Self-suppression of common-mode noises of the ... - OSA Publishing

Vol. 26, No. 12 | 11 Jun 2018 | OPTICS EXPRESS 15384

Self-suppression of common-mode noises of the different fiber optic interferometric accelerometers YI DUO,1,2,3 HE XIANGGE,1,2 LIU FEI,1,2 GU LIJUAN,2,4 ZHANG MIN,2,* QIU XIAOKANG,5 AND YE HAN6 1School

of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China of Ocean Research, Peking University, Beijing 100871, China 3Currently with the College of Physics and Energy, Shenzhen University, 518060, China 4School of Physics, Peking University, Beijing 100871, China 5Department of electronic engineering, Tsinghua University, Beijing, 100084, China 6Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China *[email protected] 2Institute

Abstract: This study proposes two new fiber optic interferometric accelerometers with the utilization of the push-pull structure, one is based on the principle of triple low-reflectivity fiber Bragg gratings, and the other is based on the 1x3 unbalanced Michelson interferometer. The proposed accelerometers are capable of suppressing the common-mode noises (CMNs) by themselves without additional reference accelerometers, and therefore reducing the volume and the cost of the sensing system. Besides, the accelerometers can also suppress the sensor noises caused by the environment, and therefore show better CMNs suppression effect than the traditional method of using the reference accelerometer. The two accelerometers are experimentally verified and show respectively an improvement of 33 dB and 28 dB in CMNs suppression at 100 Hz. Both presented fiber optic accelerometers show huge advantages for the large-scale quasi-distributed oil and gas reservoir monitoring applications. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (060.2310) Fiber optics; (060.2370) Fiber optics sensors; (060.3735) Fiber Bragg gratings.

References and links 1.

N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, and S. R. Lai, “A 3-component fiber-optic accelerometer for well logging,” Opt. Commun. 234(1–6), 153–162 (2004). 2. J. M. D. Freitas, “Recent developments in seismic seabed oil reservoir monitoring applications using fibre-optic sensing networks,” Meas. Sci. Technol. 22(5), 052001 (2011). 3. G. Gagliardi, M. Salza, P. Ferraro, P. D. Natale, A. D. Maio, S. Carlino, G. D. Natale, and E. Boschi, “Design and test of a laser-based optical-fiber Bragg-grating accelerometer for seismic applications,” Meas. Sci. Technol. 19(8), 085306 (2008). 4. A. D. Kersey, M. J. Marrone, and M. A. Davis, “Polarisation-insensitive fibre optic michelson interferometer,” Electron. Lett. 27(6), 518–520 (1991). 5. M. Pang, H. P. Zhou, M. Zhang, F. Lin, N. Zeng, and Y. B. Liao, “Analysis and amelioration about the crossaxis sensitivity of a fiber-optic accelerometer based on compliant cylinder,” J. Lightwave Technol. 26(3), 365– 372 (2008). 6. J. M. D. Freitas, J. P. F. Wooler, and P. J. Nash, “Measurement of sensor axis misalignment in fibre-optic accelerometers,” Meas. Sci. Technol. 17(7), 1819–1825 (2006). 7. P. Nash, A. Strudley, R. Crickmore, and J. DeFreitas, “High efficiency TDM/WDM architectures for seismic reservoir monitoring,” in 20th International Conference on Optical Fibre Sensor (2009), paper 75037T. 8. S. Niu, Y. Hu, Z. Hu, and H. Luo, “Fiber fabry-perot hydrophone based on push-pull structure and differential detection,” IEEE Photonics Technol. Lett. 23(20), 1499–1501 (2011). 9. Q. Jiang and M. Yang, “Simulation and experimental study of a three-axis fiber Bragg grating accelerometer based on the pull–push mechanism,” Meas. Sci. Technol. 24(11), 115105 (2013). 10. Z.-G. Guan, D. Chen, and S. He, “Coherence multiplexing of distributed sensors based on pairs of fiber Bragg gratings of low reflectivity,” J. Lightwave Technol. 25(8), 2143–2148 (2007). 11. J. Sancho, S. Chin, D. Barrera, S. Sales, and L. Thévenaz, “Time-frequency analysis of long fiber Bragg gratings with low reflectivity,” Opt. Express 21(6), 7171–7179 (2013). 12. S. Dyer, K. Rochford, and A. Rose, “Fast and accurate low-coherence interferometric measurements of fiber Bragg grating dispersion and reflectance,” Opt. Express 5(11), 262–266 (1999).

