1. Introduction

Lever measurements are increasingly essential in many practical applications of civil engineering, such as weapons and satellite attitude [1]. Fiber-optic lever (tilt) sensors have received considerable attention in various sensing applications due to their many advantages, such as high sensitivity, low cost and long-distance signal transmission for remote operation [2].

Generally, most fiber-optic lever sensors need a proof mass in order to provide the inertia [3]. Due to the gravitation of the proof mass, the tilt angle can be converted into the strain, displacement, and pressure, which can be measured using the fiber sensor [4]. Fiber-optic lever sensors have been classified into two categories according to the proof mass: solid mass and liquid mass. The gravity components of the solid mass applied to the fiber sensor vary with the tilt angle, which is detected using different fiber sensors, such as fiber bragg grating [5], long-period grating [6] and photonic crystal fiber [7]. However, the size of many solid masses, such as iron balls [8,9], is very large, resulting in a complex fabrication process and a bulky device. The liquid mass is always based on a mobile microbubble in the liquid [10,11]. This microbubble can flow along the inwall of the microcavity and stay at a vertex to achieve a state of mechanical equilibrium, which induces a change in the optical path difference. Fiber-optic lever sensors based on liquid mass possess a compact size, good linearity and high directional sensitivity. However, both the solid mass and the liquid mass forms suffer from a low shock survival rating under strong shock and vibration conditions due to their large inertia. In recent years, thermal convection-based sensors have attracted attention due to their high shock reliability and proof-mass-free configuration [12–15]. Instead of using a proof mass, thermal convection with an electrical heater in an enclosed chamber is used to overcome the disadvantages of a proof-mass-type sensor. In general, almost all thermal convection-based lever sensors are based on an electronic heater and a detector. Thus, they inevitably face some long-standing challenges, such as electromagnetic interference and remote detection.

In this letter, we propose and experimentally demonstrate a proof-mass-free all-fiber lever sensor based on thermal convection with a Co²⁺-doped microfiber heater. A section of the Co²⁺-doped fiber was etched to form a microfiber. The Co²⁺-doped microfiber can be heated through a pump laser, which generates a symmetrical temperature profile inside a hermetic chamber due to thermal convection. Two micro-single mode fibers (micro-SMFs) are placed perpendicular to the Co²⁺-doped microfiber to form a Michelson interferometer. With different tilt angles, the temperature is distributed along the same direction corresponding to the horizontal axis, while the temperature profile at the two micro-SMFs is asymmetric. Hence the tilt angle can be detected by interrogating the Michelson interferometer. The thermal convection-based fiber lever sensors are large dynamic range, compact size and able to distinguish the tilt direction.

2. Fabrication of the fiber optic lever sensor

The sensing structure is shown in Fig. 1(a). A circular steel plane with the diameter of 34mm and height of 31mm was employed. In the center, a hemispherical cavity with a diameter of 10 mm and a depth of 5 mm was fabricated to form a chamber. Four rectangular grooves, with a width of 130 µm, were fabricated using laser micromachining in four sides of the hemispherical cavity, which were distributed symmetrically in the circular steel plane. In this way, two grooves along the same direction were perpendicular to other two grooves. The depth of each groove was 200 µm. The Co²⁺-doped fiber was inserted into two grooves and fixed using polyamide. The commercial Co²⁺-doped fiber was purchased from CorActive High-Tech Co., which can absorb light from a pump laser operating at 1480 nm and generates heat. Due to the uniform size of the grooves and the Co²⁺-doped fiber (125 µm), the Co²⁺-doped fiber was placed in the centre of the hemispherical cavity. A section of the standard SMF was cleaved using a fiber cleaver (S183PM, Fitel), and the cleaved SMF was fixed onto a precision translation stage (MT1-Z8, ThorLabs). The SMF was then inserted into the other rectangular grooves, which were vertical to the Co²⁺-doped fiber. The distance between the end facet of the SMF and the Co²⁺-doped fiber was adjusted to 200 µm precisely, as shown in Fig. 1(b). Next, the process was repeated using a second SMF, which was inserted and fixed in the other groove. The distance between the end facet of the second SMF and the Co²⁺-doped fiber was also 200 µm. Hence two SMFs were placed symmetrically on two sides of the Co²⁺-doped fiber, as shown in Fig. 1(b).

