Investigation into improving resolution of strain measurements in BOTDA sensors. Ander Zornoza Indart

Transcription

1 Investigation into improving resolution of strain measurements in BOTDA sensors BY Ander Zornoza Indart Eng., Universidad Publica de Navarra, Pamplona, 2008 M.S., Universidad Publica de Navarra, Pamplona, 2009 THESIS Submitted as partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering in the Graduate College of the University of Illinois at Chicago, 2014 Chicago, Illinois Defense Committee: Dr. Farhad Ansari, Chair and Advisor Dr. Thomas Royston, Bioengineering Dr. Didem Ozevin

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3 Acknowledgments The author of this thesis would like to thank the Fulbright program for the scholarship provided to complete the MS in Civil Engineering at UIC between fall 2012 and spring iii

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5 Table of contents Introduction to the thesis 0.1-Motivation Objectives of the thesis Structure of the thesis... 2 Chapter 1: Introduction to BOTDA systems 1.1.-Introduction Fundamentals of BOTDA BOTDA measuring principle BOTDA performance parameters Temperature or strain error and repeatability Temperature and strain resolution Spatial resolution Model to evaluate the performance of BOTDA Conclusions Chapter 2: State of the art of BOTDA sensors 2.1-Introduction Factors that limit BOTDA Improved BOTDA systems Techniques to improve spatial resolution Techniques to extend measuring range Techniques to discriminate strain and temperature Conclusions Chapter 3: Fiber optic coils for strain, temperature and spatial resolution improvement in BOTDA 3.1-Introduction Coils theory Experimental results of comparing coils and no coils Conclusions Chapter 4: Conclusions Cited literature v

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7 List of tables 1.I: Example of error and repeatability values in different sections of the fiber II: Example of the resolution of different strain gauge sensing systems using different number of quantification bits III: Different strain resolution definition values for the sections of the fiber IV: Summary table of the performance parameters per section of the fiber V: FoM examples from literature (Soto, 2013) I: examples of improvement for different systems with different coils II: Calculation of improvement obtained with the coils III: Calculation of improvement obtained with the coils I: Definition of the parameters that describe the quality of the system I: Definition of the parameters that describe the quality of the system...63 vii

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9 List of figures Figure 1.1: Schematic of the Stimulated Brillouin Scattering 6 Figure 1.2: BOTDA time of flight operating principle..9 Figure 1.3: BOTDA trace for a given frequency difference between pump and probe. The amplitude decays exponentially when the BFS is similar. In the section with a slightly higher amplitude, the BFS is closer to the difference between pump and probe.9 Figure 1.4: BOTDA sweep operating principle..10 Figure 1.5: Reconstruction of the spectra along the fiber after the sweep. We can clearly see the section with difference in BFS 10 Figure 1.6: Measured spectrum at a location in the fiber (blue) and the Lorentzian fit (red) 11 Figure 1.7: Spectra reconstruction after the fit 11 Figure 1.8: Distributed strain or temperature measurement without moving average (blue) with moving average (red) 13 Figure 1.9: three traces before (a) and after reference compensation (b). The cyan trace is at the same conditions as the reference, while the red and green are not. We can see that the actual difference with the reference is clearer after the compensation 14 Figure 1.10: Error and repeatability calculation in point sensors, like strain gauges or FBGs 17 Figure 1.11: One hundred distributed measurements with BOTDA with the fiber at a constant strain and no temperature variations.18 Figure 1.12: Error and repeatability calculation at different locations of a fiber using BOTDA. The repeatability in each case is different.20 Figure 1.13: Error calculation in BOTDA using the average strain at each location along the fiber 20 Figure 1.14: Distributed error in BOTDA example. The red markers correspond to the maximum values in each section..21 Figure 1.15: Repeatability calculation in BOTDA using twice the standard deviation of strain at each location along the fiber. The red markers correspond to the maximum values in each section..21 Figure 1.16: examples of resolution in strain gauges (a), FBGs (b) and BOTDA sensors (c)..23 Figure 1.17: Example of several repeated measurement on a location on the fiber using BOTDA (orange line with dots). The horizontal lines correspond to the resolution of 0.1 of the system calculated ix

10 taking into account the frequency difference stability. The actual repeatability is 4.56, much worse than the theoretical resolution 26 Figure 1.18: Relationship between BFS and strain for an example with 18- standard deviation. The black straight line corresponds to the theoretical data without noise, the straight red lines corresponds to the boundaries of the standard deviation, the dashed lines correspond to the boundaries of twice the standard deviation and the dotted lines to the boundaries of three times the standard deviation..26 Figure 1.19: Example of 18 increments in a 4.8m long section of the fiber for an example with 18- standard deviation (a). The straight thick lines correspond to the theoretical values, while the thin lines correspond to the measurements. Example of 54 increments in a 4.8m long section of the fiber for an example with 18- standard deviation (b)..27 Figure 1.20: Distribution of samples in a Gaussian profile referred to the standard deviation. 27 Figure 1.21: Resolution calculation in BOTDA using the standard deviation of strain at each location along the fiber. The red markers correspond to the maximum values in each section.. 28 Figure 1.22: Spatial resolution calculation example. 29 Figure 1.23: graphical explanation of the parameters to calculate SNR in a BOTDA trace...32 Figure 2.1: Convolution of the Brillouin spectrum with short pulse spectrum..38 Figure 2.2 Strong leakage level pulses to pre-excite the acoustic wave in order to obtain high spatial resolution BOTDA measurements.40 Figure 2.3 Principle of operation of PPP-BOTDA.40 Figure 2.4: Principle of operation of Dark pulse BOTDA Figure 2.5: Operation principle of double pulse BOTDA...41 Figure 2.5: Operation principle of double pulse BOTDA 41 Figure 2.7: Operation principle of simplex coded BOTDA.42 Figure 3.1: Schematic example of coiled fiber glued to structure..46 Figure 3.2: schematic of effect of strain in the coil when deformation is longitudinal (a) or generated by a point load applied in the center of the coil (b).47 Figure 3.3: example of a measurement in a coil. The strain in the coil is uniform, so the average can be taken as the significant value 48 Figure 3.4: (a) the proposed coil. (b)rod, deck, coil and temperature compensating wrapped fiber..51 x

11 Figure 3.5: Reference distributed measurement of strain along the fiber. Note that reference compensation is needed since the different fibers spliced together have different reference BFS or strain..53 Figure 3.6: strain measured in the 3rd coil with different tensions applied to the rod (a) and two particular cases to show the uniformity of the strain applied to the coil (b)..53 Figure 3.7: Strain measured along the fiber for (a) coil 1 (b) coil 2 and (c) coil 4 in the thirteen measurements taken.55 Figure 3.8: standard deviation of each point along each of the coils..56 Figure 3.9: Measured strain in the coils for the 13 measurements 56 xi

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13 Summary Structural health monitoring contributes to the safety and extension of the lifetime of structures. There are several techniques for structural health monitoring, most of them based on different types of sensors. Fiber optics has been proven as a very good technology since it is lightweight, has low signal loss, is immune to electromagnetic interferences and offers the possibility of remote sensing and multiplexing. Therefore, as in telecommunications technology, the application of fiber optics to structural health monitoring has resulted in great breakthroughs during the last decades. Furthermore, one of the advantages that fiber optic sensors offer is obtaining distributed measurements with a certain spatial resolution. In this approach, the whole fiber optic line is the sensor, instead of having sensors placed in given positions. Between the different technologies that perform fiber optic distributed measurements, Brillouin optical time domain analysis (BOTDA) is the one with better performance. BOTDA sensors are based in the stimulated Brillouin scattering phenomenon characterization. This is a phenomenon that has a strong dependence on strain and temperature. However, there is still much room for improvement in these sensors since they do not meet the minimum quality criteria for some structural health monitoring applications. Also, survey of literature indicates that the parameters that define the performance of the sensor and specially the resolution of measurements are not thoroughly defined. This is due to the infancy of this technology and the fact that unlike localized sensing technologies the measurement parameters in distributed sensing are dependent on spatial characteristics of the sensor. In this thesis, a method for the computation and presentation of measurement resolutions in BOTDA sensors is defined based on an exhaustive literature review. Moreover, an important improvement in BOTDA quality is presented by creating fiber optic coils and special data processing, which is a non-instrument-based enhancement. An improvement of 1.73 times the strain resolution and repeatability and a reduction of the spatial resolution from 20cm to 7.7cm are experimentally demonstrated. xiii