#330419 Journal © 2018

https://doi.org/10.1364/OE.26.015384 Received 26 Apr 2018; revised 27 May 2018; accepted 29 May 2018; published 4 Jun 2018


13. O. H. Waagaard, E. Rønnekleiv, S. Forbord, and D. Thingbø, “Suppression of cable induced noise in an interferometric sensor system,” Proc. SPIE 7503, 75034Q (2009). 14. O. H. Waagaard and E. Rønnekleiv, “Reduction of crosstalk in inline sensor arrays using inverse scattering,” Proc. SPIE 7004, 70044Z (2008). 15. S. Knudsen, G. B. Havsgard, A. Berg, D. Thingbø, F. Bostick, and M. Eriksrud, “High resolution fiber-optic 3-C seismic sensor system for in-well imaging and monitoring applications,” in 18th International Conference on Optical Fibre Sensor (2006), paper FB2. 16. Z. Zhi, W. Zhenzhen, and S. Lian, “Fiber-reinforced polymer-packaged optical fiber Bragg grating strain sensors for infrastructures under harsh environment,” J. Sens. 16(1), 1–18 (2016). 17. C. Zhang, D. Jiang, and L. Liang, “Application of fiber Bragg grating for safety monitoring of cantilever crane of huge crane barge,” in International Conference on Optical Communications and Networks (2010), pp. 60–64. 18. T. H. T. Chan, L. Yu, H. Y. Tam, Y. Q. Ni, S. Y. Liu, W. H. Chung, and L. K. Cheng, “Fiber Bragg grating sensors for structural health monitoring of tsing-ma bridge: Background and experimental observation,” Eng. Struct. 28(5), 648–659 (2006). 19. L. P. Canal, R. Sarfaraz, G. Violakis, J. Botsis, V. Michaud, and H. G. Limberger, “Monitoring strain gradients in adhesive composite joints by embedded fiber Bragg grating sensors,” Compos. Struct. 112, 241–247 (2014). 20. F. Liu, S. Xie, X. Qiu, X. Wang, S. Cao, M. Qin, X. He, B. Xie, X. Zheng, and M. Zhang, “Efficient commonmode noise suppression for fiber-optic interferometric sensor using heterodyne demodulation,” J. Lightwave Technol. 34(23), 5453–5461 (2016).

1. Introduction Fiber optic accelerometers have been widely used for acoustic and vibration detection in numerous industrial applications, for example, in the explorations of oil and gas reservoir, micro-seismic monitoring and well logging [1–3]. They offer various advantages such as high sensitivity, immunity to the electromagnetic interference, easiness to form a network when compared with the traditional electronic sensors. Among all types of fiber optic accelerometers, the Michelson interferometer with a compliant cylinder structure is the most classic and widely applied one [4–7]. P.Nash et al. have reported a time and wavelength based multiplexing architecture combining up to 256 sensor channels onto a single optical fiber pair [7]. This type of accelerometer is based on the mass-spring system, and the external vibration acceleration can be detected by demodulating the phase changes of the interferometric light. In addition, the push-pull structure of the accelerometer has been reported [8,9], which is used to increase the device reliability and reduce the disturbance due to its symmetrical structure. In recent years, the fiber optic accelerometers based on low-reflectivity Fiber Bragg Gratings (FBGs) have been reported [10–15].O.H.Waagaard et al. have reported a fiber optic seismic monitoring network system for the permanent tubing conveyed installation in oil and gas well [13,14]. When compared with the traditional accelerometer based on the Michelson interferometer, the low-reflectivity FBGs require only one single fiber with no other additional optical devices, and therefore largely reduces the cost and volume of the sensing system. Besides, they can realize an N-level quasi-distributed sensing network by simply fabricating certain numbers of gratings along a single fiber [16–19]. All these advantages make them the promising candidates for the applications of large-scale quasi-distributed sensing networks. The common-mode noises (CMNs) are frequently generated in fiber optic sensing systems [20], mainly from the sensing system devices themselves and the environment, and their frequency distributions vary from several tens to several thousand hertz, which influence greatly the noise floor performance and the weak signal detection especially for the largescale quasi-distributed sensing network. Nowadays, the noise floor varying from −86~-100 dB rad2/Hz is an acceptable range in the oil/gas reservoir monitoring applications [15], and therefore, in order to reduce the noise level of the sensing network system, the CMNs should be suppressed, and the suppression effect of CMNs is an important parameter to assess the system performances. F.Liu et al. have proposed a traditional method for the CMNs suppression, as indicated in Fig. 1 [20], it shows a dual-pulse heterodyne fiber optic interferometric system. The system is based on an unbalanced Michelson interferometer, where two Acousto-Optic modulators are driven to generate a dual-pulse, and the external acoustic/vibration information is demodulated by the heterodyne algorithm. In order to


suppress the CMNs, an additional reference accelerometer is used. This type of the reference accelerometer is specially designed to be much less sensitive to the external vibration signal than the sensing accelerometer. The CMNs here refer to the noises shared by both the sensing accelerometer and the reference accelerometer, which cover all the noises induced from the front common path of the sensing system, such as the amplified spontaneous emission noise (ASE) of the EDFA, the amplitude caused by the AOM driver, the phase noise and the relative intensity noise (RIN) of the laser, etc. These noises lead to the common contribution to the output interferometric signal. Then the CMNs can be suppressed by subtracting the demodulated phase of the reference interference pulse 02 from the sensing interference pulse 01.

