## A novel fast phase correlation algorithm for peak wavelength detection of fiber Bragg grating sensors |

Optics Express, Vol. 22, Issue 6, pp. 7099-7112 (2014)

http://dx.doi.org/10.1364/OE.22.007099

Acrobat PDF (3014 KB)

### Abstract

Fiber Bragg Gratings (FBGs) can be used as sensors for strain, temperature and pressure measurements. For this purpose, the ability to determine the Bragg peak wavelength with adequate wavelength resolution and accuracy is essential. However, conventional peak detection techniques, such as the maximum detection algorithm, can yield inaccurate and imprecise results, especially when the Signal to Noise Ratio (SNR) and the wavelength resolution are poor. Other techniques, such as the cross-correlation demodulation algorithm are more precise and accurate but require a considerable higher computational effort. To overcome these problems, we developed a novel fast phase correlation (FPC) peak detection algorithm, which computes the wavelength shift in the reflected spectrum of a FBG sensor. This paper analyzes the performance of the FPC algorithm for different values of the SNR and wavelength resolution. Using simulations and experiments, we compared the FPC with the maximum detection and cross-correlation algorithms. The FPC method demonstrated a detection precision and accuracy comparable with those of cross-correlation demodulation and considerably higher than those obtained with the maximum detection technique. Additionally, FPC showed to be about 50 times faster than the cross-correlation. It is therefore a promising tool for future implementation in real-time systems or in embedded hardware intended for FBG sensor interrogation.

© 2014 Optical Society of America

## 1. Introduction

1. K.O. Hill, Y. Fujii, D. C. Johnsen, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. **32**, 647–649 (1978). [CrossRef]

2. G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse folographic method,” Opt. Lett. **14**, 823–825 (1989). [CrossRef] [PubMed]

3. K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. **15**(8), 1263–1276 (1997). [CrossRef]

6. X. Shu, Y. Liu, D. Zhao, B. Gwandu, F. Floreani, L. Zhang, and I. Bennion, “Dependence of temperature and strain coefficients on fiber grating type and its application to simultaneous temperature and strain measurement,” Opt. Lett. **27**(9), 701–703 (2002). [CrossRef]

7. S. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodulation system for guided-wave Bragg grating sensors,” IEEE Photonics Technol. Lett. **4**(5), 516–518 (1992). [CrossRef]

8. G. A. Ball, W. W. Morey, and R. K. Cheo, “Fiber laser source/analyzer for Bragg grating sensor array interrogation,” J. Lightwave Technol. **12**(4), 700–703 (1994). [CrossRef]

9. R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett. **31**(20), 2975–2977 (2006). [CrossRef] [PubMed]

9. R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett. **31**(20), 2975–2977 (2006). [CrossRef] [PubMed]

10. C. G. Atkins, M. A. Putnam, and E. J. Friebele, “Instrumentation for interrogating many-element fiber Bragg grating arrays,” Proc. SPIE **2444**, 257–267 (1995). [CrossRef]

11. A. Ezbiri, S. E. Kanellopoulos, and V. A. Handerek, “High resolution instrumentation system for fiber-Bragg grating aerospace sensors,” Opt. Commun. **150**, 43–48 (1998). [CrossRef]

12. J. M. Gong, J. M. K. MacAlpine, C. C. Chan, W. Jin, M. Zhang, and Y. B. Liao, “A novel wavelength detection technique for fiber Bragg grating sensors,” IEEE Photonics Technol. Lett. **14**(5), 678–680 (2002). [CrossRef]

13. C. Caucheteur, K. Chah, F. Lhommé, M. Blondel, and P. Mégret, “Autocorrelation demodulation technique for fiber Bragg grating sensor,” IEEE Photonics Technol. Lett. **16**(10), 2320–2322 (2004). [CrossRef]

14. C. Huang, W. Jing, K. Liu, Y. Zhang, and G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photonics Technol. Lett. **19**(9), 707–709 (2007). [CrossRef]

