A highly sensitive liquid-level sensor based on dual-wavelength single-longitudinal-mode fiber laser is proposed and demonstrated. The laser is formed by exploiting two parallel arranged phase-shift fiber Bragg gratings (ps-FBGs), acting as ultra-narrow bandwidth filters, into a double-ring resonators. By beating the dual-wavelength lasing output, a stable microwave signal with frequency stability better than 5 MHz is obtained. The generated beat frequency varies with the change of dual-wavelength spacing. Based on this characteristic, with one ps-FBG serving as the sensing element and the other one acting as the reference element, a highly sensitive liquid level sensor is realized by monitoring the beat frequency shift of the laser. The sensor head is directly bonded to a float which can transfer buoyancy into axial strain on the fiber without introducing other elastic elements. The experimental results show that an ultra-high liquid-level sensitivity of 2.12 × 107 MHz/m within the measurement range of 1.5 mm is achieved. The sensor presents multiple merits including ultra-high sensitivity, thermal insensitive, good reliability and stability.
© 2012 OSA
Liquid level sensing is important for modern industries in many specific fields, such as fuel storage and biochemical systems. Different kinds of liquid level sensing techniques based on electrical , mechanical , and optical methods [3–7] have been reported. Among those, electrical liquid-level sensors are widely employed while their applicability is limited if the liquid to be monitored is conductive, potentially explosive or erosive. Optical fiber sensors offer many advantages under these rigorous conditions due to its intrinsic properties such as non-conducting, anti-erosion and immune to electromagnetic interference . However, some of the liquid level detection methods based on optical fiber need special treatment of FBG like etching , and some need other elastic element like bending cantilever beam  to perform indirect measurement, which adds the instability and complexity of the sensors, as well as limits the sensor’s resolution of no more than 1 micrometer (μm). For most applications, a liquid level resolution of 1 μm is generally satisfactory, while for certain applications in geophysical research and oil industry, a much higher liquid level detection resolution down to nanometer (nm) is required . For instance, it can be applied to a water-tube tilt-meter or a hydrostatic system, which have great potential applications in the field of earth tide studies, dam surveys, estimation of subsurface permeability variations and some other geophysical explorations. Recently, optical sensors based on erbium-doped fiber laser (EDFL) [10, 11] have recently attracted considerable attention due to the properties of high sensitivity and compact size. However, it is well known that fiber lasers are usually of multi-longitudinal-mode (MLM) operation with mode hopping due to a long cavity and very narrow longitudinal mode spacing. The selection of its operation wavelength has been achieved by using different optical filtering techniques, including Lyot–Sagnac filter , equivalent ps-FBG , parallel arranged FBGs with saturable absorber , or serial connection of the FBG . Previously, several approaches for realizing dual-wavelength single longitudinal mode (SLM), for instance, based on an ultra-narrow transmission-band FBG or a FBG pair used as a Fabry-Perot filter have been proposed and demonstrated and show impressive operation performance [16, 17], however, those configurations are made up of a single fixed filter to provide dual-wavelength operation, which limits the tunability of the generated dual wavelength and its application in the optical fiber sensing system. Q. SUN et al presented an approach to realize channel-switchable single-/dual-wavelength SLM lasers and switchable beat frequency generation in the THz frequency regime, while a piece of unpumped polarization maintaining erbium-doped fiber as the saturable absorber and two band-pass filters to realize wavelength tunability are required, making the structure high-cost and complicated .
In this work, for the first time to our knowledge, a liquid level sensor based on double-ring fiber laser assisted by beat frequency interrogation is proposed and experimentally demonstrated. We design a double-ring fiber laser incorporating two parallel arranged ps-FBGs, which is capable of supporting dual-wavelength SLM operation with the assistance of a uniform FBG serving as a coarse wavelength selection component. One ps-FBG is directly bonded to a float which can transfer buoyancy into axial strain on the fiber and the other one is fixed nearby free of strain, acting as the reference element. By monitoring the beat frequency shift of the dual-wavelength lasing, the liquid level variation is demodulated and recorded. Without other elastic element like cantilever or corrugated tube between the liquid and the sensor, the detection system is free of the strain transfer retardation which may affect the measuring accuracy. Experimental results of ultra-high sensitivity, good reliability and stability are also presented.
