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Abstract
We present an axial strain applied in-fiber Mach-Zehnder interferometer (MZI) for acceleration measurement. A thin core fiber is sandwiched between two single-mode fibers with core offset to form the MZI. A controlled high fringe visibility in the transmission spectrum is obtained by applying an axial strain, leading to a large slope at the quadrature point. The MZI is then clamped to work as an accelerometer. Experimental results show that the resolution achieves 86 ng/√Hz (g is gravity of 9.8 m/s2), the dynamic range reaches as large as 104.1 dB and the linearity of acceleration response is as high as 99.994%. Moreover, the resonance frequency can be tailored by the clamped fiber length and applied axial strain. The proposed sensor is attractive for practical applications due to low temperature crosstalk, compact size and high sensitivity.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber optic accelerometers (FOAs) have a large and diverse number of applications, such as machinery or civil infrastructures health monitoring, intruder detection, seismic events monitoring, and oil and gas exploitation, due to their unique merits: electromagnetic immunity, chemical resistance, robustness in harsh environments, flexibility and multiplexing capabilities. Different applications require tailored sensor characteristics. For instance, to monitor earthquakes or civil infrastructures (buildings, bridges, etc.), the FOAs that respond to low frequencies (below a few tens of hertz) are required. However, health monitoring of machines demands the FOAs that respond to medium or high frequencies (from a few hundred hertz to several kilohertz) [1,2].
In recent years, various types of FOAs have been developed. The intensity-modulated FOAs [3,4] have simple structures, however, the performance is poor. Interferometer based FOAs [5–9] are highly sensitive but, in general, they require a special demodulation circuit and tend to be complex and high cost. Fiber Bragg grating (FBG) or tilted grating based FOAs [10–12] are well developed, however, the sensors work below a few hundred hertz and require a high cost interrogation system. Modal interferometer based FOAs have the characteristics of low cost and compactness while the accuracy is not high enough and the dynamic range is few reported. FOAs based on fiber tapering [13], offset splicing [14], collapses in photonic crystal fibers [15,16], 45 degree splicing [17–19] or long period gratings [20] have been reported. In-fiber Mach-Zehnder interferometers (MZIs) are promising modal inteferometers in sensing area. Axial strain induced wavelength shift in transmission spectrum of the MZI were extensively studied as strain gauges [21–24]. However, as far as we know, axial strain induced interference fringe visibility variation in the transmission spectrum and its effect on acceleration measurement has not been reported.
In this paper, we propose an axial strain applied FOA based on an in-fiber MZI for transverse vibration sensing for the first time to our best knowledge. The MZI is simply fabricated by fusion splicing a section of thin core fiber (TCF) between two single-mode fibers (SMFs). In particular, an axial strain is applied to acquire a controlled high visibility in the transmission spectrum to improve the sensitivity and dynamic range. We describe the principle and fabrication of the FOA, and experimentally demonstrate the viability for accurate acceleration measurement with a tailored operating frequency bandwidth.
2. Sensor configuration and principle
The schematic configuration of the FOA is shown in Fig. 1(a), one end of a TCF (Cor Active SCF-UN-3/125-25) is fusion spliced with a standard SMF by an arc fusion splicer (Fujikura FSM-60S), and the other end is fusion spliced with a core offset of 3 µm by manual core alignment. The core and cladding diameters of the TCF are 2.58 µm and 125 µm, respectively. The FOA is ready to sense transverse vibration once two ends of the fiber are clamped.
Fig. 1. (a) Schematic configuration of the proposed FOA, and (b) slopes at Q points of simulated normalized transmission spectra of different fringe visibility.
