-\tau _{\mathrm {j}}-\tau _{z}}{\omega }}\right)\tag{15}\end{align*} 其中 z 是 MI 的半臂长度，τ z =((2 n f z）/C） 表示 MI 引起的时间延迟。

After the interference of two beams of light, the optical power of the interference signal is as follows:

View Source\begin{align*} I\left ({t }\right)=&\left [{ {e_{\textrm {r}} \left ({t }\right)+e_{\textrm {d}} \left ({t }\right)} }\right]\times \left [{ {e_{\textrm {r}} \left ({t }\right)+e_{\textrm {d}} \left ({t }\right)} }\right]^{\ast } \\=&\sum \limits _{\textrm {i=1}}^{\textrm {N}} {A_{\textrm {i}}^{2}exp \left ({{-2\alpha \frac {C\tau _{\textrm {i}}}{n_{\textrm {f}}}} }\right)rect\left ({{\frac {t-\tau _{\textrm {i}}}{\omega }} }\right)} \\&+\sum \limits _{\textrm {j=1}}^{\textrm {N}} {A_{\textrm {j}}^{2}exp \left ({{-2\alpha \frac {C\tau _{\textrm {j}}}{n_{\textrm {f}}}} }\right)rect\left ({{\frac {t-\tau _{\textrm {j}} -\tau _{\textrm {z}}}{\omega }} }\right)} \\&+2\sum \limits _{\textrm {i=1}}^{\textrm {N}} {A_{\textrm {i}}} \sum \limits _{\textrm {j=1}}^{\textrm {N}} {A_{\textrm {j}} cos \left ({{\Delta \varphi } }\right)} \times exp \left [{ {-\alpha \frac {C\left ({{\tau _{\textrm {i}} +\tau _{\textrm {j}}} }\right)}{n_{\textrm {f}}}} }\right] \\&\times rect\left ({{\frac {t-\tau _{\textrm {i}}}{\omega }} }\right)rect\left ({{\frac {t-\tau _{\textrm {j}} -\tau _{\textrm {z}}}{\omega }} }\right)\tag{16}\end{align*}

经过两束光的干扰后，干涉信号的光功率如下：

I(t)==[er(t)+ed(t)]×[er(t)+ed(t)]∗∑i=1NA2iexp(−2αCτinf)rect(t−τiω)+∑j=1NA2jexp(−2αCτjnf)rect(t−τj−τzω)+2∑i=1NAi∑j=1NAjcos(Δφ)×exp[−αC(τi+τj)nf]×rect(t−τiω)rect(t−τj−τzω)(16)

View Source\begin{align*} I\left ({t }\right)=&\left [{ {e_{\textrm {r}} \left ({t }\right)+e_{\textrm {d}} \left ({t }\right)} }\right]\times \left [{ {e_{\textrm {r}} \left ({t }\right)+e_{\textrm {d}} \left ({t }\right)} }\right]^{\ast } \\=&\sum \limits _{\textrm {i=1}}^{\textrm {N}} {A_{\textrm {i}}^{2}exp \left ({{-2\alpha \frac {C\tau _{\textrm {i}}}{n_{\textrm {f}}}} }\right)rect\left ({{\frac {t-\tau _{\textrm {i}}}{\omega }} }\right)} \\&+\sum \limits _{\textrm {j=1}}^{\textrm {N}} {A_{\textrm {j}}^{2}exp \left ({{-2\alpha \frac {C\tau _{\textrm {j}}}{n_{\textrm {f}}}} }\right)rect\left ({{\frac {t-\tau _{\textrm {j}} -\tau _{\textrm {z}}}{\omega }} }\right)} \\&+2\sum \limits _{\textrm {i=1}}^{\textrm {N}} {A_{\textrm {i}}} \sum \limits _{\textrm {j=1}}^{\textrm {N}} {A_{\textrm {j}} cos \left ({{\Delta \varphi } }\right)} \times exp \left [{ {-\alpha \frac {C\left ({{\tau _{\textrm {i}} +\tau _{\textrm {j}}} }\right)}{n_{\textrm {f}}}} }\right] \\&\times rect\left ({{\frac {t-\tau _{\textrm {i}}}{\omega }} }\right)rect\left ({{\frac {t-\tau _{\textrm {j}} -\tau _{\textrm {z}}}{\omega }} }\right)\tag{16}\end{align*}

The parameter Δφ=(4πfnfz/C)+(4πfnf(lj−li)/C) represents the phase difference engendered by the half arm length and the distance between the j -th and the i -th scatterers.
参数 Δφ=（4πf n f z/C）+（4πf n f ( l j − l i ）/c） 表示由半臂长度和 j 之间的距离产生的相位差 -th 和 i -th 散射器。

