sensors Article
A Wide-Range Displacement Sensor Based on Plastic Fiber Macro-Bend Coupling Jia Liu 1,2 , Yulong Hou 1, *, Huixin Zhang 1 , Pinggang Jia 1 , Shan Su 1 , Guocheng Fang 2 , Wenyi Liu 1,2 and Jijun Xiong 1,2 1
2
*
Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; [email protected] (J.L.); [email protected] (H.Z.); [email protected] (P.J.); [email protected] (S.S.); [email protected] (W.L.); [email protected] (J.X.) Science and Technology on Electronic Test & Measurement Laboratory, North University of China, Taiyuan 030051, China; [email protected] Correspondence: [email protected]; Tel.: +86-351-355-8768
Academic Editor: Vittorio M. N. Passaro Received: 14 November 2016; Accepted: 17 January 2017; Published: 20 January 2017
Abstract: This paper proposes the strategy of fabricating an all fiber wide-range displacement sensor based on the macro-bend coupling effect which causes power transmission between two twisted bending plastic optical fibers (POF), where the coupling power changes with the bending radius of the fibers. For the sensor, a structure of two twisted plastic fibers is designed with the experimental platform that we constructed. The influence of external temperature and displacement speed shifts are reported. The displacement sensor performance is the sensor test at different temperatures and speeds. The sensor was found to be satisfactory at both room temperature and 70 ◦ C when the displacement is up to 140 mm. The output power is approximately linear to a displacement of 110 mm–140 mm under room temperature and 2 mm/s speed at 19.805 nW/mm sensitivity and 0.12 mm resolution. The simple structure of the sensor makes it reliable for other applications and further utilizations, promising a bright future. Keywords: POF; macro-bend; coupling; displacement sensor
1. Introduction Displacement is an important physical quantity of solid mechanics, and displacement measurements are required in a variety of applications, such as precision alignment, position monitoring, vibrations analysis and robotics [1–3]. Since a decade ago, a number of displacement measurement sensors, such as inductance, capacitance, ultrasonic and fiber-optic displacement sensors [4], have been developed. Their inductance type transducer exhibits a good linear response in the measurement and no electrical contact, as the displacement changes with the inductance. However, problems include: the low frequency response, coil heating, and electromagnetic attraction and large size [5]. Capacitance-type displacement sensors have high sensitivities, but the parasitic capacitance influences the measurement result [6]. Also, the inductance and capacitance displacement sensor increases the fabrication cost. Conversely, fiber-optic sensors retain many advantages compared with the aforementioned sensors, such as fast speed, electrical passivity, and immunity to electromagnetic interferences, and provide possibility for measurement of displacement. Currently, fiber-optic grating displacement sensors are more widely used, for example, Cantilever beam type fiber-optic grating displacement sensor with linear response of 0.058 nm/mm within a displacement range of 0–20 mm [7]. Jicheng Li et al. obtain sensor information via the external displacement parameters modulated the Sensors 2017, 17, 196; doi:10.3390/s17010196
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Bragg wave, and achieve measurement range of 550 mm with 14 pm/mm sensitivity and 0.142 mm accuracy, but the fabrication process is more complicated [8]. Compared with the fiber-optic grating displacement sensors, intensity-modulated sensors offer a simpler and lower cost approach to detect the displacement. Among intensity-modulated ones, the macro-bending system is easier to implement, showing a good potential for displacement applications. For example, Erik et al. [9] present a glove-based sensor based on the light intensity attenuation owing to the fact that fiber micro-bending losses are correlated to the variations in flexing angle, with a sensitivity of 1.80◦ , and can be suitable for applications in measurement angular displacements of a robot. Arifin et al. [10] scraped away the outer surface of the cladding to improve the sensitivity of the displacement measurements, and achieve maximum sensitivity of 0.2401 µW/mm and finest resolution of 4.2 µm, but the measurement range is only 0–15 mm. Based on the fiber fundamental core mode coupling and the Whispering Gallery modes (WGMs) induced by the reflection at the clad-coat interface, a length of acrylic jacket fiber has been stripped, then coated with absorbent coating material. This achieves a measurement displacement of 0–30 mm [11]. However, from the above literature, as optical fiber displacement sensors on the basis of macro-bend loss usually use a single fiber with treatment, there is no doubt that the treatment decreases the sensor robustness. Conversely, perfection plastic fiber in macro-bend, because of its advantage of flexibility, has a good robustness and shows good potential in the displacement sensing field. In previous work, we have realized liquid level detection based on effect of the Cladding Mode Frustrated Total Internal Reflection (CMFTIR) in POF, with the extinction ratio of the liquid level probe of 4.18 dB [12]. This paper further proposes a wide-range displacement sensor, the strategy and fabrication of an all plastic fiber wide-range displacement sensor, by using the macro-bend coupling effect which causes power transmission and variation between two twisted bending plastic optical fibers. This structure has a good robustness and the fiber does not need pretreatment. Through the Beam Quality Analyzer analyzing the energy transmission from one fiber to another, it can be seen that the optical field distribution and the coupling power change with the bending radius of the two twisted fiber. The displacement sensor performance is tested at different temperatures and speeds and is found to be satisfactory at both room temperature and 70 ◦ C when the displacement is up to 140 mm. The output power is approximately linear with displacement of 110 mm–140 mm under room temperature and 2 mm/s speed with 19.805 nW/mm sensitivity and 0.12 mm resolution. The retrace error of the system is less than 0.05 nW/mm. 2. Sensor Design and Sensing Principles The displacement sensor system is shown in Figure 1. It consists of an LED optical source (LEDD1B, Thorlabs, Newton, NJ, USA), a Power Meter (S120vc, Thorlabs), a fixed plate of the diameter of 8 cm, a guard cylinder with a diameter of 1 cm placed in the plate groove to prevent the bent radius of fibers that are too small to break the sensor when the fiber free end is moving. A temperature sensor monitored the temperature of fiber in real time. A macro-bend structure of two twisted naked plastic optical fibers in the plate groove works as the sensing element which is fixed on the Heating platform (MS-H280-Pro). One end of the two twisted optic fibers is the ‘fixed end’, and the other end, the ‘free end’. The free end of two twisted fibers is fixed on the motorized stage (Y200MC). The fixed end of receiving fiber is covered with a black hat to shield the visible light, and the free end of the fiber is connected to power meter. The fixed end of transmitting fiber is connected to optical source, and the other end is covered with a black hat to shield visible light. The Motorized stage is used to draw the free end of the two twisted fibers to achieve displacement shifts.
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(a)
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Figure 1. System of wide-range displacement sensor (a) and Displacement sensor experiment device (b). Figure 1. System of wide-range displacement sensor (a) and Displacement sensor experiment device (b).