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15 Introduction to the thesis 0.1-Motivation Structural health monitoring (SHM) is an important research field in civil engineering that consists of monitoring parameters of the structures to address the state of the structures (Ansari, 2005). This contributes to a longer lifetime of the structures and their safety. There are several structural health monitoring techniques which depend on each application. Optical fibers, following the trend in telecommunications, have become a good solution for structural health monitoring via fiber optic sensors. These sensors, when glued to a structure, can measure different parameters such as strain, temperature, gas concentration by variations of the signals transmitted in the fiber optics. Furthermore, fiber optic sensors offer some crucial advantages when compared to other technologies (Culshaw, 2010). Fiber optics are very light and small. This makes them very appealing for applications were weight is an issue. Also they are immune to electromagnetic interference so they can be applied in high electrical power supply structures. The low loss of optical fibers and their passive nature (no power source is needed but in transmitters and receivers) allow remote sensing and multiplexing possibilities very hard to achieve with other technology. There are different types of fiber optic sensors, and in this thesis we will differentiate between point and distributed sensors. Point sensors, the same as most electrical sensors, can measure in a single location where the sensor is deployed. In distributed sensors however, the whole fiber is the sensor, which can be several tenths of kilometers long. The measurands are obtained along the fiber at a certain resolution without blind spots. These sensors are based in different scattering phenomena such as Rayleigh, Raman and Brillouin. Brillouin sensors, mainly through the Brillouin time domain analysis (BOTDA) technique are the ones achieving better performance, since they are capable of measuring over 100-km long fibers at near meter spatial resolutions. Due to the 1

16 Introduction to the thesis requirements of some applications, the latest advances in BOTDA sensors do not meet the desired quality criteria. Furthermore, the parameters that quantify the quality of the sensors are not clearly defined in the literature due mainly to the infancy of this technology and the fact that unlike localized sensing technologies the measurement parameters in distributed sensing are dependent on spatial characteristics of the sensor. 0.2-Objectives of the thesis The objectives of this thesis are to define properly the parameters that affect the quality of the sensors and to develop better quality BOTDA sensors. With these two objectives in mind, we will contribute to find more suitable solutions for structural health monitoring applications and unify the definition of parameters used to quantify the quality of the sensors. In order to achieve these goals, we have focused on an exhaustive literature survey about the performance parameters of BOTDA and on developing a special fiber optic gluing technique and data processing technique. In order to do so, we defined the following tasks: Detailed research of BOTDA operating principle and performance parameters measurement. From this research, find the definition and the procedures to calculate and present the performance parameters. These parameters include error, repeatability and resolution. Study of the state of the art. Investigation of Coiled fiber measurements with BOTDA and performance improvement Structure of the thesis Following the three tasks defined in the previous section, the content of this dissertation is divided in four main chapters. In the first chapter a detailed explanation of BOTDA operating principle and all of the steps to make a measurement are presented. Special attention is given to the definition and calculation of different 2

17 Introduction to the thesis performance parameters such as spatial resolution, strain or temperature resolution, repeatability and error. Furthermore, the model of figure of merit calculation to compare the quality of different BOTDA systems is described. A complete state of the art study of BOTDA is presented in chapter two. The main factors that limit the BOTDA performance are explained: Spatial resolution, non-linear phenomena, signal to noise ratio (SNR) and discrimination of strain and temperature. The latest improved BOTDA systems are discussed by explaining their operating principle and how they contribute to the mitigation of the limiting factors. The solution proposed in the thesis, creating fiber coils in certain locations of the structure while using BOTDA instruments, is discussed in chapter three. The theoretical geometry of the coils and the improvement in spatial resolution and strain or temperature resolution are presented. This theory is demonstrated by experimental measurements with actual coils built in the laboratory. Finally, in chapter four the conclusions of the thesis are presented. 3

18 Chapter 1: Introduction to BOTDA systems 1.1.-Introduction Fiber optic sensors are a great breakthrough in SHM, since they offer possibilities which are hard to achieve with other technologies. Fiber optics are lightweight, offer the capability of multiplexing and are immune to electromagnetic interferences. This offers the possibility to monitor huge structures of hundreds of kilometers accurately. Fiber optic sensors can be divided into point sensors and distributed sensors. Point sensors are usually multiplexed in a fiber optic network and are able to measure given points of the network in a structure. There are different types of point sensors such as Fiber Bragg gratings (FBG) or interferometers (Higuera, 2002). They are made by processing a point on a fiber. FBG s are the most used point fiber optic sensors. They can mainly measure strain and temperature, but some special configurations allow measuring tilt, corrosion and other phenomena. Although these sensors can measure with high accuracy at high speed and at long distances, the measurement is given in a single point per sensor. Distributed sensors however, measure long distances at a given spatial resolution. In this case, the fiber optic itself is the sensor, without the need for fabrication of the sensor. There are different types of fiber optic distributed sensors. Raman distributed sensors are based on Raman scattering effect. They can measure in several kilometer fiber-optics but with limited performance. Rayleigh distributed sensors such as optical time domain reflectometers (OTDR) take advantage of Rayleigh scattering effect (Desforges, 1986). OTDR s have been widely used in fiber optic communications in order to localize defects on networks, but their sensing capabilities are limited. Sensors based in Brillouin scattering are the most promising distributed sensing technology nowadays for SHM. Due to the capability of stimulating Brillouin scattering in fiber optics with Brillouin optical time 4

19 Introduction to BOTDA systems domain analysis (BOTDA) technology, measurements of up to 240km fiber optics at meter spatial resolutions have been achieved (Soto, 2014). This is because stimulated Brillouin scattering is a relatively strong scattering effect which is dependent with strain and temperature. In this dissertation a solution to improve BOTDA system quality is presented. Therefore, in this chapter an introduction to BOTDA technology is presented, starting from the fundamentals and explaining the measuring principle and the parameters that define the performance of these sensing systems fundamentals of BOTDA Stimulated Brillouin scattering is a nonlinear phenomenon that occurs in fiber optics when a pump wave and a probe wave counter-propagate and energy transfer between the two waves occurs via an acoustic phonon (Agrawal, 2006). This energy transfer in relationship with the acoustic phonon is dependent with strain and temperature, so BOTDA sensors take advantage of this. Figure 1.1 depicts the interaction of stimulated Brillouin scattering. A pump and probe wave are traveling in opposite directions in a fiber generating an acoustic wave due to electrostriction effect. The acoustic wave generates a periodic density variation, and thus a periodic refractive index variation. A fraction of the light through Bragg diffraction is transferred from the pump to the probe wave. The refractive index variation is travelling since it is generated by the acoustic wave, and travelling at the same velocity of the acoustic wave. So due to Doppler Effect, the frequency of the transferred energy is down-shifted. This process amplifies the acoustic wave, stimulating the whole process. Note that the power levels at which stimulated Brillouin scattering (SBS) is not negligible in fiber optics and is relatively low compared, for instance, with Raman scattering. 5

20 Chapter 1 Electrostriction/acoustic wave/ refractive index perturbation Probe wave scattering Pump wave Depleted pump Probe+scattering The Brillouin frequency shift (BFS) is given by: Figure 1.1: Schematic of the Stimulated Brillouin Scattering. ν B = 2nv a λ (1.1) Where v a is the acoustic velocity in the fiber, n the effective refractive index of the fiber, and the wavelength of the pump wave. In typical commercial single mode fibers, this frequency shift is around 11GHz. The Brillouin gain is given by: g B (ν) = g max(δν B /2) 2 (ν ν B ) 2 +(ν B /2) 2 (1.2) which corresponds to a Lorentzian profile, where g max is the maximum Brillouin gain, B is the Brillouin frequency shift, B is the Brillouin bandwidth and is the difference between pump and probe frequency. The maximum gain is given by: g max = 2πn7 p 2 12 γ 2 (1.3) cλ P ρ0 v a Δν B where 0 is the density of the fiber, p 12 is the longitudinal elasto-optic coefficient of the fiber, is a factor that depends on the polarization orientation of pump and probe waves and P the pump wavelength. When the pump and probe waves have the same polarization, this last factor reaches its maximum value. Finally the dependence between the Brillouin frequency shift (BFS) with temperature and strain is given by: 6

