ABSTRACT 1. INTRODUCTION

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1 Dynamic shape sensing using a fiber Bragg grating mesh Douglas Bailey, Nikola Stan, Spencer Chadderdon, Daniel Perry, Stephen Schultz, Richard Selfridge Department of Electrical and Computer Engineering, Brigham Young University, 459 Clyde Building, Provo, UT ABSTRACT When fiber Bragg gratings (FBG) are tightly packed in a mesh and their peaks get close at a distance on the order of individual FBG spectrum widths, they start overlapping and there is a distance below which both peaks won t be detectable anymore using standard peak detection method. Ability to determine locations of individual peaks even after they overlap allows more gratings in a mesh and an increase in shape sensing resolution. We use a linear interpolation method to estimate peak locations when peaks overlap and become undetectable with standard peak finding technique. We test this algorithm on experimentally obtained data and compare peak locations obtained by the algorithm to exact peak locations. We analyze the error to show that algorithm performs well when velocity of peaks stays uniform during peak crossing. However, the error rapidly increases if the velocity changes during crossing and the maximum error can occur in a situation when peaks change direction during peak crossing. Keywords: shape sensing, fiber Bragg grating, peak tracking, interpolation, mesh. 1. INTRODUCTION Shape sensing is useful in a variety of applications including medicine 1, health monitoring of structures such as offshore oil vessels 2, windmills 3, spacecrafts 4, etc. Knowing an object s shape allows evaluation of its condition during stress or its position in relation to other objects. One common method of shape sensing involves the use of Fiber Bragg gratings (FBG). FBGs have very high strain sensitivity and thus can be used to measure even the smallest changes in shape. Research has been done in using multiple FBG sensors configured in arrays to detect shape changes 1,3,4,5,6. Parallel FBG arrays forming a mesh provide sensitivity over a wider area and multiple dimensions. The accuracy of the shape sensing depends on the number of FBGs used. Commonly, FBG peaks in an FBG array are spread out over a wide wavelength range to prevent them from interacting and crossing each other. When a number of such FBG sensors are packed together in an array, they span a wide wavelength range. As the total number of FBGs and the wavelength range increases, the interrogation difficulties emerge such as nonlinearity of broadband sources and filters over a wide wavelength range. In order to avoid these interrogation problems, individual FBG peaks can be packed closer together in wavelength, however at the expense of allowing the overlapping and crossing of two adjacent FBG peaks in certain cases. For example, suppose two adjacent FBG peaks are close in wavelength and large strain is induced in one of them, but not the other. In this case one peak will overlap the other and at one point it will be impossible to detect both peak locations. Both peaks will again be detectable only after the strained FBG peak crosses to the other side of the stationary FBG peak or returns back, but then the two peaks also need to be correctly identified. In this paper we propose a solution to the problem of detecting and identifying FBG peaks packed in a narrow wavelength range. Our algorithm assumes that a peak moves linearly from the moment it becomes obscured by the adjacent peak to the moment when it is detectable again. The algorithm finds the last known location before the crossing and the first known location after the peak has become detectable again and then it linearly interpolates the values between the two points. In this paper, in Section 2, we first provide background on the use of FBGs in detecting strain and we show how close two peaks can be to each other to still be detectable. In Section 3 we present the proposed linear interpolation algorithm for estimating peak locations during peak crossing. Section 4 describes the experimental setup and measurement results with analysis of the linear interpolation approach. In conclusion, the problem and proposed solution are reviewed and the main results are summarized. Smart Sensor Phenomena, Technology, Networks, and Systems Integration 2013, edited by Kara J. Peters, Wolfgang Ecke, Theodoros E. Matikas, Proc. of SPIE Vol. 8693, SPIE CCC code: X/13/$18 doi: / Proc. of SPIE Vol