 

Fig. 1. (a) The circular steel plane. (b) Microscope image of the crossed Co²⁺-doped fibers and SMFs. (c) HF tapering process. (d) Microscope image of the crossed Co²⁺-doped microfibers and micro-SMFs. (e) The circular steel plane with lid. (f) Schemes in the hermetic chamber.

Download Full Size | PDF

The entire circular plane was then immersed in hydrofluoric acid (HF) to taper the fiber, as shown in Fig. 1(c). The Co²⁺-doped microfibers and two micro-SMFs, with a diameter of 10 µm, were formed by immersion in HF for 130 min, as shown in Fig. 1(d). Both the circular plane and the microfibers were then washed three times with distilled water to remove any remaining HF. The entire device was coated with a gold film. Hence the end facets of the micro-SMFs were also coated with the gold film (∼15 nm). As a result, the reflectivity of the microfiber end facet is increased to improve the visibility of the Michelson interferometer. Finally, the circular plane was covered with a lid, and the gap between the circular plane and the lid was sealed with epoxy glue, as shown in Fig. 1(e). As a result, a hermetic chamber was constructed with two hemispherical cavities in the circular plane and lid, respectively, as shown in Fig. 1(f).

3. Principle of the fiber optic lever sensor

The principle of the fiber lever sensor is based on the thermal convection. When the Co²⁺-doped microfiber is heated using the pumped laser, a gradient temperature field is formed in the hermetic chamber. The convective current and temperature distribution in the chamber are simulated by using Comsol software, as shown in Fig. 2. The center region in the chamber is defined as the heater of Co²⁺-doped microfiber, of which the temperature is set as 250°C. The size of simulated space for the convective current is set as 6.4mm. The density and thermal conductivity of the air in the chamber are 1.29 Kg/m³ and 0.024 W/(m.K), respectively. The air surrounding the Co²⁺-doped microfiber (heat source) becomes less dense and rises away from the Co²⁺-doped microfiber due to the high thermal gradient [15]. At the same time, cooler air (away from the Co²⁺-doped microfiber) moves near to the Co²⁺-doped microfiber to replace the heated air. When the heated air rises further away from the Co²⁺-doped microfiber, the heated air is cooled and then falls down. This cooled air is heated again when it falls near to the Co²⁺-doped microfiber. The repeated movement of the heated and cooled air achieves an equilibrium state, forming a convective current, as shown in Fig. 2(a). Due to the central location of the Co²⁺-doped microfiber, a symmetrical temperature field is distributed in the hermetic chamber, as shown in Fig. 2(b). Hence the temperature along two opposite areas, corresponding to the two microfibers, is equal. Note that, although the temperature distribution is symmetric along the horizontal axis, the temperature distribution along the vertical axis is asymmetric due to the convective current, as shown in Fig. 2(b).

 

Fig. 2. The convective current (a) and temperature distribution (b) without tilt. (c) The convective current (top) and temperature distribution (bottom) with angles from –80° to 80°. (d) Temperature of the two micro-SMFs and the temperature difference of two opposite areas corresponding to two micro-SMFs at each angle.