21 Introduction to BOTDA systems ν (T,δε)= ν (T,0 )+ Aδ B B + B(T 0 T0 ) (1.4) where is the strain difference in the medium, a fiber optic in this case. Constants that relate temperature and strain variations are A, the strain sensitivity (the constant that relates strain variations with BFS variations) and B, the temperature sensitivity (the constant that relates the temperature variations with BFS variations), while T 0 is the reference temperature. Therefore, by monitoring some of the parameters of the SBS, the temperature and strain can be measured. Also, in order to get distributed measurements special care and special techniques must be used. In order to get distributed strain and temperature measurement in a fiber optic, the SBS phenomena along the fiber must be characterized. There are several methods to characterize SBS along the fiber and each of them gives name to a different stimulated Brillouin distributed sensing family. In Brillouin optical frequency domain analysis (BOFDA) the spectral characterization of the fiber is obtained (Garus, 1996). In Brillouin optical correlation domain analysis (BOCDA), the correlation of pump and probe waves in each location of the fiber is used (Hotate, 2000). In Brillouin optical time reflectometry (BOTDR), the spontaneous Brillouin scattering is characterized along the fiber (Horiguchi, 1995). Finally, Brillouin optical time domain analysis (BOTDA) sensors are the most popular Brillouin based sensors, and are presented in detail in the following section BOTDA measuring principle BOTDA is essentially a time of flight technique (Horiguchi, 1985). Its origin is in OTDR devices, which are here briefly explained as a first step to understand BOTDA. In OTDR a pulse is launched to a fiber, and because of Rayleigh scattering a portion of the light is reflected (Desforges, 1986). This light is measured in the same end of the fiber where the pulse is launched. The reflected energy is proportional to the loss of the fiber, and the time of arrival to the end is related to the length of the fiber. These devices are used to calculate loss in fibers and localize defects in fibers. These defects are localized with a spatial 7

22 Chapter 1 resolution proportional to the pulse duration. In BOTDA access to both ends of the fiber is needed and in contrast to OTDR, two counter-propagating waves are needed. In one end a pulsed pump wave is launched, while in the other end a continuous probe wave is launched, as depicted in figure 1.2 (a). We will call the end where the pump pulse is launched the beginning of the fiber from now on. The spatial resolution of the measurements is given by the duration of the pulse, as described by the following equation: vg T z = 2 (1.5) where T is the temporal length of the pump pulse and v g is the group velocity in the fiber. The time to space conversion of the modified continuous signal is given by the following equation: vg t z 2 (1.6) where t is the time since the pulse entered the fiber. When the frequency difference between pump and probe is near the Brillouin frequency shift, the pump generates gain in the probe wave, and this gain depends on the SBS characteristics of each location along the fiber. Figure 1.3 shows the probe power after interacting with the pump pulse. This trace will be called BOTDA trace from now on. Note that in this particular case, at the end of the fiber the Brillouin gain is different. It is greater. This is because in this part of the fiber the frequency difference between pump and probe is closer to the Brillouin frequency shift than in the rest of the fiber. This could be given for example, from a different strain or temperature in that part of the fiber. If the frequency shift over the fiber is similar, we can see that the amplitude decays exponentially: the further from the beginning of the fiber, the lower amplitude of the signal. This is due to the loss in the fiber. Also, this signal is usually very noisy because Brillouin amplification is low, less than %1, so a number of averages are recommended at each acquisition. 8

23 Introduction to BOTDA systems Pulsed pump Continuous stokes Fiber optic BOTDA interaction signal Figure 1.2: BOTDA time of flight operating principle. The pump and probe frequency difference is swept and the corresponding BOTDA trace captured for each frequency difference, so the Brillouin spectrum at each location can be reconstructed. Note that the frequency difference between pump and probe at each point of the sweep must be very stable and carefully fixed. The frequency range chosen for the sweep gives the total range of temperature or strain measured, so it must be carefully chosen. Figure 1.4 shows a schematic of the sweep: while sweeping the frequency and capturing the BOTDA trace, we have enough information to reconstruct the Brillouin spectrum. Exponential decay Section with different BFS Amplitude No interaction No interaction Length of fiber Distance Figure 1.3: BOTDA trace for a given frequency difference between pump and probe. The amplitude decays exponentially when the BFS is similar. In the section with a slightly higher amplitude, the BFS is closer to the difference between pump and probe. 9

24 Chapter 1 Amplitude Stokes wave sweep range BFS Frequency difference Pump wave Optical frequency Amplitude Amplitude Amplitude probe distance distance distance Figure 1.4: BOTDA sweep operating principle. The next step is a reconstruction of a measurement: getting the spectra for each location. In figure 1.5 an example of this reconstruction is shown. We can see that the final part of the fiber has a different Brillouin frequency shift, thus the Brillouin spectrum is moved. BFS difference Figure 1.5: Reconstruction of the spectra along the fiber after the sweep. We can clearly see the section with difference in BFS. After the reconstruction, since the measurements are noisy, a fit to the Lorentzian profile at each location is performed. Note that the fit is performed following the Lorentzian profile described in equation (1.2). In figure 1.6 an example of the spectrum for a location before and after the fit are 10

25 Introduction to BOTDA systems shown. We can see that before the fit is performed it is hard to obtain an accurate measurement of the peak, whereas after performing the fit, the peak is very clear. Furthermore, the reconstruction after the fit is way cleaner now, as depicted in figure 1.7. Amplitude Frequency Figure 1.6: Measured spectrum at a location in the fiber (blue) and the Lorentzian fit (red). Figure 1.7: Spectra reconstruction after the fit. From the fit several parameters are obtained at each location: the BFS, the amplitude, the linewidth 11

26 Chapter 1 The BFS is calculated as the frequency at which the maximum of the Lorentzian profile is obtained. From all the parameters obtained this is the most important, since it is proportional to strain and temperature. The next step is calculating the strain or temperature from the BFS, following equation (1.4) with the BFS dependence constants, A and B, for the fiber deployed. Figure 1.8 depicts an example of the distributed temperature along the fiber after performing the measurement and data processing. This is the output of most BOTDA instruments and what the user will see. We can see this data is noisy too. Therefore, a last step can also be performed: a moving average of the data. The moving average is performed with the following equation: ν B_ave (z) = 1 i=z+n 1 ν B (i) 2N 1 i=z N 1 (1.7) where N 1 is the number of samples of the moving average. The bigger the number of samples of the moving average, the greater the smoothing. However, the equivalent length of the number of samples must be less than the spatial resolution, otherwise the spatial resolution of the system can be compromised. In figure 1.8 the data after a moving average of 5 samples is also shown. It is clear that the data is less noisy. Note that the noise increases with distance, and this is because the Brillouin gain, and therefore the BOTDA trace amplitude, is smaller at the end of the fiber. 12

27 Introduction to BOTDA systems Strain or temperature Distance (1Km/div) Figure 1.8: Distributed strain or temperature measurement without moving average (blue) with moving average (red). Finally, in some cases, due to pre-strain variations while placing the fiber in the structure, temperature variation along the structure, splicing different fibers the BFS varies along the fiber. This variation may not be related to the strain or temperature we are measuring, so the best way to avoid errors is to compensate with a reference measurement. A reference measurement is a measurement where the strain and temperature of the fiber are known, and the compensation consists in subtracting the reference from the actual measurement. Figure 1.9 shows an example of compensation. In figure 1.9 (a) we can see three measurements. In all cases the BFS variations are the same for the three measurements along the fiber but in the last section. This section has been highlighted and marked as BFS difference in the figure. In figure 1.9(b) the compensation has been performed, and we can see that in the first section of the fiber, the BFS did not vary between the different measurements. However in the last section the variations between the measurements can be noticed. Therefore, after compensation the variations are compared to the reference and the actual changes that have happened in the structure can be clearly measured. This compensation can be performed before or after the conversion from BFS to strain or temperature, as long as the reference and the measurement have the 13

28 Chapter 1 same units. BFS difference BFS difference BFS BFS Distance Distance (a) (b) Figure 1.9: three traces before (a) and after reference compensation (b). The cyan trace is at the same conditions as the reference, while the red and green are not. We can see that the actual difference with the reference is clearer after the compensation BOTDA performance parameters The objective of the research in BOTDA is mainly to improve the quality of the measurements and reduce the cost of the instrumentation. Therefore we want fast and accurate measurements in long fibers at small spatial resolutions. Furthermore we want this cost reduction not to have an impact in the measurement quality. In point sensors systems, such as strain gauges or Fiber Bragg Grating (FBG) sensing systems, the output of the sensing instrument is just a measurement for a given location per sensor. Then, the quality of the measurement depends only in how good we measure the strain or temperature in the given sensor and how fast we can measure. However, we can find that manufacturers use different parameters to define the performance of the system. So sometimes it can be hard to differentiate between the true performance of the system and marketing hype (Polvino, 2011). For example some manufacturers give information about strain resolution (National Instruments, 2014; Fiber Sensing, 2014), while others use repeatability (Micron Optics, 2014). 14