Transverse vibration induced fiber length change [5] is far smaller than that of axial stretch while the operating principles are in common. As an axial stretch or a transverse vibration is applied on the MZI, the intensity of the MZI can be written as [13]
A laser is set at quadrature bias wavelength (2πneffL/λ=π/2) [15] and the transmission light is detected by a photo detector (PD), as Δϕ is small, the output voltage of the PD can be written as
As the amplitude of stimulating acceleration is a, the acceleration sensitivity is derived as
The axial strain not only induces the wavelength shift, but also changes the intensities of the fundamental core mode and a dominant high-order cladding mode that affect the visibility in the transmission spectrum. According to Eq. (1), the normalized transmission spectra of different fringe visibility of 57.7 dB, 29.8 dB and 13.1 dB are calculated and plotted in Fig. 1(b) by assuming that neff is 0.02 and L is 4 mm. It shows that the fringe visibility is high as Icladding is close to Icore. Figure 1(b) shows that a high visibility produces a large slope. It is known from Eq. (4) that a large slope KQ leads to a high sensitivity.
Without applied axial strain, the resonance frequencies of transverse vibrations of a cylinder with clamped ends can be given as [16]
where l, R, E, and ρ are the length, radius, Young modulus and density of the clamped fiber, respectively, n is any natural number except zero.The proposed sensor can be approximated as a string once an axial strain is applied and the resonance frequencies can be written as
3. Simulation and sensor fabrication
3.1 Simulation
Beam propagation method (BPM) is used for simulation, the analysis was performed by using BeamPROP toolbox of RSoft. As the core and cladding RIs of the SMF are 1.4457 and 1.4378, and the core and cladding RIs of the TCF are 1.4594 and 1.4378. Assuming that the lead-in and lead-out SMFs are 1 mm, and the TCF length is 4 mm, normalized power (LP01) is launched, the propagation field distribution and the normalized propagating power along the MZI at 1550 nm are simulated in Fig. 2(a). Owing to the core mismatch and offset, a part of the light is transmitted along the core of the TCF, and the other part is leaked to the outside, which mainly includes the excited high-order cladding mode. The height coded display mode of electric field distribution along the MZI is plotted in Fig. 2(b). An obvious interference is observed due to the interference between the core mode and the leaked high-order cladding mode.
Fig. 2. (a) Propagation field distribution and the normalized propagating power, and (b) height coded display mode of electric field distribution along the MZI with 4mm TCF at 1550 nm.
Then the wavelength was scanned from 1510 nm to 1610 nm with interval of 0.5 nm for the MZIs with TCF lengths of 4 mm, 6 mm and 10 mm, the simulated normalized transmission spectra of the MZIs are plotted in Fig. 3. It can be seen from Fig. 3 that the free spectral range (FSR) decreases when the TCF length increases. There are 3, 4 and 7 dips for the normalized transmission spectra with TCF lengths of 4 mm, 6 mm and 10 mm, respectively.
Fig. 3. Simulated normalized transmission spectra of the MZIs with TCF lengths of 4 mm, 6 mm and 10 mm.
3.2 Sensor fabrication
The sensor fabrication process is shown in Fig. 4, one super luminescent diode (SLD) is applied as the light source. Figure 3(a) shows that the MZI is fixed on two stages with a distance of 20 cm by an optical adhesive (NORLAND 81). The optical adhesive was cured by an ultraviolet curing lamp. One stage is fixed and the other is removable. The stage was moved forward a distance of 20 µm every time and the transmission spectra were recorded by an optical spectrum analyzer (OSA, Yokogawa 6370C). Figure 4(b) shows an aluminum block (35 mm×15 mm×5 mm) with a groove that is placed adjacently to the MZI, and a glass capillary is used to carry the optical adhesive to the edges of the groove to fix the fiber when the highest visibility in the transmission spectrum is achieved. Then the optical adhesive on the two stages is removed by an acetone solution. The sensor before package is shown in Fig. 5(a). Another aluminum block is screwed with the former block to package the MZI to form the FOA, which is shown in Fig. 5(b).
Fig. 4. Sensor fabrication process: (a) applying an axial strain, (b) clamping the MZI and removing the optical adhesive on the stages.