Download Full Size | PDF

When the sensing element is tilted with an angle, the natural direction of the air convection is always opposite to gravity due to the effect of natural buoyancy. Figure 2(c) shows the convective current (top) and temperature distribution (bottom) with angles from –80° to 80°. The air convection at each tilt angle remains vertical with respect to the horizontal axis and is opposite to gravity. As a result, the temperature field generated by the Co²⁺-doped microfiber remains in the original state. However, the opposite positions of the two micro-SMFs are changed. Due to the rotation, one micro-SMF is much closer to the maximum thermal field than the other micro-SMF depending on the direction of rotation. Thus, in the temperature field the locations of the two micro-SMFs are not symmetrical to the “central axis of temperature gradient” due to the asymmetric temperature distribution along the vertical axis. They are no longer on the same isothermal line with angles from –80° to 80°, as shown in Fig. 2(c). In this way, the temperatures along two opposite areas, corresponding to the two micro-SMFs, are different. In order to calculate the temperature difference between two micro-SMFs, the temperature at individual pixels along the micro-SMF axial from −800 to −200 µm and from 200 to 800 µm are summed. The red and blue solid lines in Fig. 2(d) show the temperature of two micro-SMFs (–800 to −200 µm and 200 to 800 µm) at each angle. The temperature changes of the micro-SMFs are opposite to the other one. Then two temperature along different micro-SMFs are subtracted to calculate the temperature difference, as shown in Fig. 2(d). The temperature difference presents a sinusoidal variation with the tilt angle because the natural convection of air can also be regarded as a pendulum within a hermetic chamber. The temperature difference, $\Delta T$, induced by the “gas pendulum” is expressed as $\Delta T \propto g\sin \theta .$, where g is gravity and $\theta$ is the tilt angle [16].

4. Experiment and discussion

The sensor was fixed on a rotation stage (GCD-01, Daheng Optics.) with a step precision of 0.1°, as shown in Fig. 3(a). In the experiments, the tilt angle with clockwise direction is defined as a positive value ($+ \theta$), and the tilt angle with anticlockwise direction is defined as a negative value ($- \theta$), as shown in inset of Fig. 3(a). An amplified spontaneous emission (ASE) with a wavelength ranging from 1525 to 1565 nm was illuminated into two micro-SMFs through a 2×2 fiber coupler as a light source. The light beams in the two micro-SMFs are propagated along the fiber and reflected at the end facet. The two reflected light beams are coupled into the output of the 2×2 coupler, which form a Michelson interferometer. Hence the 2×2 fiber coupler can split the ASE light into two micro-SMFs, and combine two reflected light of micro-SMFs to form a Michelson interferometer. The reflection spectrum is detected using an optical spectrum analyser (OSA, AQ6370D, YOKOGAWA, Inc.). When the temperature difference between the two micro-SMFs is changed, the wavelength of the interferogram fringe is shifted to a longer wavelength (increase of optical path difference, OPD) or a shorter wavelength (decrease of OPD) due to the variation of the OPD of the Michelson interferometer. Hence the tilt angle can be detected by interrogating the wavelength shift of the reflection spectrum. A 1480 nm tunable pump laser is illuminated into the Co²⁺-doped microfiber via a 1480/1550 nm wavelength division multiplexing (WDM) (WD1450B, Thorlabs). The clockwise direction is defined as positive tilt angle, while the anticlockwise direction is defined as negative tilt angle, as shown in inset in Fig. 3(a). Through the thermographic camera, it can be observed that the Co²⁺-doped microfiber is heated by using the pump laser, as shown in the insets in Fig. 3(b). Figure 3(b) shows the relationship between the temperature of the Co²⁺-doped microfiber, measured by using the thermographic camera once the temperature was stable, and the pump heating laser power. The temperature was increased as a function of the heating laser power, indicating the heating of the Co²⁺-doped microfiber. The linear fitting curve of the temperature is $y = 0.54x + 11.8$. Figure 3(c) shows the reflection spectrum of the Michelson interferometer with the tilt angle of 0°. Two adjacent valleys at the wavelengths of 1541.94 and 1546.62 nm are chosen in the interference fringe. Hence the difference in length between the two micro-SMFs can be calculated as $d = {\lambda _1}{\lambda _2}/(2n({\lambda _2} - {\lambda _1})\textrm{ = 175}\mu \textrm{m}.$.

