## Coherence characterization of narrow-linewidth beam by C-OFDR based Rayleigh speckle analysis |

Optics Express, Vol. 19, Issue 21, pp. 19790-19796 (2011)

http://dx.doi.org/10.1364/OE.19.019790

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### Abstract

A novel method for characterizing the amplitude of a coherence function with respect to a delay between two optical waves is proposed and demonstrated by using a distributional Rayleigh speckle analysis based on C-OFDR. This technique allows us to estimate both the coherence time of the laser and that of the spectral profiles from the measured amplitude of the coherence function, if the symmetry of the spectrum can be assumed. The spectral width obtained in the experiment agrees roughly with that obtained using a delayed self-heterodyne method.

© 2011 OSA

## 1. Introduction

1. T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. **16**(16), 630–631 (1980). [CrossRef]

2. L. Richter, H. Mandelberg, M. Kruger, and P. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum Electron. **22**(11), 2070–2074 (1986). [CrossRef]

4. P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. **20**(1), 30–32 (1984). [CrossRef]

## 2. Principle and system configuration

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

6. K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry using phase-decorrelated reflected and reference lightwaves,” J. Lightwave Technol. **15**(7), 1102–1109 (1997). [CrossRef]

*E*be the electrical amplitude of the measured beam with duration

_{q}(t)*T*. Here,

*q*denotes the number of the samples of the lightwave. Consider a single reflection point with the round trip time

*τ*, the back-reflected beam

*τ*is the distance from the spectrum center and

_{i}*g*is frequency sweep rates. Note that the coherence function is defined bywhere

*τ*is the sum of those from the scattering centers with random reflectivities [7]:where

*s*th measurement, and we analyze the correlation between the two measurements.

*q ≠ s*), and

*i ≠ j*) are statistically independent of each other. Then by using the Kronecker delta expression, we obtain,andwhere

## 3. Experimental method

8. 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]

*g*= 500 and 125 GHz/s.

*ΔF = gT*, was always set at 8 GHz, which was extended with three doublers and band pass filters, a mixer and an oscillator to step the frequency down to a suitable level, corresponding to a theoretical resolution,

*Δτ =*1/

*ΔF,*of 125 ps (round trip time). The sweep range determines the maximum linewidth which can be observed by the system. As described later, since

*N*( = 1000) neighboring samples of the backscattered intensities are used for the statistical analysis to obtain a single value of the coherence function,

*γ*(

*t*), the interval of the obtained

*γ*(

*t*) is larger than

*NΔτ*. Supposing that the domain of the coherence function is ~1/

*Δν*, 1/

*Δν*>

*NΔτ*, or

*ΔF*>

*NΔν*is needed to acquire the profile of the coherence function. For example, when

*N*= 1000, it is supposed that the linewidth up to a few MHz can be observed with the sweep range of 8 GHz.

^{TM}1617-AC-FC), then filtered by electrical filters, and acquired with 8 bit A/D converters (NI PXI-5154) with a sampling rate of 1 GHz. These data were sent to a personal computer to analyze the coherence function.

## 4. Experimental results

*T*= 16 ms and

*T*= 64 ms, respectively, and there is no clear difference between them. The obtained coherence functions decrease monotonically with respect to τ, and it appears that τ providing

*S*(ν) in accordance with the Wiener-Khinchin theorem [9],

*S*(ν)s were 520 and 116 kHz in Fig. 5(a) and (b) after Gaussian fitting, respectively. The spectral width of LUT (I) obtained in the experiment coincides well with that obtained by DSHM assuming that the profile is Gaussian. On the other hand, an approximately 1.7-fold difference is seen between those values in LUT (II). A possible reason for the discrepancy is that the proposed method observes the spectrum of the 16 ~64 ms length signals, while DSHM observes the beat with the 0.4 ms delayed signal (80 km-fiber). If the signal includes a slow frequency drift, the above discrepancy is acceptable.

## 6. Conclusion

## References and links

1. | T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. |

2. | L. Richter, H. Mandelberg, M. Kruger, and P. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum Electron. |

3. | S. A. Havestad, Y. Xie, A. B. Sahin, Z. Pan, A. E. Willner, and B. Fischer, “Delayed self-heterodyne interferometer measurements of narrow linewidth fiber lasers” |

4. | P. Healey, “Fading in heterodyne OTDR,” Electron. Lett. |

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

6. | K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry using phase-decorrelated reflected and reference lightwaves,” J. Lightwave Technol. |

7. | J. W. Goodman, “Statistical Optics,” in |

8. | 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. |

9. | M. Born and E. Wolf, |

**OCIS Codes**

(030.0030) Coherence and statistical optics : Coherence and statistical optics

(120.3180) Instrumentation, measurement, and metrology : Interferometry

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: July 5, 2011

Revised Manuscript: August 23, 2011

Manuscript Accepted: August 23, 2011

Published: September 26, 2011

**Citation**

Masaaki Inoue, Yusuke Koshikiya, Xinyu Fan, and Fumihiko Ito, "Coherence characterization of narrow-linewidth beam by C-OFDR based Rayleigh speckle analysis," Opt. Express **19**, 19790-19796 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-19790

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### References

- T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett.16(16), 630–631 (1980). [CrossRef]
- L. Richter, H. Mandelberg, M. Kruger, and P. McGrath, “Linewidth determination from self-heterodyne measurements with subcoherence delay times,” IEEE J. Quantum Electron.22(11), 2070–2074 (1986). [CrossRef]
- S. A. Havestad, Y. Xie, A. B. Sahin, Z. Pan, A. E. Willner, and B. Fischer, “Delayed self-heterodyne interferometer measurements of narrow linewidth fiber lasers” in Proceedings of lasers and Electro-Optics,2000(CLEO 2000), pp. 310–311.
- P. Healey, “Fading in heterodyne OTDR,” Electron. Lett.20(1), 30–32 (1984). [CrossRef]
- W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett.39(9), 693–695 (1981). [CrossRef]
- K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Coherent optical frequency domain reflectometry using phase-decorrelated reflected and reference lightwaves,” J. Lightwave Technol.15(7), 1102–1109 (1997). [CrossRef]
- J. W. Goodman, “Statistical Optics,” in Wiley-Interscience, (NJ & Oxford, 2000)
- 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. Born and E. Wolf, Principles of Optics 7th ed. (Cambridge University Press, 1999).

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