15. L. Negri, A. Nied, H. Kalinowsky, and A. Paterno, “Benchmark of peak detection algorithms in fiber Bragg grating interrogation and a new neural network for its performance improvement,” Sensors **11**, 3466–3482 (2011). [CrossRef]

16. L. Gui and S. T. Wereley, “A correlation-based continuous window-shift technique to reduce the peak-locking in digital PIV evaluation,” Experiments Fluids **32**, 506–517 (2002). [CrossRef]

17. A. C. Eckstein and J. Charonko, “Phase correlation processing for DPIV measurements,” Experiments Fluids **45**, 485–500 (2008). [CrossRef]

18. M. Raffel, C. Willert, and J. Kompenhans, *Particle Image Velocimetry—A Practical Guide* (Springer, 1998). [CrossRef]

19. K. T. Christensen, “On the influence of peak-locking errors on turbulance statistics compared from piv ensembles,” Experiments Fluids **36**(3), 484–497 (2004). [CrossRef]

20. J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. **8**(12), 1379–1392 (1997). [CrossRef]

## 2. Fast Phase Correlation (FPC) working principle

*R*(

*λ*), where

_{j}*λ*represents the

_{j}*j*element of the wavelength vector and

^{th}*j*=1,2,...,(

*N*−1). The number of samplings

*N*depends on the wavelength scanning range

*λ*−

_{max}*λ*and on the wavelength resolution

_{min}*δλ*.

*R′*(

*λ*), for

_{j}*j*=1,2,..., (

*N*−1). Assuming that there is no distortion of the spectrum, the perturbed spectrum

*R′*(

*λ*) can be rewritten as where Δ

_{j}*λ*is the wavelength shift between

*R*and

*R′*. In order to evaluate Δ

*λ*, the FPC algorithm first computes the fast Fourier trasforms ℜ(

*k*) and ℜ′(

*k*) of

*R*(

*λ*) and

_{j}*R′*(

*λ*) respectively with

_{j}*k*indicating the generic Fourier spectral line and

*M*the maximum number of spectral lines considered in the analysis.

*k*, starting from

*k*= 2 to

*k*=

*M*, an estimation

*λ*is then obtained taking the median value of the previously computed estimates The choice of the median instead of other metrics, such as the mean, stems from considering the robustness of the computation: the median is less sensitive to outliers. It must be noted that one normally chooses

*M*=

*N*. In this case, however,

*M*can be set to be considerably lower than

*N*, since only the first few frequency lines of

*R*and

*R′*contain energy. Such an energy distribution is due to the shape of both spectra

*R*and

*R′*, which can be approximated by “sinc” functions. If the main lobe width of these sinc functions is indicated by

*r*, then the Fourier transforms ℜ and ℜ′ result to be rectangular-shaped, with energy distributed only within the frequency band 0−

_{B}*r*/2. Therefore, the narrower is the peak, the lower is the number of spectral lines

_{B}*M*required for the analysis. When

*M*<<

*N*, as in Eqs. (3)–(4), the FPC algorithm avoids to compute (

*N*−

*M*) ×

*N*terms for each of the FFT in Eqs. (3)–(4), with a consequent advantage in terms of execution speed.

## 3. Simulation and results

### 3.1. Simulation of FBG under dynamical strain

*z*is the mode direction of propagation,

*R*(

*z*) and

*S*(

*z*) are the amplitudes of the forward-and backward-propagating modes.

*k*and

_{dc}*k*are respectively the “dc” and “ac” self-coupling coefficients. For a uniform grating

_{ac}*k*and

_{dc}*k*can be expressed as [21, 22

_{ac}22. H. Y. Ling, K. T. Lau, W. Jin, and K. C. Chan, “Characterization of dynamic strain measurement using reflection spectrum from a fiber Bragg grating,” Opt. Commun. **270**, 25–30 (2007). [CrossRef]

*n*

_{eff}is the effective index modulation,

_{0},

*λ*= 2

_{D}*n*

_{eff}Λ

_{0}is the designed Bragg wavelength and

*ν*is the fringe visibility. Assuming that the length of the grating is

*L*, the reflecivity is given by Using the T-matrix formulation Eq. (11) can be computed as follows: where

