1. Introduction

Since Optical Frequency Domain Reflectometry (OFDR) is proposed and demonstrated by W. Eickhoff [1], 1981, numerous achievements on its mechanism and potential applications emerge in past decades [2,3]. Initially, as a promising method for diagnosis and maintenance of the optical fiber networks, OFDR is utilized to statically identify and locate the breakpoints, fiber loss, and connectors [4–7]. With Fast Fourier Transformation (FFT) based demodulation in Frequency Domain, the time-varying temperature, strain, vibration, and birefringence can be qualitatively located and observed [2,3].

However, a fully functional distributed temperature and strain sensor requires quantitative measurements of real-time variations. In 1998, M. Froggatt and J. Moore from the Langley Research Center, NASA, proposed a distributed fiber sensing mechanism based on Rayleigh scattering and OFDR [8]. B. Soller, A. Sang, S. Kreger and D. Gifford then optimized this mechanism using the coherent detection, Mach-Zehnder Interferometer reference, and active polarization control [9–13]. The sensor with improved spatial resolution at cm or mm and 10 m fiber length has been applied in strain monitoring of the composite blades of the CX-100 wind turbines, ultra-low temperature measurement of the superconducting cables, and liquid Sodium leakage detection in a Sodium-cooled Fast Neutron Reactor (SFNR) [14–18]. Precise reconstruction of the gradient in temperature or strain claims a higher spatial resolution and a larger number of sensors for detailed data analysis. Nevertheless, a sub-mm spatial resolution still remains unresolved because of the degeneration in cross-correlation of Rayleigh spectra at a high spatial resolution. The degeneration results from position-deviation, which is caused by the changes in Optical Path, due to the thermal-/elastic-optic effects. Moreover, position-deviation accumulates along the fiber and becomes obvious at the fiber end, which makes the high spatial resolution and long sensing length difficult to achieve at the same time.

In this paper, we propose and demonstrate a 0.5 mm spatial resolution distributed fiber strain and temperature sensor with position-deviation compensation based on OFDR. The compensation for the accumulated position-deviation along the fiber helps maintain the cross-correlation of the Rayleigh spectra, which degenerates at a higher resolution. Experimental results reveal that with this technique, a 0.5 mm strained fiber segment is recognized at the end of a 25 m fiber with 50000 equivalent sensors. The temperature repeatability of ± 0.9 °C (12.5 pm) is obtained from 50 °C to 500 °C with a gold-coated fiber, and the strain accuracy of ± 15 µɛ is also achieved within ± 2500 µɛ. For a fully functional distributed fiber sensor, the 0.5 mm resolution at the 25 m fiber end is the highest spatial resolution ever reported to the best of our knowledge. This promising technique with such good performances is designed for sensing applications in harsh environment.

2. Principles

The schematic setup of the polarization dependent coherent OFDR system is illustrated in Fig. 1. A tunable laser is employed as a wavelength (frequency) scanning coherent source (TLS, Linewidth of 1.5 MHz, power of 10 mW, 1515 nm-1565 nm, Phoenix-HS 1200, Luna Corp.). The polarized light propagates through an 8:2 polarization-coupler (PC), splitting 80% power into a heterodyne coherent detection (HCD) module, while the other 20% goes to a reference Michelson interferometer (RMI). Reflected from two Faraday Rotation Mirrors (FRMs), the beams generate an interference at a 1:1 coupler. The interference is harvested by a photo detector (PD) after optimized by a variable optical attenuator (VOA). As a reference clock for nonlinear scanning, the interference is used to resample the original Rayleigh scattering and calibrate the TLS. It ensures the spectral repeatability during each scan-detection cycle.

 

Fig. 1. Schematic illustration of the OFDR based distributed fiber sensing system.

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The light in HCD module again splits through another 8:2 PC, injecting into a fiber under test (FUT) (80%) via a hybrid circulator and into a 2 m delay fiber (20%), respectively. Both the backward Rayleigh scattering signals and the local light split into the S/P polarizations by two polarization beam splitters (PBSs). The polarized beams interfere at the couplers C₁ and C₂ according to their corresponding polarization. Finally, polarization dependent interferences are received by the Balanced Photo Detectors (BPDs), and then collected by a 4-chanel digital data acquisition (DAQ) card, which is controlled and trigged by a data processor (DP).

Demodulation based on optical frequency shift in Rayleigh spectra is realized by solving the cross-correlation between the reference and measured Rayleigh spectra as follows. Firstly, the Rayleigh spectra are extracted from S/P interferences, which are resampled and calibrated with a normalized clock signal from the RMI. Then, Rayleigh scattering of each distributed sensor is mapped to its corresponding position via the FFT. After divided, extracted and then filtered, the signals in frequency domain are used to reconstruct the Rayleigh spectra in time domain by the inverse FFT (IFFT). Finally, the measurand is associated and described with the optical frequency shift between the static reference spectrum and the dynamic measured spectrum.

