## Realization of nano static strain sensing with fiber Bragg gratings interrogated by narrow linewidth tunable lasers |

Optics Express, Vol. 19, Issue 21, pp. 20214-20223 (2011)

http://dx.doi.org/10.1364/OE.19.020214

Acrobat PDF (1011 KB)

### Abstract

Aiming at realizing a static strain sensor of nano-strain resolution, which is required in most geophysical applications, this paper presents a thorough analysis on the strain resolution of a fiber Bragg grating (FBG) static strain sensor interrogated with a narrow linewidth tunable laser. The main noise sources of the sensor are discussed, and the strain resolution is deduced with a cross-correlation algorithm. The theoretical prediction agrees well with our experimental result, and the analysis is further validated by numerical simulations. Based on the analysis, the paper provides the guidelines for optimizing this type of sensor to realize ultra-high resolution. It is shown that with properly designed FBGs and interrogation systems, nano static strain resolution can be realized, as we recently demonstrated in experiment.

© 2011 OSA

## 1. Introduction

1. 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. **15**(8), 1442–1463 (1997). [CrossRef]

2. M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fibre Bragg gratings in structural health monitoring - Present status and applications,” Sens. Actuators A Phys. **147**(1), 150–164 (2008). [CrossRef]

3. B. Lissak, A. Arie, and M. Tur, “Highly sensitive dynamic strain measurements by locking lasers to fiber Bragg gratings,” Opt. Lett. **23**(24), 1930–1932 (1998). [CrossRef] [PubMed]

4. D. Gatti, G. Galzerano, D. Janner, S. Longhi, and P. Laporta, “Fiber strain sensor based on a pi-phase-shifted Bragg grating and the Pound-Drever-Hall technique,” Opt. Express **16**(3), 1945–1950 (2008). [CrossRef] [PubMed]

5. A. Arie, B. Lissak, and M. Tur, “Static fiber-Bragg grating strain sensing using frequency-locked lasers,” J. Lightwave Technol. **17**(10), 1849–1855 (1999). [CrossRef]

## 2. Typical system configuration

*λ*with a step of

_{i}*dλ*. The reflectivity of the sensing FBG is labeled as

*R*(

*λ*), while the reflectivity of the reference FBG is labeled as

_{i}*R*(

_{R}*λ*). Assuming the two FBGs have the same spectra shape when the sensing FBG experiences strain variation, which is widely accepted, the reflectivity satisfies:where Δ

_{i}*λ*is the wavelength shift caused by strain.

*ε*= Δ

*λ*/

*dλ*is the corresponding index shift. A certain algorithm is then employed to demodulate the wavelength shift Δ

*λ*by comparing the two spectra.

## 3. Major noise sources

### 3.1. Relative intensity noise

*R*

_{elec}.

### 3.2. The wavelength repeatability of the tunable laser

*δ*

_{1}

*λ*. Since the reflectivity of the FBG is a function of the wavelength,

*δ*

_{1}

*λ*is converted into an error in reflectivity. The converting coefficient is the differential coefficient of the FBG’s spectrum, as shown in Fig. 3 . This error in reflectivity is expressed as

*R*'(

*λ*)·

*δ*

_{1}

*λ*, where

*R*'(

*λ*) is the differential coefficient of the FBG’s spectrum. Generally

*δ*

_{1}

*λ*is much smaller than the absolute wavelength inaccuracy of the laser. Because the Bragg wavelength is determined by comparison between logged spectra, the absolute wavelength inaccuracy is of less importance.

### 3.3. Linewidth of the tunable laser

*δ*

_{2}

*λ*describes the deviation range of quick frequency jitter of the laser. Similar to the wavelength repeatability, the quick frequency jitter is also converted into the error in the measured reflectivity. The amplitude is not larger than

*R*'(

*λ*)·

*δ*

_{2}

*λ*, as it is averaged to some extent during the integration time.

