## Compensation of laser frequency tuning nonlinearity of a long range OFDR using deskew filter |

Optics Express, Vol. 21, Issue 3, pp. 3826-3834 (2013)

http://dx.doi.org/10.1364/OE.21.003826

Acrobat PDF (1035 KB)

### Abstract

We present a simple and effective method to compensate the optical frequency tuning nonlinearity of a tunable laser source (TLS) in a long range optical frequency-domain reflectometry (OFDR) by using the deskew filter, where a frequency tuning nonlinear phase obtained from an auxiliary interferometer is used to compensate the nonlinearity effect on the beating signals generated from a main OFDR interferometer. The method can be applied to the entire spatial domain of the OFDR signals at once with a high computational efficiency. With our proposed method we experimentally demonstrated a factor of 93 times improvement in spatial resolution by comparing the results of an OFDR system with and without nonlinearity compensation. In particular we achieved a measurement range of 80 km and a spatial resolution of 20 cm and 1.6 m at distances of 10 km and 80 km, respectively with a short signal processing time of less than 1 s for 5 × 10^{6} data points. The improved performance of the OFDR with a high spatial resolution, a long measurement range and a short process time will lead to practical applications in the real-time monitoring, test and measurement of fiber optical communication networks and sensing systems.

© 2013 OSA

## 1. Introduction

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

2. B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express **13**(2), 666–674 (2005). [CrossRef] [PubMed]

4. D. P. Zhou, Z. Qin, W. Li, L. Chen, and X. Bao, “Distributed vibration sensing with time-resolved optical frequency-domain reflectometry,” Opt. Express **20**(12), 13138–13145 (2012). [CrossRef] [PubMed]

5. E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express **16**(17), 13139–13149 (2008). [CrossRef] [PubMed]

6. K. Yuksel, M. Wuilpart, and P. Mégret, “Analysis and suppression of nonlinear frequency modulation in an optical frequency-domain reflectometer,” Opt. Express **17**(7), 5845–5851 (2009). [CrossRef] [PubMed]

5. E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express **16**(17), 13139–13149 (2008). [CrossRef] [PubMed]

6. K. Yuksel, M. Wuilpart, and P. Mégret, “Analysis and suppression of nonlinear frequency modulation in an optical frequency-domain reflectometer,” Opt. Express **17**(7), 5845–5851 (2009). [CrossRef] [PubMed]

2. B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express **13**(2), 666–674 (2005). [CrossRef] [PubMed]

**spatial**resolution up to be micrometers, but a measurement range is limited to a few tens of meters. Although a frequency multiplication method was proposed to increase a measurement range without increasing the path difference of an auxiliary interferometer [7], an increased measurable range is still limited by the frequency multiplication hardware and phase noise (jitter) of a clock signal. The second class method is to use algorithms to suppress a TLS nonlinearity after the data acquisition. In this class method, several types of algorithms are proposed to compensate the laser frequency tuning nonlinearity effect by using obtained optical frequency or phase information of a TLS from an auxiliary interferometer. One of those algorithms is the re-sampling technique that re-samples these main beating interference signals with an accurate equidistant optical frequency grid based on the optical frequency information of the TLS by the interpolation algorithms (such as linear and cubic spline interpolations) [6

6. K. Yuksel, M. Wuilpart, and P. Mégret, “Analysis and suppression of nonlinear frequency modulation in an optical frequency-domain reflectometer,” Opt. Express **17**(7), 5845–5851 (2009). [CrossRef] [PubMed]

8. T. J. Ahn, J. Y. Lee, and D. Y. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation,” Appl. Opt. **44**(35), 7630–7634 (2005). [CrossRef] [PubMed]

9. S. Vergnole, D. Lévesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express **18**(10), 10446–10461 (2010). [CrossRef] [PubMed]

9. S. Vergnole, D. Lévesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express **18**(10), 10446–10461 (2010). [CrossRef] [PubMed]

10. Z. Ding, T. Liu, Z. Meng, K. Liu, Q. Chen, Y. Du, D. Li, and X. S. Yao, “Note: Improving spatial resolution of optical frequency-domain reflectometry against frequency tuning nonlinearity using non-uniform fast Fourier transform,” Rev. Sci. Instrum. **83**(6), 066110 (2012). [CrossRef] [PubMed]

