In-fiber integrated accelerometerFeng Peng, Jun Yang,* Xingliang Li, Yonggui Yuan, Bing Wu, Ai Zhou, and Libo YuanPhotonics Research Center, School of Science, Harbin Engineering University, Harbin 150001, China
Significant progress has been achieved in the develop-ment of fiber-optic accelerometers in recent years. Dif-ferent types of fiber-optic accelerometers have beenproposed [1–3] and developed for a range of applications,which include oil and gas reservoir monitoring, earth-quake monitoring, intruder detection, and machinerymonitoring [4]. In this Letter, a novel compact in-fiberintegrated accelerometer based on a special designedtwin-core fiber is proposed and investigated. This typeof accelerometer has a more compact integration andsmaller size than the traditional fiber-optic acceler-ometers. In addition, this accelerometer could auto-matically compensate the variation of environmenttemperature because both of the cores in the twin-corefiber would be affected equally.The configuration of the in-fiber integrated accelera-
tion sensing system is shown in Fig. 1. In the sensingelement, the in-fiber integrated sensing element is com-posed of a solid frame and a twin core, which is speciallydesigned and fabricated in our laboratory. The twin-corefiber was inserted through two thin steel pipes, and thepipes were fixed at proper locations of the fiber usingepoxy. Then, the steel pipes were fixed on the solid framethrough epoxy.The cross-section view of the twin-core fiber is pres-
ented in Fig. 2. The diameters of the two cores are 7:3 μm,and the distance between the two cores is 53 μm. To im-prove the performance of the integrated fiber acceler-ometer, the refractive indices of the two cores aredesigned to be a little different (1.4693 and 1.4699).Figure 3 shows the refractive index distributionmeasuredwith a fiber refractive index profile (S14, Photon Kinetics,Inc) based on the refracted near-field technique [5].The fused and tapering technique was employed to
couple light from a single-mode fiber into the twin-corefiber. The light from the single-mode fiber is coupled intothe cores of the twin-core fiber when it transmits throughthe taper zone between the single-mode and twin-corefiber. Theoretically, the coupling efficiency between asingle-core and a twin-core fiber can reach more than90% [6]. In the present work, the actual efficiency is about79.4% (1 dB loss).For the interferometer optical setup in our case, the
optical differential phase shift Δϕ in the sensing elementinduced by the vibration can be represented as [7,8]
Δϕ ¼ 2πλ ΔL
�n1
�1 − c
n21
2
�þ n2
�1 − c
n22
2
��; ð1Þ
where λ is the wavelength of the laser light propagatingin the twin-core fiber, ΔL represents the difference ofthe core length between the two cores, the parameterc ¼ 0:204 [9] is a constant, and n1 and n2 are the refrac-tive indices of the two cores in the twin-core fiber,respectively.
According to [10,11], the length difference between thetwo cores ΔL is given by
ΔL ¼ d · L2
8EI· F; ð2Þ
where E is the Young’s modulus of quartz, d is the dis-tance between the two cores, L represents the effectivelength of the twin-core fiber, and I ¼ πr40=4 representsthe inertia moment of the bending simple supportedbeam, in which r0 is the radius of the fiber’s crosssection.
From Newton’s second law, we have F ¼ Ma, in whicha is the vibration acceleration, M ¼ 17m0=35þm is thetotal mass [12], including the effective mass of the twin-core fiber 17m0=35 and the loading mass m.
Substitute Eq. (2) into Eq. (1), and the accelerometer’ssensitivity Δϕ=a can be expressed by
Δϕa
¼ π · d · L2
4 · λ · EI
�n1
�1 − c
n21
2
�þ n2
�1 − c
n22
2
��·M: ð3Þ
Fig. 1. (Color online) In-fiber integrated acceleration sensingsystem based on a twin-core fiber Michelson interferometer.
The deflection along the neutral axes of the bendingfiber beam may be described as [13]
x ¼ F12EI
y
�y2 −
34L2
�: ð4Þ
Therefore, the maximum deflection of the fiber simplesupported beam is
X ¼ −FL3=48EI: ð5ÞBy Hook’s law, we have F ¼ −KX and the stiffness
coefficient of the twin-core fiber can be represented as
K ¼ 48EI=L3: ð6ÞThen, the resonance frequency of the in-fiber inte-
grated accelerometer f n is given by
f n ¼ 12π
�KM
�1=2
¼ 12π
�48EI
ð17m0=35þmÞL3
�1=2
: ð7Þ
In order to investigate the performance of the in-fiberintegrated accelerometer, a testing system is establishedfor measuring the vibration acceleration, as shown inFig. 4. The solid frame, including the in-fiber integratedaccelerometer, is vertically mounted onto a vibrationstage, and a piezoelectric accelerometer is verticallymounted on the frame quite near the fiber accelerometerfor calibrating. We monitor the amplitude of the outputsignal of the accelerometer during the process of care-fully rotating the fiber accelerometer. When the ampli-tude of the signal reaches a maximum, the applied
force can be considered to be parallel to the plane ofthe two cores and perpendicular to the fiber axis, andwe consider that the fiber accelerometer measures thesame component of the acceleration as the piezoelectricaccelerometer does. In addition, all of the other experi-mental setups are fixed on a vibration insulation table forpreventing impacts from the vibration.
