## Abstract

A novel method to realize high spatial resolution distributed strain measurement is proposed based on phase demodulation scheme of optical frequency domain reflectometry (OFDR). Strain information can be demodulated directly by analyzing the phase change of Rayleigh backscattered light. Strain location can be obtained with high spatial resolution by cross-correlation method using a wide scanning range of tunable laser source. Based on the above scheme, breakpoint detection with 0.1 mm spatial resolution has been demonstrated, static and dynamic strain up to 100 Hz could be distributedly measured with 10 cm spatial resolution over 200 m sensing fiber, and the minimum measurable strain is about 1 με.

© 2017 Optical Society of America

## 1. Introduction

Distributed fiber strain sensor has the advantages of dielectric and nonconductivity, small in size, immune to electromagnetic interference, high sensitivity, high spatial resolution and long range, which has attracted extensive attentions in sensing and detecting applications such as aerospace smart structures, material processing, leak detection in oil and gas pipelines, perimeter monitoring and so on [1,2]. There has been a great deal of research in the last three decades contributing to the development of distributed fiber strain sensors and related technologies, such as distributed fiber interferometer strain sensor [3–6], Brillouin scattering light based distributed fiber sensor [7–10], Rayleigh scattering light based distributed fiber sensor [11–18]. Among them, the optical fiber interferometer sensors, such as the MZI and Sagnac loop type [3–6], have operated with high sensivity but low spatial resolution (usually tens of meters). The Brillouin scattering light based sensor, such as Brillouin optical time domain reflectometer (BOTDR) [7,8] and Brillouin optical time domain analysis (BOTDA) [9,10], can achieve submeter spatial resolution, tens of kilometers sensing range and static / dynamic strain measurement; however, minimum measurable strain is usually limited to be above 10 με, which could not meet the high sensivity requirements of some applications [2]. The Rayleigh scattering light based sensor, especially the phase optical time domain reflectometry (φ-OTDR) [11–13], can perform with high sensivity and long range, but except the optical frequency domain reflectometry (OFDR) [16–18], most of these technologies are lack of the slow varing strain and static strain measurement capability. Although all these technological solutions mentioned above can achieve distributed fiber strain detection, only the Rayleigh scattering light based OFDR sensor can achieve high spatial resolution, high sensitivity and static / dynamic strain measurement at the same time.

The OFDR system is based on swept-wavelength homodyne interferometry, and it provides local information when the Rayleigh-backscatter signal is measured as a function of frequency in a complex fashion and processed using the Fourier transform into the time domain, where a map of the reflections as a function of length internal of sensing fiber can be constructed. After M. Froggatt firstly applied OFDR system in distributed static strain measurement [16], researchers have proposed various optical configurations and demodulation methods to promote strain detection performance.

The optical configuration of conventional OFDR sensor system contains two interferometers: an auxiliary interferometer which is used to provide external clock signal to the acquisition system and a main interferometer which is used to detect strain information [16–18]. Besides, an experimental setup by combining OFDR and OTDR configuration was reported to detect dynamic strain as well [19,20]. Another OFDR system based on external modulator to generate scanning laser output was applied in acoustic sensing, which can omit the auxiliary interferometer and simplify the system [21,22].

In terms of demodulation scheme, the method of measuring Rayleigh backscatter spectrum shift by cross-correlation calculation is widely accepted and adopted in OFDR sensor system. Rayleigh backscattered light caused by the random fluctuations of the index of fiber can be seen as the reflective spectrum of a weak and random period fiber Bragg grating (FBG). External strain will affect the reflective spectrum of the weak FBGs, and this spectrum shift can be obtained by cross-correlation calculation between the reference spectrum signal and perturbation spectrum signal. Based on this demodulation method, a time-solved OFDR sensor system was reported to measure static and dynamic strain [17,18]. However, cross-correlation analysis is so heavily dependent on the reference signal that the instability of laser source scan will cause a measurement error easily. A set of unperturbed signal must be selected deliberately as a reference signal, which increases the inconvenience of the strain measurement of the system as well.

External strain disturbances will directly result in the variation of refractive index, length and fiber core, and these changes will further affect the phase of light propagating in the fiber. Hence, demodulating the phase change of light is an efficient and reliable scheme to detect strain. Directly and efficiently phase demodulation scheme can prevent strain detection from being affected by the instability of tunable laser source. In this paper, we present a novel phase-OFDR scheme based on phase demodulation method. Cross-correlation is only used in this scheme to determine the perturbed location, which can ensure the high spatial resolution of strain detection. We demonstrate με dynamic strain detection in this scheme with a spatial resolution of 10 cm over 200 m sensing fiber, and the minimum measurable strain is about 1 με. We believe that the result in this paper will help to facilitate the simplification and performance improvement of OFDR sensor system and can promote the development of distributed fiber strain sensing field.

