## Abstract

A novel time-gated digital optical frequency domain reflectometry (TGD-OFDR) technique with high spatial resolution over long measurement range is proposed and experimentally demonstrated. To solve the contradictory between the tuning rate of lightwave frequency, which determines the spatial resolution, and the measurable distance range in traditional OFDR, our proposed scheme sweeps the frequency of probe beam only within a time window, while the local reference remains a frequency-stable continuous lightwave. The frequency-to-distance mapping is digitally realized with equivalent references in data domain. In demonstrational experiments, a 1.6-m spatial resolution is obtained over an entire 110-km long fiber link, proving that the phase noises of the laser source as well as environmental perturbations are well suppressed. Meanwhile, the dynamic range was 26 dB with an average of only 373 measurements. The proposed reflectometry provides a simple-structure and high-performance solution for the applications where both high spatial resolution and long distance range are required.

© 2015 Optical Society of America

## 1. Introduction

Optical reflectometry is a powerful technique for noninvasive diagnoses of fiber optic devices and systems, and for distributed fiber optic sensing. A well-known example is the optical time domain reflectometry (OTDR), which is widely used for tests of long-range fiber links [1–3]. The dynamic range of OTDR, however, decays rapidly as its spatial resolution increases [2]. Although various coding methods such as frequency-division-multiplexing [3] and wavelength coding [4] have been developed to improve the dynamic range by increasing the equivalent number of measurements, further improvement is limited because the intrinsic trade-off between the spatial resolution and the dynamic range.

Optical frequency domain reflectometry (OFDR), on the other hand, provides both high spatial resolution and large dynamic range [5–7]. In this case, however, a trade-off between the spatial resolution and the distance range occurs alternatively, as described below.

In a typical OFDR system, lightwave from a laser source is linearly chirped and split into two beams. One beam is launched into the fiber under test (FUT) as a probe, and the other works as a reference for coherent detection. Reflections/backscatterings at different locations along the FUT exhibit different time delay with respect to the reference lightwave. Due to the chirp of the laser, the interference between the probe and the reference produces a beat signal whose frequency depends on the traveling time difference between the two lightwaves, and on the chirp rate of the laser. Meanwhile, the distance of reflection along FUT is mapped to the frequency of the beat signal. Obviously, the duration of the laser chirp must be longer than the maximum time delay of the FUT, to make sure that even the farthest reflected lightwave of the FUT can meet the reference lightwave. The highest beat frequency is the product of the maximum time delay of FUT and the laser chirp rate. Therefore, the beat frequency becomes higher as the laser chirp rate is greater and the measurable distance range (the length of FUT) gets longer.

On the other hand, OFDR’s performance of spatial resolution is limited by the phase noise of the laser source and environmental perturbations [8, 9]. In [10], Fan *et al*. developed a phase-noise-compensated OFDR technique, which estimates and compensates the phase noise of the laser source with a reference interferometer and a cascaded algorithm. They also showed that the environmental perturbations can be effectively reduced by sweeping the lightwave frequency at a higher rate [11, 12]. In fact, a higher laser chirp rate is effective to suppress the phase noise of the laser source as well. Unfortunately, a high laser chirp rate together with a long measured distance range generates a very high beat frequency, which in most cases goes beyond the sampling rate of available data acquisition devices. In other words, the allowable laser chirp rate is inversely proportional to the measurement distance range due to the limitation of the sampling rate of data acquisition. Bandwidth-division technique using multiple band-pass-filters in hardware have been developed to reduce the signal bandwidth [11], while the sampling rate is also reduced by the number of bandwidth-division. Digitally enhanced interferometry technique was used in conjunction with OFDR to realize the bandwidth-division in data processing [13], and the measurement range was not limited by the lightwave frequency sweeping period because multiple frequency sweeps can be realized in one measurements [14]; however, the larger noise floor due to the external phase modulation in digitally enhanced interferometry technique has severely restrained the dynamic range of the sensing system.

In this paper, we propose a time-gated digital OFDR (TGD-OFDR) technique, in which only the probe beam is chirped, and the chirp is gated within a narrow time window, while the reference beam remains a frequency-stable continuous lightwave; the distance-to-frequency mapping is digitally realized with an equivalent reference in data processing. Thanks to the short duration of probe pulse in this new scheme, a very high laser chirp rate is achievable independent of the length of FUT. In experiments, a chirp rate as high as 25 THz/s was achieved in the interrogation of a 110-km long FUT. A spatial resolution of 1.64 m over the entire length of FUT was obtained, which is the best spatial resolution ever reported for an OFDR with a measurement distance range over 100 km to the best of our knowledge. The dynamic range was 26 dB with an average of only 373 measurements, which is well beyond the performance of typical OTDRs requiring an average of 2^{18} measurements with comparable spatial resolution [2].

