Open Access
Add to BibSonomy
Abstract
We propose an optical frequency comb (OFC)-based strain sensing method, namely OFC sensing cavity, which is capable of radio-frequency (RF)-based strain measurement. We developed a null-method-based strain sensing system with a comb-spacing-stabilized OFC generator. We realized strain measurement from 1.83 µε to 1800 µε with a sensing fiber length of 20 mm. The measurable strain frequency range of the developed strain sensing system was from 0 to 310 Hz. Owing to the use of RF-based strain measurement, our approach would be a useful and powerful tool for sensing of strain or other physical quantities, and the concept of the OFC sensing cavity is a new aspect of OFC technology.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Strain sensing is widely applied to monitor, analyze and control load, stress, displacement, and vibration of various mechanical structures, enabling health monitoring of buildings, detection of abnormal vibration of moving objects, defect evaluation and so on [1, 2]. The conventional and the most widely employed method is an electrical strain gauge that converts the strain into a change in resistance [1]. Although electrical strain gauges are a cost-effective solution for strain sensing, electrical noise is a fundamental limit of the precision and resolution in intensity detection schemes with analogue signals.
To overcome this issue, optical methods to sense strain have been developed [3, 4]. Especially, fiber-based optical strain sensors, such as a fiber Bragg grating (FBG) sensor [5, 6] and a Brillouin scattering sensor [7–9], have been proposed and have been widely used in practical applications. These strain sensors observe the strain-encoded optical signal, e.g., optical spectrum or optical frequency, resulting from Bragg diffraction or Brillouin scattering because the conversion of strain into optical signals enables more reliable and more functional strain sensing than that into an electric signal.
To further enhance the performance, the FBG sensor has been introduced into a fiber laser cavity to monitor the shift of the optical lasing frequency related with the applied strain, namely FBG laser sensor [10]. Since the optical spectrum in the FBG laser sensor become sharper than that in a normal FBG sensor due to the laser oscillation, the performance of strain sensing, such as precision and resolution, can be further improved. In this case, the actual performance of strain sensing is limited by the performance of the optical spectrum measurement methods, such as optical spectrometer, optical interferometer, scanning wavelength meter, and so on. One promising solution to enhance the frequency response of strain sensing is the conversion of a strain-encoded optical frequency into optical intensity; however, a fundamental limit is in the detection of analogue intensity signal due to the low immunity to noise signals, leading to the decreased resolution and precision, in the same manner as with electrical strain gauges.
To overcome the limitation of optical spectrum, frequency or intensity measurement, the strain laser sensor has been expanded into radio-frequency (RF) measurement by using FBG [11], distributed feedback (DFB) [12, 13], or distributed Bragg reflector (DBR) approach [14]. While these fiber structures are used for laser oscillation of multiple polarization or longitudinal modes, they have high sensitivity to strain and other disturbances. Therefore, RF beat frequency between two polarization modes or two longitudinal modes was measured for strain sensing. Furthermore, simultaneous monitoring of strain and temperature was performed by measurement of polarization beat frequency and longitudinal beat frequency [13] or two polarization beat frequencies [14]. Since RF measurement is more precise and more cost-effective than the optical frequency or spectrum measurement, it will be a powerful tool for the laser strain sensor. In this case, the precision of strain sensing is limited by fluctuation of RF beat frequency rather than the precision of RF frequency apparatus. If more stable RF beat frequency can be used, further enhancement of the strain sensing performance will be achieved because RF measurement benefits from an excellent RF or microwave frequency standard.
