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  • Abstract
Schematics of fiber optic liquid level sensor system based on a combination of optical interferometry and leverage principle (a) Lever based system setup for liquid level measurement. (b) Photonic crystal fiber based MZI configuration.



Liquid-level measurement is very important in many areas such as fuel storage systems, chemical processing, and other industrial environments. There are many kinds of liquid-level sensing techniques that mainly based on mechanical and electrical methods [1], [2]. Electrical liquid-level sensors are widely used, but their applicability is limited if the detected liquids are conductive, potentially explosive, or erosive. Fiber optic sensor technology is becoming a mature measurement method that can monitor many physical parameters like strain, temperature in harsh environment and remote locations [3]– [4] [5] [6][7]. As a novel fiber optic sensing device, fiber gratings have been used to develop for many sensing application like strain [3], [4], temperature [5], and refractive index [6], [7], which also be used for liquid level detection. In the past decades, some fiber optic liquid level sensors have been developed with different smart and hybrid structures [8], [9]. Recently, some liquid-level sensors based on long period gratings [10], multimode fiber interferometers [11], fiber Bragg gratings (FBGs) [12]– [13] [14] [15] [16][17], fiber Sagnac [18], and fiber in-line interferometer [19], [20] had been demonstrated. However, most sensing constructions of these liquid level sensors must be immersed into the liquid, the temperature change of the liquid influences the sensor performances which introduce extra measurement error. Fiber optic sensors especially based on the in-line fiber interferometer have attracted much attention due to their compact structure and high sensitive. In addition, Dong et al. proposed a sensitive-enhanced liquid-level sensor based on side-polished FBG [12], however, the sensor fabrication of the side-polished FBG is complicated, also the mechanical strength of the sensor is reduced, which has limited practical applications.

In a previous work [21], we reported a compact fiber-optic strain sensor with a hybrid interferometric structure including a micro-cavity Fabry–Pérot interferometer and a Mach–Zehnder interferometer (MZI), which had the advantages of simplicity and low cost and achieved a competitive sensitivity compared with other existing fiber-optic sensors [17]. In this paper, we present a novel fiber-optic liquid level sensor by combining lever principle and optical interferometry together. The sensing unit is a fiber optic MZI that constructed by sandwiching a piece of photonic crystal fiber (PCF) between two standard single-mode fibers (SMFs). This sensor unit is attached with a special designed lever structure for liquid detection, the sensor sensitivity could be adjusted by using different ratio of two lever arms Formula$L_{1}$ and Formula$L_{2}$. The sensor achieved a maximum sensitivity of 111.27 pm/mm in a liquid level range as 0–50 mm. The lab-scale experiment indicates that the larger the ratio of Formula$L_{1}/L_{2}$, the higher the sensitivity. Even level-based liquid level sensor is not a new type of liquid sensor [17], also there are some PCF based MZI sensors [4], but the sensor that we report in this paper owns its unique advantages. We present a novel level structure which can be adjusted and also integrate with PCF easily, and the MZI sensor that we designed here has high strain sensitivity. Most important innovational point of this work is that we present a creative integration about a lever transducer and an optical fiber MZI sensor based on PCF, which has not been reported previously. Comparing with the level measuring method that combined with fiber optic sensor, such as a fiber Bragg grating based liquid level sensor [17] which must be fabricated using specific laser writing, phase mask, photosensitive optical fiber, the proposed sensor system owns some remarkable advantages, such as high sensitivity, low-cost, and the sensor has the tunable sensitivity, and it is suitable for application in different fields.



