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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 25 — Dec. 3, 2012
  • pp: 27465–27472
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Correcting for spatial-resolution degradation mechanisms in OFDR via inline auxiliary points

Oren Y. Sagiv, Dror Arbel, and Avishay Eyal  »View Author Affiliations


Optics Express, Vol. 20, Issue 25, pp. 27465-27472 (2012)
http://dx.doi.org/10.1364/OE.20.027465


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Abstract

The spatial resolution of OFDR is normally degraded by the laser phase noise, deviations from linear frequency scan and acoustic noise in the fibers. A method for mitigating these degradation mechanisms, without using an auxiliary interferometer, via inline auxiliary points, is presented and demonstrated experimentally. Auxiliary points are points that are a priori known to have (spatial) impulse reflectivities. Their responses are used for compensating the phase deviations that degrade the response of points that are further away from the source.

© 2012 OSA

1. Introduction

2. Theory

Consider a fiber-optic system as described in Fig. 1
Fig. 1 The experimental setup.
. Light from a laser source is launched into a measurement arm and the back-reflected beam is mixed with a reference and detected by a coherent I/Q receiver. In OFDR the frequency of the laser is varied at a nominally constant rate, γ, over a frequency range Δf. The laser output field can be expressed as:
E(t)=E0exp{j[ω0t+πγt2+θ(t)]}
(1)
where ω0 is the nominal radial frequency at t=0 and θ(t) accounts for phase noise and any other deviation from the linear frequency scan. The measurement fiber can be considered as a distributed reflector with z-dependent reflectivity r(z). The output of the coherent receiver, V(t)I(t)+jQ(t), can be expressed as:
V(t)=a0Lr(z')exp{j[2πγ2z'vt+φ(t,z')]}dz'
(2)
where, a is a constant describing the responsivity and gain of the receiver and φ(t,z) denotes the phase of the light reflected from position z due to phase noise, non-linear frequency scan and acoustic noise in the fiber, referenced to the phase in the reference arm. An approximated expression for r(z) can be obtained by taking the Fourier transform of V(t)/a and substituting f=2zγ/v where v is the group velocity of light in the fiber:
r˜(z)=1a0TV(t')exp[j(2πγ2zvt')]dt'=0Lr(z')g˜(z,z')dz'.
(3)
where
g˜(z,z')=0Texp{j[2πγ2(z'z)vt'+φ(t',z')]}dt'.
(4)
is the response of the measurement system for a spatial impulse at z'. It describes the degradation in spatial resolution due to the phase noise, deviation from linear frequency scan and acoustic noise. It can be easily shown that for the ideal case where φ(t,z)=0 Eq. (3) reduces to r˜(z)=r(z). As will be described below it is possible to extract from the data an approximation of φ(t,z) using discrete reflection points in the fiber that we term auxiliary points. In this case a better estimation of r(z) can be obtained by calculating:
r˜˜(z)=1a0TV(t')exp{j[2πγ2zvt'+φ(t',z)]}dt'=0Lr(z')g˜˜(z,z')dz'.
(5)
where
g˜˜(z,z')=0Texp{j[2πγ2(z'z)vt'+φ(t',z')φ(t',z)]}dt'.
(6)
Note that g˜˜(z,z') attains a maximum value at z=z' for all φ(t,z) where g˜(z,z') does not. The significant improvement in the spatial impulse response, which result from calculating r˜˜(z) rather thanr˜(z), is demonstrated experimentally in sec. 4.

2.1 Compensating for source phase deviations

2.2 Compensating for acoustic phase noise

As lightwave propagates in the fiber its phase is affected by acoustic noise. The phase modulations that affect two beams which were reflected from two neighboring points are highly correlated. The compensation of acoustic phase noise using an auxiliary reflection point is based on the observation that the acoustic phase noise term, at a sufficiently close point, following the auxiliary point can be expressed as:
ψ(t,zaux+Δz)ψ(t2Δz/v,zaux)+Δψ(t,zaux,zaux+Δz).
(10)
where ψ(t,z) is the acoustic phase noise which corresponds to reflection from position z and Δψ(t,z1,z2) denotes the part of the acoustic phase noise, of light reflected from z2, which is imparted on it in the fiber segment between z1 and z2. It is assumed that the acoustic noise correlation time is much longer than 2Δz/v. Thus, given an auxiliary reflection point which is sufficiently far from other strong reflections its response can be spectrally filtered and ψ(t,zaux) can be obtained from phase demodulation. Once ψ(t,zaux) is known, its properly delayed versions can be used in Eq. (10) for z>zaux, to compensate for the acoustic phase noise which was accumulated up to the auxiliary reflection point.