In Figure 1, when the free ends of twisted structure move forward, the macro-bend radius R is In Figure 1, when the free of twisted changed simultaneously. It canends be described as:structure move forward, the macro-bend radius R is changed simultaneously. It can be described as:
R
d
R2 (1) d 2π + R2 (1) R= 2π where d is the displacement of fiber free ends, R2 is the radius of the guard cylinder. fiber macro-bendofradius is smaller a certain which causes optical fiber where dThe is the displacement fiber free ends, Rthan radiusthreshold, of the guard cylinder. 2 is the mode so that the light confined in fiber originally radiateswhich outside of theoptical fiber. The The field fiberdistortion, macro-bend radius is smaller than a certain threshold, causes fiber outside generates lot light of macro-bend modes and cladding modes, where mode fieldradiation distortion, so thatathe confined inradiation fiber originally radiates outside of the fiber. radiation modes mainly from the refracted light and rayscladding and tunneling Themacro-bend outside radiation generates a lot of come macro-bend radiation modes modes, rays. where Transmission coefficients of the refraction effect and the tunneling rays are expressed by Τr and Τ t, macro-bend radiation modes mainly come from the refracted light rays and tunneling rays. respectively [13], as Transmission coefficients of the refraction effect and the tunneling rays are expressed by Tr and 12 Tt , respectively [13], as 4sin θ sin2 2 θ sin2 2 θc 1/2 T 4 sin θ sin θ − sin θc (2) (2) Trr = h 1 2 i22 sin θ sin22 θ cos22 θ 1/2 sin θ + sin θ − cos θcc
!1/2
2/3 12 2 4 sin θ sin2 θ2 2 22 3 exp − n k × R + r θ − θ ( ) 4 sin θ1 − sin θ 2 1 2c 2 Tt sin θc 1 sin2 θ2 c exp 3 n1k R r θ c θ
Tt =
sin θ c
sin θ c
3
(3)
(3)
where, k = 2π/λ is the free-space propagation constant, r is the radius of the cylindrical homogeneous thefiber, free-space is and the the radius of fiber the axis, cylindrical where, k core 2π index λ is of core, n1 is the θ is the propagation angle betweenconstant, the light rray optical θc is the homogeneous is the indexreflection, of fiber, θwhen is thethe angle between the light rayinand theThe optical minimum criticalcore, anglenfor totalcore internal light ray is propagating fiber. angle fiber axis,by θcSnell’law is the minimum is described [14], as critical angle for total internal reflection, when the light ray is propagating in fiber. The angle is described Snell’law as θc =by arcsin (4) (n2 /n[14], 1) 1
θc arcsin n 2 n1 (4) n2 is the cladding index of fiber. One part of transmitting fiber light radiates to the outside of fiber cladding when the fiber bends, is theforms cladding index of fiber. n2 then and a radiation field around at the space of cladding. An energy coupling effect occurs One part of transmitting fiber light radiates to the outside of fiber cladding fiber when the receiving fiber traverses close to the transmitting fiber enough and exposeswhen it to athe radiation bends, and then forms a radiation field around at the space of cladding. An energy coupling effect field. Then, the radiation light couples and transmits in the receiving fiber, which results in a certain occurs coupling when the in receiving fiber close to the transmitting fiber enough andisexposes it tofiber a intensity receiving thetraverses fiber without original energy. This phenomenon called the radiation field. Then, the radiation light couples and transmits in the receiving fiber, which results in macro-bending coupling effect (FMCE), with the transmission schematic shown in Figure 2. The two a certain intensity coupling in receiving the fiber without original energy. This phenomenon is called twisted structure enhances the coupling effect and stabilizes the coupling coefficient, so the two the fiber macro-bending coupling effect (FMCE), with the transmission schematic shown in Figure 2. flexible plastic optical fibers with thin cladding are essential. Step-index fibers (Mitsubishi, SK-40) The two twisted structure enhances the coupling effect and stabilizes the coupling coefficient, so the with thickness of 10 µm cladding and core diameter of 980 µm are adopted in this experiment; thus, two flexible plastic optical fibers with thin cladding are essential. Step-index fibers (Mitsubishi, the refractive index of the cladding and the core are 1.402 and 1.492, respectively. The calculation
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SK-40) with thickness of 10 μm cladding and core diameter of 980 μm are adopted in this experiment; thus, the refractive index of the cladding and the core are 1.402 and 1.492, respectively. shows that Tt isshows very small 10−8 .and It can be approximated macro-bending The calculation that and Τt isclose verytosmall close to 10−8. It canthat be the approximated thatloss theis caused by T . r loss is caused by Τr. macro-bending
Figure Macro-bend coupling effect betweentwo twofibers. fibers. Figure 2.2. Macro-bend coupling effect between
Actually, the two closely bending fibers. Actually,the theenergy energycoupling couplingsituation situationisisvery verycomplex complexbetween between the two closely bending fibers. When macro-bendinghappens, happens, more energy radiates of the transmitting fiber.at When fiber fiber macro-bending more energy radiates outsideoutside of the transmitting fiber. Refracted Refracted at cladding-environment andinto coupling intofiber, receiving fiber,outside it radiates outside of cladding-environment surface andsurface coupling receiving it radiates of the receiving the receiving fiber. However, energy is ignored because it is energy of the fiber. However, this energy isthis ignored because it is smaller than thesmaller energythan of thethe transmitting fiber transmitting coupled receiving Therefore, only the fiber energy of transmitting fiber coupled intofiber receiving fiber.into Therefore, onlyfiber. the energy of transmitting coupling into the receiving coupling into the receiving fiber should require our attention. theand coupling coefficient is C, and fiber should require our attention. So, the coupling coefficientSo, is C, the energy coupled into the the energy coupled into the receiving fiber is expressed as: receiving fiber is expressed as: (5) PP1 1=P0Pα01αC1 C (5) where α1 is the loss coefficient of transmitting fiber. where At α1 the is the losstime, coefficient of transmitting same radiation occurs in the fiber. receiving fiber in a similar way. Because there are mainly At the same time, radiation occurs in the receiving fiber inequivalent a similar to way. Because there higher order modes, the transmission loss cannot be casually transmitting fiber are loss. mainly higher order modes, the transmission loss cannot be casually equivalent to transmitting fiber loss. The loss coefficient of the higher-order modes for the step-index optical fiber is expressed as [15]: The loss coefficient of the higher-order modes for the optical fiber is expressed as [15]: " step-index 3/2 # 2 2r P0 = 2n1 k(θ2c − θ2 ) exp −2 n1 kR θ2c − θ2 − 2r 3 2 (6) P 2n k(θ 2 θ 2 ) exp 3n kR θ 2 θ 2 R (6) 0
1
c
3
1
c
R
Then output power at the free end of the receiving fiber can be expressed as: Then output power at the free end of the receiving fiber can be expressed as: P2 = P1 (1 − α2 ) = P0 α1 C (1 − α2 )
P2 P1 1 α2 P0α1C 1 α2
(7) (7)
where α2 is the loss coefficient of receiving fiber. where As α2 is thebeloss coefficient of receiving fiber. can seen from aforementioned equations, the energy coupling and transmission loss take Asbetween can be seen aforementioned equations, the energy the coupling transmission loss take place two from close fibers, and according to the calculation, outputand power of the receiving fiber place between two close fibers, and according to the calculation, the output power of the receiving changes directly with the displacement, which realizes displacement sensing based on this principle. fiber changes directly with the displacement, which realizes displacement sensing based on this 3. Experiment and Results principle. A single-fiber macro-bending structure for a displacement sensing system is shown conceptually 3. Experiment and Results in Figure 3a, with one end of the fiber connected to a Light Source (LS) and another end connected single-fiber macro-bending structure for a with displacement sensing is shown to aAPower Meter (PM), all parameters are identical Figure 1 except the system light source is laser. conceptually in the Figure 3a, with one end of the fiber to a increase, Light Source (LS) and another end The radius of macro-bend decreases with the connected displacement the output power changes connected to a Power and Meter (PM), all parameters identical with Figure the light source become disorderly unsystematic. Becauseare the background noise 1ofexcept the transmitting fiberisis laser. Thecomposed radius of of thecore macro-bend decreases influenced with the displacement increase, the output itpower mainly mode fluctuations, by the light source fluctuations, shows changes become disorderly unsystematic. Because the abackground noise of transmitting poor signal-to-noise ratio. and Especially in the case of using laser light source, thethe laser echoes the fiber is mainlywhich composed of in core fluctuations, bylarge the light source fluctuations, it interference, results themode laser output powerinfluenced undergoing fluctuations. To use the LED
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shows2017, poor ratio. Especially in the case of using a laser light source, the laser echoes Sensors 17,signal-to-noise 196 5 of 8 shows poor signal-to-noise ratio. Especially in the case of using a laser light source, the laser echoes the interference, which results in the laser output power undergoing large fluctuations. To use the the interference, which results in the laser output power undergoing large fluctuations. To use the LED as a light source is feasible, and the experimental result is shown in Figure 3b, while the change LED a light source is feasible, and the experimental result is shown in Figure 3b, while the change as a as light is feasible, experimental is shown Figure 3b, while the change rate rate of thesource output power ofand thethe fiber end duringresult outbound and in backhaul is only 0.02%. So a laser rate of output the output power of fiber the fiber end during outbound and backhaul is only 0.02%. So a laser of the power of the end during outbound and backhaul is only 0.02%. So a laser light light source is replaced by an LED source in the experiment, and a single fiber macro-bend is not light source is replaced an source LED source the experiment, and a fiber singlemacro-bend fiber macro-bend is not source replaced by anby LED in the in experiment, and a single is not suitable suitableisfor displacement detection. suitable for displacement detection. for displacement detection.
