sensors Article

High Precision Temperature Insensitive Strain Sensor Based on Fiber-Optic Delay Ning Yang, Jun Su *, Zhiqiang Fan and Qi Qiu School of OptoElectronic information, University of Electronic Science and Technology of China, Chengdu 610054, China; [email protected] (N.Y.); [email protected] (Z.F.); [email protected] (Q.Q.) * Correspondence: [email protected]; Tel.: +86-28-8320-1111 Academic Editor: Vittorio M. N. Passaro Received: 8 March 2017; Accepted: 28 April 2017; Published: 2 May 2017

Abstract: A fiber-optic delay based strain sensor with high precision and temperature insensitivity was reported, which works on detecting the delay induced by strain instead of spectrum. In order to analyze the working principle of this sensor, the elastic property of fiber-optic delay was theoretically researched and the elastic coefficient was measured as 3.78 ps/km·µε. In this sensor, an extra reference path was introduced to simplify the measurement of delay and resist the cross-effect of environmental temperature. Utilizing an optical fiber stretcher driven by piezoelectric ceramics, the performance of this strain sensor was tested. The experimental results demonstrate that temperature fluctuations contribute little to the strain error and that the calculated strain sensitivity is as high as 4.75 µε in the range of 350 µε. As a result, this strain sensor is proved to be feasible and practical, which is appropriate for strain measurement in a simple and economical way. Furthermore, on basis of this sensor, the quasi-distributed measurement could be also easily realized by wavelength division multiplexing and wavelength addressing for long-distance structure health and security monitoring. Keywords: fiber-optic delay; strain sensor; temperature insensitive; elastic coefficient

1. Introduction In order to ensure the safety of personal and public property, the precise and real-time monitoring of strain becomes more and more important in all kinds of engineering applications, such as chemical plants, gas stations, power stations, bridges, tunnels, oil pipelines, etc. [1–5]. In general, these application environments full of poisonous gas, intense radiation, and elevated temperature are dangerous to human health, so safe and efficient remote monitoring of strain is of great significance. Compared with conventional electrical sensing methods, an optical fiber strain sensor is more suitable for present applications because of its compact size, high sensitivity, multiplexing capability, immunity to electromagnetic interference, high temperature tolerance, and resistance to harsh environments. As a result, different types of fiber optic-based strain sensors have attracted attention from all over the world during recent decades. Up to now, a great amount of optical fiber strain sensors have been reported and partially commercialized. When concerning the difficulty levels of system structure and measuring principle, the Mach-Zehnder (M-Z) interferometer-based strain sensor is the simplest with very high strain sensitivity, but the cross-effect of temperature and strain is very hard to avoid. To overcome the drawback, a special fiber is used for strain measurement, which has a diameter of only 5 µm. The diameter of this fiber is much smaller than that of a typical single mode fiber (SMF), so that this fiber is extremely insensitive to environmental temperature [6,7]. For realizing the miniaturization of the system structure, the fiber in-line M-Z interferometer has become the main research focus in this field. Currently, the technical methods to realize this kind of fiber in-line M-Z structure are various, like the single-mode-multimode-single-mode structure [8,9], the mode mismatched fusion [10,11], and the Sensors 2017, 17, 1005; doi:10.3390/s17051005

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waist distorted subuliform fiber [12,13]. Furthermore, a fiber in-line M-Z interferometer is verified to have a strain sensitivity of 0.43 µε within the range of 500 µε [14]. In addition, a strain sensitivity of 15 µε and a tempereture sensitivity of 10 ◦ C within the range of 500 µε are obtained in another fiber in-line M-Z interferometer [15]. Similarly, the fiber in-line Fabry–Pérot (F-P) interferometer is also a research focus in this field. In terms of fabrication, the structure of the fiber in-line F-P interferometer is easier to realize with natural temperature insensitivity; thus it is more suitable for a fiber-optic strain sensor. At present, the research focus of this technology is to simplify the fabrication process and broaden the shape of the F-P cavity (not limited to a rectangular cavity), in ways such as using micro-electromechanical systems (MEMS) as the two reflecting surfaces of F-P cavity [16,17], using a CO2 laser or a femtosecond pulse laser for micro-structure fabrication [18] or the assistant chemical corrosion [19] and so on. Additionally, the fiber in-line F-P interferometer is able to realize a strain sensitivity of 13.5 µε [20], a sensitivity of 19.6 µε at the range of 600 µε [21], and a sensitivity of 10 µε [22]. However, the fiber in-line F-P interferometer is still not suitable for commercial applications right now becasuse of its high cost. On the contrary, Fiber Bragg Grating (FBG) has become the most mainstream technique, developed in an economic way to be applied in bridges, concrete, and dams for strain measurement. Nevertheless, the cross-effect of temperature and strain is a big issue as well for strain measurement. At present, the commonly used solutions are utilizing speical matrials or structures to make FBG temperature insensitive [23,24] or introducing one more FBG as reference [25]. In addition, the strain sensitivity of FBG could be as high as 3 µε. Similarly, the Brillouin optical time-domain reflectometer-based (BOTDR) distributed strain sensor is also marred by the cross-effect of temperature and strain [26–28], the performance of which has reached a spatial resolution of 5 cm and a strain sensitivity of 63 µε [29,30]. At present, the biggest problem with this technology is that the higher the spatial resolution required, the narrower the pulse laser that is needed, which may limit its transmission distance. As a result, the high cost and high requirement of the sensor system make this technology uncompetitive. Furthermore, with the rapid developement of these sensor technologies, fiber-optic strain sensors have been widely applied for structural monitoring in recent years. Among these applications, BOTDR and FBG techniques are the most commonly used for distributed and quasi-distributed monitoring, respectively [31]. Glisic performed a large scale test on a 13 m long concret pipeline with an exterior diameter of 30.48 cm, and a BOTR-based distributed sensor was placed along its length [32]. The main goal of this work is to achieve real-time monitoring of pipelines that are subject to permanent ground displacements induced by earthquakes. In addition, by addressing the effects of the initial non-circular cross section of a pipeline under internal pressure, the cross deformation of this non-circular pipeline was measured with a BOTDR-based distributed sensor deployed helically on it [33]. Except for pipelines, the health monitoring of bridges is also of great significance. During the construction of the Streicker Bridge, a distributed sensor and many FBG sensors were embedded in the concrete. These sensors work to acquire the important data related to the global performance of the structure, i.e from the early behavior of the concrete to the identification of damage, which is unprecedented [34]. In another application, a multiscale fiber-optic sensing network composed by FBG- and BOTDR-based sensors is employed to realize a large measurement range and to achieve a higher sensitivity [35]. Moreover, in practical applications, the sensing capability could be enhanced by incorporating distribued sensors and FBG sensors, and this combination is effective for achieving a larger measurement range [36]. Compared with all these optical fiber strain sensors mentioned above, the strain sensor proposed in this paper uses a normal single-mode fiber as the sensing and transmission medium, which makes it more cost-efficient and practical. This sensor no longer relies on precise spectrum measurement but realizes strain monitoring by measuring the phase delay induced by strain. Due to the compact size and low price of phase delay detector, this sensor is easy to integrate. In addition, this sensor could achieve a higher strain sensitivity without being affected by the cross-effect of temperature. As a result,