2. Laser configuration and sensing principle
The schematic diagram of the proposed double-ring EDFL is shown in Fig. 1 . The coarse lasing wavelength selection is carried out by means of a uniform FBG tuned by a translation stage. When π-phase shift is introduced into a uniform FBG structure, an ultra-narrow transmission-band (~0.1 pm) will open in the stopband of the original FBG. By exploiting two parallel arranged π-phase-shift FBGs with different central wavelength in the ring cavity, two lasing wavelengths identical with the ultra-narrow transmission peaks of the two ps-FBGs can be achieved, respectively. A section of erbium-doped fiber (EDF) with high gain coefficient is incorporated into the ring cavity to act as the active medium. The circulator is employed to ensure unidirectional operation and therefore avoiding the spatial hole-burning effect. Two polarization controllers (PC) and two variable optical attenuators (VOA) are used to align the polarization direction of the light entering the EDF and relax the gain competition of EDF, respectively.
As depicted in Fig. 2 , by setting the narrow transmission band of each ps-FBG in an appropriate wavelength, namely keeping certain wavelength spacing between the two ps-FBGs, and tuning the reflection band of uniform FBG to cover the two transmission bands, the dual-wavelength lasing operation can be achieved theoretically. In the simulation, the theoretical spectra of the two ps-FBGs were obtained with the following typical parameters: the refractive index of the fiber core is 1.48, the length of the ps-FBG is 20 mm, the modulation depth of the refractive index is 10−4, and the pitch of the gratings for ps-FBG1 and ps-FBG2 are 532.6 nm and 532.9 nm, respectively. As shown in the Fig. 2(a), the 3-dB bandwidth of the uniform FBG and the transmission band of ps-FBG are 0.4 nm and 0.11 pm respectively as well as the spacing between the central wavelengths of the two ps-FBGs is 80 pm. The lasing wavelength is selected by the coaction of the uniform FBG and the ps-FBGs, as illustrated in the Fig. 2(b). Provided that the length of the ring cavity is 10 m, which corresponds to the longitudinal mode frequency spacing of 15 MHz, the bandwidth of the ps-FBG’s transmission band would be narrower than that of the longitudinal mode frequency, therefore ensuring the SLM operation. The ps-FBG here plays the role of ultra-narrow filter to achieve SLM. Since there’s no need to introduce other complicated methods to compress bandwidth, the laser structure is simple and low cost.
Since the two channel laser modes share a common cavity and gain medium, the coherent lasing output can be heterodyned at the photon detector (PD). By monitoring the generated beat signals in an electrical spectrum analyser (ESA), the wavelength variation of the ps-FBG can be demodulated.
The beat frequency shift is decided by the variation of wavelength spacing according to the following equation
For the sensing ps-FBG, the wavelength tuning range of the grating in respect to strain can be expressed as 
As illustrated in Fig. 3 , one end of the sensing ps-FBG is fixed to the bottom of the container, and the other is directly bonded to a float which can transfer buoyancy into axial strain on the fiber. The sensing principle can thus be derived from the following balanced relation 
The buoyancy of the float is given by
According to the above equations, as the liquid-level varies, inducing the change of the Ffloat, thus FB changes correspondingly, forcing the stress of one ps-FBG to change and ultimately causes the shift of the central transmission peak wavelength of the sensing ps-FBG. Therefore, the wavelength spacing of the two ps-FBGs changes, which leads to the shift of the beat frequency. Based on the conversion of buoyancy into axial strain, a mechanism to measure the variation of the liquid level can be realized by detecting the beat frequency shift of the coherent lasing.
Equation (6) indicates that the liquid-level variation can be measured by monitoring the shift of beat frequency presented by ESA.