(a) (a)
(b) (b)
Figure 3. System of single fiber displacement sensor (a); Output power changes with displacement (b). Figure Figure3.3.System Systemofofsingle singlefiber fiberdisplacement displacementsensor sensor(a); (a);Output Outputpower powerchanges changeswith withdisplacement displacement(b). (b).
The Beam Quality Analyzer (BC106N-VIS/M, Thorlabs) used for analyzing the energy coupling The Beam Quality Analyzer (BC106N-VIS/M, Thorlabs) used for analyzing the energy coupling and distribution of the transmitting fiber and receiving fiber of twofor twisted opticthe fibers is also shown The Beam Quality Analyzer (BC106N-VIS/M, Thorlabs) used analyzing energy coupling and distribution of the transmitting fiber and receiving fiber of two twisted optic fibers is also shown in Figure 4. Lightofintensity at the end of the fiber and twisted the receiving fiber shown on the and distribution the transmitting fiber andtransmitting receiving fiber of two optic fibers is also shown in Figure 4. Light intensity at the end of the transmitting fiber and the receiving fiber shown on the Beam Quality Analyzer change with the displacement. Figure.4a shows the light intensity in Figure 4. Light intensity at the end of the transmitting fiber and the receiving fiber shown on the Beam Quality Analyzer change with the displacement. Figure.4a shows the light intensity distribution the transmitting fiberthe when the displacements areshows 0 mm,the 45light mm,intensity 90 mm and 135 mm. Beam QualityofAnalyzer change with displacement. Figure 4a distribution distribution of the transmitting fiber when the displacements are 0 mm, 45 mm, 90 mm and 135 mm. center to fiber edgewhen of thethe figure corresponds the optical core cladding. of theThe transmitting displacements are to 0 mm, 45 mm, fiber 90 mm andto135 mm. The light The center to edge of the figure corresponds to the optical fiber core to cladding. The light intensity gradually weakens from the center to the edge. Figure 4a shows an output power the The center to edge of the figure corresponds to the optical fiber core to cladding. Theoflight intensity gradually weakens from the center to the edge. Figure 4a shows an output power of the transmitting fiber that can befrom obtained with this system. the4agraph, energy of intensity gradually weakens the center to the edge.From Figure showsthe an mode outputfield power of the transmitting fiber that can be obtained with this system. From the graph, the mode field energy of transmitting fiber fiber that mainly thethis core, which From is determined themode multimode fiber transmitting canconcentrates be obtained in with system. the graph,bythe field energy transmitting fiber mainly concentrates in the core, which is determined by the multimode fiber transmission characteristics The center changes with radius by of the on a of transmitting fiber mainly[16,17]. concentrates in theenergy core, which is determined the macro-bend multimode fiber transmission characteristics [16,17]. The center energy changes with radius of the macro-bend on a small scale, characteristics but shifts significantly with the energy light source which means a low transmission [16,17]. The center changesfluctuations, with radius of the macro-bend on small scale, but shifts significantly with the light source fluctuations, which means a low contribution to the macro-bend coupling effect. Therefore, when a single fiber is used for a small scale, but shifts significantly with the light source fluctuations, which means a low contribution contribution to the macro-bend coupling effect. Therefore, when a single fiber is used for displacement detection, the signal-to-noise ratio is poor and fiber the output power scarcely changes with to the macro-bend coupling effect. Therefore, when a single is used for displacement detection, displacement detection, the signal-to-noise ratio is poor and the output power scarcely changes with displacement. the signal-to-noise ratio is poor and the output power scarcely changes with displacement. displacement.
Figure 4. Response Responseofofthe the transmitting receiving (b) fiber at four different displacements: transmitting (a)(a) andand receiving (b) fiber at four different displacements: (1) d Figure 4.0 Response of themm; transmitting (a) and(4) receiving (b) fiber at four different displacements: (1) d (1) d = mm; (2) d = 45 (3) d = 90 mm; d = 135 mm. = 0 mm; (2) d = 45 mm; (3) d = 90 mm; (4) d = 135 mm. = 0 mm; (2) d = 45 mm; (3) d = 90 mm; (4) d = 135 mm.
As shown in Figure 4b, the receiving fiber retains no energy when the displacement is 0 mm, and, with enhanced displacement, the light intensity increases gradually. The mode field is distorted,
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As shown in Figure 4b, the receiving fiber retains no energy when the displacement is 0 mm, and, with enhanced displacement, the light intensity increases gradually. The mode field is Sensors 2017, 17, 196 6 of 8 distorted, and the main energy concentrates near the cladding, demonstrating that the energy is coupling from the transmitting fiber due to the macro-bend effect of two twisted fibers. This energy is modulated by the concentrates macro-bend near radius, the signal-to-noise ratio is the high. Thereisare three main and the main energy theso cladding, demonstrating that energy coupling from reasons to explain why the intensity distribution is twisted irregular. The This first reason that the POFs the transmitting fiber due to light the macro-bend effect of two fibers. energy is modulated by are isotropic, but the macro-bend structure is “anisotropic”. The second reason is that the energy the macro-bend radius, so the signal-to-noise ratio is high. There are three main reasons to explain coupled into intensity the receiving fiber varies since the changes the different macro-bend why the light distribution is irregular. The energy first reason is thatwith the POFs are isotropic, but the position of the transmitting fiber. The The last second reason reason is that is the complex mode field distribution of the macro-bend structure is “anisotropic”. that the energy coupled into the receiving multimode fiber, the when the light fieldwith changes by the macro-bend, a more complex energy fiber varies since energy changes the different macro-bendproduces position of the transmitting fiber. distribution field. Thus, the energy distribution of the receiving fiber is fiber, morewhen complex thanfield the The last reason is that the complex mode field distribution of the multimode the light transmitting fiber. changes by the macro-bend, produces a more complex energy distribution field. Thus, the energy As in the above results, energy of thethan receiving fiber changes distribution of the receiving fiberthe is more complex the transmitting fiber. significantly with the displacement. plastic opticalthefiber is easy to bend, a twisted is more stable, andthe a As in theAs above results, energy of the receiving fiber structure changes significantly with two twisted optic fibers structure for displacement sensing is adopted. Figure 1 shows the schematic displacement. As plastic optical fiber is easy to bend, a twisted structure is more stable, and a of the experimental setup. The free of two twisted move Figure forward at a constant speed, two twisted optic fibers structure for ends displacement sensingfibers is adopted. 1 shows the schematic while radius of the macro-bend thetwisted fiber moves, this processatisacalled outbound. of the the experimental setup. The freeincreases ends of as two fibers and move forward constant speed, Then the radius fiber isof released at a constant speed the moves, backhaul with isthe radius of the while the macro-bend increases as theinfiber andprocess this process called outbound. macro-bend The prototype has beenprocess completed andradius the result shown in Then the fiberincreasing is releasedgradually. at a constant speed in the backhaul with the of the is macro-bend Figure 5. gradually. The prototype has been completed and the result is shown in Figure 5. increasing
Figure 5. Output power of receiving fiber changes with displacement.