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when this strain sensor is used for monitoring infrastructures, because of its basic properties, an overall low cost and high precision could be achieved with self-temperature compensation. The working principle of this strain sensor endows itself with a higher environmental tolerance and a low spatial limit. In addition, quasi-distributed strain measurement can be achieved through wavelength division multiplexing and wavelength addressing, so this sensor also shows great potential for long distance structure health and security monitoring. 2. Theoretical Basis and Sensing Principle 2.1. Theoretical Basis of Fiber-Optic Delay For a stable optical fiber that is isotropic, uniform, and linear, its optical properties are very stable when not being affected by mechanical stress, and that means that the optical fiber has a constant refractive index profile (RIP). However, when being affected by mechanical stress, the RI of the fiber will be changed, and the variation of RI is the explicit function of the stress tensor. In the Cartesian coordinate system, the strain tensor has six independent components, which are three axial components, ε xx , ε yy , and ε zz (i = j), and three shear components, ε yz , ε zx , and ε xy (i 6= j). Similarly, the stress tensor also has six independent components, which are σxx , σyy , and σzz and σyz , σzx , and σxy . Due to Hooke’s law, under the range of elastic deformation, strain is linearly related to stress, and the relationship can be expressed as: 6

εi =

∑ hij δj

(i, j = xx, yy, zz, yz, zx, xy),

(1)

j =1

where each coefficient, according to the symmetry of coordinate axis, has an inner connection as hij = h ji instead of being absolutely independent. However, in most of the practical instances in which the optical fiber may be affected by mechanical stress, the fiber is commonly placed or embedded in building walls, bridges, concrete, or some other enclosed structure, being used as a sensitive component to realize the measurement of strain or stress [37,38]. Under this condition, because of the special properties and characterizations of these enclosed structures, the shear deformation can be ignored and only the longitudinal stress is concerned (σx = σy = 0), so that the relationship between strain and stress can be simplified into [39]: 

  εx 1 F     εy  =  −υ AY εz 1

    −υ −υ 0 −υ F     1 −υ   0  =  −υ . AY −υ −υ 1 1

(2)

Here, Y is the Young’s modulus, υ is the Poisson’s ratio, F is the longitudinal mechanical force, and A is the cross-sectional area of fiber. In addition, the variation of RI can be expressed as: 

  ∆n x p11 1 −2    ∆( 2 ) = 3  ∆ny  =  p12 n n ∆nz p12

p12 p11 p12

    p12 εx p11 ε x + p12 (ε y + ε z )     p12  ε y  =  p11 ε y + p12 (ε x + ε z ) . p11 εz p11 ε z + p12 (ε x + ε y )

(3)

Introducing Equation (2) into Equation (3), the variation of RI could be finally obtained as: 

   ∆n x (1 − υ) p12 − υp11 3 −n F      ∆ny  =  (1 − υ) p12 − υp11 . 2AY p11 − 2υp12 ∆nz

(4)

As for a single-mode optical fiber, only the fundamental mode could transmit in the fiber, and it consists of two modes with perpendicular polarization directions, which are LPX 01 and LPY 01 ,

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respectively. Since the light waves transmitting in the single-mode fiber are substantially transverse waves, the variation of RI approximately satisfies ∆n = ∆n x = ∆ny so as to derive its expression as: ∆n =

−n3 [(1 − υ) p12 − υp11 ] ε z = γnε z , 2

(5)

where p12 and p11 are the elastic-optic parameter of fiber and γ = −n2 [(1 − υ) p12 − υp11 ]/2 can be regarded as the effective elastic-optic coefficient. In addition, when transmitting in a certain length of optical fiber, the optical signal will be delayed and the delay is determined by the optical path. If the fiber dispersion is not considered, the delay of the optical signal can be expressed as τ = Ln/c, where L is the length of optical fiber, c is the speed of light in a vacuum, and n is the refraction index of the optical fiber. In fact, fiber optic delay is strain dependent because of its elastic property, so that the variation of delay is: ∆τ =

(n + ∆n)( L + ∆L) nL − . c c

(6)

Here, ∆L and ∆n are the change of length and the refractive index of fiber caused by the longitudinal stress, respectively, and the equation meets the condition ∆n · ∆L < 0. Furthermore, because the longitudinal deformation is so small that ∆L and ∆n are both infinitesimal, the approximate expression ∆L · ∆n ≈ 0 is obtained. Consequently, the variation of delay can be calculated using Equations (5) and (6): ∆L · n ∆τ = (1 + γ ). (7) c In general, the value of the effective elastic-optic coefficient meets, −1 < γ < 0 and it indicates that the optical fiber delay is supposed to monotonically increase when the fiber is stretched. Here, the elastic coefficient of fiber-optic delay is defined as J = (1 + γ) · n/c, so Equation (7) could be simplified into ∆τ = JLε. Moreover, optical fiber delay is also temperature-dependent due to its thermo-optical property and thermal-expansion property, thus the total differential form of delay is: ∆τ = (