29 Introduction to BOTDA systems Things can become trickier in BOTDA systems, due to the distributed nature of the measurements. Distance and location must also be taken into account. Therefore, in distributed sensors, several parameters come into play in order to address the quality of a system. For example, the quality of a measurement at a point in the fiber may be different from another point that is placed further from the instrument and hence, more sensitive to loss in the fiber, while the measuring instrument is the same (Nikles, 2007). Also, the quality of a measurement in two fibers of different length or different loss characteristics should not be the same. The spatial resolution is also a parameter affecting the quality of the measurement. Shorter length over which strain is averaged provides higher spatial resolution. However, averaging the Brillouin gain over shorter lengths results in higher noise levels. In other words higher spatial resolutions provide more spatial detail at higher noise level. We can see that there are a lot of things to take into account: distance, spatial resolution, temperature or strain resolution and repeatability, measuring range So it is hard to compare two different instruments. For example, if an instrument is performing long distance measurements with large spatial resolution and another performing short distance with small spatial resolution which one is best? And of course we still have the ambiguity of the parameters used for the description of the performance we have in point sensors. In this section we will define the most important parameters to quantify the performance of a system. Furthermore, we will describe the procedure to measure these parameters with examples and present a summary table that clearly describes the performance of a system. Also, we will go through the latest model to calculate the ultimate quality of an instrument taking into account all of these parameters, based on the figure of merit of the system Temperature or strain error and repeatability In this section the measurement error and repeatability are discussed. The temperature or strain measurement error is the maximum difference between the measured temperature or strain and the 15

30 Chapter 1 real value (Mathworld, 2014; NIST, 1297; IEC, ). It can be expressed in absolute values, and in that case is defined as the absolute temperature or strain error. The repeatability is defined as the closeness of agreement between results of successive measurements of the same measurand carried out under the same conditions (NIST, 1297) or the precision under repeatability conditions (ISO, 3534). It can be characterized by twice the standard deviation of a set of measurements under the same conditions (IEC, ; Nikles, 2007). These definitions apply to all kind of sensors, so in order to explain how to calculate this parameter in BOTDA, we will start with the explanation of point sensors, such as strain gauges. Figure 1.10 depicts an example of one hundred repeated measurement of strain using the strain gauge. In order to calculate the error and repeatability, the average measured strain and the real value are also depicted in the figure. The average measured value of strain is 10, while the real value of the strain at which the gauge is subjected to is 8. Therefore, the error of the measurement is 2. In order to calculate the repeatability, twice the standard deviation of all the measurements (100 points) must be calculated. In this case the value is 1. Therefore, this system using strain gauges has a 2- strain error and 1- repeatability. Note that the calculation procedure for an FBG would be exactly the same: take a set of data at the same conditions, calculate the average and subtract it from the real value for the error and calculate twice the standard deviation for repeatability. As an example, the repeatability of the Micron Optics FBG sensing interrogator model sm125 is 5pm (Micron Optics, 2014) and for the Smart fibres Smartscan device as low as 0.4pm. From these values, using the sensitivity of the actual FBG sensor, the repeatability in strain or temperature can be calculated and it is equivalent to 6 and 0.48 in these cases respectively. Sometimes the values of repeatability can be given as a percentage over the whole sensing range as well. 16

31 Introduction to BOTDA systems Measured strain Average strain Real strain Strain (microstrain) Repeatability=2s Error=average-real Number of measurement Figure 1.10: Error and repeatability calculation in point sensors, like strain gauges or FBGs. In BOTDA, since the measurements are distributed additional factors must be taken into account. Note that the error and the repeatability must be measured specifying the conditions of the systems such as: number of averages, spatial resolution, length of the fiber, Brillouin spectral line-width and number of steps per complete sweep. In figure 1.11 an example of one hundred repeated measurements are presented. It corresponds to the distributed strain along a 7-km long fiber, and all the data were calculated in the same conditions: same fiber temperature, same number of averages, same moving average, same spatial resolution, same spectral width and steps We can see that the further the location, the greater the noise, as we have explained in the previous section. This means that the repeatability and the error must be calculated taking this into account (Nikles, 2007; IEC, ). In figure 1.12 the strain at four different locations (1km, 2km, 5km and 6km) are shown. The same as in figure 1.10, the repeatability and error can be calculated. The average is near 11 in each case and the real measurement is 9. However, we can see that the error and repeatability values for each location 17

32 Chapter 1 are different. Therefore, the two parameters must be calculated for each location (Nikles, 2007; IEC, ) Strain (microstrain) Distance (1km/div) Figure 1.11: One hundred distributed measurements with BOTDA with the fiber at a constant strain and no temperature variations. In order to calculate the error, we first must calculate the average of a set of measurements for each location, as shown in figure The error at each location is calculated as the subtraction between these values and the real value: (z) = (z) (z) (1.8) Where is the real strain at each location z and is the average of the measurements at that location. The greatest value of all the calculated errors is the actual error of the system. In our example it is 3.01 at the location of 6.09km, shown in figure The repeatability is calculated the same as in the case for the strain gauge or the FBG, by twice the standard deviation at each point: i i (z) = (z) = 1 n ( n i=1 i(z) (z)) 2 (1.9) 18

33 Introduction to BOTDA systems Where i is the strain at each measurement in location z and is the average at that location. Figure 1.15 shows the calculation for our example. With this data, we know the repeatability in each point, and if we want to be safe in the estimation for our system, we could use the greatest value, that is Also, some authors suggest the data at a distance of 100m from each of the ends of the fiber should be provided (IEC, ). For structural health monitoring applications, users might be interested in the repeatability or error for different sections of the fiber. For example if measurements with 5 repeatability are needed in a 2-km long section, we can use the first 2-km of the network. So in the previous system, we could use the first 2-km of fiber. In this 2-kms the repeatability is not anymore, it is lower. Therefore, as plotted in figure 1.14 and 1.15 with vertical lines, we suggest to give the values of error and repeatability per section. In table 1.I we give the values of the error and repeatability dividing the fiber in four different sections. The error and repeatability for each section are calculated as the maximum of the data in the given section, which are presented with red markers in figure 1.14 and The number of sections and their length may vary depending on the application. In this example we chose three 2-km long sections and one 1-km long section. 19

34 Chapter Strain (microstrain) Repeatability=2s Error=average-real z=1km z=2km z=5km z=6km Average strain Real strain Number of measurement Figure 1.12: Error and repeatability calculation at different locations of a fiber using BOTDA. The repeatability in each case is different average strain real strain Average strain (microstrain) Error=average-real Distance (1km/div) Figure 1.13 Error calculation in BOTDA using the average strain at each location along the fiber. 20

35 Introduction to BOTDA systems 10 9 section 1 section 2 Section 3 Section Error (microstrain) Distance (1km/div) Figure 1.14: Distributed error in BOTDA example. The red markers correspond to the maximum values in each section section 1 section 2 Section 3 Section 4 2x standard deviation of strain (microstrain) Distance (1km/div) Figure 1.15: Repeatability calculation in BOTDA using twice the standard deviation of strain at each location along the fiber. The red markers correspond to the maximum values in each section. 21

36 Chapter 1 section z(km) Error ( ) 2s 1 0-2km km- 4km 4km- 6km 6km- 7km Table 1.I: Example of error and repeatability values in different sections of the fiber Temperature and strain resolution The resolution is a parameter that has no mathematical definition and is defined uniquely in every field (Polvino, 2011). In this thesis, we will define the resolution as it is commonly defined in sensing: the smallest increment that can be measured by the system (Beckwith, 1961). Actually, although there are cases when the measurands vary continuously, many measurement devices will show output changes in discrete steps. The simplest example is a mercury thermometer: we can only measure temperature in the printed lines. So the resolution of the thermometer is the minimum spacing between these lines. In strain gauges, the minimum detectable change in voltage gives the resolution, and it is usually given by the number of quantification bits of the ADC converter. Figure 1.16(a) shows the conversion from volts to strain. It is not a continuous slope: for small voltage changes we will still measure the same strain, we will step from one value to the other. The minimum detectable change is then the size of the step and it can be calculated taking into account the number of quantification bits. For example for 6 bits we get: 22

37 Introduction to BOTDA systems R s u i n (%) = n = 2 6 = 1.56% (1.10) Table 1.II shows as an example, the resolution of different strain gauge measurement systems calculated with the previous equation. We can see that the greater the number of bits, the better the resolution of the system. The case of FBG s is very similar, the resolution of strain or temperature is given by the minimum wavelength difference that can be discriminated, as shown in figure 1.16 (b) (IEC, ). For example, for the Smartscan interrogator device from smartfibres it is less than 5pm, equivalent to 6 Smart fibres 2014 Strain Resolution Strain or temperature Resolution Strain or temperature Resolution Voltage Wavelength BFS (a) (b) (c) Figure 1.16: examples of resolution in strain gauges (a), FBGs (b) and BOTDA sensors (c). Number of bits Resolution (% of full scale) Table 1.II: Example of the resolution of different strain gauge sensing systems using different number of quantification bits. In BOTDA the concept of resolution, following the definitions and examples of strain gauges and FBG s, is given by the minimum detectable changes in BFS, as depicted in figure 1.16(c). This value is usually 23