The fitting fitting curve curve proposed proposed by by MATLAB MATLAB simulation, simulation, is is The 3 2 P2 (d) P20.003d 30.0005d 0.979d 282.2139 (d) = 0.003d + 0.0005d2 +0.979d + 282.2139
(8) (8)
In the experiment, the light source power is set at 39.027 mW. Although the output power of the In the experiment, the light source power is set at 39.027 mW. Although the output power of receiving fiber is only of nW, the resolution of the Power Meter at 1 nW is enough to be detected. The the receiving fiber is only of nW, the resolution of the Power Meter at 1 nW is enough to be detected. motorized stage is set to draw the free end of two twisted fibers at a constant speed of 2 mm/s, and The motorized stage is set to draw the free end of two twisted fibers at a constant speed of 2 mm/s, the power meter linked to the free end of the receiving fiber is used to detect the output power of and the power meter linked to the free end of the receiving fiber is used to detect the output power receiving fiber at the same time. From the result of Figure 5, under the displacement range of of receiving fiber at the same time. From the result of Figure 5, under the displacement range of 0–140 mm, the output power of the receiving fiber increases gradually, and the output power shift is 0–140 mm, the output power of the receiving fiber increases gradually, and the output power shift approximately linear with a displacement of 110 mm–140 mm. The sensitivity is 19.805 nW/mm; is approximately linear with a displacement of 110 mm–140 mm. The sensitivity is 19.805 nW/mm; accuracy, 0.12 mm resolution, respectively. For the displacement from 140 mm to 0 mm, the output accuracy, 0.12 mm resolution, respectively. For the displacement from 140 mm to 0 mm, the output power decreases in real time, while the systematic retrace error is less than 0.05 nW/mm in the power decreases in real time, while the systematic retrace error is less than 0.05 nW/mm in the experiment. When the fiber end is drawn at different speeds of 2 mm/s, 6 mm/s, 10 mm/s, as shown experiment. When the fiber end is drawn at different speeds of 2 mm/s, 6 mm/s, 10 mm/s, as shown in Figure 6a, the displacement-output power curve shows a slight overall decline. in Figure 6a, the displacement-output power curve shows a slight overall decline.
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(a)
(b)
Figure 6. power of receiving fiberfiber changes with with displacement at different speeds speeds (a); Output Figure 6. Output Output power of receiving changes displacement at different (a); power of receiving fiber changes with displacement at different temperatures (b). Output power of receiving fiber changes with displacement at different temperatures (b).
Temperature is an important factor in the external environment for displacement application. Temperature is an important factor in the external environment for displacement application. As the normal operating temperature of plastic optical fiber increases up◦ to 70 °C, the sensor is As the normal operating temperature of plastic optical fiber increases up to 70 C, the sensor is affected affected by temperature (from 25 °C to 70 °C) as shown in Figure 6b. With an increase of the by temperature (from 25 ◦ C to 70 ◦ C) as shown in Figure 6b. With an increase of the temperature, temperature, the displacement-output power curve shows an overall decline, and the sensitivity is the displacement-output power curve shows an overall decline, and the sensitivity is also decreased. also decreased. Because of the rising temperature, the light performance of the plastic optical fiber Because of the rising temperature, the light performance of the plastic optical fiber gets worse, and the gets worse, and the coupling capacity between the two twisted fibers is reduced. From the coupling capacity between the two twisted fibers is reduced. From the experimental results above, experimental results above, this system is used with displacement sensors during this development this system is used with displacement sensors during this development effort within a stable structure. effort within a stable structure. 4. Conclusions 4. Conclusions A novel optical fiber wide-range displacement sensor based on a macro-bend coupling effect A novel optical which fiber wide-range displacement sensor on aAccording macro-bend coupling effect has been developed, exhibits a good robustness and based low cost. to the principle of has been developed, which exhibits a good robustness and low cost. According to the principle of coupling between two closely optical fibers, a two twisted fibers sensing structure is designed. A Beam couplingAnalyzer betweenwas twoused closely optical the fibers, a two twistedand fibers sensing structure designed. A Quality to analyze energy coupling distribution of the twoisfibers to find Beam Quality Analyzer was used to analyze the energy coupling and distribution of the two fibers out that the fiber which has no intensity originally generates a lot of light intensity, which changes to find out that the fiber which has no intensity originally generates a lot of light intensity, which with the displacement. This structure avoids the sensing signal shifts influenced by visible light and changes with the displacement. This structure avoids the sensing signal shifts influenced by visible light sources and realizes the displacement measurement within a wide range of 0–140 mm. Moreover, light and light sources and realizes the displacement measurement within a wide range of 0–140 it is effective and stable at different temperatures and speeds. The output power is approximately mm. Moreover, it is effective and stable at different temperatures and speeds. The output power is linear with displacement of 110 mm–140 mm under room temperature and 2 mm/s speed with approximately linear with displacement of 110 mm–140 mm under room temperature and 2 mm/s 19.805 nW/mm sensitivity and 0.12 mm resolution. Compared to other sensors, the production process speed with 19.805 nW/mm sensitivity and 0.12 mm resolution. Compared to other sensors, the of this sensor is very simple, and immune to electromagnetic interference. Further work, such as production process of this sensor is very simple, and immune to electromagnetic interference. compensation for the temperature change and quantitative analysis of mutual coupling of modes and Further work, such as compensation for the temperature change and quantitative analysis of mutual interference in multimode fibers, is in progress. coupling of modes and interference in multimode fibers, is in progress. Acknowledgments: This work was supported by the National Science Fund for Distinguished Young Scholars (No. 51425505) and the National Natural SciencebyFoundation of China 51405454 and No. 51275491). Acknowledgments: This work was supported the National Science(No. Fund for Distinguished Young Scholars (No. 51425505) and the National Natural Science Foundation of China (No. 51405454 and No. 51275491). Author Contributions: Jia Liu, Yulong Hou and Wenyi Liu conceived and designed the experiments; Shan Su performed the experiments; Huixin Zhang and Guocheng Fang analyzed the data; Pinggang Jia contributed Author Contributions: Jia Liu, Yulong Hou and Wenyi Liu conceived and designed the experiments; Shan Su materials and analysis tools; Jia Liu wrote the paper. performed the experiments; Huixin Zhang and Guocheng Fang analyzed the data; Pinggang Jia contributed Conflicts Interest: authors declare materials of and analysisThe tools; Jia Liu wroteno theconflict paper. of interest.
Conflicts of Interest: The authors declare no conflict of interest. References 1.