L dn n dL + )∆T, c dT c dT

(8)

where T is temperature. Actually, the first item, dn/dT, stands for the thermo-optical property of the fiber and the second item, dL/LdT, stands for the thermal-expansion property of the fiber. Due to the fact that the value of the thermal-expansion coefficient is much smaller than that of the thermo-optical coefficient for the standard SMF-28 single-mode fiber [40], the thermal coefficient of fiber-optic delay could be similarly defined as K = dn/cdT [41] so as to further simplify Equation (8) into ∆τ = KL∆T. Therefore, the variation of fiber-optic delay induced by temperature and strain could be synthetically expressed as: ∆τ = JLε + KL∆T. (9) 2.2. Fiber-Optic Delay Based Sensing Principle According to the theoretical analysis above, a high precision detection system was designed to measure the elastic coefficient and the thermal coefficient of fiber-optic delay, and the schematic of the proposed detection system is shown in Figure 1. The detection system is composed of a vector network analyzer and an optical transceiver module, wherein the vector network analyzer is used to compare the two microwave signals of input and output ports and then the inner calculating module of vector network analyzer can work on translating the phase difference between the two microwave signals into the time delay of the entire measuring transmission optical path.

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Figure 1. 1. The The schematic schematic of of the the proposed proposed high high precision precision optical optical fiber fiber delay delay detection detection system system based based on on Figure the frequency frequencydomain domainphase phasemethod. method. the

More specifically, the offset compensation function of the vector network analyzer is utilized More specifically, the offset compensation function of the vector network analyzer is utilized during the practical measurement process, and the basic operation could be described as: the optical during the practical measurement process, and the basic operation could be described as: the optical signal is modulated by the microwave signal from port.1; after that, the modulated optical signal signal is modulated by the microwave signal from port.1; after that, the modulated optical signal transmits through the measuring optical path and is de-modulated into a microwave signal, transmits through the measuring optical path and is de-modulated into a microwave signal, importing importing into port.2. By sampling and calculating, the phase difference between the input and into port.2. By sampling and calculating, the phase difference between the input and output microwave output microwave signals could be obtained, and the vector network analyzer could work on signals could be obtained, and the vector network analyzer could work on introducing extra time delay introducing extra time delay to compensate the measured phase difference. Therefore, the phase to compensate the measured phase difference. Therefore, the phase difference between the two signals difference between the two signals can be finally eliminated by turning the compensation time can be finally eliminated by turning the compensation time delay, and the current compensation value delay, and the current compensation value is equal to the time delay of the measuring optical path. is equal to the time delay of the measuring optical path. By using the method above, the relative delay of fiber was measured by the vector network By using the method above, the relative delay of fiber was measured by the vector network analyzer within a tensile force range of 1 N to 6.5 N and with an increment step of 0.5 N. Figure 2 analyzer within a tensile force range of 1 N to 6.5 N and with an increment step of 0.5 N. Figure 2 demonstrates the experimental response of the relative delay for the rise of the tensile force, and the demonstrates the experimental response of the relative delay for the rise of the tensile force, and the variation was recorded with an increment of 0.5 N. Furthermore, the linear fit of the elastic property variation was recorded with an increment of 0.5 N. Furthermore, the linear fit of the elastic property of fiber-optic delay is presented in Figure 2 as well, wherein the standard SMF-28 type single-mode of fiber-optic delay is presented in Figure 2 as well, wherein the standard SMF-28 type single-mode fiber, produced by Corning Inc. (New York, NY, USA), was chosen as the measuring fiber for which fiber, produced by Corning Inc. (New York, NY, USA), was chosen as the measuring fiber for which the refractive index is is about 1.468, Young’s modulus is 65 GPa, the core diameter is 125 μm, and the refractive index is is about 1.468, Young’s modulus is 65 GPa, the core diameter is 125 µm, and the initial unstressed length is 15.5 cm. The experimental results indicate that the measured elastic the initial unstressed length is 15.5 cm. The experimental results indicate that the measured elastic coefficient is 0.736 ps/N and the relative delay linearly increases with the increment of longitudinal coefficient is 0.736 ps/N and the relative delay linearly increases with the increment of longitudinal strain, which is a proof of the theoretical analysis above. According to Hooke’s law, the longitudinal strain, which is a proof of the theoretical analysis above. According to Hooke’s law, the longitudinal strain is   F (Y  A) , so the elastic coefficient could be further obtained as J = 3.78 ps/km·με. As for strain is ε = F/(Y · A), so the elastic coefficient could be further obtained as J = 3.78 ps/km·µε. As for 0.113,pp12 == 0.252 0.252 and and υυ == 0.17, 0.17, its its the material material of of the the fiber, fiber,the theelastic elasticparameters parametersofofwhich whichare arepp11==0.113, the 11 12 c , the effective elastic-optic elastic-opticcoefficient coefficientisisγγ==−−0.22. elastic coefficient is effective 0.22. Combined Combined with with JJ= ((1 1 +γ) )n· n/c, the elastic coefficient calculated as J = 3.82 ps/km·με with an experimental error of 0.04 ps/km·με. is calculated as J = 3.82 ps/km·µε with an experimental error of 0.04 ps/km·µε. Based on onthe the same experimental presented in Figure 1, the coefficient thermal coefficient of Based same experimental setupsetup presented in Figure 1, the thermal of fiber-optic ◦ ◦ ◦ fiber-optic delay was measured in the temperature range from −30 ℃ to 70 ℃ with an increment delay was measured in the temperature range from −30 C to 70 C with an increment step of 3 C step of 3 ℃ the by same utilizing the same optical as in thesample, measuring the initial length which by utilizing optical fiber as in thefiber measuring the sample, initial length of which is of 95.15 m. is 95.15 m. Figure 3 presents the experimental responsefor ofthe delay forand theindicates rise of Figure 3 presents the experimental response of delay difference rise ofdifference temperature and indicates a thermal atemperature thermal coefficient of about K = 39.2coefficient ps/km·◦ C.of about K = 39.2 ps/km·℃. As aaresult, result,on onthe thebasis basisofofEquation Equation(9), (9),ififthe theinitial initial unstressed length L and elastic coefficient As unstressed length L and elastic coefficient J ofJ of a sensing fiber are known, the strain can be measured by monitoring the change of fiber-optic a sensing fiber are known, the strain can be measured by monitoring the change of fiber-optic delay in delay in an experimental environment withtemperature. a stable temperature. an experimental environment with a stable

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Figure 2. The experimental response of relative delay for the rise of the longitudinal tensile force.

