## Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry

Optics Express, Vol. 16, Issue 17, pp. 13139-13149 (2008)

http://dx.doi.org/10.1364/OE.16.013139

Acrobat PDF (334 KB)

### Abstract

The frequency-sampling method is widely used to accommodate nonlinear laser tuning in swept-wavelength interferometric techniques such as optical frequency domain reflectometry (OFDR) and swept-wavelength optical coherence tomography (OCT). In this paper we analyze the frequency-sampling method and identify two sources of sampling errors. One source of error is the limit of an underlying approximation for long interferometer path mismatches and fast laser tuning rates. A second source of error is transmission delays in data acquisition hardware. We show that the measurement system can be configured such that the two error sources cancel to second order. We present experimental verification of sampling error correction using a general swept-wavelength interferometer with a significantly nonlinear laser sweep.

© 2008 Optical Society of America

## 1. Introduction

2. E. C. Burrows and K.-Y. Liou, “High resolution laser LIDAR utilising two-section distributed feedback semi-conductor laser as a coherent source,” Electron. Lett. **26**, 577–579 (1990). [CrossRef]

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

4. S. A. Kingsley and D. E. N. Davies, “OFDR diagnostics for fibre and integrated-optic systems,” Electron. Lett. **21**, 434–435 (1985). [CrossRef]

5. D. Uttam and B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. **LT-3**, 971–977 (1985). [CrossRef]

6. U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Technol. **11**, 1377–1384 (1993). [CrossRef]

7. 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**, 1131–1141 (1997). [CrossRef]

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

8. L.-T. Wang, K. Iiyama, F. Tsukada, N. Yoshida, and K.-I. Hayashi, “Loss measurement in optical waveguide devices by coherent frequency-modulated continuous-wave reflectometry,” Opt. Lett. **18**, 1095–1097 (1993). [CrossRef] [PubMed]

9. R. Passy, N. Gisin, and J. P. von der Weid, “High-sensitivity-coherent optical frequency-domain reflectometry for characterization of fiber-optic network components,” IEEE Photon. Technol. Lett. **7**, 667–669 (1995). [CrossRef]

11. M. Yoshida, K. Nakamura, and H. Ito, “A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser,” IEEE Photon. Technol. Lett. **13**, 227–229 (2001). [CrossRef]

12. T.-J. Ahn, Y. Jung, K. Oh, and D. Y. Kim, “Optical frequency-domain chromatic dispersion measurement method for higher-order modes in an optical fiber,” Opt. Express **13**, 10,040–10,047 (2005). [CrossRef]

13. M. Froggatt, “Distributed measurement of the complex modulation of a photoinduced Bragg grating in an optical fiber,” Appl. Opt. **35**, 5162–5164 (1996). [CrossRef] [PubMed]

15. O. H. Waagaard, “Spatial characterization of strong fiber Bragg gratings using thermal chirp and optical-frequency-domain reflectometry,” J. Lightwave Technol. **23**, 909–914 (2005). [CrossRef]

16. B. Huttner, J. Reecht, N. Gisin, R. Passy, and J. P. von der Weid, “Local birefringence measurements in single-mode fibers with coherent optical frequency-domain reflectometry,” IEEE Photon. Technol. Lett. **10**, 1458–1460 (1998). [CrossRef]

17. M. Yoshida, T. Miyamoto, N. Zou, K. Nakamura, and H. Ito, “Novel PMD measurement method based on OFDR using a frequency-shifted feedback fiber laser,” Opt. Express **9**, 207–211 (2001). [CrossRef] [PubMed]

18. M. Wegmuller, M. Legré, and N. Gisin, “Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry,” J. Lightwave Technol. **20**, 800–807 (2002). [CrossRef]

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

22. B. J. Soller, D. K. Gifford, M. S. Wolfe, M. E. Froggatt, M. H. Yu, and P. F. Wysocki, “Measurement of localized heating in fiber optic components with millimeter spatial resolution,” in *Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference*, Technical Digest (CD) (Optical Society of America, 2006). Paper OFN3.