Most stable RF beat frequency can be obtained from an optical frequency comb (OFC) or a mode-locked laser because OFC inherently maintains the tight phase locking of all longitudinal modes with a strictly constant frequency separation in the broad spectral range. An OFC is a promising measurement tool in optical frequency metrology and spectroscopy owing to the ability of an OFC to act as an optical frequency ruler traceable to the frequency standard, enabling high spectral resolution and accuracy [15–17]. For strain sensing, the OFC is utilized as a dimensional converter of strain into a RF signal [18]. The OFC exhibits an inherent direct frequency link between the optical frequency domain (a few hundred THz, OFCs operating in this region exist) and the RF domain (a few tens to hundreds of MHz) without spoiling frequency uncertainty, observed as a RF beat note of each mode pair, namely RF comb beat, in OFC. Furthermore, the fundamental RF comb beat frep, corresponding to the comb spacing, is exactly given by:
where c, n, and L denote the velocity of light, the group velocity refractive index of the OFC cavity fiber, and the cavity length, respectively. By using a part of the OFC cavity as a strain sensor, a strain that occurs as a result of a change in the optical cavity length nL can be decoded with the RF signal of frep. In the previous research of OFC-based strain sensors [18], the deflection-method-like direct measurement of frep was performed. In this case, the performance of the RF spectrum analyzer or RF frequency counter limits the frequency response of strain sensing similar to the optical spectrum and frequency measurement in the conventional optical strain sensor.In the present study, to achieve OFC-based strain sensor with high frequency response, we developed a null-method-like strain sensing system with a frep-stabilized OFC generator, in which the strain was decoded by the control voltage of a piezoelectric transducer (PZT) installed for performing frep stabilization of the OFC, instead of the deflection-method-like direct measurement of frep.
2. Optical setup
The optical setup of the proposed strain sensing system with an OFC is shown in Fig. 1(a). A custom-built ring-cavity erbium-doped fiber (EDF) laser mode-locked by a nonlinear polarization rotation technique [19] was employed as an OFC generator, of which the fundamental comb spacing, the center wavelength, the spectral bandwidth and the net dispersion of the oscillator cavity at the center wavelength were 43.4 MHz, 1550 nm, 40 nm, and −0.02 ps2, respectively. The stability of the OFC generator was estimated in terms of Allan deviation as shown in Fig. 2. The Allan deviations of 3.0 × 10−9 for the gate time of 10 ms and of 1.3 × 10−9 for 1 s were realized, which respectively corresponded to the cavity length stabilities of 13.2 nm and 5.72 nm with the total cavity fiber length of 4.4 m in the repetition rate of 43.4 MHz.
Fig. 1 Strain sensing system with OFC. (a) Optical setup of OFC-based strain sensing system with comb-spacing stabilization. (b) Schematic strategy of the null method-based strain sensing with OFC. EDF, erbium-doped fiber; PD, photo detector; IWDM, wavelength division multiplexer with isolator; OC, optical coupler; DBM, double balanced mixer; SPF, short frequency pass filter; and PZT, piezoelectric transducer.
A part of the OFC cavity made of a silica-core single-mode optical fiber with a core diameter of 8.2 µm, a cladding diameter of 125 µm, and an acrylate coating diameter of 242 µm (SMF-28, Thorlabs, Inc.) was used as a strain sensing region. The part of the OFC cavity other than the sensing region was installed in a thermo-controlled box with a Peltier thermo-controller. The comb spacing of the OFC was stabilized by a double balanced mixer (DBM)-based servo control system with a ring-shaped PZT using the following procedure: The fundamental beat note of the comb spacing frep was detected by a photodetector, and the difference frequency signal of frep and the reference frequency (43.4 MHz) generated by an RF synthesizer referenced to a commercially available rubidium (Rb) atomic clock (accuracy of 5 × 10−11 and instability of 2 × 10−11 at 1 s) was extracted by a DBM and a short frequency pass filter. A proportional and integral type servo controller stabilized the comb spacing by means of a ring-shaped PZT (cutoff frequency of 1 kHz) on which several turns of a part of the OFC cavity fiber were wound. Owing to the electric stabilization of frep, a null-method-like frequency observation of frep was available at high speed, in which the control voltage of the PZT VPZT was followed as a function of strain perturbation for the frep stabilization. Therefore, high-speed strain sensing can be achieved by monitoring the compensation signal VPZT without the need for the deflection-method-like direct measurement of frep as shown in Fig. 1(b).