## 2. Principle

The schematic of our proposed time-gated digital OFDR system is shown in Fig. 1. The lightwave from a laser source is split into two beams by a coupler. The probe beam (upper) is frequency-swept and time-gated by an acousto-optic modulator (AOM), while the reference beam (lower) remains a frequency-stable continuous lightwave. The AOM is driven by a function generator (FG) generating a chirp sinusoidal waveform with chirp rate of γ and time duration of *τ _{p}*. As a result, the probe beam after AOM becomes a chirped pulse with duration of

*τ*and frequency chirp rate of γ:

_{p}*rect*() is a rectangular function,

*E*is the amplitude,

_{0}*ω*is the initial frequency, and

*γ*is the frequency chirp rate of the probe. The frequency chirp range is Δ

*f*= γ

*τ*. An example of the chirped probe pulse is shown in Fig. 2. High chirp rate and perfect linearity can be easily achieved within a narrow time-window by using AOM. Even larger chirp range can be obtained by other types of modulators like single sideband modulator [15].

_{p}Reflections at different locations along the FUT exhibit different time delay *t _{d}* with respect to the reference lightwave, which travels over a fixed path-length. The reflections can be given as:

*R*is the reflectivity at the place within FUT which corresponds to time delay

*τ*.

_{d}The reference is a continuous lightwave with constant frequency of *ω*, *E _{ref}* =

*E*exp(

_{loc}*jωt*). Here

*E*is the amplitude of the reference lightwave. The reflections with time delay

_{loc}*t*mixed with the reference lightwave, and a beat signal is generated at the balanced photo detector (BPD) as below (ignoring the DC components):

_{d}*θ*(

*t*) is the term of phase noise summarizing the phase noise of the laser source as well as the phase fluctuation induced by environmental perturbations. Equation (3) indicts that the beat signals generated by reflected lightwaves at different locations along the FUT have the same frequency chirp rate and range, but they appear within different time window according to the time delay

*τ*, as shown in Fig. 3. Although beat signals generated by reflections at adjacent locations partly overlap in time, their instantaneous frequencies are always different.

_{d}To retrieve the reflections along the FUT from the detected beat signals, a digital implementation of frequency-to-distance mapping is proposed. As shown in Fig. 3, an equivalent reference, *S _{ref_1}* = cos(

*πγt*

^{2}), is generated in data processing. The equivalent reference has the same chirp rate as the chirped pulse, working as an ideal reference as that in typical OFDR systems. The frequency difference

*F*between the detected beat signal and the equivalent reference is proportional to the corresponding time delay

*τ*by

_{d}*F*=

*γτ*. The collected data by the analog-to-digital (A/D) convertor is multiplied with the equivalent reference, and then Fourier transform is carried out to calculate the spectrum of the beat signal, completing the distance-to-frequency mapping as that in typical OFDR systems.

_{d}During the data processing, the equivalent reference is also sampled with the same rate as the A/D convertor, so the maximum frequency of the reference *f*_{max} is a half of the sampling rate of the A/D convertor according to Nyquist sampling theorem. As a result, the duration of one equivalent reference is limited to τ_{s} = *f*_{max}/γ. In case the maximum round trip time of the FUT is longer than τ_{s}, more equivalent references with proper time delays can be used for data processing. In Fig. 3, a second equivalent reference *S _{ref_2}* is illustrated for data processing, which has the same form as

*S*except for the time delay of

_{ref_1}*τ*. To make sure that the collected data from any location can be treated as a whole when taking the FFT operation, the two equivalent references should at least overlap by τ

_{ref}_{p}. So the maximum time delay for

*S*is:

_{ref_2}For even longer length of FUT, more references can be adopted similarly to cover the maximum round trip time. Finally, the obtained scattering with different equivalent references will be connected to produce the reflection information of the whole FUT.

The phase term *θ*(*t*) in Eq. (3) results in a spectrum vague during the Fourier transform of Eq. (3), which determines the spatial resolution. Since the ratio of beat frequency to distance is proportional to chirp rate of the probe lightwave, the influence of the phase noise is well suppressed by using a higher chirp rate. In our proposed scheme, the lightwave chirp only occurs in the time window *τ _{p}*, and the frequency of detected beat signal is independent of the length of FUT. Consequently, very high frequency chirp rate can be used for the suppression of phase noise no matter of the length of FUT.