In this work, we employed phase generated carrierhomodyne based on a modulated light source [14] todemodulate the optical phase shift information fromthe interference output of the in-fiber integrated acceler-ometer. Figure 5 shows the schematic diagram of thedemodulation method. A large amplitude sinusoidal mod-ulation with a frequency outside the signal band is im-posed on the drive current of the light source, and thewavelength can be changed, which will contribute to theinterference output of the in-fiber integrated acceler-ometer. The signal received by the probe detectors ismultiplied by ω0 and 2ω0, respectively. Then, low-passfilers are used to remove the term above the highestfrequency of interest. The time derivative of these twosignals, the sine and cosine terms, are respectively cross-multiplied with the cosine squared terms, to yield the de-sired sine and cosine squared terms. The output afteradding can be integrated to produce a signal that includesall of the drift information in addition to the actual signal.
Fig. 2. (Color online) End surface of the twin-core fiber.
Fig. 3. (Color online) Refractive distribution of the twin-corefiber.
Fig. 4. (Color online) Testing system of the accelerometer.
Fig. 5. (Color online) Schematic diagram of the demodulationsystem.
In the fiber-optic accelerometer, the effective length Lof the twin-core fiber is 5 cm, and there is no loadingmass on the fiber. Figure 6 shows the detected opticalphase shift versus acceleration of the accelerometerwhen the vibration frequency is 80Hz. From Fig. 6, wecan see that the experimental results give a good linearityresponse between the optical phase shift and the accel-eration. The sensitivity of the fiber accelerometer can beobtained from the slope of the trend line in Fig. 6, whichis calculated as 0:09 rad=g.Figure 7 shows the signal-to-noise ratio of the in-fiber
integrated accelerometer when the vibration frequency is200Hz. From the figure, we obtain that the background
noise is −99:37 dB, and the signal amplitude of the in-fiberintegrated accelerometer is −24:09 dB. Therefore, thesignal-to-noise ratio of the accelerometer is 75:28 dB.
The resonant frequency of the simple supported beamof the fiber accelerometer is also measured in the experi-ment for getting its working bandwidth. The amplitude-frequency characteristic is presented in Fig. 8. From thefigure, it can be seen that the resonant frequency is680Hz, and the amplitude-frequency response at frequen-cies below 500Hz is flat, which is the available bandwidthof the fiber accelerometer.
In conclusion, a compact in-fiber integrated fiber-opticaccelerometer based on Michelson interferometer con-structed with a twin-core fiber is demonstrated. The ex-perimental results show that such an accelerometer has asensitivity of 0:09 rad=g, with resonant frequency of680Hz. Compared with any other fiber-optic acceler-ometers, the size of the in-fiber integrated accelerationis small, and the weight is lighter. In addition, the accel-erometer could automatically compensate the variationof environmental temperature due to both cores of thetwin-core fiber that would be affected equally by suchchanges. Future work will focus on improving the detec-tion sensitivity and extending the response bandwidth.
This work was supported by the key project of theNature Science Foundation of Heilongjiang Province(grant ZD200810), Key Project Foster Program forUniversity and College Science and Technology Innova-tion (grant 708030) and Fundamental Research Funds forthe Central Universities (grant HEUCFZ1020) to theHarbin Engineering University. This work was also par-tially supported by the National Nature Science Founda-tion of China (NSFC), under grants 60877046, 60707013,60807032, and 60927008, to the Harbin EngineeringUniversity.
References
1. N. Zeng, C. Z. Shi, M. Zhang, L. W. Wang, Y. B. Liao, andS. R. Lai, Opt. Commun. 234, 153 (2004).
2. M. D. Todd, G. A. Johnson, B. A. Althouse, and S. T. Vohra,IEEE. Photon. Technol. Lett. 10, 1605 (1998).
3. B. Bhola and W. H. Steier, IEEE Sens. J. 7, 1759 (2007).4. D. A. Jackson, Meas. Sci. Technol. 20, 034010 (2009).5. K. I. White, Opt. Quantum Electron. 11, 185 (1979).6. L. B. Yuan, Z. H. Liu, and J. Yang, Opt. Lett. 31, 3237 (2006).7. L. B. Yuan, J. Yang, and Z. H. Liu, IEEE. Sensors. J. 8,
1114 (2008).8. A. S. Gerges, T. P. Newson, J. D. C. Jones, and D. A. Jacks,
Opt. Lett. 14, 251 (1989).9. A. Laudati, F. Mennella, M. Giordano, G. D. Altrui,
C. C. Tassini, and A. Cusano, IEEE. Photon. Technol. Lett.19, 1991 (2007).
10. L. B. Yuan, J. Yang, Z. H. Liu, and J. X. Sun, Opt. Lett. 31,2692 (2006).
11. W. X. Gou, in Mechanics of Materials (Science, 2005),pp. 151–203.
12. B. C. Wen, in Theory of Mechanical Vibration and Its
Application (High Education , 2009), pp. 24–28.13. R. G. Budynas, in Advanced Strength and Applied Stress
Analysis, 2nd ed. (McGraw-Hill, 1999), pp. 849–857.14. A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, IEEE. J.
Quantum Electron. 18, 1647 (1982).
Fig. 6. (Color online) Acceleration versus optical phasedemodulated.
Fig. 7. (Color online) Signal-to-noise ratio of theaccelerometer.