The interferometric signal includes not only the location information of the sound source, but also the phase change after demodulation. Finally, the distributed acoustic response can be measured by analyzing the backscattering power displayed. Experiments show that different acoustic sources with different intensity can be demodulated, and phase, amplitude, frequency response and location information can be obtained simultaneously.
干涉信号不仅包括声源的位置信息，还包括解调后的相位变化。最后，可以通过分析显示的背向散射功率来测量分布式声学响应。实验表明，可以解调不同强度的不同声源，同时获得相位、幅度、频率响应和位置信息。

Subsequently, on the basis of this system, they added a sensing network with 500 ultra-weak fiber Bragg gratings (UWFBG) with the same spacing of 2 m as Figure 11 [31], and carried out the experimental study of acoustic detection in water tank. The results show that when the pressure detection limit is 0.122 Pa and the frequency response is 450–600 Hz, the system successfully demodulates distributed acoustic signals with the sensitivity of −158 dB (re rad/μ Pa).
随后，在该系统的基础上，他们增加了一个具有 500 个间距为 2 m Figure 11 的超弱光纤布拉格光栅 （UWFBG） 的传感网络 [31] ，并开展了水箱声学检测的实验研究。结果表明，当压力检测限为 0.122 Pa 且频率响应为 450–600 Hz 时，系统以 −158 dB （re rad/ μ Pa） 的灵敏度成功解调分布式声学信号。

FIGURE 11.   图 11.

The Φ -OTDR-interferometer system with uwFBGs.
The Φ -带有 uwFBG 的 OTDR 干涉仪系统。

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In Φ -OTDR system, the location of sound source is an urgent concern. In order to solve this problem, many research institutes have carried out a lot of experiments, including noise elimination, signal-to-noise ratio (SNR) improvement and system performance optimization.
在 Φ 中 -OTDR 系统，声源的位置是一个紧迫的问题。为了解决这个问题，许多研究机构进行了大量实验，包括噪声消除、信噪比 （SNR） 改进和系统性能优化。

For example, Lu et al. weakened the noise power by moving differential method and average method, and at the same time, the frequency response range was expanded [71]. Under different polarization conditions, Qin et al. recommended a wavelet denoising method to eliminate random noise caused by different vibration sources and detectors [72]. Muanenda et al. used the method of cyclic pulse coding to improve the SNR of backscattered signals by 9 dB in Φ -OTDR system [73]. The main method of operation is to realize cyclic coding by modulating inter-pulse coherence and intra-pulse incoherence. Subsequently, they applied cyclic pulse coding to a distributed sensing system for simultaneous measurement of acoustic and temperature [74], which can detect acoustical vibration at 500 Hz at 5 km, and the temperature resolution is less than 0.5°. Then in order to improve the SNR of Φ -OTDR acoustic sensing system, a combination of phase difference average estimation, infinite impulse response filtering and piecewise unwrapping algorithm is expounded [75]. Moreover, a narrow linewidth light source is used to improve the system performance. Rao et.al. used the DAS system based on Φ -OTDR to measure dynamic strain, and achieved 12.6 km of sensing range and 10 m of spatial resolution [76]. They combine the I/Q demodulation and the homodyne detection of 90 mixed mode to demodulate the phase information of optical signal successfully without interferometer configuration in the experimental optical path. The experimental schematic diagram is elucidated in Figure 12.
例如，Lu 等人通过移动差分法和平均法削弱了噪声功率，同时扩大了 [71] 频率响应范围。在不同极化条件下，Qin 等人推荐了一种小波去噪方法，以消除不同振动源和探测器引起的随机噪声 [72] 。Muanenda 等人使用循环脉冲编码方法将反向散射信号的 SNR 提高了 9 dB 的 Φ -OTDR 系统 [73] .主要的作方法是通过调制脉冲间相干性和脉冲内非相干性来实现循环编码。随后，他们将循环脉冲编码应用于分布式传感系统，用于同时测量声学和温度 [74] ，该系统可以在 5 km 处检测 500 Hz 的声学振动，温度分辨率小于 0.5°。那么为了提高 Φ 的 SNR -阐述了相位差平均估计、无限脉冲响应滤波和分段解缠算法相结合的 OTDR 声学传感系统 [75] 。此外，使用窄线宽光源来提高系统性能。饶 et.al。使用基于 Φ 的 DAS 系统 -OTDR 测量动态应变，并实现了 12.6 公里的感应距离和 10 米的空间分辨率 [76] 。它们将 I/Q 解调和 90 混合模式的零差检测相结合，在实验光路中无需干涉仪配置即可成功解调光信号的相位信息。实验示意图如 Figure 12 所示。

FIGURE 12.   图 12.

Optical fiber sensing system diagram based on COTDR.
基于 COTDR 的光纤传感系统图

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