## 2. Principle

When the linearly frequency scanning coherent light provided by tunable laser source (TLS) is injected into the sensing fiber, Rayleigh backscattered light with the same frequency scanning process will propagate along the fiber and interfere with the reference light. Assuming that linear frequency tuning speed of TLS is *𝛾*, the optical field *Er(t)* of reference light can be written as:

*f*is the initial optical frequency of TLS,

_{0}*Φ(t)*is the phase term of reference light.

Supposing the round-trip time delay of backscattered Rayleigh light caused by a scatter point along the sensing fiber is *τ*. Backscattered light field *E _{s}(t)* from that point of fiber can be written as:

*R(τ)*is reflection reflectivity of the fiber,

*Φ(t-τ)*is the phase term of backscattered light which includes the extrinsic strain perturbation information.

Reference light and backscattered light are fed into two inputs of the 3 × 3 optical coupler as shown in Fig. 1. After interfering within the 3 × 3 optical coupler, the interference signal is split into three channels and each differs by 120 degree in phase [23]. Because of the time delay *τ* between the reference signal and backscattered signal, the interference signal will contain a beat frequency *f*_{b} item which value is determined by the time delay *τ* and tuning speed *𝛾*.

The optical intensity *I _{iout}* of three output channels can be written as:

*M*and

*P*are constant coefficients. When substituting the expression of

*E*and

_{r}*E*into the above intensity expressions, all of them can be expanded as:

_{s}*f*represents the beat frequency item,

_{b}= 𝛾τ*Δφ(t) = Φ(t)-Φ(t-τ)*represents the phase difference between the reference signal and backscattered Rayleigh signal.

In OFDR sensor system, different beat frequencies *f*_{b} corresponds to different location of sensing fiber. For the same area of sensing fiber, the value of beat item *f*_{b} is consistent, which indicated that spatial domain information can be extracted from each channel time domain data through Fourier transform.

After removing the direct current components of the interference signal, the differential and cross-multiply phase demodulation scheme are applied to analyze the phase information [24,25], where the derivative procedure of transforming the acquired signal into the phase signal is shown in Fig. 2. Through the analysis of demodulation algorithm and removing the linear trend 2*πf*_{b}*t* of the data, the modulated phase item of interference signal is proportional to the output voltage data *V _{out} (t)*:

When a vibration occurs on fiber, considering the photoelastic effect and strain effect and assuming the temperature around the sensing fiber being consistent, the phase variation Δ*φ(t)* can be expressed as:

*n*

_{g}is the group index of fiber,

*ξ*

_{ε}is a composite fiber strain coefficient,

*n*is a natural number, and

*k*is the wave number. Since the phase change is a periodic process, large strain might result in the phase variation above

_{0}*2π*. Therefore,

*2nπ*represents the period of phase variation, and phase unwrapped algorithm can be used to determine the exact value of cycle number count

*n*[26]. It is turned out that the strain

*ε(t)*is proportional to the output voltage

*V*as shown below:

_{out}(t)## 3. Experiment setup

The schematic diagram of the proposed OFDR system is shown in Fig. 3. This system consists of two interferometer configurations: an auxiliary interferometer and a main interferometer. The auxiliary interferometer with 106 m optical path difference is to obtain the instantaneous optical frequency of TLS [27]. The main interferometer with 3 × 3 optical coupler configuration is to demodulate phase information of Rayleigh-backscatter signal. The continuous laser output of TLS (81606A, Keysight) is split by a 90/10 optical coupler. The 10% of the output is injected into the auxiliary interferometer—an imbalance Mach-Zehnder interferometer configuration—to obtain the instantaneous optical frequency information. The output of the auxiliary interferometer is detected by a balanced photodetector (Thorlab PDB415C-AC, 100 MHz bandwidth). The 90% of the laser output is acting as probe light and split by a 3 dB optical coupler. The probe light is launched into the fiber under test (FUT, Corning SMF-28e) through a circulator and then the backscattered Rayleigh light is mixed with the reference light from reference path of the main interferometer in a 3 × 3 optical coupler. The output interference signals of the 3 × 3 optical coupler are detected by three photodetectors (New Focus 1811, 125 MHz bandwidth) associated with the data-acquisition card (DAQ), in which the data-acquisition is triggered by the external clock signal of the auxiliary interferometer. Acquisition and analysis of the sensing signal are processed by a self-designed program.