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Park, H.S.; Kim, J.M.; Choi, S.W.; Kim, Y. A Wireless Laser Displacement Sensor Node for Structural Health Monitoring. Sensors 2013, 13, 13204–13216. [CrossRef] [PubMed] Chuang, K.C.; Ma, C.C.; Wang, H.C. Simultaneous measurement of dynamic displacement and strain in a single fiber using coarse wavelength-division multiplexing and fiber Bragg-grating filter-based sensing system. Appl. Opt. 2016, 55, 2426–2434. [CrossRef] [PubMed] Yang, H.Z.; Qiao, X.G.; Luo, D.; Lim, K.S.; Chong, W.Y.; Harun, S.W. A review of recent developed and applications of plastic fiber optic displacement sensors. Measurement 2014, 48, 333–345. [CrossRef] Podhraski, M.; Trontelj, J. A Differential Monolithically Integrated Inductive Linear Displacement Measurement Microsystem. Sensors 2016, 16, 384. [CrossRef] [PubMed] Wang, B.; Long, J.; Teo, K.H. Multi-Channel Capacitive Sensor Arrays. Sensors 2016, 16, 150. [CrossRef] [PubMed] Shen, C.Y.; Zhong, C. Novel temperature-insensitive fiber Bragg grating sensor for displacement measurement. Sens. Actuat. A Phys. 2011, 170, 51–54. [CrossRef] Li, J.C.; Neumann, H.; Ramalingam, R. Design, fabrication, and testing of fiber Bragg grating sensors for cryogenic long-range displacement measurement. Cryogenics 2015, 68, 36–43. [CrossRef] Fujiwara, E.; dos Santos, M.F.M.; Suzuki, C.K. Flexinble Optical Fiber Bending Transducer for Application in Glove-Based Sensors. IEEE Sens. J. 2014, 14, 3631–3636. [CrossRef] Arifin, A.; Hatta, A.M.; Muntini, M.S.; Rubiyanto, A. Bent of plastic optical fiber with structural imperfections for displacement sensor. Indian J. Pure Appl. Phys. 2014, 52, 520–524. Moro, E.A.; Todd, M.D.; Puckett, A.D. Using a validated transmission model for the optimization of bundled fiber optic displacement sensors. Appl. Opt. 2011, 50, 6526–6535. [CrossRef] [PubMed] Hou, Y.L.; Liu, W.Y.; Su, S.; Zhang, H.X.; Zhang, J.W.; Liu, J.; Xiong, J.J. Polymer optical fiber twisted macro-bend coupling system for liquid level detection. Opt. Express 2014, 22, 23231–23241. [CrossRef] [PubMed] Durana, G.; Zubia, J.; Arrue, J.; Aldabaldetreku, G.; Mateo, J. Dependence of bending losses on cladding thickness in plastic optical fibers. Appl.Opt. 2003, 42, 997–1002. [CrossRef] [PubMed] Stigloher, J.; Decker, M.; Korner, H.S.; Tanabe, K.; Moriyama, T.; Taniguchi, T.; Hata, H.; Madami, M.; Gubbiotti, G.; Kobayashi, K.; et al. Snell’s Law for Spin Waves. Phys. Rev. Lett. 2016, 117, 037204. [CrossRef] [PubMed] Cao, H.M.; Chen, Y.P.; Zhou, Z.; Zhang, G. Theoretical and experimental study on the optical fiber bundle displacement sensors. Sens. Actuators A Phys. 2007, 136, 580–587. [CrossRef] Varallyay, Z.; Szipocs, R. Stored Energy, Transmission Group Delay and Mode Field Distortion in Optical Fibers. IEEE J. Sel. Top. Quantum Electron. 2014, 20, 0904206. [CrossRef] Liu, W.; Shi, W.X.; Yao, K.N.; Cao, J.T.; Wu, P.X.; Chi, X.F. Fiber coupling efficiency analysis of free space optical communication systems with holographic modal wave-front sensor. Opt. Laser Technol. 2014, 60, 116–123. [CrossRef] © 2017 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
A Wide-Range Displacement Sensor Based on Plastic Fiber Macro-Bend Coupling Jia Liu 1,2 , Yulong Hou 1, *, Huixin Zhang 1 , Pinggang Jia 1 , Shan Su 1 , Guocheng Fang 2 , Wenyi Liu 1,2 and Jijun Xiong 1,2 1
2
*
Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; [email protected] (J.L.); [email protected] (H.Z.); [email protected] (P.J.); [email protected] (S.S.); [email protected] (W.L.); [email protected] (J.X.) Science and Technology on Electronic Test & Measurement Laboratory, North University of China, Taiyuan 030051, China; [email protected] Correspondence: [email protected]; Tel.: +86-351-355-8768
Academic Editor: Vittorio M. N. Passaro Received: 14 November 2016; Accepted: 17 January 2017; Published: 20 January 2017
Abstract: This paper proposes the strategy of fabricating an all fiber wide-range displacement sensor based on the macro-bend coupling effect which causes power transmission between two twisted bending plastic optical fibers (POF), where the coupling power changes with the bending radius of the fibers. For the sensor, a structure of two twisted plastic fibers is designed with the experimental platform that we constructed. The influence of external temperature and displacement speed shifts are reported. The displacement sensor performance is the sensor test at different temperatures and speeds. The sensor was found to be satisfactory at both room temperature and 70 ◦ C when the displacement is up to 140 mm. The output power is approximately linear to a displacement of 110 mm–140 mm under room temperature and 2 mm/s speed at 19.805 nW/mm sensitivity and 0.12 mm resolution. The simple structure of the sensor makes it reliable for other applications and further utilizations, promising a bright future. Keywords: POF; macro-bend; coupling; displacement sensor
1. Introduction Displacement is an important physical quantity of solid mechanics, and displacement measurements are required in a variety of applications, such as precision alignment, position monitoring, vibrations analysis and robotics [1–3]. Since a decade ago, a number of displacement measurement sensors, such as inductance, capacitance, ultrasonic and fiber-optic displacement sensors [4], have been developed. Their inductance type transducer exhibits a good linear response in the measurement and no electrical contact, as the displacement changes with the inductance. However, problems include: the low frequency response, coil heating, and electromagnetic attraction and large size [5]. Capacitance-type displacement sensors have high sensitivities, but the parasitic capacitance influences the measurement result [6]. Also, the inductance and capacitance displacement sensor increases the fabrication cost. Conversely, fiber-optic sensors retain many advantages compared with the aforementioned sensors, such as fast speed, electrical passivity, and immunity to electromagnetic interferences, and provide possibility for measurement of displacement. Currently, fiber-optic grating displacement sensors are more widely used, for example, Cantilever beam type fiber-optic grating displacement sensor with linear response of 0.058 nm/mm within a displacement range of 0–20 mm [7]. Jicheng Li et al. obtain sensor information via the external displacement parameters modulated the Sensors 2017, 17, 196; doi:10.3390/s17010196
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Bragg wave, and achieve measurement range of 550 mm with 14 pm/mm sensitivity and 0.142 mm accuracy, but the fabrication process is more complicated [8]. Compared with the fiber-optic grating displacement sensors, intensity-modulated sensors offer a simpler and lower cost approach to detect the displacement. Among intensity-modulated ones, the macro-bending system is easier to implement, showing a good potential for displacement applications. For example, Erik et al. [9] present a glove-based sensor based on the light intensity attenuation owing to the fact that fiber micro-bending losses are correlated to the variations in flexing angle, with a sensitivity of 1.80◦ , and can be suitable for applications in measurement angular displacements of a robot. Arifin et al. [10] scraped away the outer surface of the cladding to improve the sensitivity of the displacement measurements, and achieve maximum sensitivity of 0.2401 µW/mm and finest resolution of 4.2 µm, but the measurement range is only 0–15 mm. Based on the fiber fundamental core mode coupling and the Whispering Gallery modes (WGMs) induced by the reflection at the clad-coat interface, a length of acrylic jacket fiber has been stripped, then coated with absorbent coating material. This achieves a measurement displacement of 0–30 mm [11]. However, from the above literature, as optical fiber displacement sensors on the basis of macro-bend loss usually use a single fiber with treatment, there is no doubt that the treatment decreases the sensor robustness. Conversely, perfection plastic fiber in macro-bend, because of its advantage of flexibility, has a good robustness and shows good potential in the displacement sensing field. In previous work, we have realized liquid level detection based on effect of the Cladding Mode Frustrated Total Internal Reflection (CMFTIR) in POF, with the extinction ratio of the liquid level probe of 4.18 dB [12]. This paper further proposes a wide-range displacement sensor, the strategy and fabrication of an all plastic fiber wide-range displacement sensor, by using the macro-bend coupling effect which causes power transmission and variation between two twisted bending plastic optical fibers. This structure has a good robustness and the fiber does not need pretreatment. Through the Beam Quality Analyzer analyzing the energy transmission from one fiber to another, it can be seen that the optical field distribution and the coupling power change with the bending radius of the two twisted fiber. The displacement sensor performance is tested at different temperatures and speeds and is found to be satisfactory at both room temperature and 70 ◦ C when the displacement is up to 140 mm. The output power is approximately linear with displacement of 110 mm–140 mm under room temperature and 2 mm/s speed with 19.805 nW/mm sensitivity and 0.12 mm resolution. The retrace error of the system is less than 0.05 nW/mm. 2. Sensor Design and Sensing Principles The displacement sensor system is shown in Figure 1. It consists of an LED optical source (LEDD1B, Thorlabs, Newton, NJ, USA), a Power Meter (S120vc, Thorlabs), a fixed plate of the diameter of 8 cm, a guard cylinder with a diameter of 1 cm placed in the plate groove to prevent the bent radius of fibers that are too small to break the sensor when the fiber free end is moving. A temperature sensor monitored the temperature of fiber in real time. A macro-bend structure of two twisted naked plastic optical fibers in the plate groove works as the sensing element which is fixed on the Heating platform (MS-H280-Pro). One end of the two twisted optic fibers is the ‘fixed end’, and the other end, the ‘free end’. The free end of two twisted fibers is fixed on the motorized stage (Y200MC). The fixed end of receiving fiber is covered with a black hat to shield the visible light, and the free end of the fiber is connected to power meter. The fixed end of transmitting fiber is connected to optical source, and the other end is covered with a black hat to shield visible light. The Motorized stage is used to draw the free end of the two twisted fibers to achieve displacement shifts.