3. Experimental results and discussion
3.1 Fiber ring laser
In our experiment, the length of EDF is 5 m and the total cavity length is 12 m, corresponding to a longitudinal mode frequency spacing of 18 MHz. The round trip loss of the cavity induced by inserted components and fusion splicing is estimated to be 8 dB and the gain coefficient of the EDF is 10 dB/m. The pumping threshold for stimulated emission is around 75 mA. However, we employ higher pump power of 150 mA to increment the output power stability. The uniform FBG is centered at 1540.35nm with a reflectivity of about 90% and a 3-dB bandwidth of 0.3 nm, which is tuned by a translation stage with the resolution of 1 μm. Two ps-FBGs are centered at 1540.914 and 1540.974 nm with a theoretically calculated 3-dB bandwidth of 0.11 and 0.10 pm, respectively. Both ps-FBGs are entirely placed on a thermoelectric cooler (TEC), ensuring the variation of the temperature less than 0.0625 K. To extract 10% of the laser output power from the ring cavity, a 90/10 coupler is used. The output power splits into two channels, with one port linked to the OSA (Yokogawa AQ6370C) and another port applied to the PD (Newport 1014), at the output of which the beating signal is monitored by an ESA (Agilent E4447A). As indicated in Fig. 1, the erbium-doped fiber amplifier (EDFA) is introduced to amplify the optical power so as to ease the influence of noise in the process of heterodyning.
By carefully tuning the wavelength of the uniform FBG until its reflection spectrum overlaps the narrow transmission spectrum of the two ps-FBGs, as well as adjusting the PCs and VOAs to an appropriate position to align the polarization direction and distribute the optical power equally, stable dual-wavelength lasing output with a wavelength spacing of 0.134 nm and side mode suppression ratio more than 40 dB is achieved, as illustrated in the inset of Fig. 4(a) . By applying the lasing output to a PD, the electrical spectrum of the coherent beat signal is observed in Fig. 4(a). The beating frequency is centered at 16.328 GHz corresponding to the frequency resolution of 200 kHz. Figure 4(b) plots six measurements taken at a time interval of 4 min. The maximum fluctuation of each peak power is less than 1.7 dB within 30 min, which indicates that the dual-wavelength lasing is stable at room temperature, in agreement with the behavior of self-injection seeding, as illustrated in .
Moreover, by means of tuning the temperature through TEC, thermal stability of the fiber laser can be investigated. In the experiment, the two ps-FBGs are placed on a single TEC to ensure that both ps-FBGs experience the same ambient temperature variation. The temperature is increased from 15 °C to 50 °C with a step of 5 °C and the corresponding frequencies shifts at different beat frequencies of 10 GHz, 20 GHz, 30 GHz, and 40 GHz are recorded, as shown in Figs. 5(a) , 5(b), 5(c), 5(d). It can be seen that all the beat frequencies experience small fluctuations as the temperature ascends. The absolute value of maximum fluctuation is less than 5 MHz, which proves the good thermal stability of the fiber laser structure. Since the 1pm wavelength shift corresponds to the 125 MHz beat frequency shift according to the Eq. (1), the wavelength resolution can be as high as 0.04 pm, owing to the frequency stability better than 5 MHz of the proposed dual-wavelength fiber ring laser. It is essential to demonstrate the thermal stability since in most sensing fields, thermal fluctuation will induce the deterioration of sensing properties and usually needs extra scheme to eliminate the effect of thermal instability.
3.2 Liquid level sensor
The experimental setup for the liquid level sensor is depicted in Fig. 6 . The dashed line divides the schematic diagram into two parts. The left part is double-ring fiber laser configuration and the right part is float type based liquid level detection configuration. Both ps-FBGs of the double-ring fiber laser are placed in the water tank with one mounted in the middle of the tank serving as sensing element and the other fixed on the side bar acting as reference element. The two ends of the sensing ps-FBG are fixed to the bottom of the water tank and the float through the flange in the bottom, respectively. The stainless float is shaped into a hollow cylinder opening upward to place the guided fiber from the sensing ps-FBG to VOA1. Both ps-FBGs are linked to the double-ring fiber laser cavity through the lead fiber. A support is mounted beside the container to support a circular board, which acts as the cover plate of the container and with a hole in the middle to match the top of float, ensuring the float to move vertically.
In many traditional liquid level sensing experiments, the liquid level is calibrated by the high-precision scale, which is easy to realize while suffers great error due to the scale’s limited resolution of lower than 1 mm. Therefore, in our experiment, aiming to increase the accuracy of the liquid level calibration, the water level is adjusted and calibrated by introducing a connecting vessel structure, as indicated in Fig. 7 . The structure is comprised of two identical water containers and a one-meter-long interconnecting rubber pipe. If the liquid level in one container changed, that in the other one would vary correspondingly due to the principle of communicating vessels. It is clear that the variation of water level is equal to half of the amount tuned by the elevating stage. In our experiment, the displacement resolution of the elevating stage is 20 μm, so the liquid level can be tuned by the step of 10 μm. However, we only choose the liquid level tuning step of 50 μm to avoid the inherited instrument error of the stage.