Fig. 1. General fiber-optic Michelson interferometric system and its CMNs suppression method [20].

The usage of the additional reference accelerometer to suppress the CMNs is widely applied by the current mainstream oil company [13,14]. However, it has also several limitations. Firstly the phase subtraction method mainly suppresses the CMNs generated from the front common path of the system such as the laser source, but it cannot suppress the noise of the sensing accelerometer caused by the environment. Secondly, the additional reference accelerometer still suffers from a weak sensitivity, and a part of useful external vibration information is also filtered in the suppression process at the same time. Finally, the usage of the additional reference accelerometer increases the system cost and size. In this paper, we demonstrate two new fiber optic accelerometers and their CMNs suppression effects are compared. One is based on the triple low-reflectivity fiber Bragg gratings, and the other is based on the 1x3 unbalanced Michelson fiber optic interferometer. The proposed accelerometers are capable of suppressing the CMNs by their own structures, and they show even better CMNs suppression effect than the traditional method using the reference accelerometer. Besides, the push-pull structure is applied to both accelerometers to ensure a high on-axis sensitivity and low cross-axis sensitivity. The experimental setup is built up and the CMN suppression effects of the two new accelerometers are analyzed and compared via power spectrums. The main performance parameters such as on-axis sensitivity, operating bandwidth, resolution, linearity and cross-axis sensitivity are finally measured and compared. To the authors’ knowledge, it is the first time that these two types of accelerometers are reported, and the proposed two accelerometers are particularly suitable for the large-scale quasi-distributed sensing system in the oil and gas reservoir monitoring applications.


2. Accelerometer structures 2.1 Triple low-reflectivity fiber Bragg gratings accelerometer Figure 2 shows the structure diagram of the proposed triple low-reflectivity fiber Bragg gratings accelerometer. Figure 2(a) demonstrates the novel structure of the fiber with triple low-reflectivity FBGs. It consists of a 23 m long polarization-maintaining optical fiber and three FBGs which are carved along the fiber with evenly spaced of 10 m. The fiber length of 10 m is designed to realize the light interference in the space, and the details will be introduced in the next paragraph. Two sections of 1.5 m additional fiber optic are designed at the two ends to facilitate the connection with the other optical devices. The polarizationmaintaining optical fiber is used to eliminate the polarization induced fading. The center wavelength of the FBGs is 1554.12 nm, and the reflectivity is 5% so that it ensures the intensities of the reflected light to be approximately equal. It should be noted that the reflectivity of each FBG is low enough so that the multiple reflections among the FBGs can be ignored. Besides, the 3 dB bandwidth of the reflection spectrum is 1 nm, which ensures that the incident light is in the flat zone of the FBG reflectivity spectrum. Figure 2(a) also indicates the pulse propagation along the fiber Bragg grating (pulses numbering is explained at the end of Fig. 2). Assuming the incident light consists of a dualpulse with a spatial separation of 20 m, when they pass through the first FBGs, about 5% light power is reflected, and the rest 95% light power goes through the second and the third FBGs in turn. Since the dual-pulse is separated in the space, the pulse-11 and the pulse-21 are reflected separately with a distance of 20 m. Besides, the distance between the pulse-11 and pulse-12 is also 20 m considering the back and forth of the incident pulse. Therefore two interference pulses 01 and 02 occur between the pulse-12 and the pulse-21, the pulse-13 and the pulse-22. Finally, the phases of the two interference pulses 01 and 02 are demodulated and subtracted, and the amplitude of the external vibration acceleration is reflected by the phase difference. Figure 2(b) demonstrates the triple low-reflectivity fiber Bragg gratings accelerometer with the push-pull structure. It consists of a coaxial pole, a metal mass, two elastic enhanced layers, a base and the 23 m long polarization-maintaining optical fiber described in Fig. 2(a). Two elastic enhanced layers are inserted below and above the metal mass and supported by the base. The two sections of the 10 m polarization-maintaining optical fiber between the FBGs are wrapped around the two elastic enhanced layers symmetrically with a pre-tensioned force, and the three FBGs are laid in the middle of the metal mass.

Fig. 2. Structure diagram of the triple low-reflectivity fiber Bragg gratings accelerometer. (a) Fiber optic with the triple low-reflectivity FBGs. (b) Cross section of the fiber optic accelerometer. (Annotation: pulse-11, pulse-12 and pulse-13 represent the reflected pulses of the front incident pulse. Pulse-21, pulse-22 and pulse-23 represent the reflected pulses of the later incident pulse. Pulse 01 and pulse 02 represent the interference pulses occurred between the returning pulse train 1 and 2.)