3. Experiment

An experimental OFDR system with an array of discrete reflectors, as depicted in Fig. 1, was constructed. A tunable laser source (orbits lightwave) with center wavelength of 1550 nm was swept in optical frequency over a frequency range of Δf0.5GHz. The light emitted from the laser was fed to a 50/50 PM splitter. One output of the splitter (the reference arm) was connected to the Local Oscillator (LO) port of a dual-polarization 90° optical-hybrid (Kylia). The second output of the splitter was connected to the measurement arm using an optical circulator. The output of the circulator (port 3) was fed into the Signal port of the dual-polarization 90° optical-hybrid. The optical hybrid's outputs were detected in pairs by four balanced photoreceivers as described in Fig. 1. The photoreceivers yielded electric signals proportional to the four quadrature components of the signal field (two for each polarization). These were sampled and stored by a data acquisition (DAQ) system. Port 2 of the circulator was used to connect the measurement arm. The measurement arm comprised an array of 10 FBGs at equal center wavelengths and 10 m spacing. It was terminated with an open to air APC connector. The total length of the FBG fiber (including one long patch-cord) was ~850 m. The first auxiliary reflection point is at the fiber adaptor between the FC-APC connector to the FC-PC connector. The choice of the position of the first auxiliary point was made according to two considerations. First, to use the approximation in Eq. (8) it is required that τaux will be smaller than the characteristic variation time of the deviations from linear sweep. Second, it is desired to keep the auxiliary beat frequency sufficiently far from the elevated response at zero beat frequency (a result mainly of non-ideal balanced detection) and from the nearest reflector. This is done to ensure that the broadened spectral response of the auxiliary reflector is sufficiently isolated from other responses. The required excess fiber length preceding and following the auxiliary reflector can change if the source induced resolution degradation is changed. In case of overlap between the spectral response of the auxiliary point and other near spectral responses, the compensation of the non-linear frequency scan is compromised. In this work the first auxiliary point was positioned 30 m from the point of zero differential delay. The reflected light from the FBG fiber was directed by the circulator to the signal port of the optical hybrid. The acquired data was then processed in order to compensate for the source phase deviations initially, and then for the acoustic phase noise as well.

4. Results

A (digital) low pass filter with a bandwidth of 9.82 KHz was used to filter out the response of the first auxiliary point. After phase demodulation and numerical integration according to Eq. (9) the estimated source phase deviation, θ(t), was found. Next, θ(t) was used for calculating θ(t)θ(t2z/v) as a function of z and for finding r˜˜(z) according to Eq. (5). The improved reflectivity graph is shown in Fig. 3
Fig. 3 Reflectivity after source phase deviation compensation (blue) and before (grey).
. The Bragg reflectors are clearly resolved as well as the reflection from the angled connector at the fiber end.

While using the first auxiliary point managed to compensate well for the source phase deviations, the responses of the Bragg reflectors were also broadened by the presence of acoustic phase noise in the fiber. To mitigate that another auxiliary point was used for extracting the acoustic phase that was accumulated between the first auxiliary point and the Bragg reflectors. Since the first reflector was found to be relatively weak the second auxiliary point was chosen to be the second Bragg reflector. Again, a (digital) band-pass filter with a bandwidth of 2 KHz was used for extracting the response of the auxiliary point and its phase, ψ(t,zaux), was found by demodulation. With ψ(t,zaux) known, the integral in Eq. (5) was calculated once again but this time V(t) was replaced with the inverse Fourier transform of the one-time compensated reflectivity, r˜˜(z), and ψ(t,zaux) substituted for φ(t,z). The twice compensated reflectivity is plotted in Figs. 4
Fig. 4 The reflectivity of the Bragg reflectors after two compensations.
and 5
Fig. 5 The reflectivity of a Bragg reflector after source phase deviation compensation (black), two compensations (blue) and the theoretical limit (red).
. All reflection peaks following the auxiliary point exhibit additional narrowing which is due to the compensation of a significant part of the acoustic phase noise that affected them. Also plotted in Fig. 5 is a theoretical reflection peak from a spatial impulse at the same position as the last FBG. The theoretical response is broadened due to numerical reasons as its frequency is not an integer multiple of the fundamental frequency step, df=1/T (T being the time duration of the response).

5. Discussion

In reflectometry of optical networks the theoretical response of many of the features is a spatial impulse. Moreover, in many situations there is preliminary knowledge about the expected positions of such reflectors. In these cases it is possible to take advantage of the expected responses and use it for improving the spatial resolution and quality of other positions in the network. The spatial resolution of OFDR is limited by the frequency scan range Δf according to: Δzv/(2Δf) [9

9. 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]

]. In our experimental setup the optical source and its frequency scan module was limited to a frequency scan range of Δf0.5GHz which determined a moderate spatial resolution of Δz200mm. It is expected, however, that the proposed method can maintain similar compensation abilities when implemented with optical sources with wider frequency scan ranges. In this case it will be possible to increase Δf by increasing the scan time or the scan rate, γ. Both actions do not have a fundamental effect on the applicability of the proposed method. An increase in the scan time may require additional memory for storing the added sample points while an increase in γ may require increasing the sampling rate. With these modifications the proposed compensation method should exhibit similar performance independent of the value of Δf. Following the compensation of the source phase deviations, the Full Width Half Maximum (FWHM) widths of all the reflection peaks (Figs. 3-5) were comparable with the z sampling step which was 193.5 mm. The acoustic noise was manifested mainly as elevated response values in the regions outside the −3 dB range. The application of acoustic phase noise compensation reduced these elevated responses and produced significantly narrower peaks. The twice compensated peaks were closer to the theoretical limit as can be seen in Fig. 5. In this example the compensated peak exhibited similar width as the theoretical limit down to −22 dB from the peak maximum. The deviation from the theoretical reflectivity is attributed to acoustical noise in the section between the second auxiliary point and the last FBG and to numerical errors inherent to the compensation method.