38 Chapter 1 given by the stability of the frequency difference between the pump and stokes waves (Oz-Optics, 2014). Some manufacturers provide it this way, and for example for the Oz-optics DSTS-F-10 BOTDA sensing instrument, which has a stability between pump and probe frequency difference of 5kHz, the temperature and strain resolutions are 0.005C and 0.1 respectively (Oz-Optics, 2014). However, we have seen that the actual repeatability values are much worse than 0.1C or 2. In figure 1.17 a zoom of one of the examples from figure 1.11 is given, for the localization at 5km. The horizontal lines correspond to the resolution with the definition given by the pump and probe frequency stability. We can see that due to the noise of the system, even if the resolution is 0.1, this will not result in the ability to discriminate between two different quantities: this 0.1 step is completely buried in noise. Therefore, some authors have defined the resolution of the system by the standard deviation of repeated measurements (Nikles, 2007), which is more realistic. This definition is used by several manufacturers in the fiber optic sensing industry such as Fiber Sensing (Fiber Sensing, 2014) or Omnisens (Omnisens, 2014). Note that other manufacturers provide the repeatability, which is just twice this value (Neubrex, 2014; Micron Optics, 2014). Some other authors use a more realistic and conservative value of three times de standard deviation to define the resolution (Polvino, 2011). In figure 1.18 an example measurement of each of the different definitions of resolution is given. In this example, the relationship between the BFS and strain is plotted for data with a standard deviation of 18. We can see that for the first definition, where the resolution is supposed to be the same as the standard deviation, most of the data are outside the boundaries. For the repeatability (two times the standard deviation) we are closer, but still a lot of data is outside the boundaries. Finally, for the case in which three times the standard deviation is used most of the data is within the boundaries. In figure 1.19 (a) the strain increments in a section of 4.8m of fiber equivalent to the standard deviation (18 ) are depicted. It is hard to differentiate between the successive measurements in most of the locations within the section. In figure 1.19 (b) however, where the increments are three times the standard 24

39 Introduction to BOTDA systems deviation, the different steps are clearly noticeable. Since the noise is Gaussian in BOTDA measurements, the data at each location under the same conditions has a Gaussian profile (Soto, 2013). From probabilistic theory we can conclude that the data within three standard deviations of the average corresponds to the 86.6%, while it is the 68.2% within two standard deviations and only 38.2% within one standard deviation, as shown in figure 1.20 (Devore, 2011). Therefore, by defining the resolution as three times the standard deviation, 86.6% of the samples are within the boundaries, so we can see that measuring the resolution as three times the standard deviation is the best approximation. Therefore, in this thesis, we propose to use three times the standard deviation of the measurement as the resolution. Note that in the case of BOTDA, the resolution must be calculated at each location, and the greatest of all values gives the actual resolution of the system. In figure 1.21 the resolution for each location in the previous example from figure 1.11 is given. It is calculated with the following expression: s u i n(z) = (z) = 1 n ( n i=1 i(z) (z)) 2 (1.11) Where i is the strain at each measurement in location z and is the average at that location.the resolution for this particular system, the maximum calculated value all along the fiber, is then We can see that the resolution is worse further from the beginning of the fiber, as expected for the loss in the fiber. Again, as in the case of error or repeatability, the conditions of the system must be specified. This is why manufacturers specify the values they give for the length of fiber, spatial resolution and loss at least (Oz optics, 2014; Neubrex, 2014; Omnisens, 2014). So, the same as for the error and repeatability, we propose to give the resolution per sections of the fiber. This can be very helpful for structural health monitoring applications, so the network can be designed taking into account the resolution needs of a given structure. For the example in figure 1.21 we have chosen to divide in four sections: three 2-km long sections and one 1-km long section. The red markers in this figure correspond to the maximum values of resolution in each of the section. In table 1.III a summary of the values per section is presented. Note that the values for the different resolution definitions are given. 25

40 Chapter 1 The value we propose, three times the standard deviation, gives the greater value, which is the most conservative, and also, as discussed, the most accurate Resolution 11.5 Strain (microstrain) Number Number of of repeated repeated measurements measurement Figure 1.17: Example of several repeated measurement on a location on the fiber using BOTDA (orange line with dots). The horizontal lines correspond to the resolution of 0.1 of the system calculated taking into account the frequency difference stability. The actual repeatability is 4.56, much worse than the theoretical resolution Strain (microstrain) s s s BFS (GHz) Figure 1.18: Relationship between BFS and strain for an example with 18- standard deviation. The black straight line corresponds to the theoretical data without noise, the straight red lines corresponds to the boundaries of the standard deviation, the dashed lines correspond to the boundaries of twice the standard deviation and the dotted lines to the boundaries of three times the standard deviation. 26

41 Introduction to BOTDA systems Strain (microstrain) Strain (microstrain) Distance (m) Distance (m) (a) (b) Figure 1.19: Example of 18 increments in a 4.8m long section of the fiber for an example with 18 standard deviation (a). The straight thick lines correspond to the theoretical values, while the thin lines correspond to the measurements. Example of 54 increments in a 4.8m long section of the fiber for an example with 18- standard deviation (b) s=86.6% 2s=68.3% s=38.2% Distribution of samples Standard deviations (A.U) Figure 1.20: Distribution of samples in a Gaussian profile referred to the standard deviation. 27

42 Chapter 1 20 section 1 section 2 Section 3 Section 4 3 x standard deviation of strain (microstrain) Distance (1km/div) Figure 1.21: Resolution calculation in BOTDA using the standard deviation of strain at each location along the fiber. The red markers correspond to the maximum values in each section. section z(km) s repeatability 2s resolution 3s 1 0-2km km-4km km-6km km-7km Table 1.III: Different strain resolution definition values for the sections of the fiber Spatial resolution As discussed in chapter 1 of this thesis, in conventional BOTDA systems, the spatial resolution is related to the duration of the pump pulse. The actual relationship is given by equation (1.5). In more sophisticated BOTDA techniques such as in PPP-BOTDA, or in the double-pulse BOTDA, which are introduced in the next chapter, equation (1.5) must be slightly modified. In order to come up with a 28

43 Introduction to BOTDA systems unified spatial resolution definition, it has been proposed to use the minimum length of fiber where the temperature can be measured within the specified measurement error and repeatability. In order to calculate the spatial resolution, hotspots must be created in the fiber. These hotspots are part of a fiber optic sensor of length L 1 exposed to a measurable temperature or strain change greater than the temperature and strain repeatability, and is measured with reference devices. The spatial resolution is equal to the length between the last sample point at reference temperature and the first sample point at >90% of the hot spot reference temperature increase if the following sample points within L 1 show the temperature of the hotspot within the specified spatial temperature resolution. Figure 1.22 shows an example of a hotspot within the spatial resolution. The hotspot is 20C hotter than the rest of the fiber. The spatial resolution is 0.5m in this case, since it takes 0.5m to reach 90% of the temperature change, and after that, the specifications regarding error, repeatability and resolution are met for at least 0.5m. Instead of using the slope, is also possible to measure the length of the fiber where the temperature or strain are measured accurately, as depicted in figure 1.22 as well Spatial resolution Specification met Temperature (C) Measured strain 100% 90% distance (m) Figure 1.22: Spatial resolution calculation example. 29

44 Chapter Summary table of performance parameters Finally, we propose to put all the parameters we have calculated into one table. In this table, the error, the repeatability and the strain or temperature resolution can be specified for every section of the fiber. Table 1.IV is an example of the summary table for the data from figure This table must always be presented with data corresponding to the conditions of the measurement, because if the conditions vary, the parameters must be calculated again. This example corresponds to a simulation for a the total length of the fiber of 7km, loss of the fiber of 2.5dB, a spatial resolution of 10m, a number of averages of 2 10 and moving averages of 16, a Brillouin spectral line-width of 40MHz and number of steps per complete sweep of 400 at 1MHz steps. This parameters must always be provided with the table. section z(km) Error ( ) repeatability 2s resolution 3s 1 0-2km km-4km km-6km km-7km Table 1.IV: Summary table of the performance parameters per section of the fiber. 1.5-Figure of merit of BOTDA We have seen there are several parameters that must be specified in order to quantify the quality or performance of BOTDA devices. Depending on the actual application, different parameters might be interesting or important for the user. For example, for a portable BOTDA device, the warm-up time and measuring time might be the most important parameters, since users may require a fast response of the device while measuring in different locations. However, some other parameters, like the measuring range, spatial resolution and temperature or strain resolution, are directly related to the performance quality of the device. In this section we will concentrate in quantifying the overall performance or the 30