Next, the theoretical on-axis sensitivity and the cross-axis sensitivity of the presented triple low-reflectivity fiber Bragg gratings accelerometer are discussed respectively. Generally speaking, the on-axis sensitivity is desired as higher as possible and the cross-axis sensitivity is desired as lower as possible to avoid disturbing the on-axis measurements. When an external vibration is exerted vertically on the accelerometer (on-axis), the metal mass compresses one of the elastic enhanced layers and another expands, then the deformations of the two elastic enhanced layers are converted respectively to the radial expansion and the compression in the sensing fiber 1 and 2, which finally leads to the phase changes in the same amplitude but opposite direction, as indicated in Fig. 3(a), therefore the on-axis sensitivity doubles by subtracting the interference phase 01 and 02. However, when the vibration is exerted horizontally on the accelerometer (cross-axis), the two elastic enhanced layers deform in the same manner, therefore the phases between the two sensing fibers vary with the same amplitude and same direction, and the interferometric light is suppressed by subtracting the interference phase 01 and 02. Finally, the cross-axis sensitivity is reduced to zero theoretically.

Fig. 3. On-axis and cross-axis sensitivity of the triple low-reflectivity fiber Bragg gratings accelerometer.

2.2 1x3 unbalanced Michelson fiber optic accelerometer Figure 4 represents the structure diagram of the proposed 1x3 unbalanced Michelson fiber optic accelerometer. Figure 4(a) shows the structure of the 1x3 fiber optic interferometer. It is based on the unbalanced Michelson interferometer, which consists of one input optical fiber and three output optical fibers. The length of the three output optical fibers are respectively 0.5 m, 10.5 m and 20.5 m, and each fiber optic is collected with a Faraday mirror to eliminate the polarization induced fading. Figure 4(a) also shows the pulse propagation in the 1x3 fiber optic Michelson interferometer. The dual-pulse with a 20 m spatial separation is injected into the interferometer. When the first pulse passes through the three fiber optic beams, three pulses are reflected successively by the Faraday mirrors with separations of 20 m and 40 m, and they generate the returning pulse train 3. Since the dual-pulse is separated in the space, the second pulse goes through the same path but leaves a spatial delay of 20 m, and they generate the returning pulse train 4. Similar to Fig. 2(a), the two interference pulses 03 and 04 occur between the pulse-32 and pulse-41, the pulse-33 and the pulse-42, and the phase subtraction between the two interference pulses 03 and 04 reflects the amplitude of the external vibration acceleration. The 1x3 fiber optic Michelson interferometer is then wrapped onto the push-pull structure, which is indicated in Fig. 4(b). The push-pull structure is similar to Fig. 2(b), with two grooves designed in the middle of the metal mass in order to settle the optical coupler and the three Faraday mirrors. The 0.5 m long fiber is directly wrapped onto the middle metal mass, the 10.5 m length fiber and the 20.5 m length fiber are wrapped respectively onto the upper and the lower elastic enhanced layers.


Fig. 4. Structure diagram of the 1x3 unbalanced Michelson fiber optic accelerometer. (a) 1x3 fiber optic interferometer. (b) Cross section structure of the fiber optic accelerometer.

Next, the theoretical on-axis sensitivity and the cross-axis sensitivity of the presented 1x3 Michelson fiber optic accelerometer are discussed respectively. As indicated in Fig. 5 (a), this accelerometer is equivalent to two unbalanced Michelson interferometers, specifically speaking, with the 0.5 m and the 10.5 m fiber optics as the two beams of the first equivalent interferometer, and the 10.5 m and the 20.5 m fiber optics as the two beams of the second equivalent interferometer. When the external vibration is exerted vertically on the accelerometer (on-axis), the fiber optics wrapped around the upper and lower elastic enhanced layers deform radially in the opposite direction. Since the phase sensitivity is proportional to the sum of the two interferometric beams of the fiber length, the external vibration of the second equivalent interferometer leads to a phase amplitude 3 times bigger than the first equivalent interferometer, therefore the on-axis sensitivity becomes 4 times high by subtracting the interference phases 04 from the interference phases 03. On the other hand, when the vibration is exerted horizontally on the accelerometer (cross-axis), the two elastic enhanced layers deform in the same manner, and the cross-axis sensitivity is suppressed by subtracting the two interference phases. Here it should be especially explained that the horizontal external vibration is suppressed twice by the two equivalent Michelson interferometers, therefore, theoretically speaking, the theoretical suppression effect of crossdisturbance of the presented 1x3 Michelson fiber optic accelerometer is better than that of the triple low-reflectivity fiber Bragg gratings accelerometer.

Fig. 5. On-axis sensitivity and cross-axis sensitivity of the 1x3 Michelson accelerometer.