24. G. D. VanWiggeren, A. R. Motamedi, and D. M. Baney, “Single-scan interferometric component analyzer,” IEEE Photon. Technol. Lett. **15**, 263–265 (2003). [CrossRef]

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

26. D. K. Gifford, B. J. Soller, M. S. Wolfe, and M. E. Froggatt, “Optical vector network analyzer for single-scan measurments of loss, group delay, and polarization mode dispersion,” Appl. Opt. **44**, 7282–7286 (2005). [CrossRef] [PubMed]

27. S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. **22**, 340–342 (1997). [CrossRef] [PubMed]

28. S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express **11**, 2953–2963 (2003). [CrossRef] [PubMed]

29. K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Spatial-resolution improvement in long-range coherent optical frequency domain reflectometry by frequency-sweep linearisation,” Electron. Lett. **33**, 408–410 (1997). [CrossRef]

30. K. Iiyama, L.-T. Wang, and K. ichi Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. **14**, 173–178 (1996). [CrossRef]

8. L.-T. Wang, K. Iiyama, F. Tsukada, N. Yoshida, and K.-I. Hayashi, “Loss measurement in optical waveguide devices by coherent frequency-modulated continuous-wave reflectometry,” Opt. Lett. **18**, 1095–1097 (1993). [CrossRef] [PubMed]

31. K.-Y. Huang and G. M. Carter, “Coherent optical frequency domain reflectometry (OFDR) using a fiber grating external cavity laser,” IEEE Photon. Technol. Lett. **6**, 1466–1468 (1994). [CrossRef]

15. O. H. Waagaard, “Spatial characterization of strong fiber Bragg gratings using thermal chirp and optical-frequency-domain reflectometry,” J. Lightwave Technol. **23**, 909–914 (2005). [CrossRef]

32. M. Kobayashi, K. Takada, and J. Noda, “Optical-frequency encoder using polarization-maintaining fiber,” J. Lightwave Technol. **8**, 1697–1702 (1990). [CrossRef]

6. U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Technol. **11**, 1377–1384 (1993). [CrossRef]

6. U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Technol. **11**, 1377–1384 (1993). [CrossRef]

## 2. Sampling errors in triggered swept-wavelength interferometry

### 2.1. Sampling errors intrinsic to interferometric triggering

*ϕ*(

*t*) is a time-varying phase and

*E*

_{0}is a constant amplitude. In this case the instantaneous optical frequency of the laser is given by

*U*

_{0}=2σ|

*E*

_{0}|

^{2}. Next we Taylor expand the function

*ϕ*(

*t*+τ) about

*t*:

**11**, 1377–1384 (1993). [CrossRef]

^{-1}.

^{-1}, the

*i*

^{th}interval will depart from τ

^{-1}by some amount

*δ*ν

*, i.e., Δν*

^{I}_{i}*=τ*

_{i}^{-1}+

*δ*ν

*. We use the superscript*

^{I}_{i}*I*to denote that the sampling error derived here is the intrinsic error present in the frequency-sampling method, distinct from sampling errors due to delays in the DAQ hardware, which are treated in the next section.

*δ*ν

*, we consider the set of times ti at which triggers occur. These times are each separated by one period of the fringe pattern described by Eq. (3). The phase of the fringe pattern, represented in Eq. (5), will experience a change of 2*

^{I}_{i}*π*between

*t*and

_{i}*t*

_{i+1}. To express the evolution of a single period mathematically, we subtract the right side of Eq. (5) at time

*t*from the same expression at time

_{i}*t*

_{i+1}, yielding

*δ*ν

*represents a sampling error intrinsic to interferometric triggering that depends on the interferometer path mismatch and the derivatives of the tuning rate. This error couples to the final measurement through the Fourier transform, leading to both amplitude and phase errors. These errors impose a limit on the interferometer path length differences allowable in an SWI system for a given laser that exhibits nonlinear wavelength tuning. This limit can be extended, however, by using sampling errors due to delays in the DAQ hardware to cancel the intrinsic sampling errors to second order.*

^{I}_{i}### 2.2. Sampling errors due to data acquisition delays

*Ũ*that varies as a simple cosine in frequency (as is the case when higher-order sampling errors can be neglected):

*t*that correspond to sampling intervals of equal optical frequency:

_{i}*δt*that includes two components: the differential optical delay between the trigger signal and the sampled signal, and the electronic delay between a trigger event and the moment a voltage value is recorded by the data acquisition hardware. Such a finite delay will necessarily exist because of optical and electronic transmission delays if the analog clock and data channels are not carefully path-matched. Because of this delay, the data is not sampled at the times

*t*, but rather at the set of times

_{i}*t*+

_{i}*δt*. The effect of this delay is to perturb each frequency interval of the sampled data by an amount