Fig. 1 illustrates this fiber optic liquid sensor and its experimental setup. As shown in Fig. 1(a), the sensing unit is an in-line compact fiber optic Mach–Zehnder interferometer (MZI) sensor which is clamped between one free arm of a special designed lever and a fixed holder; a hanging stick is adhered to the other side of the lever and dipped into a liquid tank. A broadband light source provides light to the fiber MZI, its transmission spectra is detected by an optical spectrum analyzer. The configuration of the fiber optic MZI is shown in Fig. 1(b), two standard SMFs are spliced with a piece of PCF to form a MZI structure. The lead-in SMF/PCF splice causes the collapse of the microholes in the PCF, which acts as a mode splitter. For the lead-out PCF/SMF joint, the splicing point works as a mode combiner. Therefore, using a commercial fusion splicer, the PCF together with the two splicing points forms the MZI unit. Collapses of the microholes in the PCF with a momentarily changed profile breaks the adiabaticity of light power and generate higher-order cladding modes. Therefore, a light beam from the first splicing point is coupled in both core and cladding of the PCF, then propagate it to the second splicing point. These modes are combined by the second splicing point into the lead-out fiber, which is detected by the optical spectrum analyzer. A phase difference is thus introduced which generate a periodic oscillation spectrum due to optical path difference.

Figure 1
Fig. 1. Schematics of fiber optic liquid level sensor system based on a combination of optical interferometry and leverage principle. (a) Lever based system setup for liquid level measurement. (b) Photonic crystal fiber based MZI configuration.

The phase difference between the core and cladding modes after propagating through a fiber length can be written asFormulaTeX Source$$\Delta\phi_{m} = {2\pi \over \lambda}(n_{co, eff} - n_{cl, m, eff})L = {2\pi \over \lambda}\Delta n_{m, eff}L\eqno{\hbox{(1)}}$$where Formula$m$ is the order of cladding modes, Formula$\Delta{\rm n}_{{\rm m}, {\rm eff}} = {\rm n}_{{\rm co}, {\rm eff}} - {\rm n}_{{\rm cl}, {\rm m}, {\rm eff}}, n_{co, eff}$ and Formula$n_{cl, m, eff}$ are the effective refractive index of the fundamental mode and the Formula$m$([a-z]+) th-order cladding modes, respectively. L is the length of the PCF between two splicing point, Formula$\lambda$ is free-space wavelength. Thus, the wavelength of the dip Formula$\lambda_{m}$ is given byFormulaTeX Source$$\lambda_{m} = {2\Delta n_{m, eff} \cdot L \over m}.\eqno{\hbox{(2)}}$$When the FPI is subjected to external perturbations, the wavelength shift is FormulaTeX Source$$\Delta\lambda = \left({\delta\Delta n_{eff} \over \Delta n_{eff}} + {\delta L \over L}\right)\lambda_{m}\eqno{\hbox{(3)}}$$where Formula$\delta\Delta n_{eff}$ and Formula$\delta L$ are the variations of Formula$\Delta n_{eff}$ and Formula$L$, respectively, Formula$\delta L/L = \varepsilon_{\rm z}$ is the axial strain of the fiber.

As shown in Fig. 1(a), the lever is equalized initially, it is driven by the buoyancy of the liquid and increases buoyancy during the liquid level rises. The Formula${\rm F}_{1}$ and Formula${\rm F}_{2}$ are the buoyancy of the stick and the tension of the MZI, respectively. The buoyancy from the liquid can be displayed below:FormulaTeX Source$$F_{1} = \rho gV = \rho gsH\eqno{\hbox{(4)}}$$where Formula$\rho$ denotes the density (or specific gravity) of the liquid and Formula$g$ is gravitational acceleration. And Formula$H$ is the liquid level and Formula$s$ is the cross-sectional area of the hanging stick used in the structure. The basic of lever principle can be indicated asFormulaTeX Source$$\eqalignno{F_{1}L_{1} = &\, F_{2}L_{2} \cr F_{2} = &\, F_{1}L_{1}/L_{2}&\hbox{(5)}}$$then we get,FormulaTeX Source$$F_{2} = \rho gsHL_{1}/L_{2}.\eqno{\hbox{(6)}}$$

Based on mechanics of materials, longitudinal strain is applied to the MZI and the deformation on the cross section is neglected, the tension the MZI subjected can be estimated as follows: FormulaTeX Source$${\delta L \over L} = {F_{2} \over AE} = {\rho gsL_{1} \over AEL_{2}}H\eqno{\hbox{(7)}}$$where Formula$E$ is the Young's modulus of the fused silica, and Formula$A$ is the area of silica on the section. The value of Formula$\delta\Delta n_{eff}/\Delta n_{eff}$ is much smaller than the value of Formula$\delta L/L$, we neglect the effect of Formula$\Delta n_{eff}$.