Three FOAs labeled S1, S2 and S3 were fabricated and the main parameters are presented in Table 1. Figure 6(a) shows the spatial frequencies and transmission spectra of the proposed MZIs without axial strain. It can be observed that there is only one dominant spatial frequency for each MZI. The spatial frequencies of MZIs with L of 4 mm, 6 mm and 10 mm are 0.02999 nm−1, 0.03998 nm−1 and 0.06997 nm−1, respectively. As the spatial frequency equals neffL/λ2 mentioned in Ref. [25], the effective RI difference between the fundamental core mode and the dominant high-order cladding mode are 0.018, 0.016 and 0.0168 at the wavelength of 1550 nm. Figures 6(b)–6(d) show the transmission spectra of the MZIs under axial strain from 0 µε to 1200 µε. It is observed that the selected fringe visibility of S1, S2 and S3 are 52.0 dB, 39.6 dB and 13.5 dB, and the selected Q points are 1545.6 nm, 1546 nm and 1550.3 nm, respectively. Compared with the simulated results, the measured transmission spectra in Figs. 6(b)–6(d) are similar with the curves in Fig. 3.
Fig. 6. (a) Spatial frequencies and transmission spectra of the proposed sensors without axial strain, and the spectra of (b) S1, (c) S2 and (d) S3 under different axial strains.
Table 1. Parameters of the proposed FOAs.
In order to investigate the characteristic of temperature crosstalk of the FOA. S1 was placed in an incubator and heated from 30 °C to 90 °C with a step of 10 °C. The transmission spectra under different temperatures are captured by the OSA. The temperature responses of dip 1 (1521.56 nm), dip 2 (1553.16 nm) and dip 3 (1585.56 nm) are plotted in Fig. 7. The temperature responses of dip 1, dip 2 and dip 3 are 35.6 pm/°C, 41.4 pm/°C and 42 pm/°C, respectively. The results show that the temperature crosstalk of the FOA is relatively low, moreover, as the ambient temperature fluctuation is an extra low frequency signal mentioned in Ref. [26], the temperature induced noise can be filtered by a high pass filter in the signal processing circuit. If the FOA is subjected to a large temperature excursion and the system deviates from the Q point, the laser source can be feedback controlled to restore the wavelength to the Q point.
4. Experimental setup and results
4.1 Experimental setup
Experimental setup for acceleration measurement is illustrated in Fig. 8, (a) laser module (RIO ORION) is set at Q point wavelength. Both FOA and a reference accelerometer (RA, B&K 8305) are fixed vertically to a vibrator (B&K 4809) driven by a signal generator (Tektronix AFG1022). A frequency sweep is applied to the vibrator to generate an acceleration of 20.4 mg (0.2 m/s2). The light intensity is detected by a PD (Thorlabs PDB450C), then acquired by a panel (B&K 3160-A-022) and processed by the software (B&K PULSE Labshop). The signal of RA is amplified by a conditioning amplifier (B&K 2691-0S1) and then obtained by the panel. The amplitude of acceleration and SNR of the FOA at the stimulating frequency are read from the software.
4.2 Acceleration sensitivity and resolution
According to Eqs. (4) and (5), the measured acceleration sensitivity and resolution frequency responses are plotted in Fig. 9. Figure 9(a) shows that the frequency responses of S1, S2 and S3 are flat below 1300 Hz, 2500 Hz and 600 Hz, the average sensitivities in the flat frequency band are 5.86 mV/g, 3.47mV/g and 22.73mV/g. Figure 9(b) shows that the average resolutions are 0.13 mg/√Hz, 0.17 mg√Hz and 43 µg√Hz in the flat frequency bands, respectively. The resolutions of S1, S2 and S3 are 0.19 µg√Hz, 1.03 µg√Hz and 86 ng√Hz at the resonance frequencies of 1400 Hz, 3100 Hz and 758 Hz, respectively.
Fig. 9. Measured sensitivity-frequency responses and (b) resolution-frequency responses of the proposed FOAs.