*δ*ν

*:*

^{D}_{i}*δt*will be the same and

*δ*ν

*=0 for all*

^{D}_{i}*i*. But if the tuning rate of the laser is changing, the frequency change over each

*δt*will be different, and the frequency spacing between sampling points will no longer be uniform. To account for changes in tuning rate, we expand ν(

*t*+

*δt*) as

*δt*can be controlled by adding a delay line to either the trigger channel or the measurement channel. Therefore it is possible to force

*δ*ν

*=0 by appropriately path-matching the system such that*

^{D}_{i}*δt*=0. This strategy does not always yield the best system performance, however. Instead, a nonzero sampling error due to the DAQ delay can be used to cancel the intrinsic sampling errors derived in Sec. 2.1 through a prudent choice of

*δt*.

### 2.3. Correcting sampling errors

*t*+

_{i}*δt*, and the frequency spacing between acquisitions is

*δ*ν

*has been converted from*

^{I}_{i}*n*to

*n*-1 in order to start the summation at

*n*=1. It is often the case that the sampling errors are dominated by the first-order terms of the two sums. In this case we can neglect the higher-order terms, and the frequency spacing becomes

*δt*may be controlled using delay lines in the system. Therefore, we can set

*δt*=τ/2, which will drive the error term to zero and result in a cancelation of the sampling errors. This yields error-free sampling to second order in

*ϕ*(

*t*) and is valid as long as

*τ*

^{3}(

*d*

^{2}ν/

*dt*

^{2})≪1.

*δ*ν

*and*

^{I}_{i}*δ*ν

*differs by a factor of 1/*

^{D}_{i}*n*. Therefore cancelation of any single term in the error expansion is possible through the proper choice of

*δt*, but the required

*δt*is different for each term. In general, to drive the

*n*

^{th}order term of the sampling error to zero, the DAQ delay must be

*δt*=τ(

*n*+1)

^{-1}/

*n*.

## 3. Measurement of laser tuning rate variations

*t*) from the phase of this expression. The first step is to perform an FFT, which results in positive and negative sidebands corresponding to exp[±

*i*2

*π*ν(

*t*)τ] as shown in Fig. 2(B). Next, a digital filter is used to select a single sideband through a multiplication by the rect function overlaid on Fig. 2(B). Before transforming back to the time domain via an inverse FFT, the filtered data is shifted such that the selected sideband occupies the DC location in the data array, as shown in Fig. 2(C). The result of the inverse FFT is a data set corresponding to a single complex exponential. The phase of this exponential is plotted in red in Fig. 2(D), and the unwrapped phase is shown in black. Had we not performed the shift in the frequency domain, the phase would vary too rapidly to reliably unwrap. After unwrapping, a linear phase must be added to compensate for the shift according to the Fourier shift theorem. This results in a measurement of ν(

*t*). A numerical derivative may then be performed to get the tuning rate.

## 4. Experimental setup and results

*τ*=516 ns between the two paths. This delay is chosen to be much less than the coherence length of the laser to avoid fringe fading due to coherence effects, but large enough such that approximation (6) is not valid. The laser wavelength is swept at a nominal rate of 40 nm/s, so for this combination of tuning rate and relative interferometer delay, τ

_{t}^{2}

_{t}(

*d*ν/

*dt*)≈1.3.

_{m}=13.2 ns. For this interferometer inequality (6) holds, since τ

^{2}

_{t}(

*d*ν/

*dt*)≈10

^{-3}. Therefore the sampled fringe pattern is well described by Eq. (10) in the absence of sampling errors. Sampling errors will cause the phase of the sampled fringe pattern to deviate from linearity as a function of optical frequency.

^{-1}because the sampling errors average to zero for the given laser tuning characteristics.

_{t}=516 ns and a laser tuning rate of 40 nm/s.

*δt*for the system was 567±5 ns. The uncertainty associated with this value is dominated by the uncertainty in the measurement of the electronic delay. Since a value of τ

_{t}/2=258 ns is necessary to correct sampling errors, and addition of delay to the measurement path contributes negative delay to

*δt*, 309±5 ns must be added to the measurement path.