The buoyancy Formula$F_{1}$ will increase as the stick depth of immersion into the liquid increases. Thus, the tension of the MZI Formula$F_{2}$ will increase according to the proportion of Formula$L_{1}/L_{2}$. Therefore, the interference spectra will shift when the liquid level increases or decreases. The liquid level can be detected and evaluated by measuring the resonance wavelength shift.



We use a commercial fusion splicer (Fujikura, FSM-50s) to fabricate the sensor. An 8 mm PCF was spliced between a lead-in SMF and lead-out SMF in a manual mode. As shown in Fig. 1(b), the PCF we selected is Grapefruit photosensitive photonic crystal fiber from Fiberhome Technology Company, LTD., its core and outside diameters are 8 Formula$\mu\hbox{m}$ and 125 Formula$\mu\hbox{m}$, respectively. The air holes in the cladding have diameter of about 33.8 Formula$\mu\hbox{m}$ in radial direction. We chose a discharge intensity as 40 bit (bit is a default unit of discharge intensity of the splicer) and arc time as 500 ms to conduct the splicing process in the sensor fabrication. Under these splicing conditions, the microholes of PCF are collapsed over a length of a few hundred micrometers around two splicing points of PCF which forms a MZI. Fig. 2 shows a typical transmission spectra of this MZI. The dip in the transmission spectrum is generated by the interference between the cladding modes and the core mode.

Figure 2
Fig. 2. Transmission spectrum of fiber optic MZI sensing structure. The inset photograph shows the cross section of PCF (left) and the splice area between SMF and PCF (right).

Fig. 3 shows the experimental transmission spectra of the fabricated sensor with a 7.8 : 1 ratio of Formula$L_{1}/L_{2}$ for various liquid levels. As shown in Fig. 3, the dip of interference shifts to shorter wavelengths as the liquid level increases. Therefore, we apply this device for liquid level measurement. The PCF length we used to fabricate the MZI is 8 mm. To induce the tension on the MZI, we secured it between two bond points with a 5 cm separation, only the section between the bond points was subjected to the tension while the liquid level increases.

Figure 3
Fig. 3. Experimental transmission spectra of fiber optic MZI sensor shift with liquid levels.

A broadband light source provides light with an output wavelength range from 1500 nm to 1600 nm, an optical spectrum analyzer (Yokogawa, AQ6370) with a spectral resolution of 0.02 nm were used to measure the transmission spectra. The total length of the lever D is 10.5 cm Formula$(L_{1} + L_{2})$, the radius and length of the hanging stick of this structure is 10 mm and 9 cm, respectively. The hanging stick is a hollow plastic rods which is lightweight and can subject enough buoyancy. When the liquid level increases, the buoyancy F1 on the left end of the lever will increase. On the right hand, an axial tension is applied to the MZI, the length of the PCF and the effective refractive indices of the modes supported by the PCF all change, which results a modification in the relative phases of the MZI. Consequently, the interference pattern shifts with the axial tension, the tension of the MZI Formula$F_{2}$ will increase according to the proportion of Formula$L_{1}/L_{2}$.

To investigate the influence of Formula$L_{1}/L_{2}$ ratio on sensor sensitivity, some different ratios are tested in our experiment. Fig. 4(a)–(c) show the transmission spectra of the same MZI with different ratios, respectively. From Fig. 4, the wavelengths of the dips shift to shorter wavelengths monotonically when liquid level increasing. It indicates that the variation trends are similar as the liquid level increases, but the wavelength shift ranges are different, and the sensor with larger level ratio have larger wavelength shift ranges.

Figure 4
Fig. 4. Transmission spectra variation with different level ratio Formula$L_{1}/L_{2}$. (a) 2 : 1. (b) 2.5 : 1. (c) 7.8 : 1.