## 3. Experimental setup

The configuration of experimental setup is shown in Fig. 4. A fiber laser (NKT, E15) with a nominal linewidth of 1 kHz is used as the light source. The AOM is driven by a function generator (Tektronix, AFG3252C) with frequency sweeping range from 150 MHz to 250 MHz in a time window of 8 μs, only limited by the bandwidth of the AOM. To increase the lightwave frequency chirp range, a double-pass configuration with a Faraday rotator mirror (FRM) is employed. After passing through the AOM twice, the probe beam chirps from 300 MHz to 500 MHz. With the time window of 8 μs, the laser chirp rate is up to 25 THz/s, corresponding to a ratio of distance to beat frequency of 4 mm/kHz. Since the insertion loss of the AOM increases as the driven frequency deviates from its optimized frequency, the full width at half maximum (FWHM) of the spectrum of the probe pulse is measured to be 84 MHz, corresponding to a theoretical spatial resolution of 1.2 m.

To eliminate the influence of polarization fluctuation, a polarization diversity scheme is employed in the detection. A pair of high speed balanced photo detectors (Thorlabs, PDB480C) are used to receive the beat signals from two orthogonal polarization states. The beat signals have a frequency range from 300 MHz to 500 MHz, and are collected by a high speed analog-to-digital convertor (NI, 5185) with a sampling rate of 3.125 GS/s and 8-bit resolution. If frequency down-conversion devices are adopted to reduce the central frequency of the beat signal before data acquisition, a lower sampling rate will be applicable for the data acquisition. To reduce the Rayleigh speckle noise or so-called fading noise [16], 373 measurements at 16 different laser wavelengths are carried out.

The FUT is composed of four spools of single mode fiber under ordinary (not sound isolated) laboratory environment with a total length of 110.7 km. Angled physical contact (APC) connectors are used to connect the spools of fiber, and the far end of FUT is equipped with an open physical contact (PC) connector (4% reflection). Besides, the pigtail of the circulator that leads to the spools of fiber is also a part of FUT, and its length is 1.02 m.

In the experiments, the acquisition time of the A/D convertor is 1.28 ms, a little longer than the maximum round trip time considering the length of the FUT. The maximum frequency of the equivalent references is set to 1.5 GHz, and 25 references are used during data processing with time offset interval of 52 μs. The data processing time in one measurement is less than 0.5 s using a personal computer equipped with Intel Core-i7 3770 CPU and 8 GB Memory. Even higher data processing speed can be achieved with parallel computation technique.

## 4. Experimental results and discussion

Figure 5 shows the reflectivity of the back scattered and reflected lightwave along the FUT after averaging of 373 measurements. Five peaks appear on the trace, corresponding to the fiber connectors within the FUT as well as the open far end. The dynamic range is measured to be 26 dB, which can be further improved if more measurements are taken for averaging.

Figure 6(a) shows two close reflections caused by the pigtail of the circulator. The two reflections are clearly separated with a dimple of 0.8 dB deep, and the distance of 1.0 m is the same as the actual length of the pigtail. The spatial resolution at this position is calculated to be 1.2 m considering the 3dB width of the 2.2 m, which agrees well with the theoretical resolution considering the effective chirp range of 84 MHz. As shown in Fig. 6(b)-6(d), the spatial resolution at 29 km, 80 km, and 110 km were 1.38 m, 1.55 m, and 1.64 m, respectively. The reason for spatial resolution degeneration is the accumulation of phase noise during the measurement. The overall spatial resolution degeneration on the entire FUT is 37% (1.64 m at 110 km far-end, 1.2 m at near-end). For comparison, the spatial resolution at 80-km far-end is 3 times broader than that at the near-end of FUT even after careful nonlinear phase compensation in [17]. The comparison shows the high efficiency of our proposed method in phase noise suppression. The dynamic margin of 2.5 dB in Fig. 6(d) supports another 10 km of FUT, showing that the measurable distance range is equal to the fiber length demonstrated in [9]. However, the spatial resolution in our experiment is two orders of magnitudes better than that of 200 m given in [9].

## 5. Summary

In summary, we proposed a novel time-gated digital OFDR (TGD-OFDR) technique with high spatial resolution over long measurement range. In the proposed configuration, frequency-stable local oscillator is employed for coherent detection, while the distance-to-frequency mapping is realized in data domain. This technique allows high frequency chirp rate which is independent of the length of FUT, efficient in suppressing of both laser phase noise and environmental perturbations. In the demonstrational experiments, a frequency chirp rate of 25 THz/s with effective tunable range of 84 MHz is obtained in the investigation of 110 km FUT. A spatial resolution better than 1.64 m was obtained along the entire length of FUT, which is the best spatial resolution ever reported for an OFDR over 100 km to the best of our knowledge. This new technique has great potential in applications where both long measurement range and high spatial resolution are required.

## Acknowledgment

This work was partly supported by the National Natural Science Foundation of China under Grant 61275097, 61307106, 61575001, and 61327812.

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