2 2. BACKGROUND Fiber Bragg grating (FBG) is an optical fiber sensor that reflects light propagating through the fiber in a narrow wavelength range. The central wavelength is called the Bragg wavelength and is given by λ B = 2NΛ, (1) where Λ is the period of the grating and N is the effective index of the optical fiber mode. Applied strain results in a change in the grating period Λ and a change in the effective index of the fiber. The combination of these two effects results in a shift of the entire reflection spectrum. The shift for a standard FBG is 1.2 pm/με 7. The most common method for determining the strain is to track of the peak reflection 7. Peak c E Qo.a Relative wavelength [nm] Figure 1. Fiber Bragg grating reflection spectrum with the peak indicated by the dashed line. Figure 1 shows the reflection spectrum of a grating in terms of normalized optical power and relative wavelength where zero corresponds to the location of the Bragg wavelength or the peak in the reflection spectrum. As strain changes, the spectrum will shift right or left depending respectively on tensile or compressive nature of induced strain. The shape of the spectrum remains unchanged if applied strain is uniform along the grating length, which will be the case if strain changes are negligible over the length of 1 cm which is the standard length of FBGs. This means that strain can be dynamically measured by locating the peak of FBG reflection spectrum in time. In this paper all peak detection is performed using Matlab function findpeaks(). This function finds all local maximums in a given spectrum and returns the highest maximum in a specified range, i.e. within the minimum peak distance (MPD). The MPD parameter has to be big enough to include all local minima on a single FBG peak but not to include local minima on adjacent FBG peak in multiple FBG configurations. The upper limit for MPD parameter is the closest distance of two peaks in a multiple FBG configuration where both peaks are still detectable. Proc. of SPIE Vol

3 I I II I I I I I I I I I I I I I I I I I I I I Detected peak Undetected peak a 0) 0.8- N 0.6- E Z Q E5; Wavelength [nm] Wavelength [nm] (a) (c) $ Wavelength [nm] (b) Wavelength [nm] (d) Figure 2. Peak detection of two FBG spectra when: (a) peaks are far apart (detected peaks shown in dashed lines), (b) lower reflection peak is barely detectable, (c) lower reflection peak is undetectable (actual location of undetectable peak shown in dash-dot line), (d) two peaks perfectly match. Figure 2 illustrates the limitation in detecting two FBG peaks in a multiple FBG configuration. When two peaks are far apart, Figure 2a shows that the peak detection functions independently for both peaks. When peaks get close enough so their distance is on the order of individual FBG spectrum widths, Figure 2b shows that they start interacting with each other and there is a minimum distance at which both peaks are still detectable, the minimum detectable distance (MDD). This distance will depend on the difference in reflectivity between two peaks, specifically the spectral width of the higher reflectivity peak at the reflectivity level at the maximum of the smaller peak. For example, if the smaller reflectivity peak was half the reflectivity of the higher peak, MDD would be half the 3dB width of the higher peak. When peaks come closer to each other than distance MDD, Figure 2c shows that only the higher reflectivity peak will be detectable. In these two critical cases (Figure 2b and Figure 2c) the spectrum shapes can be hardly visually distinguished. It should be noted that the closer in reflectivity two peaks are, the smaller their MDD will be, i.e. the closer they will be able to come together and still be both detectable. Figure 2d shows the extreme case when two peak locations match and the lower reflectivity peak is entirely hidden by the higher reflectivity peak. In this case Figure 2d shows that the spectrum looks nearly identical to spectrum of just the higher reflectivity FBG peak. In order to address the problem of peak tracking in a tightly packed FBG array configuration, we made an experimental setup to obtain practical shape sensing data. Shape sensing resolution is reduced to just two points by using only two FBGs in an array, but this doesn't limit the generality of the analysis, nor the conclusions. PD TIA FFP M 50:50 ISO 50:50 4- FBG FBG LD LD OSC FGEN Figure 3. Experimental setup. Figure 3 shows the experimental setup used for obtaining the practical shape sensing data. Amplified spontaneous emission (ASE) light source and Erbium doped fiber amplifier (EDFA) generate a broadband optical signal that is incident on two FBG sensors connected through a 2x2 50:50 splitter. The two FBG sensors can be independently strained to simulate different shape sensing scenarios. In the parallel branch of the splitter are two tunable lasers coupled through a 2x1 50:50 splitter with an isolator. Laser light and FBG reflections go through the Micron Optics FFP-TF2 fiber Fabry Perot (FFP) tunable filter with a narrow passband and then to the photodetector (PD), transimpedance Proc. of SPIE Vol

