## Spatially continuous distributed fiber optic sensing using optical carrier based microwave interferometry |

Optics Express, Vol. 22, Issue 15, pp. 18757-18769 (2014)

http://dx.doi.org/10.1364/OE.22.018757

Acrobat PDF (2853 KB)

### Abstract

This paper reports a spatially continuous distributed fiber optic sensing technique using optical carrier based microwave interferometry (OCMI), in which many optical interferometers with the same or different optical path differences are interrogated in the microwave domain and their locations can be unambiguously determined. The concept is demonstrated using cascaded weak optical reflectors along a single optical fiber, where any two arbitrary reflectors are paired to define a low-finesse Fabry-Perot interferometer. While spatially continuous (i.e., no dark zone), fully distributed strain measurement was used as an example to demonstrate the capability, the proposed concept may also be implemented on other types of waveguide or free-space interferometers and used for distributed measurement of various physical, chemical and biological quantities.

© 2014 Optical Society of America

## 1. Introduction

1. K. Grattan and T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators A Phys. **82**(1–3), 40–61 (2000). [CrossRef]

2. A. D. Kersey, T. A. Berkoff, and W. W. Morey, “Multiplexed fiber Bragg grating strain-sensor system with a fiber Fabry - Perot wavelength filter,” Opt. Lett. **18**(16), 1370–1372 (1993). [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]

4. Y. Wang, J. Gong, B. Dong, W. Bi, and A. Wang, “A quasi-distributed sensing network with time-division-multiplexed fiber Bragg gratings,” IEEE Photon. Technol. Lett. **23**(2), 70–72 (2011). [CrossRef]

6. J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, and H. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. **3**(5), 1062–1072 (1985). [CrossRef]

7. J. Wang, B. Dong, E. Lally, J. Gong, M. Han, and A. Wang, “Multiplexed high temperature sensing with sapphire fiber air gap-based extrinsic Fabry-Perot interferometers,” Opt. Lett. **35**(5), 619–621 (2010). [CrossRef] [PubMed]

8. F. Shen and A. Wang, “Frequency-estimation-based signal-processing algorithm for white-light optical fiber Fabry-Perot interferometers,” Appl. Opt. **44**(25), 5206–5214 (2005). [CrossRef] [PubMed]

9. J. Huang, L. Hua, X. Lan, T. Wei, and H. Xiao, “Microwave assisted reconstruction of optical interferograms for distributed fiber optic sensing,” Opt. Express **21**(15), 18152–18159 (2013). [CrossRef] [PubMed]

10. B. Sutapun, M. Tabib-Azar, and A. Kazemi, “Pd-coated elastooptic fiber optic Bragg grating sensors for multiplexed hydrogen sensing,” Sens. Actuators B Chem. **60**(1), 27–34 (1999). [CrossRef]

11. L. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. Ang, P. Zu, W. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry–Perot humidity sensor,” Sens. Actuators B Chem. **169**, 167–172 (2012). [CrossRef]

12. M. Froggatt and J. Moore, “High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter,” Appl. Opt. **37**(10), 1735–1740 (1998). [CrossRef] [PubMed]

13. Y. Koyamada, M. Imahama, K. Kubota, and K. Hogari, “Fiber-optic distributed strain and temperature sensing with very high measurand resolution over long range using coherent OTDR,” J. Lightwave Technol. **27**(9), 1142–1146 (2009). [CrossRef]

14. X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. **13**(7), 1340–1348 (1995). [CrossRef]

16. M. N. Alahbabi, Y. T. Cho, and T. P. Newson, “150-km-range distributed temperature sensor based on coherent detection of spontaneous Brillouin backscatter and in-line Raman amplification,” J. Opt. Soc. Am. B **22**(6), 1321–1324 (2005). [CrossRef]

17. K. Shimizu, T. Horiguchi, Y. Koyamada, and T. Kurashima, “Coherent self-heterodyne Brillouin OTDR for measurement of Brillouin frequency shift distribution in optical fibers,” J. Lightwave Technol. **12**(5), 730–736 (1994). [CrossRef]

18. W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. **39**(9), 693–695 (1981). [CrossRef]

19. M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Simplex-coded BOTDA fiber sensor with 1 m spatial resolution over a 50 km range,” Opt. Lett. **35**(2), 259–261 (2010). [CrossRef] [PubMed]

20. Y. Dong, L. Chen, and X. Bao, “Time-division multiplexing-based BOTDA over 100 km sensing length,” Opt. Lett. **36**(2), 277–279 (2011). [CrossRef] [PubMed]

22. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photon. **1**(6), 319–330 (2007). [CrossRef]

23. J. Yao, “Microwave photonics,” J. Lightwave Technol. **27**(3), 314–335 (2009). [CrossRef]

## 2. Concept of the spatially continuous distributed sensing based on cascaded OCMI-FPIs

*Γ*and

_{i}*Γ*in Fig. 1) while suppressing other values to zero. These two reflections are then Fourier transformed back to frequency domain to reconstruct a microwave interferogram, which can be used to find the optical path difference (OPD) between the two reflectors (e.g.,

_{j}*d*). The change in the OPD between these two reflectors (e.g.,

_{ij}*Δd*) can be calculated based on the frequency shift of the microwave interferogram.

_{ij}## 3. Modeling and simulations

*t*is the time;

*E*is the electric field;

_{o}*A*is the amplitude;

*φ*is the phase;

*ω*is the angular optical frequency.

*M*is the amplitude of the modulation, which falls in the range of 0 to 1,

*Ω*is the microwave angular frequency, and

*ϕ*is the phase.

*m(t)*is the amplitude modulation term, given by

*N*is the total number of the reflectors;

*z*represents the location of the i-

_{i}*th*reflector. Note that in Eq. (5), both the optical and microwave components are functions of the locations (

*z*) of the reflectors.

_{i}*th*optical reflection) in Eq. (5) is given bywhere

*Γ*is the amplitude reflection coefficient of the i-

_{i}*th*reflector seen by the photodetector;

*c*is the speed of light in vacuum;

*n*is the effective refractive index.

*W*) of the microwave system and this delay is the same for all the paths. The second delay term is the contribution from the optical propagation delays at different reflectors.

*ω*to

_{min}*ω*. The total power of the superimposed optical waves of all the reflections is given by

_{max}*Ω*.

*g*) and synchronized microwave detection is given by

*A*and

_{eff}*Φ*are the amplitude and phase of the microwave signal, respectively. where

_{eff}*Ω*to

_{min}*Ω*), the complex microwave reflection spectrum (with both amplitude and phase) is obtained. By applying a complex and inverse Fourier-transform to the microwave spectrum, a series of cardinal sine functions are obtained at discrete reflectors, given by:

_{max}*i-th*reflector.

*z*) that can be found when the delays (

_{i}*τ*) are determined. The frequency bandwidth (

_{i}*Ω*-

_{max}*Ω*) determines the spatial resolution, i.e., the minimum distance between two adjacent reflectors to avoid an overlap of the two pulses in the time domain. The larger the microwave bandwidth, the narrower is the pulse width (sinc function) in time domain and the higher is the spatial resolution.

_{min}*g(t)*. The time domain signal after applying a gate function is thus given by

*X(t)g(t)*. The gated signal is then Fourier transformed back to the frequency domain to reconstruct the microwave interferogram, which can be used to find the optical distance between the two reflectors (e.g.,

*d*). The reconstructed OCMI-FPI interferogram is thus given bywhere

_{ij}*G(Ω)*is the inverse Fourier transform of the gate function

*g(t)*;

*τ*is the time delay of the gate function. As shown in Eq. (13), the reconstructed microwave FPI interferogram in spectrum domain is in essence a convolution of the microwave signal

_{0}*S*and

*G(Ω)*. Here we define the optical path difference (OPD) of the OCMI-FPI is

*A*) and phase (

_{eff}*Φ*) spectra based on Eq. (11). Figures 2(c) and 2(d) plot the calculated results based on Eqs. (12) and (13), respectively. As shown in Fig. 2(c), the 8 reflectors can be clearly identified at the corresponding locations. A Hanning window function was applied to the time-domain signal shown in Fig. 2(c) to cut out a section including the 4th and 5th reflectors. The center of the Hanning window was located at the center between the two reflectors and the width of the window was chosen to be 1.22 ns. The cut-out section of the time-domain signal was then Fourier transformed back into the frequency domain as shown in Fig. 2(d), where an interferogram can be clearly identified. The reconstructed interferogram is the result of the microwave interference of the two reflected signals at the 4th and 5th reflectors. The FSR was found to be 1.005 GHz, which matched well with that calculated based on Eq. (15).