As the liquid level variation ranging from 0 to 1.5 mm with a step of 50 μm, the beat frequencies of the dual-wavelength fiber ring laser are recorded. The resolution of the frequency scanning is 910 kHz. For each liquid level, the experiment is repeated for ten times to minimize the random errors, and the average data is used to analyze the performance of the liquid level detection system. By using linear regression fits, as illustrated in Fig. 8 , the beat frequency shift is in direct proportion to the change of liquid level, with high sensitivity of 2.12 × 107 MHz/m. Within the whole range of about 1.5 mm, a good linearity of 0.986 is achieved. In this experiment, corresponding to the frequency stability of 5 MHz, the liquid level measuring accuracy could reach up to 0.295 μm.
As the liquid level changes in two directions, it is essential to do the experiment both in the condition of the level increase and decrease to investigate the hysteresis of the sensor. As shown in Fig. 9 , the red fit line marketed by the upward-pointing triangle indicates the process of increasing while the blue fit line marketed by the downward-point triangle indicates the opposite process. It is obvious that the two fit lines are almost coincided and both in a good linearity within the variation of 1.5 mm. The slope of the fitting curve for the level increasing and decreasing process is 21.2127 and 21.2494 respectively, which indicates that the system is of great repeatability and stability. As shown in the inset of Fig. 9, half the maximum deviation is 200 MHz, less than 0.5% comparing with entire measurement range of 45 GHz. A possible cause of this slight error roots in the fixing method between the fiber and the connector, where inevitable will introduce gum that suffers little retardation.
In addition to the merit of ultra-high sensitivity, thermal insensitive is another outstanding feature for the proposed liquid level detection method. In the sensor system configuration, both the sensing and reference ps-FBGs are fixed in the same water tank so as to experience identical temperature fluctuation, therefore, the narrow transmission band of each ps-FBG shifts simultaneously while the wavelength spacing remains unchanged. Therefore, the beat frequency is supposed to be the same in spite of the variation of the ambient temperature, which has been demonstrated in the thermal stability experiment mentioned above.
It should be noted that the measurement range is 1.5 mm, which seems to be a little small for some industrial applications. However, it is enough for the high-precision sensing fields with small parameter changes such as seismic precursor and geophysical exploration. Furthermore, we could expand the measurement range remarkably by increasing the bandwidth of uniform FBG as well as employing the frequency reduction technique.
In addition, as shown in Eq. (6), the sensitivity of the liquid-level detection is determined by the coefficient of Δν, which can be enhanced by choosing the material of the fiber grating with low Young’s modulus, such as poly fiber grating. As the Young’s modulus of the poly FBG is about 30% of the glass FBG, the sensitivity can be enhanced about two orders of magnitude.
In this work, a liquid level sensor based on double-ring fiber laser is proposed and demonstrated. Measurement of liquid level can be realized by monitoring the beat frequency shift of two coherent lasing outputs, resulting from the change of the wavelength spacing between the sensing and the reference ps-FBGs. The sensing head is directly bonded between the float and water tank bottom through flange, which is free of the strain transfer retardation. The experimental results show ultra-high sensitivity of 2.12 × 107 MHz/m with measurement range of 1.5 mm, hysteresis of less than 0.5%, and good linearity of 0.986. This technique has the advantage of effectively controlling the wavelength spacing, simple structure, and easy fabrication, resulting in high sensitivity as well as good reliability and stability. Furthermore, the performance of the sensor can be markedly improved by optimizing the parameter of the FBGs and adopting the technique of frequency reduction to expand measurement range and lower the system cost. The structure also shows the capability for other parameter measurement such as temperature, strain, displacement, etc., which presents great potential in high-precision sensing areas.
This work is supported by Major Program of National Natural Science Foundation of China (No. 60937002), the National Natural Science Foundation of China (No. 60907037, No. 61275004) and the China Scholarship Council Scholarship (No. 20113022).