4 amplifier (TIA) and into the oscilloscope (OSC). The spectrum, which includes the two laser peaks and two FBG reflection peaks, is captured by sweeping the narrow passband of the FFP filter over the relevant wavelength range. The FFP wavelength is controlled with a sinusoidal signal from a function generator (FGEN) which is also observed on the oscilloscope. -a ñ elength i i -----Inpr-Y _ 11 _,_' -6- Normalized power [ %] w Voltage Figure 4. Spectrum interrogation method and data representation in time: (a) sinusoidal wavelength tuning voltage with a period Δ t, (b) measured optical signal, (c) extracted optical spectra and (d) false color representation of the spectra in time. Figure 4 shows the captured spectrum data and its representation. All graphs have the time axes aligned and are synchronized in time. Figure 4a illustrates that Δ t is the period of the sine waveform controlling the transmission wavelength of the FFP. Figure 4.b shows the observed optical signal. The full spectrum is captured twice during a single period Δ t, once during the rising and once during the falling edge of the sinusoid. One of these two spectra can be discarded in order to avoid problems of asymmetric filter response and spectral alignment. Since every FFP control voltage value corresponds to a wavelength value, voltage values in Figure 4a can be directly converted to wavelength values and combined with the extracted spectra in Figure 4c to represent full spectrum data in time. Figure 4d shows how the spectral data can be combined as a false color image to visualize how the spectrum changes over time. 3. LINEAR INTERPOLATION ALGORITHM In order to estimate peak location when two FBG peaks overlap, i.e. get closer than MDD, we suggest using a simple linear interpolation algorithm. The algorithm is applied on a data set containing time varying spectrum measurements such as described in Section 2. First, peak tracking is performed on all spectra in the given data set and arrays are Proc. of SPIE Vol

5 created with each peak s location in time. The two FBG peaks can be distinguished because of their different reflected optical power, i.e. reflectivity. The FBG with the higher reflectivity (FBG2) will always have a detectable peak, while the FBG with the lower reflectivity (FBG1) will have a detectable peak only when its distance from FBG2 is greater than MDD. Search array for zeros Search for peaks Find peak locations before and after zeros Insert a zero value when peak not found 'if Linear interpolation of peak locations between two end points (a) (b) Figure 5. Block diagram of linear interpolation algorithm showing: (a) method of adding zeros when the peak is not found, and then (b) linear interpolation between two known peak locations. Figure 5 shows a block diagram of the linear interpolation algorithm. First, peak detection is performed by applying Matlab findpeaks() function on all the measured spectra. Arrays are created with detected peak locations and zero values when multiple peaks cannot be detected. These zero values are then sequentially searched for in the resulting arrays. When the first zero in a sequence is found, the value immediately before it is recorded and the subsequent zeros are skipped to the first non-zero value. These zero values are then replaced by a series of values generated by linear interpolation between the two recorded non-zero values Ê 1551 g Detected peaks Interpolated values Minimum detectable distance (MDD) E Time [ms] Figure 6. Locations of FBG1 and FBG2 peaks as functions of wavelength and time. The continuous solid line represents the peak locations of FBG2 and the solid line with a discountinuity is FBG1. The dashed line indicates the MDD between two peaks. Dotted line represents the interpolated values when peaks are closer than MDD. Figure 6 shows locations of FBG1 and FBG2 peaks in time and illustrates how the linear interpolation algorithm works. Solid lines represent locations of detected FBG peaks using Matlab findpeaks() function. Discontinuity in FBG1 peak location curve happens when it approaches FBG2 at a distance closer than MDD, which is indicated with dashed lines. The missing values in the FBG1 peak location curve are populated using linear interpolation between two nearest known peak locations, which is shown with a dotted line. Proc. of SPIE Vol