Figure 2. The experimental response delayfor forthe therise rise longitudinal tensile Figure 2. The experimental responseof ofrelative relative delay ofof thethe longitudinal tensile force.force.

Figure 3. The experimental response of relative delay for the rise of temperature. Figure 3. The experimental response of relative delay for the rise of temperature.

Figure 3. The experimental response of relative delay for the rise of temperature. 3. Design and Analysis of Strain Sensor 3. Design and Analysis of Strain Sensor 3. Design and of Analysis of Strain Sensor 3.1. Design Strain Sensor 3.1. Design of Strain Sensor Based on the discussion above, the relationship between delay and strain is set up, and the 3.1. Design of Strain Sensor discussion above, the between delaydue andtostrain is set and the strainBased couldon be the measured by detecting the relationship change of delay. However, Equation (9),up, fiber-optic Based on the discussion above, the relationship between delay and strain is set up, and the strain could be measured by detecting the change of delay. However, due to Equation (9), fiber-optic delay is both strain-dependent and temperature-dependent, so the measurement of strain will bestrain delay is both strain-dependent and temperature-dependent, so the measurement of strain will bedelay couldaffected be measured by detecting the change as of well. delay. due to Equation (9), fiber-optic by the cross-effect of temperature ToHowever, solve this problem, an extra reference optical affected by the cross-effect of temperature as well. To solve this problem, an extra reference optical path is introduced to predigest this process by detecting difference of optical is both strain-dependent and temperature-dependent, sothe thedelay measurement oftwo strain willsignals be affected path is introduced to predigest this process detecting delay difference two optical signals instead. This schematic process can presented as: this the by the cross-effect of temperature asbe well. Tobysolve problem, an extra of reference optical path is instead. This schematic process can be presented as: introduced to predigest this process by detecting the delay difference of two instead. . optical signals(10) 1   0  JL   1   0    1   2    0   2   JL   1   0   1 presented  0  JL   1 as:  0    1   2    0   2   JL   1   0  . This schematic process can be (10) Here, τ0 and τ1 are the delays of the sensing fiber at strain ε0 and ε1, respectively, and τ2 is the and τ1 arefiber. the delays of the sensing fiber at strain ε0 carrier and ε1,wave respectively, andrelated τ2 is the delayHere, of theτ0reference Furthermore, the(τdelay of the optical is linearly to (10) τ1 − τ0 = JL (ε 1 − ε 0 ) → 1 − τ2 ) − ( τ0 − τ2 ) = JL ( ε 1 − ε 0 ) . delay of the reference fiber. Furthermore, the delay of the optical carrier wave is linearly related to the phase of the modulating signal with a proportionality coefficient of 2πf, so that Equation (10) the phase of the modulating signal with a proportionality coefficient of 2πf, so that Equation (10) could into: of the sensing fiber at strain ε and ε , respectively, and τ is the Here,be τ further and τ transformed are the delays 0 1 2 could be0further 1transformed into: delay of the reference fiber. Furthermore,the delay of the optical carrier wave is linearly related to the ,     2  fJL      (11) 1 0 1 0 1   0  2 fJL   1   0  , of 2πf, so that Equation (10) (11) phase of the modulating signal with a proportionality coefficient could be where Δφ0 and Δφ1 are the obtained phase differences at strain ε0 and ε1, respectively, and f is the further transformed into: where Δφ0 of and Δφ 1 are the obtained differencesthe at strain ε0 and ε1of , respectively, is the frequency the modulating signal.phase Consequently, measurement strain couldand be ffinally ∆φ − ∆φ = 2π f JL ε − ε , (11) ( ) frequency of the modulating signal. Consequently, the measurement of strain could be finally 0 0 1 1 achieved by the detection of phase difference so as to simplify the measurement process. achieved by the detection of phase difference so as to simplify the measurement process.

where ∆φ0 and ∆φ1 are the obtained phase differences at strain ε0 and ε1 , respectively, and f is the frequency of the modulating signal. Consequently, the measurement of strain could be finally achieved by the detection of phase difference so as to simplify the measurement process.

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Sensors 2017, 17,terms, 1005 of 14 In practical the environmental temperature is quite hard to keep stable, and the 7variation of temperature is an insurmountable cross-effect for the measurement of strain. Thus Equation (11) In practical terms, the environmental temperature is quite hard to keep stable, and the variation couldSensors be further as: 2017, 17,rewritten 1005 7 of 14

of temperature is an insurmountable cross-effect for the measurement of strain. Thus Equation (11) could be further rewritten as: In practical terms, the environmental is quite ∆ψ = 2π f JL(temperature ε 1 − ε 0 ) + 2π f K∆Lhard · ∆Tto(tkeep ), stable, and the variation (12) of temperature is an insurmountable  cross-effect 2 fJL   1 for  0  the  2measurement fK L  T (t ) , of strain. Thus Equation (11) (12) could bethe further rewritten as: where ∆ψ is variation of phase difference, ∆L is the length difference between sensing path and where Δψ is the variation of phase difference, ΔL is the length difference between sensing path and reference path, and ∆T(t) is the temperature function another advantage of the   2 fJL  1   0 related  2related  fK to Lto  time. T (t ) ,Hence, function (12) reference path, and ΔT(t) is the temperature time. Hence, another advantage of introduced reference path is path to compensate for theforeffect of temperature on the sensing path, which the introduced reference is to compensate the effect of temperature on the sensing path, where Δψ isthis the variation of phase difference, ΔL is the length temperature difference between sensing path and is beneficial for strain sensor to resist the environmental fluctuations. In addition, which is beneficial for this strain sensor to resist the environmental temperature fluctuations. In reference path, and ΔT(t) is the temperature function related to time. Hence, another advantage of the lengths of the sensing path and reference are urged to be equal. addition, lengths of sensing path andpath reference path are urged to be equal. the introduced reference path is to compensate for the effect of temperature on the sensing path, which is beneficial for this strain sensor to resist the environmental temperature fluctuations. In addition, the lengths of sensing path and reference path are urged to be equal.

Figure 4. The schematic structure of a fiber-optic delay-based strain sensor.

Figure 4. The schematic structure of a fiber-optic delay-based strain sensor.