As the push-pull structure takes advantage of two symmetrically placed elastic enhanced layers, it is reasonable to consider only one of them as a sample when estimating the theoretical sensitivity of the accelerometer, and then double the sample sensitivity for the onaxis sensitivity of the triple low-reflectivity fiber Bragg gratings accelerometer and quadruple it for the on-axis sensitivity of the 1x3 Michelson fiber optic accelerometer. The theoretical sensitivity of a single compliant cylinder structure is expressed as:


dφ n2 8π 2 nbvNM ( )0 [1 − (1 − v f ) p12 − v f p11 ] = a 2 λ HAK A = 1−

NE fn S fn EHb(b 2 − a 2 )

[b 2 (2v 2 + v − 1) − a 2 (1 + v)]

(1)

(2)

where n is the refractive index of the fiber. H,b,a are respectively the height, the outer radius and the inner radius of the elastic enhanced layer. E,v are respectively the Young’s modulus and the Poisson ratio of the elastic enhanced layer. N is the loop number of the wrapped fiber. M is the mass, λ is the wavelength, K is the system stiffness and A is a variable which describes the effects of the wrapped fiber on the elastic enhanced layer. E fn , S fn are respectively the Young’s modulus and the Poisson ratio of the fiber optic, and p11 , p12 are the elasto-optic coefficients. 2.3 Advantages of the newly designed accelerometers When compared with the traditional accelerometer, the presented two newly designed accelerometers show several advantages. Firstly, they count the subtraction of two interference pulses, and if one of the interference pulses is used for sensing, then the other may be considered as the reference accelerometer, vice versa. Therefore they are capable to suppress the CMNs by their independent structures without additional reference accelerometers, therefore reduce the cost and volume of the sensing system, showing potentially huge advantages especially for the large-scale quasi-distributed sensing system. Secondly, the two interference pulses generated from the accelerometers share the same noise caused by the external environment, and therefore the subtraction of two interference phases can also suppress the sensor noise caused by the external environments except for the traditional CMNs generated from the front common path of the systems. Finally, the on-axis sensitivity becomes doubly high for the triple low-reflectivity fiber Bragg gratings accelerometer, and 4 times high for the 1x3 Michelson fiber optic accelerometer, while the cross-axis sensitivity is largely suppressed for both new accelerometers due to the utilization of the push-pull structure. 3. Experimental setup The experimental setup of the fiber optic accelerometer system is built up to verify the suppression effects of the CMNs of the newly designed accelerometers, as shown in Fig. 6. Firstly the polarization-maintaining laser (center wavelength: 1554 nm) is selected as the light source, with two optical couplers and two acoustic-optic modulators to generate heterodyne dual pulses. In detail, the laser generates the continuous wave light, then, AOM1 and AOM2 are driven by the AOM driver and modulate the continuous wave light into the two pulses with a frequency shift of 100 MHz and 100.05 MHz respectively. A 20 m long delay polarization-maintaining optical fiber is placed after the AOM1 to separate the two pulses in the time domain. The two AOMs modulate the continuous wave to form a dual pulse train with the pulse width of 80 ns and the pulse repetition frequency of 200 kHz. Here the newly designed two fiber optic accelerometers and the traditional one using the reference accelerometer are compared for the CMNs suppression performance, and three tests are conducted under the same environmental conditions. During the first test, the dual-pulse train is connected with the triple low-reflectivity fiber Bragg gratings accelerometer by a polarization-maintaining circulator, and it returns the interference pulses 01 and 02. Then the returned interference pulses are launched into the demodulation module, they are converted into the electric signal by the photoelectric conversion and the data are collected by the highspeed acquisition card with a sampling frequency of 100 MS/s. The phase changes are finally demodulated based on the heterodyne demodulation algorithm [9], and the demodulated


phase of the triple low-reflectivity fiber Bragg gratings accelerometer is obtained by subtracting the phases of the interference pulses 01 from 02. During the second test, the dual pulse train is connected with the 1x3 fiber optic Michelson accelerometer by the circulator, and then it returns the interference pulses 03 and 04. Similar to the above, the two interference pulses are launched into the demodulation module, and the final demodulated phase of the 1x3 fiber optic Michelson accelerometer is obtained by subtracting the phase of the interference pulse 03 from 04. During the third test, the traditional CMNs suppression method using the reference accelerometer is considered. The dual pulse train is separated into two branches by the optical coupler 3, and they are discussed separately. The first dual pulse train is connected with the sensing accelerometer which is fabricated based on the principle of an unbalanced Michelson interferometer with two fiber beams of unequal lengths of 0.5 m and 10.5 m. The 10.5 m fiber is wrapped around the elastic enhanced layer and the 0.5 m fiber is wrapped directly around the metal mass. The dimension of the sensing accelerometer is half of the push-pull structure. The second dual pulse train is firstly connected with the delay fiber in order to distinguish spatially with the interference pulse generated by the sensing accelerometer, and then it transmits into a reference accelerometer. The reference accelerometer is also fabricated based on the principle of the unbalanced Michelson interferometer, two beams of fiber are wrapped directly around an aluminum cylinder without elastic enhanced layers so that it is insensible to the external vibration. Both the sensing accelerometer and the reference accelerometer eliminate the polarization induced fading by the reflection of the Faraday Rotation Mirror (FRM). The sensing accelerometer generates the interference pulse 05 and reference accelerometer generates the interference pulse 06, and the traditional method to suppress the CMNs is to subtract the phase of the reference interference pulse 06 from the sensing interference pulse 05.

