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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 3 — Feb. 11, 2013
  • pp: 3826–3834
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Compensation of laser frequency tuning nonlinearity of a long range OFDR using deskew filter

Zhenyang Ding, X. Steve Yao, Tiegen Liu, Yang Du, Kun Liu, Junfeng Jiang, Zhuo Meng, and Hongxin Chen  »View Author Affiliations


Optics Express, Vol. 21, Issue 3, pp. 3826-3834 (2013)
http://dx.doi.org/10.1364/OE.21.003826


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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 × 106 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

Optical frequency-domain reflectometry (OFDR) [1

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

] has been attracting considerable attention for a number of applications, including optical communication networks monitoring [2

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]

], and distributed optical fiber sensing [3

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,” IEEE Conference Avionics Fiber-Optics and Photonics, 2006 (IEEE, 2006) pp. 38–39.

,4

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]

]. In an OFDR system, the interference signals are collected as a function of optical frequency of a tunable laser source (TLS). A Fast Fourier transform (FFT) is then used to convert this frequency domain information to a desired spatial information, where it requires that the interference signals are sampled at an equal interval of the optical frequency. However, any frequency tuning nonlinearity of a TLS gives a rise of non-uniform sampling interval of the optical frequency when the signal is sampled by an equal time interval which, in turn, results in spreading of the reflection peak energy, deteriorating the spatial resolution and reducing the peak’s amplitude [5

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

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]

].

In this paper, we present a simple but effective technique to reduce a degradation of the optical frequency tuning nonlinearity of a TLS in a long range OFDR by using the deskew filter. The deskew filter (also called Residual Video Phase filter) was originally applied to compensate a frequency tuning or frequency chirp nonlinearity in a Frequency Modulated Continuous Wave Synthetic Aperture Radar (FMCW SAR) [15

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]

17

17. W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Synthetic Aperture Radar (Artech House, 1995).

]. For our proposed technique an auxiliary interferometer is implemented to obtain the required nonlinear phase of a TLS. The nonlinear laser frequency or phase noises of the beating signals that were acquired from the main OFDR interferometer can be compensated by the deskew filter for the entire spatial domain beating signals by one time calculation so as to have a high computational efficiency. In theory the proposed method could eliminate any laser frequency tuning nonlinearity completely provided that the nonlinear phase of a TLS can be estimated accurately. Using the proposed method, we demonstrated that the reflection peaks that were undetectable due to the frequency tuning nonlinearity of the TLS can be measured with a significantly improved spatial resolution. In particular, in our OFDR system we observed a spatial resolution of 20 cm and 1.6 m at distances of 10 km and 80 km, respectively, that is about 93 times enhancement when compared with that of the same OFDR system without nonlinearity compensation. If the TLS has a better tuning linearity and wider tuning frequency range, a spatial resolution of our OFDR could be further improved. Moreover this method doesn’t require numerous measurements for the data averaging and thereby a total signal processing time is short, e.g. less than 1 s for data size of 5 × 106. 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

An OFDR interferometer provides beating signals that are produced by the optical interference between two light signals originating from the same linearly chirped high coherent light source. One signal Es(t)is reflection or backscattering light from an optical path of a fiber under test (FUT) while another Er(t)follows a reference path of the interferometer. For a TLS having a linear optical frequency tuning speed γ, an optical field Er(t) can be written as
Er(t)=E0exp{j[2πf0t+πγt2+2πe(t)]},
(1)
wheref0 is the optical frequency,e(t) is the nonlinear phase or phase noise of the TLS.

By assuming that a reflection reflectivity is r(τ) at a delay time τand αis the fiber attenuation coefficient, a reflectivity with the fiber attenuation can be written as R(τ)=r(τ)exp(ατc/n), where c is the light speed in vacuum and n is the refractive index of fiber. Then Es(t) of reflection with the reflectivity can be expressed as

Es(t)=R(τ)E0exp{j[2πf0(tτ)+πγ(tτ)2+2πe(tτ)}.
(2)

TheEr(t) and Es(t) can also be considered as the local oscillator (LO) signals and received signals from the FUT, respectively. Thus, an AC coupled beat signal I(t) generated by the interferences of the LO light Er(t) and received signals Es(t)can be written as
I(t)=2R(τ)E02cos{2π[f0τ+fbt+12γτ2+e(t)e(tτ)]},
(3)
where the beat frequencyfb=γτ. Because different beat frequencies fb correspond to the different locations (i.e. fiber distances) in a spatial domain, the last term e(t)e(tτ) is a source of the laser frequency tuning nonlinearity effect, i.e. a nonlinear phase or phase noise of the TLS. This could also be understood as a beating between the LO light nonlinear phase e(t) and received signal’s nonlinear phase e(tτ).