*m*is the number of sections in which the grating is divided and

*T*is the

_{r}*r*transfer matrix In order to simulate the dynamical behavior of the FBG, the following strain function along the

^{th}*z*axis is assumed where

*C*

_{0}is a constant. In this circumstance, the design wavelength

*λ*in (9) becomes where

_{D}22. H. Y. Ling, K. T. Lau, W. Jin, and K. C. Chan, “Characterization of dynamic strain measurement using reflection spectrum from a fiber Bragg grating,” Opt. Commun. **270**, 25–30 (2007). [CrossRef]

23. Y. J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. **8**, 355–377 (1997). [CrossRef]

*p*

_{11}and

*p*

_{12}are the components of the fibre-optic strain tensor and

*υ*is the Poisson’s ratio. At each time step, the developed Matlab script recalculates the value of

*λ*and refreshes the value of

_{D}*k*needed for the computation of the reflectivity according to Eq. (11). This numerical procedure was used to simulate the behavior of an FBG with

_{dc}*L*= 10

^{−2}m, Λ

_{0}= 10

^{−7}m,

*n*

_{eff}= 1.452,

*ν*= 1,

*p*

_{11}= 0.121,

*p*

_{12}= 0.270,

*υ*= 0.17. The Bragg wavelength of the grating in a strain-free state is 1540.16 nm. The normalized reflectivity was computed for a uniform strain of

*C*

_{0}= 10

^{−4}

*με*. Figure 1 shows the normalized reflectivity and the wavelength shift Δ

*λ*as a function of time.

_{D}*ε*(

*z*), the reflectivity can be directly calculated from the exact solution. However, the transfer matrix-method was hier used in order to implement a procedure capable to perform the analysis on any kind of grating subjected to any kind of axial strain. In future works a similar procedure will be used to simulate and analize the behavior of FBG under dynamical non uniform strain fields.

### 3.2. Processing of simulated FBG spectra and performance analysis

*R*(

*k*) while the reflectivity at each time instant was taken as the vector

*R′*(

*k*). To simulate signals with different signal-to-noise ratios, white Gaussian noise (AWGN) was added to the instantaneous reflectivity. Signals were generated for SNR values of 30 dB up to 60 dB in steps of 5 dB. For each SNR level, the wavelength shift was computed 500 times to determine the statistics of the peak detection error. Figure 2 provides a graphical explanation of the procedure.

*σ*and accuracy

_{SNR}*δ*of the FPC algorithm for each SNR were computed according with the following definitions: where Δ

_{SNR}*λ*is the calculated wavelength shift for the given SNR at the

_{SNR,n}*n*repetition and Δ

^{th}*λ*is the corresponding shift of the design wavelength obtained from Eq. (16). It is worth to notice that lower values of

_{D}*σ*and

*δ*indicate better precision and accuracy.

*M*=7. Four different sample resolutions

*δλ*were considered: 10 pm (Figs. 3(a) and 4(a)), 25 pm (Figs. 3(b) and 4(b)), 30 pm (Figs. 3(c) and 4(c)) and 35 pm (Figs. 3(d) and 4(d)). The results show that, although both FPC and CCA perform generally better than the MDA, the comparison of both precision and accuracy changes from one wavelength shift Δ

*λ*to another. This is due to the peak locking effect, which is low for high resolution (

*δλ*=10 pm) but becomes dominant as the resolution decreases (

*δλ*=35 pm). Because of peak locking, an algorithm could be erroneously considered more or less precise and accurate than another. For example, looking at Figs. 3(c) and 4(c), at SNR=60 dB and Δ

*λ*=7 pm, the precision of FPC, CCA and MDA are respectively 0.14 pm, 0.09 pm and 0.77 pm. So one would conclude that the FPC precision improves by 82% compared to MDA but decreases by 35% compared to CCA. In terms of accuracy, for the same SNR and wavelength shift, the FPC shows improvements of 89% and 63% compared to MDA and CCA, respectively. However, when Δ