### 3.4. Wavelength stability of the tunable laser

## 4. Cross-correlation algorithm

*λ*from the measured spectra, because this algorithm is proved to have very good resolution compared with other algorithms such as the centroid detection algorithm (CDA) and the least square fitting algorithm (LSA) [7–9

9. G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett. **14**(15), 823–825 (1989). [CrossRef] [PubMed]

*R*(

*λ*) and

_{i}*R*

_{R}(

*λ*) are equal to zero if the indices lie outside their ranges. This assumption is acceptable as long as the sampling range covers the whole principal peaks of both FBGs.

_{i}*C*(

*j*) has the maximum at

*j*=

*ε*, where the two spectra overlap completely and

*ε*is demodulated from the index when

*C*(

*j*) is at its maximum. Due to the random errors in the measured reflectivity, the retrieved

*ε*deviates from Δ

*λ*/

*dλ*, and the deviation range is the resolution of the sensor. It should be mentioned that although the index of maximum

*C*(

*j*) falls into an integer which is the nearest to

*ε*,

*ε*can be precisely calculated either by interpolation or by curve-fitting around the maximum.

*ε*= 0 is assumed to simplify the analysis without any influence on the resolution.

*C*(

_{R}*j*) in Eq. (4) is the auto-correlation curve of the real spectrum without noise, as shown in Fig. 4 (the black dashed line). It has a peak (labeled P) at

*j*= 0 and declines when

*j*diverges from 0. The second term

*C*(

_{N}*j*) is the cross-correlation of the real spectrum and the random noise. It makes the actual cross-correlation curve

*C’*(

*j*) fluctuate, as shown as the red line in Fig. 4. Because only the relative amplitude is concerned with the position of the maximum, we shift

*C’*(

*j*) to pass through point P, the peak of

*C*(

_{R}*j*), as shown as the dashed red line in Fig. 4. The random noise makes the shifted curve fluctuate around the auto-correlation curve. The deviation is a function of the index

*j*:

*Δ*and

_{N,elec}*Δ*are the noises caused by the relative intensity noise and the wavelength inaccuracy, respectively.

_{N,λ}*Δ*has a mean of zero and a standard deviation as:

_{N}*C’*(

*j*) appears in the region satisfying

## 5. Model of FBG’s spectrum

*N*-order Gaussian curve is employed as the model of the FBG’s spectrum for quantitative analysis:where

*λ*=

*λ*

_{0}+

*i*·

*dλ*,

*dλ*is the wavelength sweep step and

*λ*

_{width}=

*w*·

*dλ*is the full width at 1/

*e*maximum of the FBG’s spectrum.

*n*is the order of Gaussian function, working as a shape parameter in the model. For FBGs with smooth spectra (maximum reflectivity less than 80%),

*n*is 1; for a high reflectivity FBG with a spectrum of a flat peak and sharp slopes,

*n*is a large integer. With this expression, we obtain following expressions around

*j*= 0:

*w*varies from 16 to 1024, and

*n*varies from 1 to 5, the approximation of Eqs. (9) and (10) has an error less than 1%. For Eq. (11), the error is less than 5% for

*n*= 1 and a little larger when

*n*≥ 2. With above approximations we calculate the resolution with Eq. (7) aswhere

*λ*is the wavelength resolution of the sensor,

_{R}*dλ*the wavelength sweep step of the laser,

*σ*(Δ

*R*) the standard deviation of the relative intensity noise,

*σ*(

*δλ*) the standard deviation of wavelength inaccuracy. From the wavelength resolution, the strain resolution can be simply deduced by the strain-wavelength coefficient of about 1.2 pm/με.

## 6. Guidelines for sensor design and optimization

### 6.1. FBG spectrum

*n*is shown in Fig. 6 . The 1st-order Gaussian shape FBG has better resolution with narrower bandwidth, which is more preferable in practice because it requires smaller wavelength tunable range, and then can achieve higher measurement speed. We can see from Fig. 6 that, with the given

*dλ*,

*δλ*, and Δ

*R*, which are practical values for commercially available devices, nano-strain resolution is achievable with a proper FBG.