3. Results
3.1 Static strain sensing
To validate our method, we first investigated the static response of the developed OFC-based strain sensor. The relationship between the control voltage VPZT and the applied displacement is shown in Fig. 3. VPZT was indirectly obtained from the voltage-monitor output of the PZT driver. A static strain perturbation was applied by means of a 20 mm-long block-shaped PZT attached at the strain sensing region. The relation between the displacement of the sensing region and VPZT applied to the block-shaped PZT was initially calibrated by means of frep observed with a frequency counter referenced to the Rb atomic clock. VPZT was linearly varied depending on the displacement applied to the sensing region, while frep of the OFC was stabilized at 43.4 MHz. The displacement sensitivity, defined as the slope of the least squares linear fit of Fig. 3, was 4.10 V/µm. When the strain was defined as the relative displacement of the 20 mm-long sensing region, the same length as the block-shaped PZT, a strain sensitivity of 82.0 mV/µε was obtained.
Fig. 3 Relationship between compensation signal VPZT and applied displacement in static strain sensing. The solid line indicates the linear least-squares fit to the experimental data (solid circles).
The fluctuation of the control voltage VPZT was about 150 mV with the bandwidth of 100 MHz, indicating that the sensing limit of the minimum displacement was 36.6 nm. Assuming a 20 mm-long sensing region, the sensing limit of the minimum strain was estimated to be 1.83 µε. On the other hand, we confirmed the strain sensor worked up to a control voltage VPZT of at least 150 V, corresponding to a displacement of 36.6 µm or a strain of 1.83 mε with a 20 mm-long sensing region. Based on theoretical speculation, the sensing limit of the maximum strain may be limited by the yield strain of the optical fiber [20] used in the strain sensing region, which might reach 10 mε or larger. These results confirmed the static strain sensing capability of our strain sensing system with a comb-spacing-stabilized OFC generator.
3.2 Dynamic strain sensing
The dynamic strain sensing capability of the strain sensing system was also evaluated. The frequency response of the control voltage VPZT is shown in Fig. 4. A displacement of 150 nm, corresponding to a strain of 7.90 µε with a 20 mm-long sensing region, was applied to the strain sensing region by the 20 mm-long block-shaped PZT. The cutoff frequency, defined as the frequency at which the control voltage VPZT was attenuated by −3 dB from that at the zero frequency, was 310 Hz, whereas the frequency response of the block-shaped PZT attached to the optical fiber of the strain sensing region was higher than 5 kHz (data not shown). This result indicated that the proposed strain sensor could be capable of dynamic strain sensing owing to its strain sensing strategy based on the frep stabilization. Higher frequency response up to sub-MHz can be realized by using an electro-optic modulator (EOM) in place of PZT for the servo controlling [21]; but in general, the maximum detectable strain might be decreased due to the trade-off relationship between the frequency response and displacement of the actuators. The PZT, EOM, or other actuators for the servo controller should thus be chosen depending on the applications to realize adequate frequency response and displacement.
Fig. 4 Frequency response of compensation signal VPZT. A displacement of 150 nm, or a strain of 7.90 µε over a 20 mm-long sensing region, was applied to the strain sensing region.