Fig. 6. Experimental setup. (Annotation: The red lines represent the polarization-maintaining optical fibers, the yellow lines the normal fiber optics, and the blue lines the electric cables. The red pulses represent the input pulses, and the green pulses the output interference pulses. The blue cylinder represents the compliant cylinder with the elastic enhanced layer, and the purple one without elastic enhanced layers.)

Typical performance parameters for the accelerometer include on-axis sensitivity, operating bandwidth, linearity, cross-axis sensitivity and resolution (also named as “minimum detectable acceleration”). Therefore the test platform is also built up to measure the above parameters of the two accelerometers, and their performances are compared. During the onaxis sensitivity test (seen in Fig. 7), the fiber optic accelerometer and a standard piezoelectric accelerometer are both placed on an electrodynamic shaker to suffer the same vibration. The


vibration acceleration is measured by the piezoelectric accelerometer while the phase change of the interferometric light is demodulated based on the heterodyne demodulation algorithm, and therefore the on-axis sensitivity (defined as the ratio between the phase change and the acceleration) can be estimated. Then the sensitivity response in function of frequency is measured by varying the vibration frequency. During the linearity test, the frequency is fixed at 180 Hz to ensure that the accelerometer works in the flat bandwidth. The fiber optic accelerometer is still fixed on the electrodynamic shaker shown in Fig. 7. Considering the dynamic range limit of the system, the vibration acceleration amplitude varies from 0 to 1g (1g = 9.8 m/s2) for the 1x3 fiber optic Michelson accelerometer, and 0 to 2g for the triple low-reflectivity fiber Bragg gratings accelerometer. The light phases are collected by the demodulation system, and the linearity relationship curves between the accelerations and the light phases can be obtained. During the direction pattern test, a rotatable mechanical fixture is used. As seen in Fig. 8, the accelerometer is placed on the rotatable fixture which is connected to the electrodynamic shaker, and the sensitivities at different orientations of the axis are obtained by rotating the fixture. Here the accelerometer sensitivity is calibrated every 15 degrees, and the direction pattern of a single cycle is finally plotted by connecting all the 24 (360 degrees/15 degrees = 24) sensitivity values in each direction. Finally the cross-axis sensitivity is calculated according to the direction pattern.

Fig. 7. Sensitivity test setup.

Fig. 8. Direction pattern test setup.

4. Results and analyses The test results are discussed as follows. Firstly the CMNs suppression effect of the two fiber optic accelerometers is discussed separately. The noise floor of the accelerometer sensing system is measured and presented in the form of power spectral density (PSD). The result of the triple low-reflectivity fiber Bragg gratings accelerometer is shown in Fig. 9, where the signal 1(blue curve) and the signal 2(black curve) represent the PSDs of the interference phase 01 and 02, and the red curve represents the PSD after the phase subtraction between the


interference pulses 01 and 02. It is observed that the PSD curve of the noise floor of the signals 1 and 2 are nearly coincident and undistinguishable due to their adjacent position, and the PSDs are respectively −63.48 dB rad2/Hz and −63.68 dB rad2/Hz at 100 Hz, with a difference of only 0.20 dB. However, the noise level decreases significantly after the subtraction of interference phase, and the PSD reduces to −96.50 dB rad2/Hz with a suppression of about 33 dB at 100 Hz, this phenomenon confirms the theoretical analysis as discussed in section 2.3. The suppression effect tends to be less efficient at higher frequency (1 kHz ~10 kHz) since most of the CMNs distribute within the low-frequency range.

Fig. 9. Suppression effect of common-mode noise of the triple low-reflectivity fiber Bragg gratings accelerometer in the frequency domain. (dB rad2/Hz = 20 ⋅ log10rad2/Hz, same for Fig. 10, Fig. 11.)

Then, the CMNs suppression effect of the 1x3 unbalanced fiber optic Michelson accelerometer is discussed, and the result is shown in Fig. 10. The signal 1(blue curve) and 2(black curve) represent the PSDs of the interference phase 03 and 04, and the red curve represents the PSD after the phase subtraction between the interference pulses 03 and 04, which reflects the CMNs suppression effect of the 1x3 unbalanced fiber optic Michelson accelerometer. Similar to Fig. 9, the noise level decreases significantly after the subtraction of interference phase, and the PSD of noise floor after suppression is −91.32 dB rad2/Hz at 100 Hz with a suppression of about 28 dB. It also shows an obvious suppression up to about 1.3 kHz.