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(a)
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Figure 1. System of wide-range displacement sensor (a) and Displacement sensor experiment device (b). Figure 1. System of wide-range displacement sensor (a) and Displacement sensor experiment device (b).
In Figure 1, when the free ends of twisted structure move forward, the macro-bend radius R is In Figure 1, when the free of twisted changed simultaneously. It canends be described as:structure move forward, the macro-bend radius R is changed simultaneously. It can be described as:
R
d
R2 (1) d 2π + R2 (1) R= 2π where d is the displacement of fiber free ends, R2 is the radius of the guard cylinder. fiber macro-bendofradius is smaller a certain which causes optical fiber where dThe is the displacement fiber free ends, Rthan radiusthreshold, of the guard cylinder. 2 is the mode so that the light confined in fiber originally radiateswhich outside of theoptical fiber. The The field fiberdistortion, macro-bend radius is smaller than a certain threshold, causes fiber outside generates lot light of macro-bend modes and cladding modes, where mode fieldradiation distortion, so thatathe confined inradiation fiber originally radiates outside of the fiber. radiation modes mainly from the refracted light and rayscladding and tunneling Themacro-bend outside radiation generates a lot of come macro-bend radiation modes modes, rays. where Transmission coefficients of the refraction effect and the tunneling rays are expressed by Τr and Τ t, macro-bend radiation modes mainly come from the refracted light rays and tunneling rays. respectively [13], as Transmission coefficients of the refraction effect and the tunneling rays are expressed by Tr and 12 Tt , respectively [13], as 4sin θ sin2 2 θ sin2 2 θc 1/2 T 4 sin θ sin θ − sin θc (2) (2) Trr = h 1 2 i22 sin θ sin22 θ cos22 θ 1/2 sin θ + sin θ − cos θcc
!1/2
2/3 12 2 4 sin θ sin2 θ2 2 22 3 exp − n k × R + r θ − θ ( ) 4 sin θ1 − sin θ 2 1 2c 2 Tt sin θc 1 sin2 θ2 c exp 3 n1k R r θ c θ
Tt =
sin θ c
sin θ c
3
(3)
(3)
where, k = 2π/λ is the free-space propagation constant, r is the radius of the cylindrical homogeneous thefiber, free-space is and the the radius of fiber the axis, cylindrical where, k core 2π index λ is of core, n1 is the θ is the propagation angle betweenconstant, the light rray optical θc is the homogeneous is the indexreflection, of fiber, θwhen is thethe angle between the light rayinand theThe optical minimum criticalcore, anglenfor totalcore internal light ray is propagating fiber. angle fiber axis,by θcSnell’law is the minimum is described [14], as critical angle for total internal reflection, when the light ray is propagating in fiber. The angle is described Snell’law as θc =by arcsin (4) (n2 /n[14], 1) 1
θc arcsin n 2 n1 (4) n2 is the cladding index of fiber. One part of transmitting fiber light radiates to the outside of fiber cladding when the fiber bends, is theforms cladding index of fiber. n2 then and a radiation field around at the space of cladding. An energy coupling effect occurs One part of transmitting fiber light radiates to the outside of fiber cladding fiber when the receiving fiber traverses close to the transmitting fiber enough and exposeswhen it to athe radiation bends, and then forms a radiation field around at the space of cladding. An energy coupling effect field. Then, the radiation light couples and transmits in the receiving fiber, which results in a certain occurs coupling when the in receiving fiber close to the transmitting fiber enough andisexposes it tofiber a intensity receiving thetraverses fiber without original energy. This phenomenon called the radiation field. Then, the radiation light couples and transmits in the receiving fiber, which results in macro-bending coupling effect (FMCE), with the transmission schematic shown in Figure 2. The two a certain intensity coupling in receiving the fiber without original energy. This phenomenon is called twisted structure enhances the coupling effect and stabilizes the coupling coefficient, so the two the fiber macro-bending coupling effect (FMCE), with the transmission schematic shown in Figure 2. flexible plastic optical fibers with thin cladding are essential. Step-index fibers (Mitsubishi, SK-40) The two twisted structure enhances the coupling effect and stabilizes the coupling coefficient, so the with thickness of 10 µm cladding and core diameter of 980 µm are adopted in this experiment; thus, two flexible plastic optical fibers with thin cladding are essential. Step-index fibers (Mitsubishi, the refractive index of the cladding and the core are 1.402 and 1.492, respectively. The calculation
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SK-40) with thickness of 10 μm cladding and core diameter of 980 μm are adopted in this experiment; thus, the refractive index of the cladding and the core are 1.402 and 1.492, respectively. shows that Tt isshows very small 10−8 .and It can be approximated macro-bending The calculation that and Τt isclose verytosmall close to 10−8. It canthat be the approximated thatloss theis caused by T . r loss is caused by Τr. macro-bending
Figure Macro-bend coupling effect betweentwo twofibers. fibers. Figure 2.2. Macro-bend coupling effect between
Actually, the two closely bending fibers. Actually,the theenergy energycoupling couplingsituation situationisisvery verycomplex complexbetween between the two closely bending fibers. When macro-bendinghappens, happens, more energy radiates of the transmitting fiber.at When fiber fiber macro-bending more energy radiates outsideoutside of the transmitting fiber. Refracted Refracted at cladding-environment andinto coupling intofiber, receiving fiber,outside it radiates outside of cladding-environment surface andsurface coupling receiving it radiates of the receiving the receiving fiber. However, energy is ignored because it is energy of the fiber. However, this energy isthis ignored because it is smaller than thesmaller energythan of thethe transmitting fiber transmitting coupled receiving Therefore, only the fiber energy of transmitting fiber coupled intofiber receiving fiber.into Therefore, onlyfiber. the energy of transmitting coupling into the receiving coupling into the receiving fiber should require our attention. theand coupling coefficient is C, and fiber should require our attention. So, the coupling coefficientSo, is C, the energy coupled into the the energy coupled into the receiving fiber is expressed as: receiving fiber is expressed as: (5) PP1 1=P0Pα01αC1 C (5) where α1 is the loss coefficient of transmitting fiber. where At α1 the is the losstime, coefficient of transmitting same radiation occurs in the fiber. receiving fiber in a similar way. Because there are mainly At the same time, radiation occurs in the receiving fiber inequivalent a similar to way. Because there higher order modes, the transmission loss cannot be casually transmitting fiber are loss. mainly higher order modes, the transmission loss cannot be casually equivalent to transmitting fiber loss. The loss coefficient of the higher-order modes for the step-index optical fiber is expressed as [15]: The loss coefficient of the higher-order modes for the optical fiber is expressed as [15]: " step-index 3/2 # 2 2r P0 = 2n1 k(θ2c − θ2 ) exp −2 n1 kR θ2c − θ2 − 2r 3 2 (6) P 2n k(θ 2 θ 2 ) exp 3n kR θ 2 θ 2 R (6) 0
1
c
3
1
c
R
Then output power at the free end of the receiving fiber can be expressed as: Then output power at the free end of the receiving fiber can be expressed as: P2 = P1 (1 − α2 ) = P0 α1 C (1 − α2 )
P2 P1 1 α2 P0α1C 1 α2
(7) (7)