According to the principle above, a fiber-optic delay based strain sensor is depicted in Figure 4. Figure 4. The schematic structure of a fiber-optic delay-based strain sensor.

In this sensor, the principle optical transmitter composeddelay of two distributed lasers According to the above, a is fiber-optic based strain feedback sensor is(DFB) depicted in with Figure 4. wavelengths of λ a and λ1, respectively. Theoftwo light beams arefeedback coupled and modulated and In thisfixed sensor, the optical transmitter is composed two distributed (DFB) lasers with According to the principle above, a fiber-optic delay based strain sensor is depicted in Figure 4.fixed then pass through the sensing areas behind after being divided by a wavelength division wavelengths of λ and λ , respectively. The two light beams are coupled and modulated and then a the optical 1 In this sensor, transmitter is composed of two distributed feedback (DFB) lasers with pass multiplexer (WDM). The WDM usedbeing in thisdivided sensor is a three-port device, including a com port, a through sensing areas a wavelength division (WDM). fixedthe wavelengths of λabehind and λ1, after respectively. The twoby light beams are coupled andmultiplexer modulated and pass port and a reflect port. The com port is accessible for all wavelengths and is connected to a then pass the sensing areas behind afterincluding being divided a a wavelength division The WDM usedthrough in this sensor is a three-port device, a com by port, pass port and a reflect transmission optical fiber. The pass port is similar to a filter for the wavelength of λ1, being multiplexer (WDM). The WDM used in this sensor is a three-port device, including a com port, port. The com port is accessible for all wavelengths and is connected to a transmission opticala fiber. connected to a sensing fiber, so the light beam λ1 is regarded as the sensing light. On the contrary, pass port port and a reflect The com is accessible forbeing all wavelengths andaissensing connected to aso the The pass similar to aport. filter for the port wavelength connected fiber, the reflectis port is accessible to all wavelengths except of forλλ1i;, thus it is connected to to the reference fiber, transmission optical fiber. The pass port is similar to a filter for the wavelength of λ 1, being light and beam theassensing light.light. On After the contrary, thelight reflect port accessible to all 1 is regarded theλlight beam λa is as used the reference that the two beams areisde-modulated connected to a sensing fiber, so the light beam λ1 is regarded as the sensing light. On the contrary, wavelengths except fora λVector it is connected to the reference and thethe light beam λa is used and imported into Meter (VVM), which is usedfiber, to measure phase difference i ; thusVoltage the reflect port is accessible to all wavelengths except for λi; thus it is connected to the reference fiber, thelight. two After input that microwave with high precision. In addition, a piezoelectric as thebetween reference the twosignals light beams are de-modulated and imported into a Vector and the light beam λa is used as the reference light. After that the two light beams are de-modulated ceramics-based optical fiber stretcher, with athe controlling voltage range of the 0–120 V input and amicrowave radial Voltage (VVM), is used to measure phase difference andMeter imported intowhich a Vector Voltage Meter (VVM), which is used tobetween measure thetwo phase difference deformation resolution of 4 nm, was used to realize the generation and control of strain in signals with high addition, signals a piezoelectric ceramics-based fiber stretcher,this with a between the precision. two input In microwave with high precision. In optical addition, a piezoelectric sensor. controlling voltage range of 0–120 V and a radial deformation resolution of 4 nm, was used to realize ceramics-based optical fiber stretcher, with a controlling voltage range 0–120 V and a radial Tunable Laser(λi) Microwave Source deformation resolution 4 nm, in was used to realize the generation and control of strain in this the generation and control of strain this sensor. sensor. Tunable Laser(λi)

Microwave Source RF

Coupler

Fiber Stretcher

M-Z Modulator

LD (λa)

RF

Coupler

Fiber Stretcher

WDM-λ1

M-Z Modulator A

LD (λa)

Fiber Stretcher

O/E

Vector Voltage Meter

WDM-λ1 B A

O/E O/E

Fiber Stretcher

WDM-λa

WDM-λN

Vector Voltage Meter

Figure 5. The fiber-optic delay based quasi-distributed strain sensor. O/E B

WDM-λa

WDM-λN

Figure 5. The fiber-opticdelay delay based based quasi-distributed strain sensor. Figure 5. The fiber-optic quasi-distributed strain sensor.

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One significant significant advantage advantage of of the the designed designed sensor sensor is is that that it it is cascade-able, cascade-able, which which means means that that aa One quasi-distributed strain strain sensor sensor could could be be simply simply realized realized by by connecting connecting several several basic basic sensor sensor units units in in quasi-distributed series with with slightly slightly modifications. modifications. Figure Figure 55 presents presents the the schematic schematic structure structure of of the quasi-distributed quasi-distributed series strain sensor, sensor, in byby a tunable laser whose wavelengths is λiis(iλ=i (i 1–N) and strain inwhich whichaaDFB DFBlaser laserisisreplaced replaced a tunable laser whose wavelengths = 1–N) there are a pair of WDMs being placed beside each sensing area. In addition, by changing the output and there are a pair of WDMs being placed beside each sensing area. In addition, by changing the wavelength of the tunable laser, each sensing area could measured in sequence. output wavelength of the tunable laser, each sensing areabecould be measured in sequence. 3.2. Calibration Calibration of of Strain Strain 3.2. Before the radial displacement of the in the in controlling voltage Before the sensing sensingexperiment, experiment,thethe radial displacement of stretcher the stretcher the controlling range of 0 V–120 V was tested, and the obtained data is presented in Figure 6. The experimental voltage range of 0 V–120 V was tested, and the obtained data is presented in Figure 6. The results demonstrate (1) its radial not linear with controlling voltage and (2) experimental results that demonstrate thatdisplacement (1) its radial isdisplacement is not linear with controlling during the rising falling of controlling voltage, the displacement at each voltage and (2) and during theprocesses rising and falling processes ofradial controlling voltage, the testing radial voltage point is different, and the displacement curve during the falling process of voltage has a bigger displacement at each testing voltage point is different, and the displacement curve during the curvature. Therefore, whenhas theafiber-optic stretcher Therefore, is used for when strain control, every testing point must falling process of voltage bigger curvature. the fiber-optic stretcher is used be calibrated in advance, and the point fallingmust process voltage is suitable be chosen directly for strain control, every testing be of calibrated inmore advance, andtothe falling for process of verifying the accuracy of the calibration result. voltage is more suitable to be chosen for directly verifying the accuracy of the calibration result.