Fig. 10. Suppression effect of common-mode noise of the 1x3 unbalanced fiber optic Michelson accelerometer in the frequency domain.

Next, the CMNs suppression effect between the different fiber optic accelerometers is compared, and the results are plotted in Fig. 11. The red curve represents the CMNs suppression effect of the triple low-reflectivity fiber Bragg gratings, the black curve for the 1x3 fiber optic Michelson accelerometer, and the blue curve for the traditional method.


Obviously, the two newly designed fiber optic accelerometers show better performances of CMNs suppression than the traditional method especially during 70 Hz~1 kHz, and the noise levels are respectively −91.32 dB rad2/Hz and −96.50 dB rad2/Hz at 100 Hz, which meet the requirements for the current oil/gas reservoir monitoring applications. Regarding the noise level lower than 70 Hz, the CMNs suppression effects of the two new accelerometers are insignificant when compared with the traditional method due to the strong low-frequency turbulence of the test environment, which increases the uncertainty of measurements. Besides, by comparison between the presented two new fiber optic accelerometers, it is observed that the 1x3 unbalanced fiber optic Michelson accelerometer shows better CMNs suppression than the triple low-reflectivity fiber Bragg gratings one, especially from 125 to 1 kHz. This phenomenon may be explained that the light pulses propagate independently along the three unbalanced interferometric beams in the 1x3 fiber optic Michelson accelerometer, which helps to avoid the aliasing effect before the interference. While in the triple low-reflectivity fiber Bragg gratings accelerometer, the reflected light pulse from the following grating is still influenced by the previous gratings, which leads to the increase of the noise level.

Fig. 11. Comparison of suppression effect of common-mode noise between the three different fiber optic accelerometers in the frequency domain.

Next, the on-axis sensitivities of the two fiber optic accelerometers are discussed. The vibration frequency varies from 20 Hz to 3150 Hz. The accelerometer sensitivity at each frequency point is measured and the frequency response curve is plotted in Fig. 12. The operating frequency bandwidth, defined as the sensitivity fluctuation within which is less than 3 dB, covers from 20 Hz to 1250 Hz for both the triple low-reflectivity fiber Bragg gratings accelerometer and the 1x3 fiber optic Michelson accelerometer. Actually, in the applications of the micro-seismic monitoring, the frequency distribution of the signal is lower than 500 Hz, and therefore the operating frequency range for both two accelerometers meets the needs of the actual micro-seismic monitoring applications. Within this operating bandwidth, the average on-axis sensitivity is 32.20 dB rad/g for the triple low-reflectivity fiber Bragg gratings accelerometer and 39.07 dB rad/g for the 1x3 fiber optic Michelson accelerometer, and the minimum detectable acceleration (defined as the ratio between the noise floor and the sensitivity) at 100 Hz are estimated respectively as 367 ng/ Hz and 312 ng/ Hz . Besides, it should be noted that the theoretical values for the on-axis sensitivity are 32.39 dB rad/g and 38.41 dB rad/g with the parameters listed in Table 1 according to the Eqs. (1)-(2) for both accelerometers, and the experimental average sensitivities show good agreement with the theoretical ones.


60 1x3 Michelson 3 FBGs

Sensitivity (dB rad/g)

50

40

30

20 10

1

10

2

10

Frequency(Hz)

3

10

4

Fig. 12. On-axis sensitivity of the two fiber optic accelerometers. (dB rad/g = 20 ⋅ log10 rad/g, same for Fig. 14.) Table 1. Theoretical parameters of the accelerometer. L(m) 10

Efn (GPa) 73

Sfn (m2) 1.22 ×10

−8

E(GPa)

v

H(mm)

b(mm)

a(mm)

n

M(kg)

P11

P12

2.6

0.37

18

16.5

14.5

1.457

0.057

0.12

0.27

Figure 13 shows the comparison results for the linearity of the two fiber optic accelerometers, and the linearity is defined as the vibration acceleration changing slope versus the demodulated phase of the interferometric light. The discrete points are the measured data and the blue curve is the first order linear fitting result. The acceleration varies from 0 to 2g and the corresponding demodulated phase varies from 3.7 rad ~84.5 rad for the triple low-reflectivity fiber optic accelerometer, the average phase sensitivity is calculated as 41.47 rad/g with fluctuation rate less than 4.70%. As for the 1x3 Michelson fiber optic accelerometer, the acceleration varies from 0 to 1g due to the dynamic range limit of the system, and the corresponding demodulated phase varies from 4.0 rad ~80.8 rad, the average phase sensitivity is calculated as 80.51 rad/g with fluctuation rate less than 4.33%. The results show a good linearity between the acceleration amplitude and the demodulated optical phase with linearity coefficients of 0.9994 and 0.9995, which indicates good linearity performances of both two fiber optic accelerometers. 150 1x3 Michelson:experimental recording 1x3 Michelson:first order fitting 3 FBGs:experimental recording

100

3 FBGs: first order fitting

Phase (rad)

Linearity coefficient 0.9995

50

Linearity coefficient 0.9994

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Acceleration (g)

Fig. 13. Linearity of the two fiber optic accelerometers.