## 5. Summary and conclusions

^{2}(

*d*ν/

*dt*)≪1 is no longer valid. The second source can be present even for small path length differences and tuning rates and is due to transmission delays in data acquisition hardware. We further show that by introducing an optical delay line into the swept-wavelength measurement system, these errors can effectively cancel one another to second order. This eases the restrictions on the interferometer delay and laser tuning curve necessary for using the frequency-sampling method from τ

^{2}(

*d*ν/

*dt*)≪1 to τ

^{3}(

*d*

^{2}ν/

*dt*

^{2})≪1. In the case where intrinsic sampling errors are negligible, errors due to DAQ delays can be removed by using the delay line to match the measurement channel path length to the trigger channel path length. Correction of sampling errors was experimentally verified, showing an order of magnitude improvement in the phase error of the sampled interferogram.

## References and links

1. | A. Hymans and J. Lait, “Analysis of a frequency-modulated continuous-wave ranging system,” Proc. IEEE |

2. | E. C. Burrows and K.-Y. Liou, “High resolution laser LIDAR utilising two-section distributed feedback semi-conductor laser as a coherent source,” Electron. Lett. |

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

4. | S. A. Kingsley and D. E. N. Davies, “OFDR diagnostics for fibre and integrated-optic systems,” Electron. Lett. |

5. | D. Uttam and B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. |

6. | U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Technol. |

7. | 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. |

8. | L.-T. Wang, K. Iiyama, F. Tsukada, N. Yoshida, and K.-I. Hayashi, “Loss measurement in optical waveguide devices by coherent frequency-modulated continuous-wave reflectometry,” Opt. Lett. |

9. | R. Passy, N. Gisin, and J. P. von der Weid, “High-sensitivity-coherent optical frequency-domain reflectometry for characterization of fiber-optic network components,” IEEE Photon. Technol. Lett. |

10. | M. Froggatt, T. Erdogan, J. Moore, and S. Shenk, “Optical frequency domain characterization (OFDC) of dispersion in optical fiber Bragg gratings,” in |

11. | M. Yoshida, K. Nakamura, and H. Ito, “A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser,” IEEE Photon. Technol. Lett. |

12. | T.-J. Ahn, Y. Jung, K. Oh, and D. Y. Kim, “Optical frequency-domain chromatic dispersion measurement method for higher-order modes in an optical fiber,” Opt. Express |

13. | M. Froggatt, “Distributed measurement of the complex modulation of a photoinduced Bragg grating in an optical fiber,” Appl. Opt. |

14. | H. Rosenfeldt, C. Knothe, J. Cierullies, and E. Brinkmeyer, “Evolution of amplitude and dispersion spectra during fiber Bragg grating fabrication,” in |

15. | O. H. Waagaard, “Spatial characterization of strong fiber Bragg gratings using thermal chirp and optical-frequency-domain reflectometry,” J. Lightwave Technol. |

16. | B. Huttner, J. Reecht, N. Gisin, R. Passy, and J. P. von der Weid, “Local birefringence measurements in single-mode fibers with coherent optical frequency-domain reflectometry,” IEEE Photon. Technol. Lett. |

17. | M. Yoshida, T. Miyamoto, N. Zou, K. Nakamura, and H. Ito, “Novel PMD measurement method based on OFDR using a frequency-shifted feedback fiber laser,” Opt. Express |

18. | M. Wegmuller, M. Legré, and N. Gisin, “Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry,” J. Lightwave Technol. |

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

20. | M. Froggatt, B. Soller, D. Gifford, and M. Wolfe, “Correlation and keying of Rayleigh scatter for loss and temperature sensing in parallel optical networks,” in |

21. | D. K. Gifford, B. J. Soller, M. S. Wolfe, and M. E. Froggatt, “Distributed fiber-optic temperature sensing using Rayleigh backscatter,” in |

22. | B. J. Soller, D. K. Gifford, M. S. Wolfe, M. E. Froggatt, M. H. Yu, and P. F. Wysocki, “Measurement of localized heating in fiber optic components with millimeter spatial resolution,” in |

23. | M. Froggatt, D. Gifford, S. Kreger, M. Wolfe, and B. Soller, “Distributed strain and temperature discrimination in unaltered polarization maintaining fiber,” in |

24. | G. D. VanWiggeren, A. R. Motamedi, and D. M. Baney, “Single-scan interferometric component analyzer,” IEEE Photon. Technol. Lett. |

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

26. | D. K. Gifford, B. J. Soller, M. S. Wolfe, and M. E. Froggatt, “Optical vector network analyzer for single-scan measurments of loss, group delay, and polarization mode dispersion,” Appl. Opt. |