6. Conclusions

A method for mitigating resolution degradation mechanisms in OFDR was introduced and demonstrated experimentally. The method is based on in-line auxiliary points with pre-known reflectivities and does not require a separate auxiliary interferometer. By filtering out the responses of these auxiliary points it is possible to estimate the undesired phase terms which result from mechanisms such as the non-linear scan of the laser, the phase noise of the laser and acoustic phase noise in the fibers. Once these phase terms are extracted they are used for obtaining a compensated response with enhanced resolution. In addition to resolution enhancement in static OFDR measurements, the proposed method can be used for extracting the acoustical signals in dynamic OFDR acoustic sensors.

References and links

1.

M. K. Barnoski and S. M. Jensen, “Fiber waveguides: a novel technique for investigating attenuation characteristics,” Appl. Opt. 15(9), 2112–2115 (1976). [CrossRef] [PubMed]

2.

M. Tateda and T. Horiguchi, “Advances in optical time-domain reflectometry,” J. Lightwave Technol. 7(8), 1217–1224 (1989). [CrossRef]

3.

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

4.

H. Barfuss and E. Brinkmeyer, “Modified optical frequency domain reflectometry with high spatial resolution for components of integrated optic systems,” J. Lightwave Technol. 7(1), 3–10 (1989). [CrossRef]

5.

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(2), 666–674 (2005). [CrossRef] [PubMed]

6.

G. Mussi, N. Gisin, R. Passy, and J. P. von derWeid, “−152.5 dB sensitivity high dynamic-range optical frequency-domain reflectometry,” Electron. Lett. 32(10), 926–927 (1996). [CrossRef]

7.

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

8.

X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency domain reflectometry with measurement range beyond laser coherence length realized using concatenative reference method,” Opt. Lett. 32(22), 3227–3229 (2007). [CrossRef] [PubMed]

9.

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]

10.

Y. Koshikiya, X. Fan, and F. Ito, “Influence of acoustic perturbation of fibers in phase-noise compensated optical frequency domain reflectometry,” J. Lightwave Technol. 28(22), 3323–3328 (2010).

OCIS Codes
(060.2300) Fiber optics and optical communications : Fiber measurements
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(060.2630) Fiber optics and optical communications : Frequency modulation
(060.4230) Fiber optics and optical communications : Multiplexing
(120.1840) Instrumentation, measurement, and metrology : Densitometers, reflectometers
(060.3735) Fiber optics and optical communications : Fiber Bragg gratings

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: August 9, 2012
Revised Manuscript: September 27, 2012
Manuscript Accepted: September 28, 2012
Published: November 27, 2012

Citation
Oren Y. Sagiv, Dror Arbel, and Avishay Eyal, "Correcting for spatial-resolution degradation mechanisms in OFDR via inline auxiliary points," Opt. Express 20, 27465-27472 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-25-27465


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References

  1. M. K. Barnoski and S. M. Jensen, “Fiber waveguides: a novel technique for investigating attenuation characteristics,” Appl. Opt.15(9), 2112–2115 (1976). [CrossRef] [PubMed]
  2. M. Tateda and T. Horiguchi, “Advances in optical time-domain reflectometry,” J. Lightwave Technol.7(8), 1217–1224 (1989). [CrossRef]
  3. W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett.39(9), 693–695 (1981). [CrossRef]
  4. H. Barfuss and E. Brinkmeyer, “Modified optical frequency domain reflectometry with high spatial resolution for components of integrated optic systems,” J. Lightwave Technol.7(1), 3–10 (1989). [CrossRef]
  5. 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. Express13(2), 666–674 (2005). [CrossRef] [PubMed]
  6. G. Mussi, N. Gisin, R. Passy, and J. P. von derWeid, “−152.5 dB sensitivity high dynamic-range optical frequency-domain reflectometry,” Electron. Lett.32(10), 926–927 (1996). [CrossRef]
  7. S. Venkatesh and W. V. Sorin, “Phase noise considerations in coherent optical FMCW reflectometry,” J. Lightwave Technol.11(10), 1694–1700 (1993). [CrossRef]
  8. X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency domain reflectometry with measurement range beyond laser coherence length realized using concatenative reference method,” Opt. Lett.32(22), 3227–3229 (2007). [CrossRef] [PubMed]
  9. 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]
  10. Y. Koshikiya, X. Fan, and F. Ito, “Influence of acoustic perturbation of fibers in phase-noise compensated optical frequency domain reflectometry,” J. Lightwave Technol.28(22), 3323–3328 (2010).

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