The tuning range ΔF of TLS is 20 nm and the tuning speed 𝛾 is setting to be 20nm/s. The maximum beat frequency generated by the FUT is approximate 5 MHz, so the sampling rate of DAQ is chosen to be 20 Ms/s for gathering original data. Figure 4 shows that an approximately 200 m single mode fiber is applied as sensing fiber, which is connected with a short fiber by a pair of angled physical contact (APC-APC). There is a small gap between two contacts and the end of the short fiber is equipped with an open APC connector. Some high refractive index glue (n≈1.473) is smeared over the end of the fiber to reduce the Fresnel reflection. A 30 cm long fiber is wrapped on a PZT that provides quantitative strain to the fiber.

## 4. Result and discussion

#### 4.1 Strong reflection point detection

The measurement range of the conventional OFDR sensor system is limited by the optical path difference of the auxiliary interferometer, which is determined as a quarter of the optical path difference according to the Nyquist sampling criteria [17]. For increasing the sensing range, the interpolation algorithm is applied in our work [27]. Due to the instability of TLS, conventional OFDR sensor system needs the auxiliary interferometer to provide external clock signal to revise the sampling rate of DAQ. Although auxiliary interferometer can reduce spatial resolution degradation of OFDR, sensing length is limited by the optical path difference of the auxiliary interferometer as well. The method of using interpolation algorithm can overcome the restrictions on the sensing range of the auxiliary interferometer, where the sensing length is only limited by the hardware and the coherent length of TLS. Therefore, OFDR sensor system with interpolation algorithm has the capability of long distance detection. In this paper, the function of auxiliary interferometer is to continuously monitor and record the instantaneous frequency of sweeping laser source, and monitoring data is used as a corrected parameter in interpolation algorithm.

An approximately 200 m SMF equipped with an open APC connector is used as FUT. Time domain data acquired by DAQ is transformed through Fast Fourier transform (FFT) to spatial domain data. Figure 5 shows the Raleigh backscattered signal as a function of distance and the strong reflection point caused by the Fresnel reflection of an open APC connector (without connecting with a short fiber). The signal to noise ratio (SNR) of the strong reflection point is about 20 dB. The sensing length is approximately twice as the optical path difference of the auxiliary interferometer because of the optimization of interpolation algorithm. It is obvious that the spatial resolution of strong reflection point is about 0.1mm as shown in the inset of Fig. 5. The theoretical spatial resolution *Δz* of OFDR sensor is determined by: *Δz = c/2n _{g}ΔF*. When the scanning range

*ΔF*of TLS is 20 nm, theoretical spatial resolution

*Δz*is about 0.04 mm. The effective spatial resolution is close to the theoretical spatial resolution when the scanning range of TLS is 20nm. With larger scan range of TLS, higher resolution can be obtained, but the system’s acquisition performance requirements will increase as well.

For further demonstrating the effective spatial resolution of multipoint detecting, an about 2 m long fiber is connected after the FUT but there is a small gap between two APC connectors. Figure 6 shows the Raleigh backscattered signal as a function of distance and two strong reflection peaks caused by two contacts. Obviously, two peaks can be discriminated and the distance between two APC connectors is about 2 mm. The second reflection peak is 7 dB less than that of the first reflection peak, which is induced by the attenuation. Although this system can achieve breakpoint detection with a spatial resolution of 0.1 mm, in multipoint discrimination, the amount of the data is adjusted for achieving better SNR. Therefore, the spatial resolution of single point in Fig. 6 is about 0.8 mm, which the spatial resolution is slightly degraded due to the change of the size of the data. But it is enough to distinguish two reflection points where the spacing is about 2 mm.

#### 4.2 Vibration detection

After transforming the time domain data into spatial data as shown in Fig. 5, the spatial data is divided into several sections and the length of each fiber section determines the effective spatial resolution *Δx = NΔz* of strain detection where *Δz* is the theoretical spatial resolution and *N* is an integer number which determines the length of fiber section. The cross-correlation calculation between the perturbed data and unperturbed data is used to determine the vibration location of the FUT. The Rayleigh backscattered light information of the whole fiber will be recorded as the unperturbed data when there is no strain affecting the sensing fiber. For static and dynamic strain, the cross-correlation calculation results will be different. When there is no strain affecting the sensing fiber, the result of cross-correlation will present a single peak as shown in Fig. 7(a). If the result of cross-correlation calculation is still a peak but with a location shift compared with Fig. 7(a), this fiber section might be a perturbed region affected by static uniform strain. If result of calculation becomes multiple peaks, the segment might be a perturbed region affected by non-uniform static strain or dynamic strain. Figure 7(b) represents the region of sensing fiber perturbed by static uniform strain and Fig. 7(c) represents the region where is perturbed by dynamic strain. According to the results of cross-correlation analysis, the region affected by strain can be directly obtained. In this paper, for obtaining proper detection SNR, an overall section containing *N =* 1000 data points is used to calculate the cross-correlation and the effective spatial resolution of strain detection is about 10 cm.