27. | S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. |

28. | S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express |

29. | K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Spatial-resolution improvement in long-range coherent optical frequency domain reflectometry by frequency-sweep linearisation,” Electron. Lett. |

30. | K. Iiyama, L.-T. Wang, and K. ichi Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. |

31. | K.-Y. Huang and G. M. Carter, “Coherent optical frequency domain reflectometry (OFDR) using a fiber grating external cavity laser,” IEEE Photon. Technol. Lett. |

32. | M. Kobayashi, K. Takada, and J. Noda, “Optical-frequency encoder using polarization-maintaining fiber,” J. Lightwave Technol. |

33. | K. Takada, “High-resolution OFDR with incorporated fiber-optic frequency encoder,” 4, 1069–1072 (1992). |

34. | T.-J. Ahn and D. Y. Kim, “Analysis of nonlinear frequency sweep in high-speed tunable laser sources using a self-homodyne measurement and Hilbert transformation,” Appl. Opt. |

**OCIS Codes**

(060.2300) Fiber optics and optical communications : Fiber measurements

(120.3180) Instrumentation, measurement, and metrology : Interferometry

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: June 27, 2008

Revised Manuscript: August 4, 2008

Manuscript Accepted: August 5, 2008

Published: August 12, 2008

**Virtual Issues**

Vol. 3, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Eric D. Moore and Robert R. McLeod, "Correction of sampling errors due to
laser tuning rate fluctuations in
swept-wavelength interferometry," Opt. Express **16**, 13139-13149 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13139