4. Discussion
Since the proposed method was based on compensation of the displacement ΔL applied to the sensing region of the OFC cavity, the control voltage VPZT is expressed as
with the assumption that the control voltage was linearly proportional to the displacement ΔL, as shown in Fig. 3, where the proportionality coefficient is C. This indicates that the proposed system predominantly worked as a displacement sensor. For strain sensing, the strain sensitivity depends on the sensing cavity length, that is,where ε represents the strain defined as the relative change in the sensing cavity length ΔL/L. Since the total fiber length without the optical components and the EDF was about 3 m in the case of the comb spacing of 43.4 MHz in our setup, the maximum fiber length available for strain sensing was 3 m as well. If we were to employ a 3 m-long fiber as the sensing region, the sensing limit of the minimum strain shown in our demonstration of the static strain sensing would correspond to 12.2 nε. Although the maximum strain of the proposed strain sensor is limited in such a large sensing region because of the limited compensation displacement of the PZT, e.g., a compensation displacement of 36.6 µm, as shown above, which corresponds to 1.2 µε, the proposed method has the potential to realize sub-nano-strain sensing with the use of a long sensing fiber. If we need to expand the dynamic range of the strain sensing, we can combine other PZTs with large displacement or other actuators, such as a translational stage. Although the frequency response of the strain sensor depends on the actuator employed in this strain sensor, the selectivity of the dynamic range of the strain and its frequency response is an advantage of our method using a comb-spacing-stabilized OFC generator.The fluctuation of the control voltage VPZT, which is a result of changes in the optical cavity length and limited the observable minimum strain of the proposed method, might be due to thermal perturbation in OFC cavity including the sensing region. The relationship between the thermal perturbation δT and its resultant change in optical cavity length δ(nL) is expressed as,
where L, αn, and αf represent the original cavity length of the OFC generator, and thermo-optic and thermal expansion coefficients of the optical fiber used for the OFC cavity, respectively. As a result, to reduce the fluctuation of the cavity length, reduction of the cavity length, thermal isolation of the optical fiber, and/or the use of an optical fiber with lower thermo-optic and thermal expansion coefficients are required. Reducing the cavity length suggests the use of an OFC generator with a large comb spacing, in other words, with a high frep. If we employed an OFC generator with a comb spacing of a few hundred MHz, the fluctuation of the cavity length could be reduced to about 1/2 to 1/10 compared with the OFC generator used in this study. Thermal isolation of the optical fiber can be realized by using a thermo-controlled box, like the one we employed in this study. The typical expansion coefficient and the temperature coefficient of a SiO2 fiber used in this study were 1.0 × 10−5 K−1 and 5.5 × 10−7 K−1, respectively. As the result of the sensing limit of the minimum strain of 1.83 µε that was realized in this study, the thermal stability in our demonstration might be 0.183 K or less at the sensing region and 7.7 × 10−4 K or less at the other OFC cavity fiber, respectively. Further thermal compensation can be realized by using in situ monitoring of the ambient temperature and its feedback control of the OFC cavity fiber, which might be suitable for strain sensing of material exhibiting high temperature fluctuations and for long-term strain sensing to avoid temperature drift depending on its environment. Unfortunately, the number of available optical fibers with lower thermo-optic and thermal expansion coefficients is very limited, and so reducing the cavity length and implementing thermal stabilization of the cavity fiber are good solutions for reducing the fluctuations of the control voltage VPZT in this method.Finally, we compare the OFC-based strain sensor with FBG- [11], DFB- [12, 13], or DBR-based strain laser sensor [14]. While both sensors are available in RF region, main difference between them is in linewidth of RF beat signal. Linewidth of RF comb beat can go down below 1 Hz without active stabilization, which is much lower than that of RF beat signal between polarization or longitudinal modes. Such narrow-linewidth RF beat signal enables us to fully benefit from high-precision RF measurement based on the frequency standard, leading to the enhanced performance in strain sensing. Unfortunately, the insufficient suppression for thermal perturbation in OFC cavity makes this benefit blurred in the presented results. However, if the OFC cavity is optimized for the strain sensing, we believe that the OFC-based sensing scheme still has space for improvement of the strain sensing performance. Another approach is to perform simultaneous sensing of strain and temperature based on two RF parameters of OFC in the same manner as DFB [13] or DBR laser sensor [14]; for example, frep and a carrier-envelope-offset frequency fceo, another important RF parameter in OFC. Work is in progress to measure strain and temperature simultaneously by use of frep and fceo.