**17**(7), 5845–5851 (2009). [CrossRef] [PubMed]

10. Z. Ding, T. Liu, Z. Meng, K. Liu, Q. Chen, Y. Du, D. Li, and X. S. Yao, “Note: Improving spatial resolution of optical frequency-domain reflectometry against frequency tuning nonlinearity using non-uniform fast Fourier transform,” Rev. Sci. Instrum. **83**(6), 066110 (2012). [CrossRef] [PubMed]

12. F. Ito, X. Fan, and Y. Koshikiya, “Long-range coherent OFDR with light source phase noise compensation,” J. Lightwave Technol. **30**(8), 1015–1024 (2012). [CrossRef]

*et al.*presented a method that uses main interference signals to mix with a predicted phase of the TLS to achieve an OFDR with a measurement range of 2 km and a spatial resolution of 1 mm [11,13

13. Luna, “Optical backscatter reflectometer (Model OBR 4600)”, http://lunainc.com/wp-content/uploads/2012/11/NEW-OBR4600_Data-Sheet_Rev-03.pdf.

*et al*. introduced a novel OFDR system with the measurement range of 40 km and the spatial resolution of 5 cm [12

12. F. Ito, X. Fan, and Y. Koshikiya, “Long-range coherent OFDR with light source phase noise compensation,” J. Lightwave Technol. **30**(8), 1015–1024 (2012). [CrossRef]

14. Y. Koshikiya, X. Fan, and F. Ito, “Long range and cm-level spatial resolution measurement using coherent optical frequency domain reflectometry with SSB-SC modulator and narrow linewidth fiber laser,” J. Lightwave Technol. **26**(18), 3287–3294 (2008). [CrossRef]

12. F. Ito, X. Fan, and Y. Koshikiya, “Long-range coherent OFDR with light source phase noise compensation,” J. Lightwave Technol. **30**(8), 1015–1024 (2012). [CrossRef]

**30**(8), 1015–1024 (2012). [CrossRef]

**30**(8), 1015–1024 (2012). [CrossRef]

**30**(8), 1015–1024 (2012). [CrossRef]

15. M. Burgos-García, C. Castillo, S. Llorente, J. M. Pardo, and J. C. Crespo, “Digital on-line compensation of errors induced by linear distortion in broadband LFM radars,” Electron. Lett. **39**(1), 116–118 (2003). [CrossRef]

^{6}. The reported approach in this paper can result a significantly improvement for an OFDR instrument system that could be developed as a powerful tool for a real-time fiber optical network testing and optical fiber sensing which has both the high spatial resolution and long measurement range.

## 2. Algorithm principle

### 2.1 Basic theory of the OFDR

*n*is the refractive index of fiber. Then

### 2.2 Principle and signal processing of the deskew filter algorithm

*Step one:*The beat signals with laser frequency tuning nonlinearities are acquired as described in Eq. (4). Assuming a nonlinear function

*S*(

_{e}*t*) is known (its detailed estimation will be discussed in below next section), a distance independent LO light nonlinear phase in the beat frequency signal can be eliminated by following multiplicationIn Eq. (5) the received signal’s nonlinearity

*τ*) must be implemented to the beat frequency signals and this can be achieved by using the deskew filter that can be expressed as

*Step two:*The deskew filter is applied to

*Step three:*The linear beat signals

### 2.3 Nonlinear phase estimation

*t.*Thus an estimation of

## 3. Experimental results and discussion

### 3.1 Setup

**3.2** Nonlinear phase estimation

*e*(t)is estimated by using a method as mentioned above from measured beat signal of an auxiliary interferometer with 50 m and 10 km reference delay fiber as shown in Figs. 3(a) and 3(b). The estimated phases using 10 km reference delay fiber are shown in Fig. 3(e).

18. G. Giampieri, R. W. Hellings, M. Tinto, and J. E. Faller, “Algorithms for unequal-arm Michelson interferometers,” Opt. Commun. **123**(4-6), 669–678 (1996). [CrossRef]

### 3.3 Tuning nonlinearity compensation of main interferometer

19. S. Venkatesh and W. V. Sorin, “Phase noise consideration in coherent optical FMCW reflectometry,” J. Lightwave Technol. **11**(10), 1694–1700 (1993). [CrossRef]

*n*is the refractive index of fiber and

20. J. P. von der Weid, R. Passy, G. Mussi, and N. Gisin, “On the characterization of optical fiber network components with optical frequency domain reflectometry,” J. Lightwave Technol. **15**(7), 1131–1141 (1997). [CrossRef]

^{6}data points in a personal computer with Intel Core i7 2600 CPU and a 8 GB cache memory. This method indicates a powerful tool for a real-time optical fiber network monitoring and optical fiber sensing applications with a high spatial resolution and a long measurable range.