_{eff}## 4. Experimental demonstration

### 4.1 System implementation

### 4.2 Strain measurement using OCMI-FPIs

### 4.3 Spatially continuous measurement of distributed strains

## 6. Conclusion

## Acknowledgments

## References and links

1. | K. Grattan and T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators A Phys. |

2. | A. D. Kersey, T. A. Berkoff, and W. W. Morey, “Multiplexed fiber Bragg grating strain-sensor system with a fiber Fabry - Perot wavelength filter,” Opt. Lett. |

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

4. | Y. Wang, J. Gong, B. Dong, W. Bi, and A. Wang, “A quasi-distributed sensing network with time-division-multiplexed fiber Bragg gratings,” IEEE Photon. Technol. Lett. |

5. | B. A. Childers, M. E. Froggatt, S. G. Allison, T. C. Moore Sr, D. A. Hare, C. F. Batten, and D. C. Jegley, “Use of 3000 Bragg grating strain sensors distributed on four 8-m optical fibers during static load tests of a composite structure,” Proc. SPIE |

6. | J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, and H. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. |

7. | J. Wang, B. Dong, E. Lally, J. Gong, M. Han, and A. Wang, “Multiplexed high temperature sensing with sapphire fiber air gap-based extrinsic Fabry-Perot interferometers,” Opt. Lett. |

8. | F. Shen and A. Wang, “Frequency-estimation-based signal-processing algorithm for white-light optical fiber Fabry-Perot interferometers,” Appl. Opt. |

9. | J. Huang, L. Hua, X. Lan, T. Wei, and H. Xiao, “Microwave assisted reconstruction of optical interferograms for distributed fiber optic sensing,” Opt. Express |

10. | B. Sutapun, M. Tabib-Azar, and A. Kazemi, “Pd-coated elastooptic fiber optic Bragg grating sensors for multiplexed hydrogen sensing,” Sens. Actuators B Chem. |

11. | L. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. Ang, P. Zu, W. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry–Perot humidity sensor,” Sens. Actuators B Chem. |

12. | M. Froggatt and J. Moore, “High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter,” Appl. Opt. |

13. | Y. Koyamada, M. Imahama, K. Kubota, and K. Hogari, “Fiber-optic distributed strain and temperature sensing with very high measurand resolution over long range using coherent OTDR,” J. Lightwave Technol. |

14. | X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. |

15. | J. Dakin, D. Pratt, G. Bibby, and J. Ross, “Distributed optical fibre Raman temperature sensor using a semiconductor light source and detector,” Electron. Lett. |

16. | M. N. Alahbabi, Y. T. Cho, and T. P. Newson, “150-km-range distributed temperature sensor based on coherent detection of spontaneous Brillouin backscatter and in-line Raman amplification,” J. Opt. Soc. Am. B |

17. | K. Shimizu, T. Horiguchi, Y. Koyamada, and T. Kurashima, “Coherent self-heterodyne Brillouin OTDR for measurement of Brillouin frequency shift distribution in optical fibers,” J. Lightwave Technol. |

18. | W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. |

19. | M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Simplex-coded BOTDA fiber sensor with 1 m spatial resolution over a 50 km range,” Opt. Lett. |

20. | Y. Dong, L. Chen, and X. Bao, “Time-division multiplexing-based BOTDA over 100 km sensing length,” Opt. Lett. |

21. | J. Huang, X. Lan, H. Wang, L. Yuan, and H. Xiao, “Optical carrier-based microwave interferometers for sensing application,” Proc. SPIE |

22. | J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photon. |

23. | J. Yao, “Microwave photonics,” J. Lightwave Technol. |

24. | K. Bisshopp and D. Drucker, “Large deflection of cantilever beams,” Q. Appl. Math. |

**OCIS Codes**

(060.2310) Fiber optics and optical communications : Fiber optics

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

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(060.5625) Fiber optics and optical communications : Radio frequency photonics

**ToC Category:**

Sensors

**History**

Original Manuscript: May 15, 2014

Revised Manuscript: July 15, 2014

Manuscript Accepted: July 18, 2014

Published: July 25, 2014

**Citation**

Jie Huang, Xinwei Lan, Ming Luo, and Hai Xiao, "Spatially continuous distributed fiber optic sensing using optical carrier based microwave interferometry," Opt. Express **22**, 18757-18769 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-18757