where α2 is the loss coefficient of receiving fiber. where As α2 is thebeloss coefficient of receiving fiber. can seen from aforementioned equations, the energy coupling and transmission loss take Asbetween can be seen aforementioned equations, the energy the coupling transmission loss take place two from close fibers, and according to the calculation, outputand power of the receiving fiber place between two close fibers, and according to the calculation, the output power of the receiving changes directly with the displacement, which realizes displacement sensing based on this principle. fiber changes directly with the displacement, which realizes displacement sensing based on this 3. Experiment and Results principle. A single-fiber macro-bending structure for a displacement sensing system is shown conceptually 3. Experiment and Results in Figure 3a, with one end of the fiber connected to a Light Source (LS) and another end connected single-fiber macro-bending structure for a with displacement sensing is shown to aAPower Meter (PM), all parameters are identical Figure 1 except the system light source is laser. conceptually in the Figure 3a, with one end of the fiber to a increase, Light Source (LS) and another end The radius of macro-bend decreases with the connected displacement the output power changes connected to a Power and Meter (PM), all parameters identical with Figure the light source become disorderly unsystematic. Becauseare the background noise 1ofexcept the transmitting fiberisis laser. Thecomposed radius of of thecore macro-bend decreases influenced with the displacement increase, the output itpower mainly mode fluctuations, by the light source fluctuations, shows changes become disorderly unsystematic. Because the abackground noise of transmitting poor signal-to-noise ratio. and Especially in the case of using laser light source, thethe laser echoes the fiber is mainlywhich composed of in core fluctuations, bylarge the light source fluctuations, it interference, results themode laser output powerinfluenced undergoing fluctuations. To use the LED
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shows2017, poor ratio. Especially in the case of using a laser light source, the laser echoes Sensors 17,signal-to-noise 196 5 of 8 shows poor signal-to-noise ratio. Especially in the case of using a laser light source, the laser echoes the interference, which results in the laser output power undergoing large fluctuations. To use the the interference, which results in the laser output power undergoing large fluctuations. To use the LED as a light source is feasible, and the experimental result is shown in Figure 3b, while the change LED a light source is feasible, and the experimental result is shown in Figure 3b, while the change as a as light is feasible, experimental is shown Figure 3b, while the change rate rate of thesource output power ofand thethe fiber end duringresult outbound and in backhaul is only 0.02%. So a laser rate of output the output power of fiber the fiber end during outbound and backhaul is only 0.02%. So a laser of the power of the end during outbound and backhaul is only 0.02%. So a laser light light source is replaced by an LED source in the experiment, and a single fiber macro-bend is not light source is replaced an source LED source the experiment, and a fiber singlemacro-bend fiber macro-bend is not source replaced by anby LED in the in experiment, and a single is not suitable suitableisfor displacement detection. suitable for displacement detection. for displacement detection.
(a) (a)
(b) (b)
Figure 3. System of single fiber displacement sensor (a); Output power changes with displacement (b). Figure Figure3.3.System Systemofofsingle singlefiber fiberdisplacement displacementsensor sensor(a); (a);Output Outputpower powerchanges changeswith withdisplacement displacement(b). (b).
The Beam Quality Analyzer (BC106N-VIS/M, Thorlabs) used for analyzing the energy coupling The Beam Quality Analyzer (BC106N-VIS/M, Thorlabs) used for analyzing the energy coupling and distribution of the transmitting fiber and receiving fiber of twofor twisted opticthe fibers is also shown The Beam Quality Analyzer (BC106N-VIS/M, Thorlabs) used analyzing energy coupling and distribution of the transmitting fiber and receiving fiber of two twisted optic fibers is also shown in Figure 4. Lightofintensity at the end of the fiber and twisted the receiving fiber shown on the and distribution the transmitting fiber andtransmitting receiving fiber of two optic fibers is also shown in Figure 4. Light intensity at the end of the transmitting fiber and the receiving fiber shown on the Beam Quality Analyzer change with the displacement. Figure.4a shows the light intensity in Figure 4. Light intensity at the end of the transmitting fiber and the receiving fiber shown on the Beam Quality Analyzer change with the displacement. Figure.4a shows the light intensity distribution the transmitting fiberthe when the displacements areshows 0 mm,the 45light mm,intensity 90 mm and 135 mm. Beam QualityofAnalyzer change with displacement. Figure 4a distribution distribution of the transmitting fiber when the displacements are 0 mm, 45 mm, 90 mm and 135 mm. center to fiber edgewhen of thethe figure corresponds the optical core cladding. of theThe transmitting displacements are to 0 mm, 45 mm, fiber 90 mm andto135 mm. The light The center to edge of the figure corresponds to the optical fiber core to cladding. The light intensity gradually weakens from the center to the edge. Figure 4a shows an output power the The center to edge of the figure corresponds to the optical fiber core to cladding. Theoflight intensity gradually weakens from the center to the edge. Figure 4a shows an output power of the transmitting fiber that can befrom obtained with this system. the4agraph, energy of intensity gradually weakens the center to the edge.From Figure showsthe an mode outputfield power of the transmitting fiber that can be obtained with this system. From the graph, the mode field energy of transmitting fiber fiber that mainly thethis core, which From is determined themode multimode fiber transmitting canconcentrates be obtained in with system. the graph,bythe field energy transmitting fiber mainly concentrates in the core, which is determined by the multimode fiber transmission characteristics The center changes with radius by of the on a of transmitting fiber mainly[16,17]. concentrates in theenergy core, which is determined the macro-bend multimode fiber transmission characteristics [16,17]. The center energy changes with radius of the macro-bend on a small scale, characteristics but shifts significantly with the energy light source which means a low transmission [16,17]. The center changesfluctuations, with radius of the macro-bend on small scale, but shifts significantly with the light source fluctuations, which means a low contribution to the macro-bend coupling effect. Therefore, when a single fiber is used for a small scale, but shifts significantly with the light source fluctuations, which means a low contribution contribution to the macro-bend coupling effect. Therefore, when a single fiber is used for displacement detection, the signal-to-noise ratio is poor and fiber the output power scarcely changes with to the macro-bend coupling effect. Therefore, when a single is used for displacement detection, displacement detection, the signal-to-noise ratio is poor and the output power scarcely changes with displacement. the signal-to-noise ratio is poor and the output power scarcely changes with displacement. displacement.
Figure 4. Response Responseofofthe the transmitting receiving (b) fiber at four different displacements: transmitting (a)(a) andand receiving (b) fiber at four different displacements: (1) d Figure 4.0 Response of themm; transmitting (a) and(4) receiving (b) fiber at four different displacements: (1) d (1) d = mm; (2) d = 45 (3) d = 90 mm; d = 135 mm. = 0 mm; (2) d = 45 mm; (3) d = 90 mm; (4) d = 135 mm. = 0 mm; (2) d = 45 mm; (3) d = 90 mm; (4) d = 135 mm.