From Eq. (6), the theoretical resonance frequencies of the sensors are 1404 Hz, 1404 Hz and 770 Hz by considering E=72 GPa and ρ=2200 kg/m3. The experimental results are basically consistent with theoretical values except S2. The measured resonance frequency of S2 is much higher than the theoretical calculation due to the applied tension. The measured resonance frequency of S2 is 2.21 times of that of S1. And from Eq. (7), the calculated resonance frequency of S2 is 2.35 times of S1. The results show that the operating frequency bandwidth can be adjusted by the clamped fiber length and the applied axial strain.
4.3 Linearity and dynamic range
The linearity test was performed by increasing the amplitude of applied acceleration. 1 KHz, 1 KHz and 400 Hz are selected from the flat working frequency bands for S1, S2 and S3. As shown in Fig. 10, the amplitude of output voltage responses linearly to that of acceleration. The linearity of S1 is 99.994% in the range of 2.5-10143 mg, the linearity of S2 is 99.989% in the range of 2.5-10204 mg and the linearity of S3 is 99.961% in the range of 2.5-1020 mg, respectively.
The software (B&K Pulse labshop) has the function of signal total harmonic distortion (THD) measurement. Keeping increasing the amplitude of stimulating acceleration till the THD of the testing signal reaches 1%. The dynamic ranges equal the SNRs when THD reaches 1%. The time domain waveforms of RA, S1, S2 and S3 are plotted in Figs. 11(a), 11(c) and 11(e) when the testing signal THD reached 1%. The corresponding frequency spectra of RA, S1, S2 and S3 are plotted in Figs. 11(b), 11(d) and 11(f). The noise floors of S1, S2 and S3 are −125 dB, −126 dB and −126 dB, and the amplitude at stimulating frequencies are −20.9 dB, −27 dB and −30.8 dB, thus the dynamic ranges of FOAs are 104.1 dB, 99 dB and 93.2 dB, respectively. A short TCF length and a large fringe visibility lead to a large dynamic range. The results demonstrate that the dynamic range of the FOAs have relationship with the slope at Q point and TCF length, which are consistent with Eq. (3).
Fig. 11. (a) Waveform and (b) frequency spectrum of RA and S1 @1 KHz, (c) waveform and (d) frequency spectrum of RA and S2 @1 KHz and, (e) waveform and (b) frequency spectrum of RA and S3 400 Hz (see Visualization 2).
4.4 Discussion
As shown in Table 2, compared to intensity modulated FOA, Michelson interferometer (MI) based FOAs, Fabry-Perot interferometer (FPI) based FOAs, and fiber Bragg grating (FBG) or tilt FBG based FOAs, our proposed FOAs show the merits of good detection capability, large dynamic range, simple fabrication process and low cost. Compared with modal interferometer based FOAs, the proposed FOAs have better resolutions, wider working frequency bands and larger dynamic ranges.
Table 2. Comparison of FOAs with different configurations.
5. Conclusion
In conclusion, a tailor-able FOA based on an in-fiber MZI has been proposed and experimentally demonstrated. Axial strain was employed to improve the performance of the FOA. Large fringe visibility of 52 dB in the transmission spectrum of the MZI was achieved. Three FOAs were fabricated with flat operating frequency bands below 1300Hz, 2500 Hz and 600 Hz, and the average resolutions are 0.13 mg/√Hz, 0.17 mg√Hz and 43 µg√Hz, respectively. Furthermore, the operating frequency bandwidth can be tailored by the clamped fiber length and the applied axial strain. The dynamic range of the FOA reaches as large as 104.1 dB, the linearity is as high as 99.994%, and the resolution achieves 86 ng/√Hz at the resonance frequency of 758 Hz. Moreover, the measured temperature crosstalk is 41.4 pm/°C. Owing to the advantages of low cost, large dynamic range, compactness, flexible design and high sensitivity, the FOA has promising prospects in vibration measurement.
Funding
National Natural Science Foundation of China (51627804); Provincial Key R&D Program of Anhui (1804a0802214); National Key Research and Development Program of China (2016YFC0301902).
Disclosures
The authors declare no conflicts of interest.
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