*λ*=20 pm, because of the peak locking, the improvement introduced by the FPC compared to MDA reaches the 93% for precision and the 83% for accuracy. At the same time, compared to CCA, the precision decreases by 64% while the accuracy improves by 62%. This happens because the proposed FPC algorithm exhibits a less evident peak locking phenomenon compared to the MDA and CCA techniques. Figures 3 and 4 also show how the wavelength resolution affects the detection performances. The resolution has an attenuated influence on the FPC precision, which deteriorates only slightly when the resolution decreases from 10 to 35 pm, especially for SNR levels above 45 dB. This makes the selection of the spectral resolution quite flexible. The effect of the resolution on the accuracy is more evident, however. The accuracy of the FPC can be up to 50 times worse going from

*δλ*=10 pm to

*δλ*=35 pm. Besides precision and accuracy, the computation time is another key factor for the evaluation of the performance of the proposed FPC algorithm. Table 1 reports the FPC computation performance in comparison with the MDA and CCA algorithms. To ease the comparison, all the values have been normalized using the execution time of the MDA algorithm as a reference. The analysis was performed with an

*Intel*®

*Core*

^{™}*i*7 – 3740

*QM CPU*@2.70 GHz processor. It is evident that the FPC has the best performance, independently from the number of samples

*N*used for the analysis. More specifically, the FPC is 5 to 6.35 times faster than the MDA and 30.15 to 50.18 times faster than the CCA.

*N*=500, the time for a single phase correlation calculation is about 1 ms. From a practical point of view this means that, the proposed FPC algorithm would allow real time measurements at a scanning frequency of about 1 kHz. Tables 2 and 3 show the precision and accuracy of the peak detection algorithm when Δ

*λ*=0 and SNR=55 dB.

## 4. Experiments and results

24. Optical Sensing Interrogator sm125, http://micronoptics.com/uploads/library/documents/datasheets/instruments.

*με/sec*. The FBGs reflected spectra are measured by the interrogator with a frequency of 2 Hz, stored and successively processed using the FPC, CCA and MDA algorithms. The wavelength shift of each FBG is computed using a wavelength window of 5 nm (

*N*=1001) centered around the initial Bragg wavelength. Since at each time instant the exact wavelength shift is unknown, the precision of the algorithms is evaluated here as the standard deviation of the

*L*

_{1}error between the measured data and their cubic fitting. Figures 7 – 9 report the computed wavelength shifts as function of time.

*σ*with respect to resolution. As the resolution step increases, the FPC continues to provide good sensing precision. Considering FBG1 and FBG2, the FPC peak wavelength

*σ*first shows a slight increase, then the curves remain almost flat up to a resolution of 55 pm. The

*σ*values are confined between 0.548 and 0.821 pm for FBG1 and between 0.587 and 0.891 pm for FBG2. The FPC precision is worse for FBG3, with values going from a minimum of 1.051 pm at 5 pm resolution, to a maximum 2.091 pm at a 50 pm resolution. Compared with CCA, the FPC precision is always better for FBG3. For FBG1 and FBG2 the FPC is more precise than CCA up to a resolution of 40 pm, while for values of resolution above this limit the cross correlation performs slightly better.

*σ*tends to be lower as the resolution decreases from 5 to 35 pm and becomes almost stable for higher resolutions. When the resolution step increases, the frequency bandwidth spanned by the 10 points quadratic interpolation used by the MDA also increases, allowing for a better approximation of the peak region and making the algorithm more stable. Despite this improvement, the MDA precision never reaches the same level of CCA and FPC. At a 40 pm resolution, for example, the precision of the MDA algorithm is 3.575 pm for FBG1, 4.467 pm for FBG2 and 66.71 pm for FBG3, against the 0.661, 0.701 and 1.622 pm obtained by the FPC. This results suggest that, in contrast to the MDA, the FPC could operate in combination with low resolution interrogator systems while still guaranteeing a high sensing precision.