When the perturbed area is determined, phase demodulation method as shown in the principle part is used to further analyze strain information. The voltage signal *V _{out}* will have a direct relationship with the external strain

*ε.*Based on this phase demodulation scheme, the reference signals can be avoided which must be introduced in the conventional cross-correlation analysis scheme. Therefore, the relative error between the reference signal and the perturbed signal due to the instability of TLS can be eliminated. A section of 30 cm fiber is wrapped on a PZT and different quantitative static strains are applied on it. According to the cross-correlation calculating result, the fiber section beginning from 198.9 m to 199.2 m is determined as vibration location, where the experimental results are consistent with the experimental setup.

The demodulation result of perturbed area is presented in Fig. 8. It clearly shows that the static strain increases from 1.6 με to 4.6 με at the same vibration location, where the corresponding phase variation are all less than one period. At the case of static strain, it is difficult to quantify the larger strain which induced phase variation above *2π*, unless the phase change process has been mornitored for cycle number count comfirmation based on phase unwrapped algorithm. The demodulation result of unperturbed area is smaller and random fluctuations, which can be seen as the background noise of the strain detection. According to the demodulation result, the amplitude of noise variation fluctuates within a certain range and the maximum detection error is about 1με, which is a composite noise caused by the phase noise of laser source, environmental noise and minimum quantifiable noise of DAQ. Among them, phase noise of laser might affect the detection result, but the effect of minimum quantifiable noise might be the largest source of overall noise.

In dynamic strain detection experiment, acquired time domain data need to be evenly divided into *M* segments before transforming them into spatial domain data. Assuming the sweeping time of TLS is *T*, the sampling frequency could be determined as *M/T* Hz and the maximum detectable frequency is *M/(2T)* Hz according to the Nyquist sampling criteria. In this paper, the sweeping time *T* is approximate 1 s and the *M* value is 300, which means that the sampling frequency of this dynamic strain sensor system is 300 Hz.

Figure 9(a) presents the detection result of a 20 Hz sinusoidal vibration at 199.0 m of the FUT. The vibration amplitude is about 2.3 με, where the corresponding radian of phase difference is about 2.2 rad. Comparative experiment is also carried out at the same location where there is no vibration applied. It is obviously shown that 20 Hz vibration signal can be demodulated and it can be discriminated clearly from the comparative group. Another detection result of a 100 Hz sinusoidal vibration with the same sampling frequency is exhibited in Fig. 9(b). The signal can be demodulated and distinguished from the background noise as well. But the signal waveform becomes sharp due to the limitation of sampling frequency.

Although the maximum measurable frequency of sensor system is 150 Hz according to the Nyquist sampling criteria, as the increase of signal frequency, the detection waveform will tend to become worse gradually. If the sampling frequency can further increase, the detection result will demonstrate more details of the vibration. Besides, under the condition of the total amount of data keeping consistent, there is a tradeoff between the detection SNR and *M*, *N* value. Higher sampling frequency detection can be achieved by increasing *M* value. Better spatial resolution can be obtained through decreasing *N* value as well. But increasing *M* value or lowering *N* value will affect the size of data used to analyze, which will degrade the detection SNR of strain detection. Hence, for ensuring appropriate detection SNR, the vibration frequency measurable range is from 0 to 100 Hz when the system parameters are setting as *M* = 300 and *N* = 1000. Theoretically, the frequency detection range can be improved to hundreds of Hz or KHz and keep the advantage of high spatial resolution as well.

## 5. Conclusion

A distributed optical fiber strain OFDR sensor system based on phase demodulation scheme has been demonstrated. System retains the advantage of high spatial resolution of OFDR and reference signal used in conventional OFDR method can be omitted, which the instability of TLS is overcome by cross-multiply and differentiate phase demodulation algorithm. The experimental result shows that the sensor is capable of detecting and distinguishing multiple loss points separated by millimeters. Dynamic strain information can be obtained as well, which frequency measuring range is up to 100 Hz. 10 cm spatial resolution of 200 m sensing length can be achieved. For improving the measuring range and spatial resolution, TLS with larger scanning range and DAQ with larger on-board memory can be used in this system to promote the performance.

## Funding

This work was supported by National Key Research and Development Program of China (2016YFB0402204), NSFC (61575064, U1609219), the Science and Technology Project of Guangdong (2015B090926010), Tiptop Scientific and Technical Innovative Youth Talents of Guangdong special support program (2015TQ01X322), the Fundamental Research Funds for Central Universities (2015ZP019), the High level Personnel Special Support Program of Guangdong Province (2014TX01C087), and the National Science Fund for Distinguished Young Scholars of China (61325024).

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