Figure Figure 6. 6. The The testing testingresults resultsof ofradial radialdisplacement displacementof of this this fiber-optic fiber-optic stretcher stretcher under under the the controlling controlling voltage range of 0–120 V. voltage range of 0–120 V.

Moreover, for the reason that the sensing fiber coiled on the optical fiber stretcher may impede Moreover, for the reason that the sensing fiber coiled on the optical fiber stretcher may impede its its radial displacement, the practical stretched length of the sensing fiber will deviate from the radial displacement, the practical stretched length of the sensing fiber will deviate from the theoretical theoretical value, so that we calibrated at each testing point in the voltage range of 102−24 V with a value, so that we calibrated at each testing point in the voltage range of 102−24 V with a decrement decrement step of 6 V, using the experimental setup presented in Figure 1. The number cycles of the step of 6 V, using the experimental setup presented in Figure 1. The number cycles of the sensing fiber sensing fiber coiled on this stretcher is 14, which means that the initial unstressed length of sensing coiled on this stretcher is 14, which means that the initial unstressed length of sensing fiber is 3.08 m. fiber is 3.08 m. As the variation of time delay induced by the change of controlling voltage is As the variation of time delay induced by the change of controlling voltage is specially required, the specially required, the measured time delay at 24 V was set as a zero reference, replacing the measured time delay at 24 V was set as a zero reference, replacing the absolute value with a relative absolute value with a relative value so as to simplify the subsequent data processing. value so as to simplify the subsequent data processing. Figure 7a demonstrates the experimental response of relative delay for the decrease of Figure 7a demonstrates the experimental response of relative delay for the decrease of controlling controlling voltage. If the frequency of the modulating signal is 5 GHz, the theoretical measurement voltage. If the frequency of the modulating signal is 5 GHz, the theoretical measurement precision of precision of the strain-induced fiber-optic delay is about 100 fs for this sensor, whereas the the strain-induced fiber-optic delay is about 100 fs for this sensor, whereas the measurement precision measurement precision of the vector network analyzer is as high as 1 fs. As a result, the system error of the vector network analyzer is as high as 1 fs. As a result, the system error induced by the calibration induced by the calibration is less than 1%. is less than 1%. As for the sensing fiber coiled on the piezoelectric ceramics-based optical fiber stretcher, the As for the sensing fiber coiled on the piezoelectric ceramics-based optical fiber stretcher, the following relationships could be set up as [42]: following relationships could be set up as [42]:

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∆τ = JLε = J∆L P 9 of 14 (13) ∆L T = 2π · Q · (∆ri − ∆r24 )(i = 0 − 120)   JL  J LP R = ∆L P /∆L T  (rJL   J LP(i  0  120) . LT  2  Q (13) i  r24 ) LT  2  Qand R(ritheoretical L r i   ) ( 0 120) . (13)  L 24 Here, ∆LP and ∆LT are the practical stretched lengths of the sensing fiber, P T R   L  L P T respectively, J is the elastic coefficient of the fiber-optic delay whose value is about J = 3.8 ps/km·µε, Q Here, ΔLP and ΔLT are the practical and theoretical stretched lengths of the sensing fiber, is therespectively, cycles of the coiled sensing fiber, ∆r is the radial displacement of the at the controlling the elastic ofi theand fiber-optic delay whose value is stretcher about J =sensing 3.8 ps/km·με, ΔLT arecoefficient the practical theoretical stretched lengths of the fiber, Here, ΔLJ Pisand voltage R isJ is defined as the stretching ratio. data value is presented 7b, and the Q isi, and the cycles of coiled sensing fiber, Δri The is theobtained radial displacement thein at the respectively, thethe elastic coefficient of the fiber-optic delay whose is of about Jstretcher =Figure 3.8 ps/km·με, results indicate thatofthe stretched theradial sensing fiberobtained is lessofthan theoretical controlling voltage i,practical and R issensing definedfiber, aslength the ratio. The data is presented invalue Q is the cycles the coiled Δristretching isofthe displacement the its stretcher at the Figure 7b, and the results indicate that the stretched length the sensing fiber is less than voltage i,ofand R is0.29 defined as practical the stretching ratio. The of obtained datathe is presented invalue with controlling a stretching ratio about at each testing voltage point. In addition, measured itsstretching theoretical value with aindicate stretching ratio aboutdistributed, 0.29 at eachlength testing point.fiber In addition, theto the 7b, andratio the results that theof practical stretched ofvoltage the sensing is less than of theFigure is approximately normally and its peak point corresponds measured value of the stretching ratio is approximately normally distributed, and its peak point its theoretical value with a stretching ratio of about 0.29 at each testing voltage point. In addition, the position with the biggest curvature of the displacement curve in Figure 8, which could be regarded as corresponds to the position with the biggest curvature of the displacement curveand in Figure 8, which measured value the stretching is approximately normally distributed, its peak a verification of the of accuracy of the ratio calibration. Furthermore, the response of strain to thepoint decrease could be regarded as a verification the accuracy of the calibration. Furthermore, the response of corresponds to the position with theofbiggest curvature of the displacement curve in Figure 8, which in the controlling voltage is finally obtained and presented in Figure 8, and the whole experimental strain to decrease the controlling voltage is finally obtained and presented in Figure 8, and the could be the regarded as in a verification of the accuracy of the calibration. Furthermore, the response of process was conducted in a room a voltage constant temperature. whole experimental waswith conducted in aisroom with a constant temperature. strain to the decreaseprocess in the controlling finally obtained and presented in Figure 8, and the Sensors 2017, 17, 1005

whole experimental process was conducted in a room with a constant temperature.

(a)

(b)

(a) (b) Figure 7. The calibration of strain in the voltage range of 102–24 V with a decrement step of 6 V: (a) Figure 7. The calibration of strain in the voltage range of 102–24 V with a decrement step of 6 V: (a) The The response relative delay to voltage; (b) Therange response of variation to voltage. Figure 7. The of calibration of strain in the voltage of 102–24 V withofalength decrement step of 6 V: (a)

response of relative delay to voltage; (b) The response of variation of length to voltage.