45 Introduction to BOTDA systems quality of the measurements. The goal of this approach is to quantify the improvement between different BOTDA instruments independently of the conditions of the measurement. Evaluating the performance of BOTDA has been difficult since this technique was first proposed. Therefore, several approaches throughout the history of BOTDA have been given. The first approach was to relate the SNR to the standard deviation of the strain or temperature measurements with the following equation (Horiguchi, 1995): SNR = Δ B 4 σ v 4 (1.12) where s v is the standard deviation of the measured BFS, and B is the line-width of the BOTDA spectrum. The signal to noise ratio (SNR) is the maximum electrical signal level with respect to the noise. Figure 1.23 shows a schematic of the parameters involved in the SNR for a given BOTDA trace, which is given by the following equation: SNR (z) = V2 (z) σ 2 (1.13) where V(z) is the amplitude of the signal after detection, and s 2 the variance of the noise, which is equal for any location along the fiber. Note that the SNR is dependent on the distance, z, due to fiber loss: the further the measuring location, the lower the SNR. The derivation of this equation has not been justified though, and the theory does not match very well with experimental results (Zornoza, 2012; Soto, 2013). Therefore, instead of using this equation, most of the publications that claimed an important improvement in BOTDA setups and techniques during the last years, would inform of the conditions (i.e. spatial resolution, length of the fiber ) in order to prove the quality of the measurements. However all of these parameters do not give a clear picture of the improvement achieved, unless the performance is compared to other devices working under the same conditions. 31

46 Chapter 1 Some authors have used just the SNR of the BOTDA traces to compare the performance of different BOTDA setups (Zornoza, 2012). However, in order for the SNR to be a valid indicator to estimate the quality of an instrument, it must always be measured under the same conditions. V 2 (Volts) V(z) 2 s 2 z Figure 1.23: graphical explanation of the parameters to calculate SNR in a BOTDA trace. Recently, in order to quantify the improvements in the quality of the measurement by new sophistications or techniques, a figure of merit (FoM) has been presented. This figure of merit is based on a model of the SNR behavior in BOTDA, in accordance with (Zornoza, 2012). However, it goes one step further and it links the SNR with the accuracy of the Brillouin spectrum fit and the performance parameters that affect the SNR. Therefore, after an extensive and detailed demonstration of a model relating the SNR to the temperature or strain standard deviation, an equation for the FoM is derived (Soto, 2013). For a given BOTDA device and measuring conditions, the FoM can be calculated using: F M = ( e ) ν B z Nσ v (1.14) The parameters affecting the figure of merit are the effective length of the fiber (L eff ), the loss of the fiber (α), the spatial resolution ( z), the standard deviation (s v ), the spectral line-width ( B ), the frequency step of the sweep ( ) and number of averages (N). Note that the standard deviation of the measurement is half the repeatability and a third of the resolution. Although many parameters come 32

47 Introduction to BOTDA systems into play in order to describe the performance of a BOTDA sensing instrument, these are the more important in order to quantify and compare the quality of the instrument itself. Note that any measurement can be used to calculate the FoM of a device as long as we recorded all the required data for the calculations of the parameters. It should also be pointed out that the unified definition and measuring procedures of the parameters in the previous section gives a unique possible calculation for the FoM, reducing the room for misunderstanding and going one step further in unification. Furthermore, a historic overview of the BOTDA FoM is presented in table 1.V (Soto, 2013), where it is clear that the evolution of BOTDA has led to an increase of 5 orders of magnitude over the last twenty years. Note that (Soto, 2013) uses a novel configuration method where the actual length of the fiber is 240km. This is the reason of such a high FoM (Soto, 2014). Actually it is the system with the greatest performance in literature. Reference Length (Km) Spatial resolution ( z) (m) Number of averages Frequency step ( ) (MHz) Spectral line-width ( B) (MHz) Standard deviation (s) (MHz) FoM (Bao, 1993) (Bao, 1995) (Lecoeuche, 1998) (Diaz, 2008) (Martin-Lopez, 2010) (Soto, 2011) (Soto, 2012) (Taki, 2013) (Jia, 2013a) (Jia, 2013b) (Soto,2014) Table 1.V: FoM examples from literature (Soto, 2013). 33

48 Chapter conclusions In this chapter the BOTDA technology has been introduced. We have focused on the fundamentals of BOTDA, the measuring principle and the performance parameters of BOTDA. We have seen that BOTDA systems are based on Stimulated Brillouin Scattering, a nonlinear phenomenon that has a strong dependence with strain and temperature. Using a time of flight technique, the Stimulated Brillouin scattering characteristics of a fiber are distributedly measured. The steps to perform a complete measurement in BOTDA systems are the following: 1. Obtain the BOTDA trace for each frequency in the frequency sweep between pump and probe. 2. Reconstruct the spectra along the fiber. 3. Fit each spectrum of each location along the fiber. 4. Obtain the BFS value for each location along the fiber. 5. Calculate the strain or temperature from the distributed measurement of the BFS. 6. Perform a moving average to smooth the results and reduce noise. 7. If required, compensate with a reference measurement. In order to quantify the performance of a BOTDA system many parameters come into play: spatial resolution, strain or temperature resolution, strain or temperature error, and strain or temperature repeatability. We have defined each of these parameters in detail and given the measurement procedures to calculate them. We have proposed that some of these parameters (error, repeatability and resolution) should be given per section of the fiber. This can be helpful for structural health monitoring applications, where different parts of the structure to be monitored may require different quality of the measurements. It should be mentioned that the definition of resolution we propose, three times the standard deviation, is based on probabilistic theory, and is an accurate approximation. Finally we have proposed a format to present the quality of the measurements which can be very helpful for structural health monitoring applications. This format corresponds to table 1.IV. In this table, the error, 34

49 Introduction to BOTDA systems the repeatability and the strain or temperature resolution are given for different sections of the fiber. Note that this table has to be always presented with data corresponding to the conditions of the measurement such as: total length of the fiber, the loss of the fiber, the spatial resolution the number of averages and moving averages, Brillouin spectral line-width and number of steps per complete sweep. Also we have seen that even with all the performance parameters defined, it is not enough to fairly compare the performance of different instruments unless measurements in the same conditions are presented. Recently a new model of BOTDA relation to noise and fitting of the data has led to an accurate equation for the FoM of BOTDA. This equation gives a clear idea and can be used in any kind of measurements as long as the required data and parameters are calculated. Thanks to a standardized way of measuring parameters and FoM, we can now fairly compare the performance of BOTDA systems and instruments. 35

50 Chapter 1 36

51 Chapter 2: State of the art of BOTDA sensors 2.1- Introduction After explaining the basics of BOTDA systems in the first chapter, the state of the art of the BOTDA systems is presented in this chapter. In order to relate the latest advances in BOTDA systems, first the factors that limit BOTDA will be discussed in section 2.2. Once these limiting factors are clearly presented, the solutions to minimize their effects are described in the state of the art of BOTDA systems in section Factors that limit BOTDA Some SHM applications such as crack detection require spatial resolutions in the mm-order. Theoretically, with the description we have given, this could be achieved by reducing the pulse length. However, when pulse durations are on the order of the acoustic phonon lifetime, the gain generated decays considerably, leaving it negligible for pulses of 6ns or shorter. In these cases the Brillouin spectrum is not only given by equation (1.5), but by convolution between equation (1.5) and the pulse spectrum, as depicted in figure 2.1, the shorter the pulse the wider its spectrum. So the convolution results in a wider and smaller spectrum. For example, for a 1ns long pulse, corresponding to a 10cm spatial resolution, the spectral width is 1GHz, with its energy spread over this 1GHz. Therefore, conventional BOTDA s are limited to spatial resolutions around 1m (10ns pulses). Although SBS has been previously described as a strong nonlinear effect in fiber optics, it is strong when compared to other nonlinear effects such as Raman. The gain experienced by the probe wave can be lower than 1%. Therefore care must be taken when using very long fibers or fibers with high loss, since the measurement can be buried in noise. Usually high number of averaging is used to compensate for the noise, by compromising the measuring time. Pump and probe powers can be increased to obtain a 37