A complex exponential expression is transformed from Eq. (3) by Hilbert transform that can be expressed as
I(t)=2R(τ)E02exp[j2π(f0τ+fbt+12γτ2)]Se(t)Se*(tτ),
(4)
where Se(t)=exp[j2πe(t)] and Se(tτ)=exp[j2πe(tτ)]. The symbol * represents the complex conjugate.

2.2 Principle and signal processing of the deskew filter algorithm

The nonlinear phase term e(t)e(tτ) results in a spreading of the reflection peak energy that deteriorates the spatial resolution and reduces the peak’s amplitude. In addition, the nonlinear phase’s influence is greater for a longer distance as shown in Fig. 1(a)
Fig. 1 (a) The beat signals with the tuning nonlinearity effects. The upper figure shows the instantaneous optical frequency of the LO signal (blue line) and two received test signals (red lines). The lower figure depicts those corresponded two beat signals. The beat frequencies are not constant and their shapes vary with the distance of the reflections. The spreading of the beat signal in a frequency domain is greater for the reflections at a larger distance than that of at the shorter distance. (b) Diagram blocks of the nonlinearity compensation algorithm. The diagrams on the right represent the behavior of the instantaneous beat signals at the different steps for the compensation algorithm.
. It is difficult to remove the nonlinear phase directly because it is dependent on the distance of the FUT. Fortunately this problem can be solved by processing the LO light’s nonlinear phase e(t) and received test signal’s nonlinear phase e(tτ) separately by using a deskew filter. The similar method was reported to solve a frequency chirp nonlinearity in the FMCW SAR [16

16. 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.

].

The linear beating signals can be recovered via a three-step procedure as shown in Fig. 1(b).

Step two: The deskew filter is applied to I1(t) in a frequency domain
I2(t)=F1{F{I1(t)}exp(jπf2/γ)},
(6)
where Fand F1denotes the Fourier transform and inverse Fourier transform, respectively. Inserting Eq. (5) into Eq. (6), I2(t) can be expressed as
I2(t)=2R(τ)E02exp{j2π[f0τ+fbt]}F1{Se*(f)exp(jπf2/γ)}(t),
(7)
where F1{}(t) denotes an inverse Fourier transform with time variable 𝑡 and Se*(f) is Fourier transform of Se*(t). Assuming that S(t)=F1{exp(jπf2/γ)Se*(f)}(t), S(t)is distance-independent. From Eq. (7), the linear beat signals in any arbitrary delay τcan be recovered after removing S(t).

Step three: The linear beat signals I3(t) can be obtained by removing S(t), i.e. multiplying with S*(t). S(t) can also be obtained by Se*(t)passing though the deskew filter.
S(t)=F1{F{Se*(t)}exp(jπf2/γ)}=F1{Se*(f)exp(jπf2/γ)},
(8)
and then

I3(t)=I2(t)·S*(t)=2R(τ)E02exp{j2π[f0τ+fbt]}.
(9)

From the above signal processing algorithm, one may find that theoretically any nonlinearity effect could be eliminated completely provided that the LO nonlinear phase e(t)of the TLS could be accurately estimated.

2.3 Nonlinear phase estimation

In above analysis, it is assumed that the LO nonlinear phase e(t) is known. In this section we will remove this assumption and describe how to estimate e(t) from the acquired data of an auxiliary unbalanced Michelson interferometer with a constant reference time delay. The similar estimation method is also described for FMCW SAR in [16

16. 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.

]. The normalized beat signal Iref(t) corresponding to a reference time delay τref is

Iref(t)=cos{2π[f0τref+γτreft+12γτref2+e(t)e(tτref)]}.
(10)

Using the Hilbert transform with simple signal processing algorithms, the nonlinear term e(t)e(tτref) can be obtained.