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### References

- K. Grattan and T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators A Phys. 82(1–3), 40–61 (2000). [CrossRef]
- A. D. Kersey, T. A. Berkoff, and W. W. Morey, “Multiplexed fiber Bragg grating strain-sensor system with a fiber Fabry - Perot wavelength filter,” Opt. Lett. 18(16), 1370–1372 (1993). [CrossRef] [PubMed]
- K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997). [CrossRef]
- Y. Wang, J. Gong, B. Dong, W. Bi, and A. Wang, “A quasi-distributed sensing network with time-division-multiplexed fiber Bragg gratings,” IEEE Photon. Technol. Lett. 23(2), 70–72 (2011). [CrossRef]
- B. A. Childers, M. E. Froggatt, S. G. Allison, T. C. Moore, D. A. Hare, C. F. Batten, and D. C. Jegley, “Use of 3000 Bragg grating strain sensors distributed on four 8-m optical fibers during static load tests of a composite structure,” Proc. SPIE 4332, 133 (2001).
- J. L. Brooks, R. H. Wentworth, R. C. Youngquist, M. Tur, B. Y. Kim, and H. Shaw, “Coherence multiplexing of fiber-optic interferometric sensors,” J. Lightwave Technol. 3(5), 1062–1072 (1985). [CrossRef]
- J. Wang, B. Dong, E. Lally, J. Gong, M. Han, and A. Wang, “Multiplexed high temperature sensing with sapphire fiber air gap-based extrinsic Fabry-Perot interferometers,” Opt. Lett. 35(5), 619–621 (2010). [CrossRef] [PubMed]
- F. Shen and A. Wang, “Frequency-estimation-based signal-processing algorithm for white-light optical fiber Fabry-Perot interferometers,” Appl. Opt. 44(25), 5206–5214 (2005). [CrossRef] [PubMed]
- J. Huang, L. Hua, X. Lan, T. Wei, and H. Xiao, “Microwave assisted reconstruction of optical interferograms for distributed fiber optic sensing,” Opt. Express 21(15), 18152–18159 (2013). [CrossRef] [PubMed]
- B. Sutapun, M. Tabib-Azar, and A. Kazemi, “Pd-coated elastooptic fiber optic Bragg grating sensors for multiplexed hydrogen sensing,” Sens. Actuators B Chem. 60(1), 27–34 (1999). [CrossRef]
- L. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. Ang, P. Zu, W. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry–Perot humidity sensor,” Sens. Actuators B Chem. 169, 167–172 (2012). [CrossRef]
- M. Froggatt and J. Moore, “High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter,” Appl. Opt. 37(10), 1735–1740 (1998). [CrossRef] [PubMed]
- Y. Koyamada, M. Imahama, K. Kubota, and K. Hogari, “Fiber-optic distributed strain and temperature sensing with very high measurand resolution over long range using coherent OTDR,” J. Lightwave Technol. 27(9), 1142–1146 (2009). [CrossRef]
- X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13(7), 1340–1348 (1995). [CrossRef]
- J. Dakin, D. Pratt, G. Bibby, and J. Ross, “Distributed optical fibre Raman temperature sensor using a semiconductor light source and detector,” Electron. Lett. 21(13), 569–570 (1985). [CrossRef]
- M. N. Alahbabi, Y. T. Cho, and T. P. Newson, “150-km-range distributed temperature sensor based on coherent detection of spontaneous Brillouin backscatter and in-line Raman amplification,” J. Opt. Soc. Am. B 22(6), 1321–1324 (2005). [CrossRef]
- K. Shimizu, T. Horiguchi, Y. Koyamada, and T. Kurashima, “Coherent self-heterodyne Brillouin OTDR for measurement of Brillouin frequency shift distribution in optical fibers,” J. Lightwave Technol. 12(5), 730–736 (1994). [CrossRef]
- W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981). [CrossRef]
- M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Simplex-coded BOTDA fiber sensor with 1 m spatial resolution over a 50 km range,” Opt. Lett. 35(2), 259–261 (2010). [CrossRef] [PubMed]
- Y. Dong, L. Chen, and X. Bao, “Time-division multiplexing-based BOTDA over 100 km sensing length,” Opt. Lett. 36(2), 277–279 (2011). [CrossRef] [PubMed]
- J. Huang, X. Lan, H. Wang, L. Yuan, and H. Xiao, “Optical carrier-based microwave interferometers for sensing application,” Proc. SPIE 9098, 90980H (2014).
- J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photon. 1(6), 319–330 (2007). [CrossRef]
- J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]
- K. Bisshopp and D. Drucker, “Large deflection of cantilever beams,” Q. Appl. Math. 3, 273–275 (1945).

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