52 Chapter 2 higher SNR of the system, however this cannot be arbitrarily done. High pump pulses can generate modulation instability in long optical fibers. This effect is given by the interplay between anomalous dispersion and Kerr effect (Alasia, 2005), and can be avoided using normal dispersion fiber (Dong, 2010). However, in these fibers, the maximum pulse power is limited by Raman scattering of the pulse, limiting its value to 30dBm (Foaleng, 2011). Short pulse spectrum Brillouin spectrum Resulting convolution Figure 2.1: Convolution of the Brillouin spectrum with short pulse spectrum. Nonlocal effects appear when the pump pulse power is affected by the probe wave. Its main consequence is that the measurement in a given position along the fiber is influenced by the preceding locations of the fiber, so an error is generated in the measurement. This is avoided by limiting the continuous probe wave power. For long fibers (>50km), the maximum value of the probe wave can be limited to values as low as -14dBm (Thevenaz, 2011). Therefore in BOTDA sensors there is a trade-off between measuring time, spatial resolution, pump and probe powers. An important limiting factor in BOTDA technology is the discrimination between strain and temperature effects in the Brillouin frequency shift. In equation (1.4) it is clear that the linear relationship of strain and temperature is coupled, which can suppose a potential problem in field measurements. However this problem is inherent to all kinds of optical sensors (Agrawal, 2006). In the following section the state of the art of BOTDA sensors will be given, where the current solutions to the limiting factors are discussed Improved BOTDA systems In order to relate the current state of the art of BOTDA sensors to the limiting factors we have described, 38

53 State of the art of BOTDA sensors this section is divided into the solutions given to every specific limiting factor. Therefore the solutions to improve spatial resolution, to extend the measuring range and to discriminate between strain and temperature are discussed below Techniques to improve spatial resolution As it has been discussed, measurements with spatial resolutions below 1m are complex in conventional BOTDA. However, many potential applications require better spatial resolution, ideally in the mm-range. This goal has driven an important research trend in BOTDA devices. The main idea in this research trend is to pre-excite the acoustic phonon in order to generate a weak SBS interaction before the desired SBS interaction takes place. Once this weak SBS is generated, the acoustic wave is already generated, so the broadening effect is reduced. In figure 2.2 a schematic diagram of the first technique proposed taking advantage of this effect is depicted, with a pulse that has an intentionally significant level of leakage. The leakage generates a weak interaction before the pulse arrives, so shorter pulses can be used. Resolutions of 10cm have been proven with this technique (Kalosha, 2006). The pulse pre-pump of BOTDA (PPP-BOTDA) takes the leakage technique to another level. Instead of using the whole leakage of the pulse, which can have negative effects in the measurements (Zornoza, 2010), it uses just a stepped pulse, as depicted in figure 2.3. Resolutions of up to 2cm have been achieved with this technique (Kishida, 2008). In the so-called dark-pulse BOTDA technique, depicted in figure 1.4, where a temporal suppression of a continuous wave is launched, resolutions of the same order as with PPP-BOTDA have been achieved (Brown, 2007). By using phase-shift instead of dark pulses, as depicted in figure 2.5, the gain generated is doubled, by improving the previous technique considerably (Foaleng, 2010). Finally in the double pulsed technique, depicted in figure 2.6, two different interactions, with two pulses with similar characteristics but different duration, are measured. By the subtraction of the two measurements, the spatial resolution will be equivalent to the duration difference of the pulses (Bao, 2004). Resolutions of 2cm have been achieved with this technique. 39

54 Chapter 2 Actual spatial resolution Strong leakage level Probe wave Fiber optic High resolution BOTDA interaction signal Figure 2.2 Strong leakage level pulses to pre-excite the acoustic wave in order to obtain high spatial resolution BOTDA measurements. Actual spatial resolution Pre-pump Probe wave Fiber optic High resolution BOTDA interaction signal Figure 2.3 Principle of operation of PPP-BOTDA. Actual Spatial resolution Probe wave Fiber optic High resolution BOTDA interaction signal Figure 2.4: Principle of operation of Dark pulse BOTDA. 40

55 State of the art of BOTDA sensors First pulse Spatial resolution Second pulse Probe wave Fiber optic First BOTDA interaction First BOTDA interaction subtraction High resolution BOTDA trace Figure 2.5: Operation principle of double pulse BOTDA. Spatial resolution -phase Probe wave Fiber optic High resolution BOTDA interaction signal Figure 2.6: Operation principle of phase shift BOTDA Techniques to extend the Measurement range These techniques are used to overcome loss in long fibers or due to imperfections on the fiber optic network to increase the SNR of the system. The first step in this direction has been the averaging, which has already been commented on in the BOTDA working principle. Note that from equation (1.8) the increased factor in SNR given by N averaging is equivalent to sqrt(n). However, this increases the measuring time linearly. So an important research trend in BOTDA has been to increase the SNR within 41

56 Chapter 2 the limiting factors previously explained. There are different approaches, from distributed amplification to complex signal processing and modulations of the signals. Here three main techniques will be explained: Raman distributed amplification BOTDA, Simplex coded of BOTDA and self-heterodyne based BOTDA. In Raman distributed amplification BOTDA s, apart from the regular BOTDA device, continuous signals are launched to the fiber in order to amplify the pulsed pump and continuous probe waves in the fiber. These signals can be launched in both ends or in a single end or generating a Raman laser cavity in the sensing fiber (Angulo, 2012). Measurements in fibers of 120km at 3m spatial resolutions have been reached with this technique reaching a FoM of 1,800 (Soto, 2011). Spatial resolution Pulsed Pump simplex code Probe wave Fiber optic High resolution BOTDA interaction signal Figure 2.7: Operation principle of simplex coded BOTDA. In figure 2.7 the principle of Simplex coded BOTDA is depicted. Instead of a single pulse, a series of pump pulses forming a simplex code are used. The length of each pulse gives the spatial resolution of the measurement. After the interaction between pump pulses and the continuous probe wave, the probe wave is detected and decoded. Using this technique in combination with spatial resolution enhancing techniques has led to measurements in 93km long fibers at 0.5m resolutions, obtaining a FoM of 350 (Taki, 2013). Combining these two techniques with laser noise suppression techniques have led to the greatest FoM values ever achieved in BOTDA, thus the highest performance BOTDA reported: 300,000 (Soto, 2014). 42

57 State of the art of BOTDA sensors BOTDA sensors using coherent self-heterodyne detection take advantage of coherent systems, which have been widely used in fiber optic communications. Their main principle is to modulate the signals, the continuous wave in the case of BOTDA, and benefit from amplification with the carrier in detection. Also, the phase information is not lost in the conversion in opposition to any other BOTDA technique, which can be helpful for dynamic measurements (Zornoza, 2012). An improvement of twice the FoM has been reported using this technology Techniques to discriminate strain and temperature In field applications discriminating between temperature and strain influence in the measurements is of the essence. There are several techniques in order to do so. The first solution is to place two fibers in the structure to be monitored, one subject to strain and temperature variations and the second subject only to temperature measurements, by placing it loose. The temperature fiber measurements are used for compensation, and the final strain is calculated by subtracting the temperature variations of the first fiber. This solution is widely adopted in medium to short spans of fiber, where the length of the fiber can be doubled without a big penalty in the measurement quality. There are several techniques that avoid using an extra fiber in the measurements in order to differ between temperature and strain effects. The first one is measuring the line-width of the Brillouin spectrum apart from the frequency shift. The Brillouin line-width has a dependence on temperature: when the temperature increases, so does the Brillouin line-width. Nevertheless, for strain it is kept constant (Nikles, 1997). Line-width measurements are not as accurate as frequency shift measurements, therefore, using this parameter for discrimination requires very clean measurements. Errors of 4ºC and 82 have been obtained with this technique (Bao, 2004). Some special fibers have multiple acoustic modes, which have different dependence in their Brillouin frequency shift with temperature and strain. So in these fibers, by measuring the frequency shift of each 43

58 Chapter 2 Brillouin peak generated by each acoustic mode, the temperature and strain can be measured. Accuracies of 1.8ºC and 37 have been obtained with this technique (Liu, 2012). The ultimate solution with almost a perfect discrimination of temperature and strain is based measuring the dynamic acoustic gratings in a polarization maintaining fiber apart from the Brillouin frequency shift. The temperature dependence has opposite slopes for each phenomenon, so accuracies of 0.08ºC and 3 have been achieved using this technique (Zou, 2009). 2.4-Conclusions In this chapter a state of the art description of BOTDA systems has been presented. First the physical factors that limit the BOTDA performance have been explained. These factors are mainly the spatial resolution limit, the weak signal that must be used to avoid nonlinear phenomena and the discrimination between strain and temperature. Therefore the improved BOTDA systems can be classified into techniques to discriminate strain and temperature, techniques to extend measuring range or techniques to improve spatial resolution. However, high performance at a reasonable cost is hard to obtain for some applications, so improvements are still needed. In the next chapter, a simple technique to improve the measuring quality in terms of spatial resolution and strain or temperature resolution is presented. 44