5. Conclusion
In conclusion, we proposed and experimentally demonstrated a strain sensing system with a comb-spacing-stabilized OFC generator, namely OFC sensing cavity. The strain/RF conversion nature of the OFC was effectively utilized for strain sensing from 1.83 µε to 1800 µε with a 20 mm-long sensing fiber length over strain frequencies of 0 to 310 Hz. The advantage of the OFC sensing cavity is to enable frequency-based sensing of strain at RF frequency region with excellent frequency reference.
For future research, we would like to emphasize high versatility of OFC sensing cavity in the fiber sensing application. Although a portion of a single-mode fiber cavity was directly used as the simplest fiber sensor in this paper, introduction of another strain-sensitive fiber sensor (for example, such as FBG fiber sensor) into the cavity will be possible in the same manner as the FBG laser sensor [10]. The combination of an OFC sensing cavity with the strain-sensitive fiber sensor has a potential to further improve the strain sensing performance. Furthermore, our approach can be used for not only the strain sensing but also sensing of other physical quantities, such as temperature, pressure, and so on, by using a part of the OFC cavity fiber or the intra-cavity target-sensitive sensor fiber that can modulate optical cavity length. Potential applications include biomedical sensing [22–24], electromagnetic wave sensing [25], and so on. A compact system with OFC sensing cavity might also be available by utilizing on-chip OFC generator [26]. Our approach would be a useful and powerful tool for sensing of strain or other physical quantities, and the concept of an OFC sensing cavity is a new aspect of OFC technology.
Funding
Exploratory Research for Advanced Technology (ERATO) MINOSHIMA Intelligent Optical Synthesizer Project (JPMJER1304), Japan Science and Technology Agency (JST), Japan; Grant-in-Aid for Exploratory Research (15K13384) form the Japan Society for the Promotion of Science (JSPS).
Acknowledgment
The authors also acknowledge Ms. Natsuko Takeichi and Ms. Shoko Lewis of Tokushima University for her help in the preparation of manuscript.
References and links
1. K. Hoffmann, “An introduction to stress analysis and transducer design using strain gauges,” HBM Test Measurement (2012).
2. C. K. Y. Leung, K. T. Wan, D. Inaudi, X. Y. Bao, W. Habel, Z. Zhou, J. P. Ou, M. Ghandehari, H. C. Wu, and M. Imai, “Review: optical fiber sensors for civil engineering applications,” Mater. Struct. 48(4), 871–906 (2015). [CrossRef]
3. I. Yamaguchi, “A laser-speckle strain gauge,” J. Phys. Educ. 14, 1270 (1981).
4. Y. Y. Hung, “Shearography: a new optical method for strain measurement and nondestructive testing,” Opt. Eng. 21, 213391 (1982).
5. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997). [CrossRef]
6. A. Fasano, G. Woyessa, P. Stajanca, C. Markos, A. Stefani, K. Nielsen, H. K. Rasmussen, K. Krebber, and O. Bang, “Fabrication and characterization of polycarbonate microstructured polymer optical fibers for high-temperature-resistant fiber Bragg grating strain sensors,” Opt. Mater. Express 6(2), 649–659 (2016). [CrossRef]
7. K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-based continuous-wave technique,” IEEE Photonics Technol. Lett. 14(2), 179–181 (2002). [CrossRef]
8. Y. Mizuno, N. Hayashi, H. Tanaka, Y. Wada, and K. Nakamura, “Brillouin scattering in multi-core optical fibers for sensing applications,” Sci. Rep. 5(1), 11388 (2015). [CrossRef] [PubMed]
9. Y. Weng, E. Ip, Z. Pan, and T. Wang, “Single-end simultaneous temperature and strain sensing techniques based on Brillouin optical time domain reflectometry in few-mode fibers,” Opt. Express 23(7), 9024–9039 (2015). [CrossRef] [PubMed]
10. K. P. Koo and A. D. Kersey, “Bragg grating-based laser sensors systems with interferometric interrogation and wavelength division multiplexing,” J. Lightwave Technol. 13(7), 1243–1249 (1995). [CrossRef]
11. S. Liu, Z. Yin, L. Zhang, L. Gao, X. Chen, and J. Cheng, “Multilongitudinal mode fiber laser for strain measurement,” Opt. Lett. 35(6), 835–837 (2010). [CrossRef] [PubMed]
12. O. Hadeler, E. Rønnekleiv, M. Ibsen, and R. I. Laming, “Polarimetric distributed feedback fiber laser sensor for simultaneous strain and temperature measurements,” Appl. Opt. 38(10), 1953–1958 (1999). [CrossRef] [PubMed]
13. O. Hadeler, M. Ibsen, and M. N. Zervas, “Distributed-feedback fiber laser sensor for simultaneous strain and temperature measurements operating in the radio-frequency domain,” Appl. Opt. 40(19), 3169–3175 (2001). [CrossRef] [PubMed]
14. Y. N. Tan, Y. Zhang, L. Jin, and B. O. Guan, “Simultaneous strain and temperature fiber grating laser sensor based on radio-frequency measurement,” Opt. Express 19(21), 20650–20656 (2011). [CrossRef] [PubMed]
15. S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hansch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84(22), 5102–5105 (2000). [CrossRef] [PubMed]
16. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002). [CrossRef] [PubMed]
17. T. Minamikawa, Y.-D. Hsieh, K. Shibuya, E. Hase, Y. Kaneoka, S. Okubo, H. Inaba, Y. Mizutani, H. Yamamoto, T. Iwata, and T. Yasui, “Dual-comb spectroscopic ellipsometry,” Nat. Commun. 8(1), 610 (2017). [CrossRef] [PubMed]
18. S. Wang, P. Lu, H. Liao, L. Zhang, D. M. Liu, and J. S. Zhang, “Passively mode-locked fiber laser sensor for acoustic pressure sensing,” J. Mod. Opt. 60(21), 1893–1898 (2013). [CrossRef]
19. H. Inaba, Y. Daimon, F. L. Hong, A. Onae, K. Minoshima, T. R. Schibli, H. Matsumoto, M. Hirano, T. Okuno, M. Onishi, and M. Nakazawa, “Long-term measurement of optical frequencies using a simple, robust and low-noise fiber based frequency comb,” Opt. Express 14(12), 5223–5231 (2006). [CrossRef] [PubMed]
20. K. Peters, “Polymer optical fiber sensors-a review,” Smart Mater. Struct. 20(1), 013002 (2011). [CrossRef]
21. Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F. L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010). [CrossRef] [PubMed]
22. P. Bhatia and B. D. Gupta, “Fabrication and characterization of a surface plasmon resonance based fiber optic urea sensor for biomedical applications,” Sens. Actuators B Chem. 161(1), 434–438 (2012). [CrossRef]
23. L. V. Wang and S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012). [CrossRef] [PubMed]
24. Y. Yamaoka, Y. Harada, M. Sakakura, T. Minamikawa, S. Nishino, S. Maehara, S. Hamano, H. Tanaka, and T. Takamatsu, “Photoacoustic microscopy using ultrashort pulses with two different pulse durations,” Opt. Express 22(14), 17063–17072 (2014). [CrossRef] [PubMed]
25. X. Zhang, A. Hosseini, H. Subbaraman, S. Wang, Q. Zhan, J. Luo, A. K. Y. Jen, and R. T. Chen, “Integrated Photonic Electromagnetic Field Sensor Based on Broadband Bowtie Antenna Coupled Silicon Organic Hybrid Modulator,” J. Lightwave Technol. 32(20), 3774–3784 (2014). [CrossRef]
26. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007). [CrossRef] [PubMed]