For a small τref, we can approximate e(t) for the Eq. (10) by using Taylor series as
e(t)e(tτref)e(t)'τref,
(11)
where e(t)' denotes a derivative of e(t) with respect to time t. Thus an estimation of e˜(t) can be obtained as

e˜(t)=te(μ)e(μτref)τrefdμ.
(12)

3. Experimental results and discussion

3.1 Setup

The experimental setup of our OFDR is shown as in Fig. 2
Fig. 2 Configuration of the OFDR system. The main interferometer is a modified fiber-based Mach-Zehnder interferometer. The auxiliary interferometer is an unbalanced Michelson interferometer with the 10km reference delay fiber. C1, C2, C3and C4 are 2 × 2 couplers, where C1 is a 1:99 coupler and C2, C3 and C4 are 50:50 couplers. TLS is tunable laser source. FRMs are Faraday rotating mirrors, PC is a polarization controller, PD is a photo-detector, PBS is a polarization beam splitter and DAQ is a data acquisition card.
. The main measurement interferometer is a modified fiber-based Mach-Zehnder interferometer. The TLS has a linewidth of ~1 kHz at a center wavelength 1550 nm, an optical power about 10 mw, a laser frequency tuning speed of 5 GHz/s and a tuning range of 1 GHz. A polarization diversity detection is employed to eliminate any polarization sensitivity in our main measurement interferometer. A FUT is 80 km standard single mode fiber. The sampling rate of data acquisition card (DAQ) is 25 MS/s. An auxiliary Michelson interferometer is used to obtain the nonlinear phase of the TLS, where two Faraday rotating mirrors (FRMs) are implemented to reduce any polarization fading. A length of the reference delay fiber in the auxiliary interferometer is 10 km.

3.2 Nonlinear phase estimation

The LO nonlinear phase 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)
Fig. 3 (a) and (b) are measured signals from the auxiliary interferometer in the time domain with 50 m and 10 km reference delay fiber, where only a part of the entire signals are shown. (c) and (d) are local zoom-ins for figures (a) and (b). The signals from 10 km reference delay fiber interferometer is more smooth than that of from 50 m delay fiber interferometer. (e) is the estimated results of the local oscillator lights' nonlinear phase using 10 km reference delay fiber.
and 3(b). The estimated phases using 10 km reference delay fiber are shown in Fig. 3(e).

An estimation of the LO nonlinear phase e(t) determines the results of nonlinearity compensation. In theory our nonlinearity compensation algorithm could completely eliminate any nonlinearity from a TLS, provided that the nonlinearity can be estimated accurately. If e(t) cannot be estimated accurately, the beat signals of the main interferometer may still contain some residual nonlinear laser phase that could deteriorate the spatial resolution and reduce the peak amplitude of the OFDR signals.

There are two conflicting requirements for the nonlinear phase estimation. On one hand, we need to choose a small reference time delay τref so that it could yield a good estimation of the derivativee(t)'. On the other hand, if the τref is too small a differential phase e(t)e(tτref) is also too small to be easily swamped by those stochastic noises, as shown in Fig. 3(c). For example, when a length of the reference delay fiber Lrefis selected to be short, e.g. of 50 m, the e(t)e(tτref) is too small to be detected due to a low signal to noise ratio (SNR) that would induce measurement errors of e(t). In contrast, if Lref is selected to be very long, we will lost these high frequency information ofe(t) [18

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]

] that would affect the nonlinearity compensation at a far distance. Comparing to Fig. 3(c), the curve shown in Fig. 3(d) does not have much glitch (noise) and also these small and fast changes of e(t)(high frequency information) can be filtered out. Overall we have chosen an optimized value of Lref to achieve a more accurate estimation ofe(t). The more accurate the estimation of e(t) is, the better spatial resolution and the higher the peak amplitude are.