6 Height at Peak Estimate > = FBG1 Peak Height En >m Detected peaks Interpolated values Minimum detectable distance (MDD) Ves Good Peak Estimate Move FBG1 Peak Estimate 1 Sample Closer to FBG FBG Time [ms] (a) (b) Figure 7. (a) Block diagram of algorithm that ensures peak estimates are plausible. (b) The dotted line represents the region where values are higher than or equal to FBG1 peak heights. We want to ensure that are estimates are within that region. The problem with this algorithm occurs when FBG1 and FBG2 peaks overlap and move together for a while before FBG1 peak comes out on the same side from which it originally came from. In this case linear interpolation creates nonrealistic peak values. To overcome this problem we extend the basic linear interpolation algorithm in the following way. Every time a data point is calculated using linear interpolation, the estimated peak location is checked for plausibility by verifying that at the estimated data point the measured spectrum has higher reflectivity than the precalculated FBG1 peak reflectivity. If this is true, then FBG1 peak is hidden behind the higher reflectivity FBG2 peak, i.e. it is located within the MDD region, and linear interpolation gives valid results. If the reflectivity of the measured spectrum at the estimated point is lower than the FBG1 peak s reflectivity, than we know that the peak cannot be there and interpolation is wrong. In this case we move the estimated point towards the location of FBG2 peak until we reach a point with reflectivity equal to FBG1 peak. This causes the FBG1 peak to be tracked as if it was moving along the edge of the MDD region until it could be detected again. Advantage of this algorithm extension is its simplicity and smoothness of the obtained peak location curve. 4. MEASUREMENTS 4.1 Linearity In Section 2, the experimental setup and spectrum measurement were described. Assuming linear response of the optical filter, every voltage value applied to FFP corresponds to a proportional wavelength value. In order to sweep the wavelength across the desired range we naturally first think of tuning FFP with a control voltage that is linear in time, e.g. a triangle waveform. However, the problem with triangle waveform is its infinite frequency content which could cause unexpected results due to FFP response to higher frequency harmonics. These problems can be avoided by driving the FFP with a sinusoid voltage with frequency content of just one single frequency. Using a sinusoid instead of a triangle waveform replaces frequency response problems with linearity problems. However, sinusoid non-linearity can be solved in two simple ways, either by appropriate calibration or by reducing the non-linearity to negligible values by increasing the sinusoid voltage amplitude. In our work we opted for the latter solution. Proc. of SPIE Vol

7 4 laser laser Y FBGsi il o -1-2 Y Figure 8. Linearity of the sinusoid filter tuning voltage at 6.4 Vpp: sinusoid edge compared to a straight line as a tuning voltage for spectrum measurement. Figure 8a shows the rising edge of the sinusoid at 1 khz and 6.4 Vppp used to drive the FFP tunable filter compared to a straight line. Also shown is the measured spectrum containing the reflection peaks of the FBGs and the two tunable laser peaks. Two tunable lasers are tuned to the two end wavelengths off the wavelength range corresponding to the total anticipated strain of the FBGs during the test. Using the known laserr wavelengths, the transmission wavelengths of the FFP are linearly mapped to the driving voltage. The wavelength span between the two lasers is 4.26 nm. Using the previously measured FFP wavelength tuning voltage rate of 4.92 pm/ /mv and FFP driving voltage at the spectrum edge of 0.47 V we can calculate that the linearity error of 0.4% in FFP driving voltage corresponds to absolute wavelength error of (470 mv)(0.4%)(4.92 pm/mv) = 9.3 pm. While linearity increases with amplitude of the driving voltage, and since this will also increasee the slope of the linear sine region, the number of samples between the two laser peaks will decrease. This means theree is a trade-off between linearity and spectral resolution. For an oscilloscope sampling rate of 25 MS/s the spectral resolution is about 4 pm. With the absolute wavelength errorr and spectral resolution on the same order, our system is now optimized. 4.2 Results FBG; FBG1 sub peak (FBG,1).may w.,j V..h.., -\,-...N ! W ravelength [nm] Figure 9. Reflection spectrum of the two FBGs used to test thee algorithms. In order to demonstrate the peak tracking algorithm, two FBGs with reflection peaks close in wavelength were subjected to uncorrelated time-varying strain. Figure 9 shows the reflection spectrum of the two FBGs, FBG1 and FBG2. The 3dB Proc. of SPIE Vol

8 widths of FBG1 and FBG2 are respectively 159 pm and 166 pm. The MDD for these two FBGs is 115 pm which corresponds to a strain value of 138 με. Ê 154' _c 155 FL> > FBG Time [ms] 400 Figure 10. FBG peak location extraction from false-color mapping of time-varying wavelength spectrum. Sub peak of FBG1 is used as reference to generate the exact FBG1 peak location. For this test, FBG1 was specifically chosen because of the presence of a large sub-peak which allows us to accurately determine exact peak locations of the two FBGs even when they cross or overlap. Figure 10 shows the time-varying spectral response of the FBG peaks with the use of the sub peak to determine the exact location of FBG1 peak as it overlaps with the FBG2 peak. This data is then used to quantify the accuracy of the peak tracking algorithm in terms of relative wavelength error. Proc. of SPIE Vol