## 4. Conclusion

^{6}. The reported technique allows an OFDR as a powerful tool for a real-time long haul optical fiber network monitoring and a long range optical fiber sensing applications that has both the high spatial resolution and long measurable range and short acquisition time. This method may also be effective for a nonlinearity compensation of a swept source optical coherence tomography (SS-OCT) and FMCW laser radar, etc.

## Acknowledgments

## References and links

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

2. | B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express |

3. | B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, “Optical frequency domain reflectometry for single- and multi-mode avionics fiber-optics applications,” |

4. | D. P. Zhou, Z. Qin, W. Li, L. Chen, and X. Bao, “Distributed vibration sensing with time-resolved optical frequency-domain reflectometry,” Opt. Express |

5. | E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express |

6. | K. Yuksel, M. Wuilpart, and P. Mégret, “Analysis and suppression of nonlinear frequency modulation in an optical frequency-domain reflectometer,” Opt. Express |

7. | K. Iiyama, M. Yasuda, and S. Takamiya, “Extended-range high-resolution FMCW reflectometry by means of electronically frequency-multiplied sampling signal generated from auxiliary interferometer,” IEICE Trans. Electron. |

8. | T. J. Ahn, J. Y. Lee, and D. Y. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation,” Appl. Opt. |

9. | S. Vergnole, D. Lévesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express |

10. | Z. Ding, T. Liu, Z. Meng, K. Liu, Q. Chen, Y. Du, D. Li, and X. S. Yao, “Note: Improving spatial resolution of optical frequency-domain reflectometry against frequency tuning nonlinearity using non-uniform fast Fourier transform,” Rev. Sci. Instrum. |

11. | M. Froggatt, R. G. Seeley, and D. K. Gifford, “High resolution interferometric optical frequency domain reflectometry (OFDR) beyond the laser coherence length, ” U.S. Pat. 7515276 (Jul. 18, 2007). |

12. | F. Ito, X. Fan, and Y. Koshikiya, “Long-range coherent OFDR with light source phase noise compensation,” J. Lightwave Technol. |

13. | Luna, “Optical backscatter reflectometer (Model OBR 4600)”, http://lunainc.com/wp-content/uploads/2012/11/NEW-OBR4600_Data-Sheet_Rev-03.pdf. |

14. | Y. Koshikiya, X. Fan, and F. Ito, “Long range and cm-level spatial resolution measurement using coherent optical frequency domain reflectometry with SSB-SC modulator and narrow linewidth fiber laser,” J. Lightwave Technol. |

15. | M. Burgos-García, C. Castillo, S. Llorente, J. M. Pardo, and J. C. Crespo, “Digital on-line compensation of errors induced by linear distortion in broadband LFM radars,” Electron. Lett. |

16. | A. Meta, P. Hoogeboom, and L. P. Ligthart, “Range non-linearities correction in FMCW SAR,” in |

17. | W. G. Carrara, R. S. Goodman, and R. M. Majewski, |

18. | G. Giampieri, R. W. Hellings, M. Tinto, and J. E. Faller, “Algorithms for unequal-arm Michelson interferometers,” Opt. Commun. |

19. | S. Venkatesh and W. V. Sorin, “Phase noise consideration in coherent optical FMCW reflectometry,” J. Lightwave Technol. |

20. | J. P. von der Weid, R. Passy, G. Mussi, and N. Gisin, “On the characterization of optical fiber network components with optical frequency domain reflectometry,” J. Lightwave Technol. |

**OCIS Codes**

(060.2300) Fiber optics and optical communications : Fiber measurements

(060.2430) Fiber optics and optical communications : Fibers, single-mode

(120.1840) Instrumentation, measurement, and metrology : Densitometers, reflectometers

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: November 27, 2012

Revised Manuscript: January 22, 2013

Manuscript Accepted: January 23, 2013

Published: February 7, 2013

**Citation**

Zhenyang Ding, X. Steve Yao, Tiegen Liu, Yang Du, Kun Liu, Junfeng Jiang, Zhuo Meng, and Hongxin Chen, "Compensation of laser frequency tuning nonlinearity of a long range OFDR using deskew filter," Opt. Express **21**, 3826-3834 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-3826