*n*= 1:

### 6.2. Sweep step of the laser source

*dλ*plays an important role in the resolution. The resolution is proportional to the square root of

*dλ*at a fixed noise level. Using a shorter sweep step (a smaller

*dλ*value) while keeping the integration time of the photo-detector constant produces the best resolution. It consumes, however, longer time to complete one sweep. If the sweep speed remains constant, on the other hand, using a shorter sweep step deduces the integration time at the photo-detector, which enhances the intensity noise level. As a result, the resolution is not necessarily improved. Therefore, the most suitable sets of parameters depend on a specific application’s requirements on the measurement speed and the resolution.

### 6.3. Wavelength repeatability and linewidth of the tunable laser source

## 7. Conclusion

## Acknowledgments

## References and links

1. | 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. |

2. | M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fibre Bragg gratings in structural health monitoring - Present status and applications,” Sens. Actuators A Phys. |

3. | B. Lissak, A. Arie, and M. Tur, “Highly sensitive dynamic strain measurements by locking lasers to fiber Bragg gratings,” Opt. Lett. |

4. | D. Gatti, G. Galzerano, D. Janner, S. Longhi, and P. Laporta, “Fiber strain sensor based on a pi-phase-shifted Bragg grating and the Pound-Drever-Hall technique,” Opt. Express |

5. | A. Arie, B. Lissak, and M. Tur, “Static fiber-Bragg grating strain sensing using frequency-locked lasers,” J. Lightwave Technol. |

6. | J. H. Chow, I. C. M. Littler, D. E. McClelland, and M. B. Gray, “Quasi-static fiber strain sensing with absolute frequency referencing,” in |

7. | Q. Liu, Z. He, T. Tokunaga, and K. Hotate, “An ultra-high-resolution FBG static-strain sensor for geophysics applications,” in Proc. of SPIE |

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

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

**OCIS Codes**

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

(120.0280) Instrumentation, measurement, and metrology : Remote sensing and sensors

(060.3735) Fiber optics and optical communications : Fiber Bragg gratings

**ToC Category:**

Sensors

**History**

Original Manuscript: July 12, 2011

Revised Manuscript: September 24, 2011

Manuscript Accepted: September 25, 2011

Published: September 30, 2011

**Citation**

Qingwen Liu, Tomochika Tokunaga, and Zuyuan He, "Realization of nano static strain sensing with fiber Bragg gratings interrogated by narrow linewidth tunable lasers," Opt. Express **19**, 20214-20223 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-20214

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### References

- 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.15(8), 1442–1463 (1997). [CrossRef]
- M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fibre Bragg gratings in structural health monitoring - Present status and applications,” Sens. Actuators A Phys.147(1), 150–164 (2008). [CrossRef]
- B. Lissak, A. Arie, and M. Tur, “Highly sensitive dynamic strain measurements by locking lasers to fiber Bragg gratings,” Opt. Lett.23(24), 1930–1932 (1998). [CrossRef] [PubMed]
- D. Gatti, G. Galzerano, D. Janner, S. Longhi, and P. Laporta, “Fiber strain sensor based on a pi-phase-shifted Bragg grating and the Pound-Drever-Hall technique,” Opt. Express16(3), 1945–1950 (2008). [CrossRef] [PubMed]
- A. Arie, B. Lissak, and M. Tur, “Static fiber-Bragg grating strain sensing using frequency-locked lasers,” J. Lightwave Technol.17(10), 1849–1855 (1999). [CrossRef]
- J. H. Chow, I. C. M. Littler, D. E. McClelland, and M. B. Gray, “Quasi-static fiber strain sensing with absolute frequency referencing,” in 19th International Coference on Optical Fiber Sensors, D. Sampson, ed. (Perth, Australia, 2008), 700429.
- Q. Liu, Z. He, T. Tokunaga, and K. Hotate, “An ultra-high-resolution FBG static-strain sensor for geophysics applications,” in Proc. of SPIE 4th European Workshop on Optical Fiber Sensors (Porto, 2010) 7653, 97–100.
- C. Huang, W. C. Jing, K. Liu, Y. M. Zhang, and G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photon. Technol. Lett.19(9), 707–709 (2007). [CrossRef]
- G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett.14(15), 823–825 (1989). [CrossRef] [PubMed]

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