The response of relative delay to voltage; (b) The response of variation of length to voltage.

Figure 8. The response of strain to the decrease in controlling voltage. Figure 8. The response of strain to the decrease in controlling voltage.

8. and The Discussion response of strain to the decrease in controlling voltage. 4. ExperimentalFigure Results 4. Experimental Results and Discussion A prototype experimental setup for testing the feasibility and practicability of the strain sensor 4. Experimental Results and Discussion presented in Figure 5 was built.setup In this wavelengths of the tunable the A prototype experimental forsensor, testingthe theoutput feasibility and practicability of the laser strainand sensor presented in Figure 5 was built. In this wavelengths of the tunable and the A prototype experimental setup for sensor, testingthe theoutput feasibility and practicability of laser the strain sensor

presented in Figure 5 was built. In this sensor, the output wavelengths of the tunable laser and the

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Sensors 2017, DFB laser are17,λi1005 = λ1

10 of 14 = 1549.32 nm and λa = 1552.12 nm, respectively. The frequency of the modulating DFB laser are λ i = λ1 = 1549.32 nm and λa = 1552.12 nm, respectively. The frequency of the signal is 5 GHz, and the bandwidth of the M-Z modulator and the two photodetectors is 10 GHz. DFB laser are λi =is 5λ1GHz, = 1549.32 nm and λa =of 1552.12 respectively. frequency of the modulating signal andtothe bandwidth the difference M-Znm, modulator and the theThe two is The vector voltage meter works measure the phase between two photodetectors microwave signals modulating signal is 5 GHz, andmeter the bandwidth the M-Z◦ the modulator the twobetween photodetectors is 10 GHz. The vector voltage works to ofmeasure phase and difference the two of port A and port B with a measurement precision of 0.1 , which is equivalent to a strain resolution 10 GHz. The vector voltage meter measure the phase of difference between the two microwave signals of port A and port Bworks with ato measurement precision 0.1°, which is equivalent to of about 4.75 µε. Due to the concerning temperature fluctuations, the impact of temperature on the signals of port and με. portDue B with a measurement precision of 0.1°, which is the equivalent to amicrowave strain resolution aboutA4.75 to the concerning temperature fluctuations, impact of measurement of strain must be evaluated as well. According to the initial parameters, the elastic a strain resolution about 4.75 με.ofDue to the concerning temperature the impact of temperature on theofmeasurement strain must be evaluated as well.fluctuations, According to the initial coefficient is J on = 3.8 ·µε, the thermal coefficient is K = 39.2 ps/km ·◦ C, and to thethe unstressed temperature theps/km measurement strain must be as well. According initial parameters, the elastic coefficient is Jof= 3.8 ps/km·με, theevaluated thermal coefficient is K = 39.2 ps/km·℃, and length of sensing fiber is 3.08 m. Combined with Equations (9) and (12), the strain error induced parameters, thelength elastic of coefficient is J = is 3.83.08 ps/km·με, the thermal K =and 39.2(12), ps/km·℃, and by the unstressed sensing fiber m. Combined withcoefficient Equationsis(9) the strain temperature fluctuations is discussed under the conditions of ∆L = 1 mm − 5 mm and ∆T = ± 10 ◦ C, the unstressed length of sensing fiber is 3.08 m. Combined with the error induced by temperature fluctuations is discussed under the Equations conditions(9) of and ΔL = (12), 1 mm − 5strain mm and the simulation results are fluctuations presented inisare Figure 9. under Thus, to achieve of−less than error induced by and temperature discussed the conditions ofachieve ΔL =error 1 amm 5error mm and ΔT = ± 10 ℃, the simulation results presented in Figure 9. Thus,atostrain strain ◦ 1%of (0.0475 µε) the fluctuation of 10fluctuation C,Thus, the length difference between and ΔT =than ± 10under ℃, and themaximum simulation results are presented in Figure 9. to of achieve error less 1% (0.0475 με) undertemperature the maximum temperature 10 ℃,a strain the length sensing path and the reference path should be controlled by less than 1.4 mm. of less than 1% (0.0475 με) under the maximum temperature fluctuation of 10 ℃, the length difference between sensing path and the reference path should be controlled by less than 1.4 mm. difference between sensing path and the reference path should be controlled by less than 1.4 mm.

Figure9.9.The The strain strain error error induced Figure inducedby bytemperature temperaturefluctuations. fluctuations. Figure 9. The strain error induced by temperature fluctuations.

Currently, the cutting precision of fiber can be controlled under one millimeter in our lab. In Currently, thethe cutting precision ofof fiber can bebe controlled under one millimeter in our lab. Currently, fiber controlled under one millimeter lab.In Inthis this experiment, thecutting delay ofprecision the sensing fiber can is 35.778 ns, and that of the reference fiberinisour 35.781 ns, experiment, the delay of the sensing fiber is 35.778 ns, and that of the reference fiber is 35.781 ns, which this experiment, the to delay of thedifference sensing fiber is 35.778 ns, and thatthe of the reference fiber between is 35.781 the ns, which is equivalent a length of about 0.6 mm. Thus, length difference is equivalent a length of about 0.6about mm.of0.6 Thus, theThus, length betweenbetween the two the paths which is equivalent to difference a length of thedifference length difference two paths istolow enough to meetdifference the requirement themm. sensor. is low enough to meet the to requirement of the sensor. two paths is low enough meet the requirement of the sensor.

(a) (a)

(b) (b)

Figure 10. The experiments for testing the strain sensitivity of this sensor: (a) The repeatability Figure 10.ofThe experiments testing the strain sensitivity of this sensor: The repeatability response phase difference for under the same experimental conditions; (b) The(a)response of degree Figure 10. The experiments for testing the strain sensitivity of this sensor: (a) The repeatability response response of phase difference under the same experimental conditions; (b) The response of degree and delay of this sensor with respect to a change in strain. of phase difference under the same experimental conditions; (b) The response of degree and delay of and delay of this sensor with respect to a change in strain. this sensor with respect to a change in strain.