9 Ê C 1550 (a) FBG1 - Linear interpolation FBG1 - Exact peak location FBG2 (b) 0_ o á> 20 o (c) ca Ê Q- 50 ó Time [ms] 600 Figure 11. (a, c) Measured spectra of the two FBGs with superimposed peak tracking data and (b, d) wavelength error as a difference between the exact peak location (solid line) and peak location computed using the interpolation algorithm (dashed line). The linear interpolation algorithm works best when FBG1 crosses FBG2 with uniform velocity. When the two peaks cross each other with little to no acceleration the error is small. Figure 11a shows a case where FBG1 moves uniformly across FBG2. Figure 11b shows that the maximum error is 20 pm, which is much less than the MDD of 115 pm. The linear interpolation algorithm yields higher error in cases where FBG1 moves with a variable velocity across FBG2. In such cases the error can be far greater. The algorithm assumes that the FBG1 is moving with a uniform velocity. If the FBG1 peak accelerates while overlapped with FBG2 the error increases rapidly. The greatest error occurs when FBG1 almost completely crosses FBG2 and then changes direction to move the other way (Figure 11c). Because FBG1 is undetectable at distances up to 115 pm from FBG2 s peak location, the maximum possible error is 230 pm. This would occur if FBG1 crossed over the FBG2 peak, moved to the maximum distance MDD on the other side and then crossed back over the FBG2 again. The linear interpolation algorithm in this case estimates peak locations that run along the edge of MDD region of FBG2 because it is unable to predict FBG1 s movement within this region. In this case interpolation algorithm estimates peak location up to 230 pm away from the actual location. This corresponds to a maximum strain error of 276 με. Future research could address this problem by considering peak tracking methods that account for the FBG spectrum width and not just on the local maxima. 5. CONCLUSION We analyze the possibilities of using multiple FBGs to sense dynamic shape changes by measuring strain induced in FBGs configured in a mesh. Since strain can, in a general case, be different on each FBG, when FBGs are packed tightly Proc. of SPIE Vol

10 in a narrow wavelength range we run into the problem of peaks crossing each other and it becoming impossible to track their exact location. We calculate the minimum detectable distance between two FBG peaks at which they are still both detectable. Then we present a linear interpolation algorithm for tracking peak locations when two FBG peaks are undetectable. We describe the experimental setup and method used for obtaining and representing shape sensing data with two FBGs. We then test the proposed algorithm on thus obtained experimental data in order to compare the peak locations estimated by the algorithm with the exact peak locations obtained by tracking a sub-peak. We show that if the velocity of FBG peaks doesn t change during peak crossing the error is less than 20 pm. On the other hand, the error increases if FBG peak has a nonzero acceleration while crossing the other peak. In a special case, if the peak changes its direction during peak crossing, the maximum wavelength error can go up to twice the minimum detectable distance, which in our specific case is 230 pm, which corresponds to 276 με maximum strain error. REFERENCE [1] Xinhua Yi; Jinwu Qian; Linyong Shen; Yanan Zhang; Zhen Zhang;, "An Innovative 3D Colonoscope Shape Sensing Sensor Based on FBG Sensor Array," Information Acquisition, ICIA '07. International Conference on, vol., no., pp , 8-11 July 2007 [2] Roberts R. D. G, Insensys Oil & Gas; Garnham S., BP; D all B., Technip;, Fatigue Monitoring of Flexible Risers Using Novel Shape-Sensing Technology, Offshore Technology Conference, [3] Hyung-joon Bang; Suk-whan Ko; Moon-seok Jang; Hong-il Kim;, "Shape estimation and health monitoring of wind turbine tower using a FBG sensor array," Instrumentation and Measurement Technology Conference (I2MTC), 2012 IEEE International, vol., no., pp , May 2012 [4] Blandino Joseph R., Duncan Roger G, Nuckels Michael C., Cadogan David, Three-Dimensional Shape Sensing for Inflatable Booms, Structures, Structural Dynamics & Materials Conference, 2005 [5] Lae-Hyong Kang, Dae-Kwan Kim, Jae-Hung Han, Estimation of dynamic structural displacements using fiber Bragg grating strain sensors, Journal of Sound and Vibration, Volume 305, Issue 3, , 21 August 2007 [6] M A Davis et al, Shape and vibration mode sensing using a fiber optic Bragg grating array, Smart Materials and Structures, Vol. 5 No. 6 (1996) [7] A. Othonos and K. Kalli, [Fiber Bragg Gratings], Artech House Publishers, (1999). Proc. of SPIE Vol