59 Chapter 3: Fiber optic coils for strain, temperature and spatial resolution improvement in BOTDA 3.1-Introduction In the previous chapters an introduction to BOTDA systems has been done, by explaining the operating and measuring principles, the parameters that describe the performance and a state of the art of the systems. We have seen that the most important parameters that influence the quality of the measurements in BOTDA are the spatial resolution, the temperature or strain resolution and the temperature or strain error. The spatial resolution depends on the device and particular technique used for BOTDA interrogation, and it is mainly given by the pump pulse duration. The smaller the spatial resolution, the greater the detail of the measurement. The temperature and strain resolution and error are specified by the manufacturer and are calculated during the instrument calibration. Nonetheless, we have explained how to calculate it for a particular system and measurement, because depending on the actual measurement parameters (length, number of averages, spatial resolution ) they vary. Furthermore these parameters are different depending on the location of the fiber, and how close to the beginning of the fiber the location is. We have seen that BOTDA resolution can be as good as a few micro-strains while measuring long fibers under meter spatial resolutions. However, depending on the structural health monitoring application, this may not be sufficient. Furthermore it has been stated that the smaller the spatial resolution, the worse the resolution of the measurement. So, the performance of commercial devices is not good enough for some applications. In this chapter a solution to improve the strain or temperature and spatial resolutions of BOTDA measurements by coiling the fiber optics is presented. The principle is coiling the fiber in some points of the structure, so the measurement at that 45

60 Chapter 3 point is repeated, without increasing the measuring time. Furthermore, the effective spatial resolution of the measurements is improved, since a greater detail in the given point is obtained. In the first section of this chapter the concept of coiling fiber and the theory behind its improvement is explained. After that the actual improvement is demonstrated by real measurements using a BOTDA device with coils and the performance parameter measurement techniques explained in the previous chapters. 3.2-Coils theory In BOTDA applications the fiber is usually glued to the structure to be monitored longitudinally. However, when we are placing the fiber optic in a structure, we can actually make loops or coils of fiber in a certain point. These loops have already been proposed in literature by Zhang et al. (Zhang, 2008) in order to measure smaller strains. In this case the loop is used to amplify the strain: the fiber loop is glued only in two points, so the actual strain occurring between the two points is given by: ave = w w (3.1) where ave is the actual strain, w the measured strain along the fiber, L w the total coil length and L the actual length between the two points. In our case, what we propose is actually creating fiber loops. These loops, that will be called coils from now on, should be completely glued to the structure, as shown in figure 3.1. This way, the same strain measurement is repeated at each loop of the coil. Fiber in Glue to attach to structure Coil Fiber out Figure 3.1: Schematic example of coiled fiber glued to structure. Figure 3.2 shows two examples of strain in the structure and the effect on the coil. In the first one longitudinal strain is applied. We can see that the coil is deformed, so the strain at this point can be 46

61 Fiber optic coils for strain, temperature and spatial resolution improvement in BOTDA measured by the coil. In the second, a vertical force applied in the coil center deforms the structure, causing the coil radius to increase. From now on we will concentrate on this second case. In conventional measurements, where the fiber is placed longitudinally, the strain variations must happen within a length equal or greater than the spatial resolution in order to be fully measurable. However, by using these coils, we can measure the strain as long as the total length of the coil is greater than the spatial resolution. Furthermore the strain is uniform in all points of the coil. load load Deformed structure Deformed structure Coil before strain Coil after strain Coil before strain Coil after strain (a) (b) Figure 3.2: schematic of effect of strain in the coil when deformation is longitudinal (a) or generated by a point load applied in the center of the coil (b) Let s take the measurement example depicted in figure 3.3. In this example the coil is 5-m long with a radius of 5cm. The load applied in the center has generated 20 in the coil. We can see that all along the length of the coil the strain is measured uniformly. The fact that the strain is uniform all along the fiber coil is in our advantage to improve the strain resolution: instead of using the measured strain at each point, the average all along the coil can be calculated. This value is the strain applied to the coil. 47

62 Chapter 3 25 Strain (microstrain) Coil length Average gives strain applied to coil Distance (m) Figure 3.3: example of a measurement in a coil. The strain in the coil is uniform, so the average can be taken as the significant value. Usually in BOTDA measurements, since the sampling interval is greater than the spatial resolution, moving average filters can be used during the data processing stage, as explained in chapter 1. These filters consist in averaging the value for a position with the previous and succeeding values. The effect of the moving average is smoothing the data, by improving the resolution N 1/2 times, where N is the number of values taken in the averaging. Therefore, the effect of coiling and calculating the average would give us a resolution improvement given by the length increase obtained in the loop, and can be expressed as: s u i n = c i e = eg a N p (3.2) where 3s coiled is resolution of strain or temperature of the coiled fiber section, 3s regular is the resolution of the measurement without coiling and N loop 1/2 is the improvement due to averaging. Therefore the value of N loop would be given by: N p = w movav (3.3) 48

63 Fiber optic coils for strain, temperature and spatial resolution improvement in BOTDA where, L movav is the Length corresponding to the N values moving average, or the length in space of the moving average. Furthermore, if the total length of the coil, L w is greater than the spatial resolution of the BOTDA device, L w >Δz, we obtain an improvement in the spatial resolution. In this case we are assuming that the strain at each point along the coil is the same, so the new spatial resolution is given by the circumference of the coil: Δz c i π (3.4) Where, r is the radius of the coil. We can furthermore calculate the improvement given in the figure of merit with and without coiling by: FoM imp vement = Δz Δz coil N loo (3.5) In table 3.I some examples of the improvement achieved using different coils are presented. For example, in the first case, we have that the spatial resolution is 1m, the moving average is 0.8m, the coil length is 5m with 30 loops of a radius of 0.03m, the spatial resolution improvement following equation (3.4) is given by: Δz imp vement = Δz Δz coil = 1m 2π(0.03m) = 5. 1 (3.6) The improvement in strain or temperature resolution, following equation (3.2) is given by: s u i n i n = 3σ la 3σ coil = N p = w movav = =.66 (3.7) Note that the improvement is exactly the same for the repeatability, since as explained in chapter 1, resolution and repeatability are proportional to standard deviation. Finally we can calculate the FoM improvement following equation (3.5): FoM imp vement = Δz Δz coil N loo = 2π(0.03m) 1m = 14.1 (3.8) Following the same procedure, the calculations for the rest of the cases are obtained. We can see that 49

64 Chapter 3 the improvement is very important, by increasing the strain/temperature resolution up to 3.98 times. Also, we can see that the spatial resolution increase is not negligible, of up to 5.31 times. This has a big impact in the FoM, which increased in all cases, with a maximum improvement of 14.1 times. Spatial resolution ( z) (m) Moving average length (L movav ) (m) Number of loops Coil radius (m) Coil length (L w ) (m) Coil spatial resolution ( z coil ) (m) Strain / temperature resolution improvement Spatial resolution improvement FoM improvement Table 3.I: examples of improvement for different systems with different coils. 3.3-Experimental results of comparing coils and no coils Three coils were fabricated for a proof of concept demonstration of the improvement of the system. The measuring instrument was a Neubrex Neubrescope NBX It is a high performance device than can measure strain and temperature at resolutions of up to 50 with 25- resolution at 2 13 averages in a 5- km long fiber with 20cm spatial resolution (Neubrex, 2014). The fiber network and parameters (number of averages ) we have, however, are different from these. So we should recalculate the parameters for our particular case. In figure 3.4 the implementation of one of the coils is shown. The fiber is carefully coiled and glued to the structure using epoxy. The hole in figure 3.4(a) corresponds to an anchorage through a rod, which will be under tension. The average diameter of the coil is 24.5mm. The coil is composed of six loops, 50

65 Fiber optic coils for strain, temperature and spatial resolution improvement in BOTDA giving us a total length of L w =0.46m. Then, the theoretical spatial resolution is near 7.7cm, calculated following equation (3.4): Δz c i π = π(1. 5c ) = 7.70c (3.9) Figure 3.4(b) shows the whole setup where the coil has been adhered with epoxy to the surface of a steel beam. Note that there is the rod at the center of the coil. The objective of the coils is to measure the local strain at the anchorage. A reference fiber, not affected by strain is needed for temperature compensation. The loose fiber wrapped around the rod is used for this, since the temperature measured at this loose fiber is the same as the one in the loop, meanwhile it is not affected by the strain at all. Note that this loose fiber just needs to be longer than the spatial resolution in order to get an accurate temperature measurement. In order to not affect the resolution, it should be longer than the coil too. In our case it is 1.3m long, and the temperature taken for compensation is the average temperature measured along its length. Note that the radius of the coil is small, only 12.25mm. The diameter of the coils was selected based on the geometric requirements of the structure subjected to test. (a) (b) Figure 3.4: (a) the proposed coil. (b)rod, deck, coil and temperature compensating wrapped fiber. Distributed strain measurements were performed in order to estimate the actual strain resolution of the system. A 100-m long fiber optic was used for the experiment and the spatial resolution was set to 51