 

Fig. 3. (a) The experimental setup. Insets show the tilt angle of the sensor. (b) The relationship between the temperature of the Co²⁺-doped microfiber and pump laser power. Insets show thermographic pictures of the Co²⁺-doped microfiber. (c) Reflection spectrum of the Michelson interferometer.

Download Full Size | PDF

The tilt angle response of the sensor was investigated. The pump laser power was set as 350 mW, and the ambient temperature was 20°C. The sensor was tilted in a clockwise direction from 0°to 80°. The reflection spectrum with different tilt angles is shown in the right inset in Fig. 4. It can be seen that the interferogram fringe experienced a red shift with increases of the tilt angle, indicating that the OPD of the Michelson interferometer increased because the tilt angle induced a change in the temperature of the two micro-SMFs. On the contrary, the interferogram fringe shifted to a shorter wavelength with the tilt angle in the anticlockwise direction, from 0°to –80°, as shown in the left inset in Fig. 4. The OPD of the Michelson interferometer is decreased due to the opposite temperature change induced by the anticlockwise tilt angle. Hence the proposed sensor has the capability to distinguish the tilt direction by interrogation of the direction of the wavelength shift. Figure 4 shows the relationship between the tilt angle and the wavelength shift of a spectrum valley at a wavelength of 1541.94 nm with tilt angles ranging from –90° to 90°. Obviously, the wavelength shift has a sine relationship with the tilt angle, which is in good agreement with the theory. The measuring range of tilt angles from –90° to 90° for the proposed lever sensor is larger than those of the other published studies [6,11]. In order to achieve linear sensitivity of the sensor, the curve was fitted in the range of 0-50°. The linear fitting curve for the mean wavelength shift measurement is $y = 0.\textrm{095}x + \textrm{0}\textrm{.185}$, as shown in Fig. 4. Therefore, the sensitivity of the thermal convection-based fiber lever sensor is 95 pm/deg within the range from −50° to 50°, which can satisfy the requirements of general lever measurement. The resolution of the OSA is 20pm, hence the precision of $\frac{{\textrm{20nm}}}{{\textrm{95nm/deg}}}\textrm{ = 0}\textrm{.21deg}$ for the proposed fiber lever sensor is achieved. It should be noted that both the micro-SMFs and the Co²⁺-doped fiber are fixed into the groove in the metal plane using polyamide. Hence during the rotation of the metal plane, the micro-SMFs and the Co²⁺-doped fiber are kept at the same attitude to the chamber. Therefore, both the micro-SMFs and the Co²⁺-doped fiber can be avoided to suffer from large strain during the rotation, which could also prevent the damage of the microfiber.

 

Fig. 4. The wavelength shift of the sensor with the tilt angle ranging from –90° to 90°. The insets show the reflection spectrum with the tilt angle in the anticlockwise (left) and clockwise (right) directions.

Download Full Size | PDF

The dependence of the sensor on the pump laser power was also studied. The Co²⁺-doped microfiber was injected with the 1480 nm laser, and the power of the laser was increased from 100 to 450 mW. Figures 5(a) and (b) show the wavelength shift and tilt sensitivity with different pump laser powers. All of the spectrum valleys exhibit a red shift with increasing tilt angle. However, the sensitivity of the sensor differs with variations in the pump laser power. The sensitivity of the sensor is increased significantly with increases in the pump laser power. The increase in the heat source temperature increases the temperature gradient, which increases the temperature difference and improves sensor sensitivity.

 

Fig. 5. The wavelength shift (a) and tilt sensitivity (b) under different pump laser powers. The wavelength shift (c) and tilt sensitivity (d) under different ambient temperatures.