3.3 Tuning nonlinearity compensation of main interferometer

In order to demonstrate an OFDR performance with our nonlinearity compensation algorithm, we applied our algorithm to process the acquired data from our OFDR which was measuring a 80 km single mode fiber. Three APC connections and one open APC connector are connected together in the FUT as shown in Fig. 2. Our experimental measurement results are shown in Fig. 4
Fig. 4 Measured Rayleigh backscattering and Fresnel reflections for a FUT length of 80-km with APC connections and open APC connector without (a) and with (b) the nonlinearity compensations. Four Fresnel reflections are at locations of 10 km, 30 km, 40 km and 80 km. The Fresnel reflections from APC connections and connector without any nonlinearity compensation cannot be detected. After a nonlinearity compensation, a spatial resolution of these reflections are significantly improved, e.g. by more than 93 times for the far-end Fresnel reflection caused by open APC connector at 80 km as shown in (c) and (f). Their spatial resolutions are 20 cm at 10 km, 50 cm at 40 km and 1.6 m at 80 km, respectively. (c)-(f)'s y axis are transformed a logarithm to a normalized linear coordinate.
. As shown in Fig. 4, a spatial resolution of the Fresnel reflection can be greatly enhanced after the nonlinearity compensation. Figure 4(a) shows that those reflections of the APC connections could not be detected due to a nonlinearity of the TLS frequency tuning . However, in contrast, those APC connection reflections can clearly be identified after the laser nonlinear frequency tuning compensation as displayed in Fig. 4(b). Comparing the reflection of a far-end open APC connector of the FUT as shown in Figs. 4(c) and 4(f), a spatial resolution by our method can increase about 93 times than that of without using any nonlinearity compensation. Our OFDR system’s theoretical spatial resolution Δz is about 10 cm based on a relationship Δz=c/2nΔF [19

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

], where cis the light speed in vacuum, n is the refractive index of fiber and ΔF is a frequency tuning range of TLS (ΔF = 1 GHz). A Δz for a reflection at 10 km is about 20 cm, which is a factor of 2 higher a theoretical value of 10 cm. TheΔzsat 40 km and 80 km are 50 cm and 1.6 m, respectively, as shown in Figs. 4(d)4(f). It should be noted that a spatial resolution of the Fresnel reflection is worse at a longer distance than that of at a shorter distance after the nonlinearity phase compensation. The reason for this degradation is that the measured beat signals from a main measurement interferometer still contain some residual “nonlinear laser phase” after the nonlinearity compensation due to the loss of high frequency information in the estimation of e(t). In order to further improve our OFDR performance, it is important to develop a more accurate estimation method of the nonlinear phase.

Measured OFDR curves shown in Fig. 4 also included Rayleigh speckle noise, residual phase noise, and so on [20

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]

] that could be reduced by using a moving median filter in the signal processing. Our proposed method has a very high computational efficiency and also doesn’t require numerous measurements for the data averaging, for example, it takes less than 1 second to complete a total data processing for 5 × 106 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

A simple and effective method to compensate a laser frequency tuning nonlinearity from a TLS in a long range OFDR system is presented and discussed. This method can be operated directly for the beating signals generated from a main OFDR measurement interferometer by using detected nonlinear phase information from an auxiliary interferometer and a deskew filter is used to compensate the laser frequency tuning nonlinearity effect for the entire spatial domain signals by one computation procedure with high efficiency. By using our proposed method we demonstrated a 93 times improvement for a spatial resolution and also achieved a measurable range of 80 km for our OFDR system. Spatial resolutions of 20 cm at 10 km and 1.6 m at 80 km were observed, respectively, in our laser frequency tuning nonlinearity compensated OFDR. It is also possible to further improve a spatial resolution by applying a wider frequency tuning range and a more accurate nonlinear phase estimation. A signal processing time is less than 1 s for a computed data size 5 × 106. 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

This work is supported by National Basic Research Program of China (973 Program, grant 2010CB327806), National Natural Science Foundation of China under Grant No. 11004150&No. 61108070, Tianjin Science and Technology Support Plan Program Funding under Grant No. 11ZCKFGX01900, China Postdoctoral Science Foundation under Grant No. 201003298, International Science & Technology Cooperation Program of China under Grants No. 2009DFB10080&No. 2010DFB13180.

References and links

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]

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,” IEEE Conference Avionics Fiber-Optics and Photonics, 2006 (IEEE, 2006) pp. 38–39.

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]

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. E89-C, 823–829 (2006).

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]

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]

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. 30(8), 1015–1024 (2012). [CrossRef]

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. 26(18), 3287–3294 (2008). [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]

16.

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.

17.

W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Synthetic Aperture Radar (Artech House, 1995).

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]

19.

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

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]

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

  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. Express13(2), 666–674 (2005). [CrossRef] [PubMed]
  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,” IEEE Conference Avionics Fiber-Optics and Photonics, 2006 (IEEE, 2006) pp. 38–39.
  4. 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]
  5. 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]
  6. 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]
  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.E89-C, 823–829 (2006).
  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. Express18(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]
  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.30(8), 1015–1024 (2012). [CrossRef]
  13. Luna, “Optical backscatter reflectometer (Model OBR 4600)”, http://lunainc.com/wp-content/uploads/2012/11/NEW-OBR4600_Data-Sheet_Rev-03.pdf .
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