References and links
1. L. R. Besprozvanny and A. R. Ball, “Liquid level sensor device,” US Patent 5,627,523 (1997).
2. G. A. Campbell and R. Mutharasan, “Sensing of liquid level at micron resolution using self-excited millimeter-sized PZT-cantilever,” Sens. Actuators A Phys. 122(2), 326–334 (2005). [CrossRef]
4. B. Yun, N. Chen, and Y. Cui, “Highly sensitive liquid-level sensor based on etched fiber Bragg grating,” IEEE Photon. Technol. Lett. 19(21), 1747–1749 (2007). [CrossRef]
7. T. Guo, Q. Zhao, Q. Dou, H. Zhang, L. Xue, G. Huang, and X. Dong, “Temperature-insensitive fiber Bragg grating liquid-level sensor based on bending cantilever beam,” IEEE Photon. Technol. Lett. 17(11), 2400–2402 (2005). [CrossRef]
8. B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003). [CrossRef]
9. Q. Liu, T. Tokunaga, and Z. He, “Realization of nano static strain sensing with fiber Bragg gratings interrogated by narrow linewidth tunable lasers,” Opt. Express 19(21), 20214–20223 (2011). [CrossRef] [PubMed]
10. Y. Zhang, M. Zhang, W. Jin, H. Ho, M. Demokan, B. Culshaw, and G. Stewart, “Investigation of erbium-doped fiber laser intra-cavity absorption sensor for gas detection,” Opt. Commun. 232(1-6), 295–301 (2004). [CrossRef]
11. D. Liu, N. Q. Ngo, S. C. Tjin, and X. Dong, “A dual-wavelength fiber laser sensor system for measurement of temperature and strain,” IEEE Photon. Technol. Lett. 19(15), 1148–1150 (2007). [CrossRef]
12. J. Liu, J. Yao, and T. H. Yeap, “Single-longitudinal-mode multiwavelength fiber ring laser,” IEEE Photon. Technol. Lett. 16(4), 1020–1022 (2004). [CrossRef]
13. X. Chen, J. Yao, and Z. Deng, “Ultranarrow dual-transmission-band fiber Bragg grating filter and its application in a dual-wavelength single-longitudinal-mode fiber ring laser,” Opt. Lett. 30(16), 2068–2070 (2005). [CrossRef] [PubMed]
14. Q. Sun, J. Wang, D. Liu, and P. Shum, “Optical generation of microwave signal using FBG-based double-ring fiber laser assisted by saturable absorber,” Microw. Opt. Technol. Lett. 53, 2478–2481 (2011).
15. M. A. Quintela, R. A. Perez-Herrera, I. Canales, M. Fernandez-Vallejo, M. Lopez-Amo, and J. M. Lopez-Higuer, “Stabilization of dual-wavelength erbium-doped fiber ring lasers by single-mode operation,” IEEE Photon. Technol. Lett. 22(6), 368–370 (2010). [CrossRef]
16. X. Chen, Z. Deng, and J. Yao, “Photonic generation of microwave signal using a dual-wavelength single-longitudinal-mode fiber ring laser,” IEEE Trans. Microw. Theory Tech. 54(2), 804–809 (2006). [CrossRef]
17. D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett. 44(7), 459–461 (2008). [CrossRef]
18. Q. Sun, J. Wang, W. Tong, J. Luo, and D. Liu, “Channel-switchable single-/dual-wavelength single-longitudinal-mode laser and THz beat frequency generation up to 3.6 THz,” Appl. Phys. B Lasers Opt. 106(2), 373–377 (2012). [CrossRef]
19. Y. Dai, Q. Sun, J. Zhang, J. Wo, and D. Liu, “Tunable dual-wavelength double-ring fiber laser and its application in highly sensitive temperature sensing,” in CLEO: Applications and Technology, OSA Technical Digest (online) (Optical Society of America, 2012), paper JW2A.75.
20. K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997). [CrossRef]
21. Y. Dai, Q. Sun, J. Wo, X. Li, M. Zhang, and D. Liu, “Highly sensitive liquid-level sensor based on weak uniform fiber Bragg grating with narrow-bandwidth,” Opt. Eng. 51(4), 044401 (2012). [CrossRef]