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### References

- W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single mode fiber,” Appl. Phys. Lett.39(9), 693–695 (1981). [CrossRef]
- B. Soller, D. Gifford, M. Wolfe, and M. Froggatt, “High resolution optical frequency domain reflectometry for characterization of components and assemblies,” Opt. Express13(2), 666–674 (2005). [CrossRef] [PubMed]
- B. Soller, S. Kreger, D. Gifford, M. Wolfe, and M. Froggatt, “Optical frequency domain reflectometry for single- and multi-mode avionics fiber-optics applications,” IEEE Conference Avionics Fiber-Optics and Photonics, 2006 (IEEE, 2006) pp. 38–39.
- D. P. Zhou, Z. Qin, W. Li, L. Chen, and X. Bao, “Distributed vibration sensing with time-resolved optical frequency-domain reflectometry,” Opt. Express20(12), 13138–13145 (2012). [CrossRef] [PubMed]
- E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express16(17), 13139–13149 (2008). [CrossRef] [PubMed]
- K. Yuksel, M. Wuilpart, and P. Mégret, “Analysis and suppression of nonlinear frequency modulation in an optical frequency-domain reflectometer,” Opt. Express17(7), 5845–5851 (2009). [CrossRef] [PubMed]
- K. Iiyama, M. Yasuda, and S. Takamiya, “Extended-range high-resolution FMCW reflectometry by means of electronically frequency-multiplied sampling signal generated from auxiliary interferometer,” IEICE Trans. Electron.E89-C, 823–829 (2006).
- T. J. Ahn, J. Y. Lee, and D. Y. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation,” Appl. Opt.44(35), 7630–7634 (2005). [CrossRef] [PubMed]
- S. Vergnole, D. Lévesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express18(10), 10446–10461 (2010). [CrossRef] [PubMed]
- Z. Ding, T. Liu, Z. Meng, K. Liu, Q. Chen, Y. Du, D. Li, and X. S. Yao, “Note: Improving spatial resolution of optical frequency-domain reflectometry against frequency tuning nonlinearity using non-uniform fast Fourier transform,” Rev. Sci. Instrum.83(6), 066110 (2012). [CrossRef] [PubMed]
- M. Froggatt, R. G. Seeley, and D. K. Gifford, “High resolution interferometric optical frequency domain reflectometry (OFDR) beyond the laser coherence length, ” U.S. Pat. 7515276 (Jul. 18, 2007).
- F. Ito, X. Fan, and Y. Koshikiya, “Long-range coherent OFDR with light source phase noise compensation,” J. Lightwave Technol.30(8), 1015–1024 (2012). [CrossRef]
- Luna, “Optical backscatter reflectometer (Model OBR 4600)”, http://lunainc.com/wp-content/uploads/2012/11/NEW-OBR4600_Data-Sheet_Rev-03.pdf .
- Y. Koshikiya, X. Fan, and F. Ito, “Long range and cm-level spatial resolution measurement using coherent optical frequency domain reflectometry with SSB-SC modulator and narrow linewidth fiber laser,” J. Lightwave Technol.26(18), 3287–3294 (2008). [CrossRef]
- M. Burgos-García, C. Castillo, S. Llorente, J. M. Pardo, and J. C. Crespo, “Digital on-line compensation of errors induced by linear distortion in broadband LFM radars,” Electron. Lett.39(1), 116–118 (2003). [CrossRef]
- A. Meta, P. Hoogeboom, and L. P. Ligthart, “Range non-linearities correction in FMCW SAR,” in IEEE International Conference on Geoscience and Remote Sensing Symposium, 2006. IGARSS 2006 (IEEE, 2006), 403–406.
- W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Synthetic Aperture Radar (Artech House, 1995).
- G. Giampieri, R. W. Hellings, M. Tinto, and J. E. Faller, “Algorithms for unequal-arm Michelson interferometers,” Opt. Commun.123(4-6), 669–678 (1996). [CrossRef]
- S. Venkatesh and W. V. Sorin, “Phase noise consideration in coherent optical FMCW reflectometry,” J. Lightwave Technol.11(10), 1694–1700 (1993). [CrossRef]
- J. P. von der Weid, R. Passy, G. Mussi, and N. Gisin, “On the characterization of optical fiber network components with optical frequency domain reflectometry,” J. Lightwave Technol.15(7), 1131–1141 (1997). [CrossRef]

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