Fig. 5 shows the sensor calibration result for different liquid level measurement. Fig. 5(a) demonstrates the fitted response of the sensitivity for the three ratios. It can be that with the liquid level increasing, the minimum transmission value of MZI decreases, the sensor with bigger ratio has higher sensitivity. In this work, the liquid level sensing range is from 0 to 50 mm, which depends on the length of the hanging stick and the mechanical strength of splice. Therefore, the sensing range can be easily varied by changing the length of the hanging stick. Actually, the measurement range can be extended by increasing the length of the stick within the extremity of mechanical strength of the MZI.

Figure 5
Fig. 5. Sensor calibration for liquid level measurement. (a) Relationship between sensitivity variation of fiber optic liquid level sensors with level arm ratio Formula$(L_{1}/L_{2})$. (b) Sensor sensitivities at different ratio of Formula$L_{1}/L_{2}$. (c) Sensor performance at different temperatures.

Fig. 5(b) presents the measured sensitivities as a function of the ratio. It indicates that the sensitivity critically depends on the ratio of Formula$L_{1}/L_{2}$. The experimental result indicates that a longer ratio of Formula$L_{1}/L_{2}$ corresponds to a higher sensitivity, which is coincident with the theoretical results that is shown as Eq. (7). In our experiment, for a lever arm ratio 7.8 : 1, the maximum sensitivity is 111.27 pm/mm. However, when the device exhibits higher sensitivity, the measurement range will be reduced since the restricted mechanical strength of splice. Thus, there is a trade-off between sensitivity and robustness in the sensor design development. In addition, we selected plastic material to construct the level arms and ceramic material as level holder, both of them have low thermal expansion coefficient, smart mechanic connections are used to fix the arms with hold together, also we used an EPO-TEK-353ND high-temperature adhesive to attach the fibers with the arms which can avoid thermal expansion at the fixing points in a temperature environment below 200 °C. As shown in Fig. 5(c), the experimental results indicate that this sensor is repeatable in a temperature range from 20–40 °C, the slight fluctuations for these tests might caused by its mechanical structure or environmental effects during the heating procedure, that can be improved by optimizing or isolating the sensing system in our future investigation.

As shown in Fig. 6, we also test the developed sensor prototype to demonstrate its characteristics for liquid levels measurement. An inset in Fig. 6 shows the sensor calibration by monitoring the minimum dip change of interference spectrum with liquid level. Based on this calibration curve, we use the sensor for liquid level measurement; the multiple test results in Fig. 6 indicate that the fluctuations of the different tests are within 5% which shows that this liquid level sensor has good repeatability. This character is extremely important in practical application. Additionally, since the sensing unit is isolated with the liquid, the temperature change of the liquid will not influence the sensor performance, it is distinguished from other previous fiber optic sensors [10]– [11] [12][13], [20].

Figure 6
Fig. 6. Measurement results of the liquid-level sensor Formula$(L_{1}/L_{2} = 7.8:1)$. The inset shows wavelength shifts as function of liquid level change.


In conclusion, we demonstrated a novel fiber optic liquid-level sensor based on optical interferometry and lever principle in this paper. The sensing unit is an in-line fiber optic Mach–Zehnder interferometer which formed by using single-mode fiber and Grapefruit photonic crystal fiber. We monitored the transmission spectra of MZI to detect liquid level. The experimental results show that for a liquid-level variation of 50 mm, the interference minima shift to shorter wavelengths as the liquid level increases, the maximum sensitivity for a 8 mm length PCF based sensor is 111.27 pm/mm. We also reveal that the larger the level arm ratio, the higher sensitivity can be achieved. Comparing with the previous works, the demonstrated fiber optic liquid sensor is low cost, easy to fabricate, in-line test and extremely sensitive. This sensor can find application in real liquid level measurement, it can also further developed to extend its sensing capabilities, for aquatic density and specific gravity measurements.


This work was supported in part by the National Nature Science Foundation of China under Grants 61137005 and 60977055 and in part by the Ministry of Education of China under Grant SRFDP-20120041110040.


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Xinpu Zhang

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Wei Peng

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Zigeng Liu

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Zhenfeng Gong

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