As shown in Figure 4b, the receiving fiber retains no energy when the displacement is 0 mm, and, with enhanced displacement, the light intensity increases gradually. The mode field is distorted,
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As shown in Figure 4b, the receiving fiber retains no energy when the displacement is 0 mm, and, with enhanced displacement, the light intensity increases gradually. The mode field is Sensors 2017, 17, 196 6 of 8 distorted, and the main energy concentrates near the cladding, demonstrating that the energy is coupling from the transmitting fiber due to the macro-bend effect of two twisted fibers. This energy is modulated by the concentrates macro-bend near radius, the signal-to-noise ratio is the high. Thereisare three main and the main energy theso cladding, demonstrating that energy coupling from reasons to explain why the intensity distribution is twisted irregular. The This first reason that the POFs the transmitting fiber due to light the macro-bend effect of two fibers. energy is modulated by are isotropic, but the macro-bend structure is “anisotropic”. The second reason is that the energy the macro-bend radius, so the signal-to-noise ratio is high. There are three main reasons to explain coupled into intensity the receiving fiber varies since the changes the different macro-bend why the light distribution is irregular. The energy first reason is thatwith the POFs are isotropic, but the position of the transmitting fiber. The The last second reason reason is that is the complex mode field distribution of the macro-bend structure is “anisotropic”. that the energy coupled into the receiving multimode fiber, the when the light fieldwith changes by the macro-bend, a more complex energy fiber varies since energy changes the different macro-bendproduces position of the transmitting fiber. distribution field. Thus, the energy distribution of the receiving fiber is fiber, morewhen complex thanfield the The last reason is that the complex mode field distribution of the multimode the light transmitting fiber. changes by the macro-bend, produces a more complex energy distribution field. Thus, the energy As in the above results, energy of thethan receiving fiber changes distribution of the receiving fiberthe is more complex the transmitting fiber. significantly with the displacement. plastic opticalthefiber is easy to bend, a twisted is more stable, andthe a As in theAs above results, energy of the receiving fiber structure changes significantly with two twisted optic fibers structure for displacement sensing is adopted. Figure 1 shows the schematic displacement. As plastic optical fiber is easy to bend, a twisted structure is more stable, and a of the experimental setup. The free of two twisted move Figure forward at a constant speed, two twisted optic fibers structure for ends displacement sensingfibers is adopted. 1 shows the schematic while radius of the macro-bend thetwisted fiber moves, this processatisacalled outbound. of the the experimental setup. The freeincreases ends of as two fibers and move forward constant speed, Then the radius fiber isof released at a constant speed the moves, backhaul with isthe radius of the while the macro-bend increases as theinfiber andprocess this process called outbound. macro-bend The prototype has beenprocess completed andradius the result shown in Then the fiberincreasing is releasedgradually. at a constant speed in the backhaul with the of the is macro-bend Figure 5. gradually. The prototype has been completed and the result is shown in Figure 5. increasing
Figure 5. Output power of receiving fiber changes with displacement.
The fitting fitting curve curve proposed proposed by by MATLAB MATLAB simulation, simulation, is is The 3 2 P2 (d) P20.003d 30.0005d 0.979d 282.2139 (d) = 0.003d + 0.0005d2 +0.979d + 282.2139
(8) (8)
In the experiment, the light source power is set at 39.027 mW. Although the output power of the In the experiment, the light source power is set at 39.027 mW. Although the output power of receiving fiber is only of nW, the resolution of the Power Meter at 1 nW is enough to be detected. The the receiving fiber is only of nW, the resolution of the Power Meter at 1 nW is enough to be detected. motorized stage is set to draw the free end of two twisted fibers at a constant speed of 2 mm/s, and The motorized stage is set to draw the free end of two twisted fibers at a constant speed of 2 mm/s, the power meter linked to the free end of the receiving fiber is used to detect the output power of and the power meter linked to the free end of the receiving fiber is used to detect the output power receiving fiber at the same time. From the result of Figure 5, under the displacement range of of receiving fiber at the same time. From the result of Figure 5, under the displacement range of 0–140 mm, the output power of the receiving fiber increases gradually, and the output power shift is 0–140 mm, the output power of the receiving fiber increases gradually, and the output power shift approximately linear with a displacement of 110 mm–140 mm. The sensitivity is 19.805 nW/mm; is approximately linear with a displacement of 110 mm–140 mm. The sensitivity is 19.805 nW/mm; accuracy, 0.12 mm resolution, respectively. For the displacement from 140 mm to 0 mm, the output accuracy, 0.12 mm resolution, respectively. For the displacement from 140 mm to 0 mm, the output power decreases in real time, while the systematic retrace error is less than 0.05 nW/mm in the power decreases in real time, while the systematic retrace error is less than 0.05 nW/mm in the experiment. When the fiber end is drawn at different speeds of 2 mm/s, 6 mm/s, 10 mm/s, as shown experiment. When the fiber end is drawn at different speeds of 2 mm/s, 6 mm/s, 10 mm/s, as shown in Figure 6a, the displacement-output power curve shows a slight overall decline. in Figure 6a, the displacement-output power curve shows a slight overall decline.
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(a)
(b)
Figure 6. power of receiving fiberfiber changes with with displacement at different speeds speeds (a); Output Figure 6. Output Output power of receiving changes displacement at different (a); power of receiving fiber changes with displacement at different temperatures (b). Output power of receiving fiber changes with displacement at different temperatures (b).
Temperature is an important factor in the external environment for displacement application. Temperature is an important factor in the external environment for displacement application. As the normal operating temperature of plastic optical fiber increases up◦ to 70 °C, the sensor is As the normal operating temperature of plastic optical fiber increases up to 70 C, the sensor is affected affected by temperature (from 25 °C to 70 °C) as shown in Figure 6b. With an increase of the by temperature (from 25 ◦ C to 70 ◦ C) as shown in Figure 6b. With an increase of the temperature, temperature, the displacement-output power curve shows an overall decline, and the sensitivity is the displacement-output power curve shows an overall decline, and the sensitivity is also decreased. also decreased. Because of the rising temperature, the light performance of the plastic optical fiber Because of the rising temperature, the light performance of the plastic optical fiber gets worse, and the gets worse, and the coupling capacity between the two twisted fibers is reduced. From the coupling capacity between the two twisted fibers is reduced. From the experimental results above, experimental results above, this system is used with displacement sensors during this development this system is used with displacement sensors during this development effort within a stable structure. effort within a stable structure. 4. Conclusions 4. Conclusions A novel optical fiber wide-range displacement sensor based on a macro-bend coupling effect A novel optical which fiber wide-range displacement sensor on aAccording macro-bend coupling effect has been developed, exhibits a good robustness and based low cost. to the principle of has been developed, which exhibits a good robustness and low cost. According to the principle of coupling between two closely optical fibers, a two twisted fibers sensing structure is designed. A Beam couplingAnalyzer betweenwas twoused closely optical the fibers, a two twistedand fibers sensing structure designed. A Quality to analyze energy coupling distribution of the twoisfibers to find Beam Quality Analyzer was used to analyze the energy coupling and distribution of the two fibers out that the fiber which has no intensity originally generates a lot of light intensity, which changes to find out that the fiber which has no intensity originally generates a lot of light intensity, which with the displacement. This structure avoids the sensing signal shifts influenced by visible light and changes with the displacement. This structure avoids the sensing signal shifts influenced by visible light sources and realizes the displacement measurement within a wide range of 0–140 mm. Moreover, light and light sources and realizes the displacement measurement within a wide range of 0–140 it is effective and stable at different temperatures and speeds. The output power is approximately mm. Moreover, it is effective and stable at different temperatures and speeds. The output power is linear with displacement of 110 mm–140 mm under room temperature and 2 mm/s speed with approximately linear with displacement of 110 mm–140 mm under room temperature and 2 mm/s 19.805 nW/mm sensitivity and 0.12 mm resolution. Compared to other sensors, the production process speed with 19.805 nW/mm sensitivity and 0.12 mm resolution. Compared to other sensors, the of this sensor is very simple, and immune to electromagnetic interference. Further work, such as production process of this sensor is very simple, and immune to electromagnetic interference. compensation for the temperature change and quantitative analysis of mutual coupling of modes and Further work, such as compensation for the temperature change and quantitative analysis of mutual interference in multimode fibers, is in progress. coupling of modes and interference in multimode fibers, is in progress. Acknowledgments: This work was supported by the National Science Fund for Distinguished Young Scholars (No. 51425505) and the National Natural SciencebyFoundation of China 51405454 and No. 51275491). Acknowledgments: This work was supported the National Science(No. Fund for Distinguished Young Scholars (No. 51425505) and the National Natural Science Foundation of China (No. 51405454 and No. 51275491). Author Contributions: Jia Liu, Yulong Hou and Wenyi Liu conceived and designed the experiments; Shan Su performed the experiments; Huixin Zhang and Guocheng Fang analyzed the data; Pinggang Jia contributed Author Contributions: Jia Liu, Yulong Hou and Wenyi Liu conceived and designed the experiments; Shan Su materials and analysis tools; Jia Liu wrote the paper. performed the experiments; Huixin Zhang and Guocheng Fang analyzed the data; Pinggang Jia contributed Conflicts Interest: authors declare materials of and analysisThe tools; Jia Liu wroteno theconflict paper. of interest.
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