Sort: Year | Journal | Reset

### References

- A. Hymans and J. Lait, "Analysis of a frequency-modulated continuous-wave ranging system," Proc. IEEE 107, 365-372 (1960).
- E. C. Burrows and K.-Y. Liou, "High resolution laser LIDAR utilising two-section distributed feedback semiconductor laser as a coherent source," Electron. Lett. 26, 577-579 (1990). [CrossRef]
- W. Eickhoff and R. Ulrich, "Optical frequency domain reflectometry in single-mode fiber," Appl. Phys. Lett. 39, 693-695 (1981). [CrossRef]
- S. A. Kingsley and D. E. N. Davies, "OFDR diagnostics for fibre and integrated-optic systems," Electron. Lett. 21, 434-435 (1985). [CrossRef]
- D. Uttam and B. Culshaw, "Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique," J. Lightwave Technol. LT-3, 971-977 (1985). [CrossRef]
- U. Glombitza and E. Brinkmeyer, "Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides," J. Lightwave Technol. 11, 1377-1384 (1993). [CrossRef]
- J. P. von derWeid, R. Passy, G. Mussi, and N. Gisin, "On the characterization of optical fiber network components with optical frequency domain reflectometry," J. Lightwave Technol. 15, 1131-1141 (1997). [CrossRef]
- L.-T. Wang, K. Iiyama, F. Tsukada, N. Yoshida, and K.-I. Hayashi, "Loss measurement in optical waveguide devices by coherent frequency-modulated continuous-wave reflectometry," Opt. Lett. 18, 1095-1097 (1993). [CrossRef] [PubMed]
- R. Passy, N. Gisin, and J. P. von der Weid, "High-sensitivity-coherent optical frequency-domain reflectometry for characterization of fiber-optic network components," IEEE Photon. Technol. Lett. 7, 667-669 (1995). [CrossRef]
- M. Froggatt, T. Erdogan, J. Moore, and S. Shenk, "Optical frequency domain characterization (OFDC) of dispersion in optical fiber Bragg gratings," in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, OSA Technical Digest Series, pp. 176-178 (Optical Society of America, 1999).
- M. Yoshida, K. Nakamura, and H. Ito, "A new method for measurement of group velocity dispersion of optical fibers by using a frequency-shifted feedback fiber laser," IEEE Photon. Technol. Lett. 13, 227-229 (2001). [CrossRef]
- T.-J. Ahn, Y. Jung, K. Oh, and D. Y. Kim, "Optical frequency-domain chromatic dispersion measurement method for higher-order modes in an optical fiber," Opt. Express 13, 10,040-10,047 (2005). [CrossRef]
- M. Froggatt, "Distributed measurement of the complex modulation of a photoinduced Bragg grating in an optical fiber," Appl. Opt. 35, 5162-5164 (1996). [CrossRef] [PubMed]
- H. Rosenfeldt, C. Knothe, J. Cierullies, and E. Brinkmeyer, "Evolution of amplitude and dispersion spectra during fiber Bragg grating fabrication," in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, OSA Technical Digest Series (Optical Society of America, 2001).
- O. H. Waagaard, "Spatial characterization of strong fiber Bragg gratings using thermal chirp and opticalfrequency-domain reflectometry," J. Lightwave Technol. 23, 909-914 (2005). [CrossRef]
- B. Huttner, J. Reecht, N. Gisin, R. Passy, and J. P. von der Weid, "Local birefringence measurements in singlemode fibers with coherent optical frequency-domain reflectometry," IEEE Photon. Technol. Lett. 10, 1458-1460 (1998). [CrossRef]
- M. Yoshida, T. Miyamoto, N. Zou, K. Nakamura, and H. Ito, "Novel PMD measurement method based on OFDR using a frequency-shifted feedback fiber laser," Opt. Express 9, 207-211 (2001). [CrossRef] [PubMed]
- M. Wegmuller, M. Legre, and N. Gisin, "Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry," J. Lightwave Technol. 20, 800-807 (2002). [CrossRef]
- M. Froggatt and J. Moore, "High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh backscatter," Appl. Opt. 37, 1735-1740 (1998). [CrossRef]
- M. Froggatt, B. Soller, D. Gifford, and M. Wolfe, "Correlation and keying of Rayleigh scatter for loss and temperature sensing in parallel optical networks," in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 2004). Paper PDP17.
- D. K. Gifford, B. J. Soller, M. S. Wolfe, and M. E. Froggatt, "Distributed fiber-optic temperature sensing using Rayleigh backscatter," in European Conference on Optical Communication, vol. 3 of ECOC 2005 Proceedings (2005). Paper We4.P.005.
- B. J. Soller, D. K. Gifford, M. S. Wolfe, M. E. Froggatt, M. H. Yu, and P. F. Wysocki, "Measurement of localized heating in fiber optic components with millimeter spatial resolution," in Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2006). Paper OFN3.
- M. Froggatt, D. Gifford, S. Kreger, M. Wolfe, and B. Soller, "Distributed strain and temperature discrimination in unaltered polarization maintaining fiber," in Optical Fiber Sensors, OSA Technical Digest (CD) (Optical Society of America, 2006). Paper ThC5.
- G. D. VanWiggeren, A. R. Motamedi, and D. M. Baney, "Single-scan interferometric component analyzer," IEEE Photon. Technol. Lett. 15, 263-265 (2003). [CrossRef]
- B. J. Soller, D. K. Gifford, M. S. Wolfe, and M. E. Froggatt, "High resolution optical frequency domain reflectometry for characterization of components and assemblies," Opt. Express 13, 666-674 (2005). [CrossRef] [PubMed]
- D. K. Gifford, B. J. Soller, M. S. Wolfe, and M. E. Froggatt, "Optical vector network analyzer for single-scan measurments of loss, group delay, and polarization mode dispersion," Appl. Opt. 44, 7282-7286 (2005). [CrossRef] [PubMed]
- S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, "Optical coherence tomography using a frequency-tunable optical source," Opt. Lett. 22, 340-342 (1997). [CrossRef] [PubMed]
- S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, "High-speed optical frequency-domain imaging," Opt. Express 11, 2953-2963 (2003). [CrossRef] [PubMed]
- K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, "Spatial-resolution improvement in long-range coherent optical frequency domain reflectometry by frequency-sweep linearisation," Electron. Lett. 33, 408-410 (1997). [CrossRef]
- K. Iiyama, L.-T. Wang, and K. ichi Hayashi, "Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry," J. Lightwave Technol. 14, 173-178 (1996). [CrossRef]
- K.-Y. Huang and G. M. Carter, "Coherent optical frequency domain reflectometry (OFDR) using a fiber grating external cavity laser," IEEE Photon. Technol. Lett. 6, 1466-1468 (1994). [CrossRef]
- M. Kobayashi, K. Takada, and J. Noda, "Optical-frequency encoder using polarization-maintaining fiber," J. Lightwave Technol. 8, 1697-1702 (1990). [CrossRef]
- K. Takada, "High-resolution OFDR with incorporated fiber-optic frequency encoder," 4, 1069-1072 (1992).
- T.-J. Ahn and D. Y. Kim, "Analysis of nonlinear frequency sweep in high-speed tunable laser sources using a self-homodyne measurement and Hilbert transformation," Appl. Opt. 46, 2394-2400 (2007). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.