Finally, the directional patterns of the two fiber optic accelerometers are analyzed. Theoretically speaking, the sensitivity at a specific direction θ is in a function form of S(= θ ) S(0) ⋅ cosθ , where S(0) is the on-axis sensitivity. The experimental results are shown in Fig. 14, where the discrete points represent the measured sensitivity values every 15 degree and the red curves represent the theoretical values. Obviously, it shows a good agreement between the experimental results and theoretical estimations for both accelerometers. Besides,


the cross-axis sensitivity and the asymmetry error are proposed to describe the directionality of the accelerometer, the cross-axis sensitivity is defined as the sensitivity at θ = 90° , and the asymmetry error is defined as the sensitivity subtraction between θ = 0° and θ = 180° . Both parameters reflect the disturbance suppression effects of the non-measurement direction, which are desired as small as possible. For the triple low-reflectivity fiber Bragg gratings accelerometer, the cross-axis sensitivity is lower than the on-axis sensitivity by 29.48 dB and the asymmetry error of the on-axis sensitivity is as low as 0.29 dB, while these two parameters are respectively 34.41 dB and 0.42 dB for the 1x3 fiber optic Michelson accelerometer. The cross-axis sensitivity suppression of the 1x3 fiber optic Michelson accelerometer is 4.93 dB better than the triple low-reflectivity fiber Bragg gratings accelerometer, which confirms the theoretical analysis in section 2.2.

30

0

330

60 90

300

50 25 (dB rad/g)

270

120

240 150

180 (a)

210

0

30

330 300

60 90

40 30 20 (dB rad/g)

10

270 240

120 150

180

210

(b)

Fig. 14. Direction pattern of the two fiber optic accelerometers. (a) 1x3 fiber optic Michelson accelerometer. (b) triple low-reflectivity fiber Bragg gratings accelerometer.

The reported two fiber optic accelerometers share the same push-pull structure and the same dimension, while one is based on the low-reflectivity fiber Bragg grating and the other on the 1x3 unbalanced Michelson interferometric structure. They are both able to realize the CMN suppression by their own structures without additional reference accelerometers. The 1x3 Michelson fiber optic accelerometer shows a better CMNs suppression especially from 125 Hz to 1 kHz since it avoids the aliasing effect before the interference, while the advantage of the low-reflectivity fiber Bragg grating accelerometer mainly reflects in that it does not need any optical device such as the coupler and the Faraday mirror in the sensing network system. In a word, both two newly designed fiber optic accelerometers show remarkable CMNs suppression effects and can be multiplied in a large-scale. Besides, from the parametrical comparisons above, it is seen that the on-axis sensitivity of the 1x3 Michelson fiber optic accelerometer is 6.7 dB higher than that of the triple low-reflectivity fiber Bragg gratings accelerometer, while the cross-axis sensitivity is 4.93 dB lower. These performances can be still improved by adjusting the dimensions, the materials and the mechanical structure design. Finally, the environmental disturbances such as the local temperature may generate the potential noises which cannot be suppressed completely by the proposed structure, and the generated noises modify slightly the noise floor performance. These will lead to the further investigations in the future. 5. Conclusions In summary, we demonstrate two new fiber optic accelerometers and their CMNs suppression performances are focused. The propose accelerometers are able to suppress the CMNs by their own structures and they show even better CMNs suppression effects than the traditional method of adding a reference accelerometer. During the experiments, a CMNs suppression improvement of 33 dB is achieved at 100 Hz for the triple low-reflectivity fiber Bragg gratings, and 28 dB for the 1x3 fiber optic Michelson accelerometer, while only 12 dB for the


traditional method using the reference accelerometer. When comparing between these two accelerometers, the 1x3 Michelson fiber optic accelerometer shows a better CMNs suppression especially from 125 Hz to 1 kHz, while the triple low-reflectivity FBGs accelerometer does not need the additional optical devices, which simplifies the sensing system structure. Both two newly designed fiber optic accelerometers provide the promising candidates for the large-scale quasi-distributed oil and gas reservoir monitoring applications. Funding National Natural Science Foundation of China (NSFC grants 61327812); National Natural Gas Hydrate Specialties (NGHS grants DD20160217); China Postdoctoral Science Foundation (CPSF grants 2017M620516).