## 5. Conclusion

## Acknowledgments

## References and links

1. | K.O. Hill, Y. Fujii, D. C. Johnsen, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. |

2. | G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse folographic method,” Opt. Lett. |

3. | K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. |

4. | A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. |

5. | Y. Yu, H. Tam, W. Chung, and M. S. Demokan, “Fiber Bragg grating sensor for simultaneous measurements of displacement and temperature,” Opt. Lett. |

6. | X. Shu, Y. Liu, D. Zhao, B. Gwandu, F. Floreani, L. Zhang, and I. Bennion, “Dependence of temperature and strain coefficients on fiber grating type and its application to simultaneous temperature and strain measurement,” Opt. Lett. |

7. | S. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodulation system for guided-wave Bragg grating sensors,” IEEE Photonics Technol. Lett. |

8. | G. A. Ball, W. W. Morey, and R. K. Cheo, “Fiber laser source/analyzer for Bragg grating sensor array interrogation,” J. Lightwave Technol. |

9. | R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett. |

10. | C. G. Atkins, M. A. Putnam, and E. J. Friebele, “Instrumentation for interrogating many-element fiber Bragg grating arrays,” Proc. SPIE |

11. | A. Ezbiri, S. E. Kanellopoulos, and V. A. Handerek, “High resolution instrumentation system for fiber-Bragg grating aerospace sensors,” Opt. Commun. |

12. | J. M. Gong, J. M. K. MacAlpine, C. C. Chan, W. Jin, M. Zhang, and Y. B. Liao, “A novel wavelength detection technique for fiber Bragg grating sensors,” IEEE Photonics Technol. Lett. |

13. | C. Caucheteur, K. Chah, F. Lhommé, M. Blondel, and P. Mégret, “Autocorrelation demodulation technique for fiber Bragg grating sensor,” IEEE Photonics Technol. Lett. |

14. | C. Huang, W. Jing, K. Liu, Y. Zhang, and G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photonics Technol. Lett. |

15. | L. Negri, A. Nied, H. Kalinowsky, and A. Paterno, “Benchmark of peak detection algorithms in fiber Bragg grating interrogation and a new neural network for its performance improvement,” Sensors |

16. | L. Gui and S. T. Wereley, “A correlation-based continuous window-shift technique to reduce the peak-locking in digital PIV evaluation,” Experiments Fluids |

17. | A. C. Eckstein and J. Charonko, “Phase correlation processing for DPIV measurements,” Experiments Fluids |

18. | M. Raffel, C. Willert, and J. Kompenhans, |

19. | K. T. Christensen, “On the influence of peak-locking errors on turbulance statistics compared from piv ensembles,” Experiments Fluids |

20. | J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. |

21. | R. Kashyap, |

22. | H. Y. Ling, K. T. Lau, W. Jin, and K. C. Chan, “Characterization of dynamic strain measurement using reflection spectrum from a fiber Bragg grating,” Opt. Commun. |

23. | Y. J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. |

24. | Optical Sensing Interrogator sm125, http://micronoptics.com/uploads/library/documents/datasheets/instruments. |

**OCIS Codes**

(050.2770) Diffraction and gratings : Gratings

(060.2370) Fiber optics and optical communications : Fiber optics sensors

(070.4790) Fourier optics and signal processing : Spectrum analysis

(070.7145) Fourier optics and signal processing : Ultrafast processing

**ToC Category:**

Sensors

**History**

Original Manuscript: December 11, 2013

Revised Manuscript: February 12, 2014

Manuscript Accepted: February 16, 2014

Published: March 19, 2014

**Citation**

A. Lamberti, S. Vanlanduit, B. De Pauw, and F. Berghmans, "A novel fast phase correlation algorithm for peak wavelength detection of fiber Bragg grating sensors," Opt. Express **22**, 7099-7112 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-7099