Download Full Size | PDF

We then tested the ambient temperature response of the sensor. Both the sensor and the rotation stage were fixed in an environmental chamber, where the temperature could be adjusted from 20°C to 140°C, with an interval of 20°C. At each measurement, the sensor was measured until the temperature was stable. Figures 5(c) and (d) show the wavelength shift and tilt sensitivity at different temperatures. The sensitivity of the sensor decreased with increases of the ambient temperature. The change of ambient temperature leads to a redistribution of the temperature field near the heat source within the chamber, and the temperature gradient is weakened.

The response time is a key factor for the sensor. The rotation angle was set as –50°, which is defined as the initial position of the test. After staying in the initial position for 10 s, the rotation angle was tilted in steps of +5°until the final angle of 50° was reached. At each angle, the sensor stayed in position for 5 s. The driven signal of the angle rotation and the wavelength shift of the sensor are shown in Fig. 6(a). The wavelength shift of the sensor shows good agreement with the driven signal. The dip signal of the wavelength shift at the beginning of each step is caused by the mechanical shove when the rotation begins to tilt. The response time of the proposed lever sensor is measured as 0.8 s, when the angle is changed from –10° to –5°, as shown in Fig. 6(b). The response time is mainly attributed to the signal delay of the rotation but is also attributable to the thermal delay generated in order to establish a new convective current after each rotation step.

 

Fig. 6. (a) The driven signal of the rotation stage and the wavelength shift of the sensor. (b) The response time of the sensor.

Download Full Size | PDF

The size of the metallic chamber and the distance between the Co²⁺-doped fiber and the micro-SMFs are two key parameters for the proposed fiber lever sensor. Especially when the ambient temperature is changed, the metallic chamber could be dilated, and the distance between the fiber could also be changed. In Ref. [13], the relationship between the size of the chamber and the sensitivity of the thermal inclinometer is investigated. The sensitivity of the thermal inclinometer is increased with the increase of the chamber size because the convective current is accelerated with the large size, resulting an increase of the temperature gradient. However, when the chamber size is larger than a certain value, the sensitivity is fixed. This is because that once a stable convective current is formed in a large size chamber, the temperature gradient is not affected by the chamber size. The diameter of the hemispherical cavity is 10 mm in the proposed fiber lever sensor, which is much larger than 10 µm of the microfiber. Therefore, the sensitivity and response time of the proposed fiber lever sensor is changed slightly with different size of the chamber. Besides, the length of the micro-SMF is increased at high temperature. At the same time, the size of the metal plane is expanded with the increase of the temperature. However, the thermal expansion coefficient ($\textrm{15} \times \textrm{1}{\textrm{0}^{\textrm{ - 6}}}$/°C) and size (34mm) of the mental plane are much larger than that of the microfiber (thermal expansion coefficient and size are $\textrm{0}\textrm{.5} \times \textrm{1}{\textrm{0}^{\textrm{ - 6}}}$/°C and 10 µm, respectively). Hence the distance between the Co²⁺-doped fiber and the micro-SMFs is increased with the increase of the temperature. As a result, the temperature gradient is also decreased because the microfiber tips are far away from the heater. Therefore, the sensitivity of the proposed fiber lever sensor is decreased and the response time is increased at high temperature due to the large distance between the Co²⁺-doped fiber and the micro-SMFs, which is in a good agreement with the experimental results shown in Fig. 5(c) and (d).

5. Conclusion

In conclusion, we have proposed and experimentally demonstrated a thermal convection-based fiber lever sensor. A Co²⁺-doped microfiber is self-heated with a pump laser acting as a heat source. Two micro-SMFs are placed orthogonally to the Co²⁺-doped microfiber, forming a Michelson interferometer. Both the temperature distribution and the convection current remain in the original state at different tilt angles, while the two micro-SMFs are not located on the same isothermal line. Therefore, the tilt angle can be detected by interrogating the wavelength shift of the Michelson interferometer induced by the temperature difference. The experimental results show that a tilt angle sensitivity of 95 pm/deg can be achieved. The proposed fiber lever sensor can be used in many fields, such as aviation (satellite attitude), automation (machine control and industrial process monitoring), and civil engineering (seismic monitoring).