Depending on the analysis above, the phase difference of port B and port A (A/B) was Depending on the range analysis above,Vthe phase difference B and A (A/B) was measured in the voltage of 102−24 with a decrement stepofofport 6 V, and the port measured value at measured in the voltage range of 102−24 V with a decrement step of 6 V, and the measured value at

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Depending on the analysis above, the phase difference of port B and port A (A/B) was measured in the voltage range of 102−24 V with a decrement step of 6 V, and the measured value at voltage Sensors 2017, 17, 1005 11 of 14 24 V was as17, the zero reference. Meanwhile, to test the repeatability of this sensor, the experimental Sensorsset 2017, 1005 11 of 14 process was repeated with the same voltage range and in aofroom with a constant voltage 24 V was many set as times the zero reference. Meanwhile, to test thedecrement repeatability this sensor, the voltage 24Combined V was set with as therepeated zero reference. Meanwhile, test the repeatability of this this experiment sensor,inthe temperature. the calibration in Section 3,to the repetition resultsand of experimental process was many times with the same voltage range decrement a are experimental process was repeated many times with the same voltage range and decrement in a room with a constant temperature. withvariation the calibration in Section 3, the is repetition results presented in Figure 10a, which show Combined that a similar of phase difference found with respect room with a constant temperature. Combined with the calibration in Section 3, the repetition results of this in experiment to a change strain. are presented in Figure 10a, which show that a similar variation of phase of this experiment are respect presented Figure which show that a similar variation of phase difference is found with to ain change in 10a, strain. The response of degree and delay of this sensor with respect to a change in strain was finally difference is found with respect to a change in strain. The response of degree and delay of this sensor with respect to a change in strain was finally obtained by measurements and equalization, shown in Figure 10b. The experimental results Themultiple response of degree and delay of equalization, this sensoraswith respect to Figure a change in The strain was finally obtained by multiple measurements and as shown in 10b. experimental demonstrate that phase difference is linear with strain, which conforms to the previous theoretical obtained by multiplethat measurements and equalization, as strain, shown which in Figure 10b. The results demonstrate phase difference is linear with conforms to experimental the previous ◦ /µε and −0.012 ps/µε, results. Moreover, the linear fitting coefficients of phase and delay are − 0.021 results demonstrate that phase difference is linear with strain, which conforms to the °/με previous theoretical results. Moreover, the linear fitting coefficients of phase and delay are −0.021 and ◦ has theoretical results. Moreover, the linear fitting coefficients of phase and delay are −0.021 °/με and of respectively. As a result, the sensor with the measurement precision of 0.1 a strain −0.012 ps/με, respectively. As a result, the sensor with the measurement precision of 0.1° hassensitivity a strain −0.012 ps/με, respectively. As a result, the sensor with the measurement precision of 0.1° has a strain 4.75 µε in the range of 350 µε. sensitivity of 4.75 με in the range of 350 με. sensitivity of 4.75 με in the range of 350 με.

Figure 11. The strain sensitivity of a sensor working at different frequencies.

Figure 11. 11. The strain workingatat different frequencies. Figure The strainsensitivity sensitivity of of aa sensor sensor working different frequencies.

As for a known strain sensor, the length of the sensing fiber and the measurement precision of

Asafor a are known strain sensor, length of the sensing fiber andthe the measurement ofof the As known strain sensor, thethe length ofway the sensing fiber measurement precision the for detector specific; thus the effective to improve its and strain sensitivity is by precision raising the the detector are specific; thus the effective way to improve its strain sensitivity is by raising the working frequency of the the effective modulating signal. Figure its 11 strain simulates the response of the phase at detector are specific; thus way to improve sensitivity is by raising the working working working frequency of the modulating signal. Figure 11 simulates the frequency response is oftruly the phase at different frequencies, which shows that the increase of working effective frequency of the modulating signal. Figure 11 simulates the response of the phase at different working different working frequencies, which shows that the increase of working frequency is truly effective in improving theshows strain that sensitivity of the sensor. In addition, duringisthe period of design, a longer the frequencies, which the increase of working frequency truly effective in improving in improving the strain of theprecision sensor. In addition, during design, a longer sensing fiber and highersensitivity measurement also work to makethe theperiod sensorofmore sensitive to strainsensing sensitivity of the sensor. In addition, duringalso thework period of design, a longer sensing fiber fiber and higher measurement precision to make the sensor more sensitive to and strain. higher measurement precision also work to make the sensor more sensitive to strain. strain.

Figure 12. The temperature insensitive response of phase difference at each controlling voltage. Figure 12. The temperature insensitive response of phase difference at each controlling voltage.

Figure 12. The temperature insensitive response of phase difference at each controlling voltage.

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To verify its temperature insensitivity, this sensor was placed in an open environment, which caused the sensor to be continuously affected by the unstable and random environmental temperature fluctuations. Under this condition, each controlling voltage was maintained for more than 20 min and measurement was repeatedly conducted several times during this period, and the obtained response is presented in Figure 12. The experimental results show an average degree fluctuation of less than 0.025◦ at each controlling voltage. On basis of the discussion above, this degree fluctuation obviously does not result from the unstable temperature and is more likely caused by the unstable working performance of the fiber stretcher and could be eliminated by averaging the multiple measured values. In this case, temperature fluctuations will no longer be a problem in practical applications. 5. Conclusions In this paper, a high precision temperature insensitive strain sensor based on optical fiber delay was reported, which is able to realize the measurement of strain by detecting delay instead of spectrum because of the elastic property of fiber-optic delay. A prototype experiment to verify its feasibility was conducted and the experimental results prove it to be feasible and practical with high precision and temperature insensitivity. To achieve an overall low cost, the vector voltage meter utilized in this paper could be simply replaced by a phase discriminator, which is increasingly mature and can be simply implemented based on functional chips with high precision. In addition, because of its working principle, the sensor has a great potential to be a substitution in the field of long distance structure monitoring. Further experiments on this study will be conducted. Acknowledgments: This work is supported by the National Natural Science Foundation of China (No. 61271030). Author Contributions: This paper was accomplished by all the authors with the assignments that Qi Qiu and Jun Su conceived and designed the structure of sensor; Zhiqiang Fan and Ning Yang designed the fiber stretcher; and Ning Yang discussed the theory, performed the experiments, analyzed the obtained data, and wrote this paper. Conflicts of Interest: The authors declare no conflict of interest.

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