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### References

- K.O. Hill, Y. Fujii, D. C. Johnsen, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978). [CrossRef]
- G. Meltz, W. W. Morey, W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse folographic method,” Opt. Lett. 14, 823–825 (1989). [CrossRef] [PubMed]
- K. O. Hill, G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997). [CrossRef]
- A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997). [CrossRef]
- Y. Yu, H. Tam, W. Chung, M. S. Demokan, “Fiber Bragg grating sensor for simultaneous measurements of displacement and temperature,” Opt. Lett. 25(16), 1141–1143 (2000). [CrossRef]
- X. Shu, Y. Liu, D. Zhao, B. Gwandu, F. Floreani, L. Zhang, I. Bennion, “Dependence of temperature and strain coefficients on fiber grating type and its application to simultaneous temperature and strain measurement,” Opt. Lett. 27(9), 701–703 (2002). [CrossRef]
- S. Melle, K. Liu, R. M. Measures, “A passive wavelength demodulation system for guided-wave Bragg grating sensors,” IEEE Photonics Technol. Lett. 4(5), 516–518 (1992). [CrossRef]
- G. A. Ball, W. W. Morey, R. K. Cheo, “Fiber laser source/analyzer for Bragg grating sensor array interrogation,” J. Lightwave Technol. 12(4), 700–703 (1994). [CrossRef]
- R. Huber, D. C. Adler, J. G. Fujimoto, “Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett. 31(20), 2975–2977 (2006). [CrossRef] [PubMed]
- C. G. Atkins, M. A. Putnam, E. J. Friebele, “Instrumentation for interrogating many-element fiber Bragg grating arrays,” Proc. SPIE 2444, 257–267 (1995). [CrossRef]
- A. Ezbiri, S. E. Kanellopoulos, V. A. Handerek, “High resolution instrumentation system for fiber-Bragg grating aerospace sensors,” Opt. Commun. 150, 43–48 (1998). [CrossRef]
- J. M. Gong, J. M. K. MacAlpine, C. C. Chan, W. Jin, M. Zhang, Y. B. Liao, “A novel wavelength detection technique for fiber Bragg grating sensors,” IEEE Photonics Technol. Lett. 14(5), 678–680 (2002). [CrossRef]
- C. Caucheteur, K. Chah, F. Lhommé, M. Blondel, P. Mégret, “Autocorrelation demodulation technique for fiber Bragg grating sensor,” IEEE Photonics Technol. Lett. 16(10), 2320–2322 (2004). [CrossRef]
- C. Huang, W. Jing, K. Liu, Y. Zhang, G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photonics Technol. Lett. 19(9), 707–709 (2007). [CrossRef]
- L. Negri, A. Nied, H. Kalinowsky, A. Paterno, “Benchmark of peak detection algorithms in fiber Bragg grating interrogation and a new neural network for its performance improvement,” Sensors 11, 3466–3482 (2011). [CrossRef]
- L. Gui, S. T. Wereley, “A correlation-based continuous window-shift technique to reduce the peak-locking in digital PIV evaluation,” Experiments Fluids 32, 506–517 (2002). [CrossRef]
- A. C. Eckstein, J. Charonko, “Phase correlation processing for DPIV measurements,” Experiments Fluids 45, 485–500 (2008). [CrossRef]
- M. Raffel, C. Willert, J. Kompenhans, Particle Image Velocimetry—A Practical Guide (Springer, 1998). [CrossRef]
- K. T. Christensen, “On the influence of peak-locking errors on turbulance statistics compared from piv ensembles,” Experiments Fluids 36(3), 484–497 (2004). [CrossRef]
- J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. 8(12), 1379–1392 (1997). [CrossRef]
- R. Kashyap, Fiber Bragg Gratings (Academic, 1999), Vol. IV.
- H. Y. Ling, K. T. Lau, W. Jin, K. C. Chan, “Characterization of dynamic strain measurement using reflection spectrum from a fiber Bragg grating,” Opt. Commun. 270, 25–30 (2007). [CrossRef]
- Y. J. Rao, “In-fibre Bragg grating sensors,” Meas. Sci. Technol. 8, 355–377 (1997). [CrossRef]
- Optical Sensing Interrogator sm125, http://micronoptics.com/uploads/library/documents/datasheets/instruments .

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