Theoretically, the spatial resolution Δz in space domain is determined and calculated by the effective scanning spectral range Δf_scan of the TLS [17]:

Figure 2 intuitively reveals the analysis above. The green and yellow blocks indicate data size of the reference and measured spectra for a single measuring point, respectively. From top to bottom, the data size decreases due to the segmentation at a higher spatial resolution, where the cross-correlation (overlap) becomes weak (small). Moreover, when the temperature or strain changes, the thermal/elastic-optic effects lead to a shift of the measured spectrum, as well as the position-deviation (offset). From left to right, the position-deviation accumulates along the fiber and becomes significant at fiber end. For the same position-deviation (offset) at different spatial resolutions of 2ω₀, ω₀, and ω₀/2, the cross-correlation (overlap) basically remains, mostly degenerates, and is totally lost, respectively. Therefore, the tradeoff is hard to achieve among the high resolution, long measuring length, and large number of sensors.

 

Fig. 2. Accumulation in position-deviation and degeneration in correlation along the fiber.

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Here, we propose a position-deviation compensation algorithm to achieve sub-mm spatial resolution at the fiber end with thousands of measuring points. By analogy with the Fiber Bragg Grating (FBG), the correlation peak is taken as the characteristic peak, and the deviation in Optical Path can be related to its wavelength shift in Eq. (2).

3. Experimental results

Figure 3(a) shows the reconstructed reference (black) and measured (red) Rayleigh spectra at a single measuring point. The spectra show noticeable wavelength-shift towards the longer spectral range, when the positive strain is axially loaded. Accordingly, the characteristic peak exhibits the same shift-direction, whether in cross-correlation (time or spectral domain Fig. 3(b)) or in convolution (frequency domain Fig. 3(c)). In this way, strain can be calculated and described with the wavelength-shift of the Rayleigh spectra, which agrees with the peak-shift in cross-correlation or convolution.

 

Fig. 3. Wavelength (a), correlation (b), and convolution (c) shift, at a distributed sensor.

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Figure 4 shows a specifically designed verification for the sub-mm resolution distributed sensor. Fiber segments are sheathed with 1-mm steel tubes and immobilized with epoxy resin under a microscope in Fig. 4(b). The spaces between these cascaded steel tubes are set as 0.5 mm, 1 mm, 2 mm, and 4 mm at the 25 m fiber end. Because of the difference in cross-section, the bare fiber and the fiber segments with steel tubes can be recognized along the strain curve, when the strain is axially loaded.

 

Fig. 4. Verification for sub-mm resolution with recognizable strained fiber segments

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Seen in Fig. 4(c), the blue scatter refers to the original data without the position-deviation compensation, while the red line indicates a strain curve after the compensation. Consistent with the analysis above, the cross-correlation degenerates at 0.5 mm spatial resolution. Here, most outliers are mistakenly recorded during the peak-seek process. Thus, the compensation is proved to be beneficial to achieve a higher spatial resolution at a longer fiber end.

Sub-mm spatial resolution is further discussed in detail in Fig. 5. The fiber segment from 2118 cm to 2140 cm is mounted between two clamps with 1400 µɛ applied, as depicted in Fig. 5(a). Partially zoomed view of the strain curve in Figs. 5(b) and 5(c) display the bare fiber and the confined fiber segments with recognizable strain differences. The strain at the confined fiber segments is about 40% of that at the bare fiber, which is inversely related to the cross-section. Moreover, the 0.5 mm, 1 mm, 2 mm, and 4 mm spaces between these cascaded steel tubes are also recognized, where the strain equals 1400 µɛ same as the rest of fiber mounted between the clamps. That means, the 0.5 mm spatial resolution sensor is achieved with 50,000 equivalent measuring points at along the 25 m fiber.

 

Fig. 5. Details of the fiber segments with recognizable strain differences.

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The positive (stretch state) and negative (squeeze state) strain is calibrated and measured with a bare fiber immobilized to an aluminous beam under four-point bending flexural. Strain circulations alternate from 0 µɛ to ± 2500 µɛ and display the strain steps towards the positive and negative direction respectively, as the black lines presents in Fig. 6. The measured strain at 0 µɛ, ±100 µɛ, ±200, ±500 µɛ, ±1000 µɛ, ±1500 µɛ, and ± 2500 µɛ shows good uniformity and repeatability during the dynamic measurements. The linearity in the strain measurement is described by the R-Square of 0.9981, while the total Uncertainty is 0.4% of the full strain range (±15 µɛ), which approaches to practical strain monitoring applications.

 

Fig. 6. Measurements of positive and negative strain circulations from 0µɛ to ± 2500µɛ

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Fig. 7. High temperature monitoring with a gold-coated fiber from 50 °C to 500 °C

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The temperature curve along an 18 m gold-coated fiber is observed in experiment in Fig. 7, varying from 50 °C to 500 °C in a Vertical Ceramic Cavity oven (Fluke). The thermal distribution is segmented into four sections, where the temperature is constant in laboratory (0∼2340 cm), flexible in the heated airflow above the oven (2340∼2350 cm), gradient along the cavity depth (2350∼2360 cm), and stable within the balance (2360∼2365 cm). The averaged wavelength-shift in 2360∼2365 cm is linearly fitted with temperature. The sensitivity is 13.92 pm/°C with the repeatability of ± 0.9 °C (12.5 pm), with R-Square of 0.9861. The high spatial resolution distributed fiber sensor also suits for high-temperature sensing, where most electronic sensors are unavailable.

4. Conclusion

We propose and demonstrate a distributed fiber temperature and strain sensor with a 0.5 mm spatial resolution. The position-deviation compensation helps maintain the cross-correlation between the reference and measured spectra. The experimental results show that the position-deviation compensation makes the 0.5 mm resolution realized at a 25 m fiber end with 50000 equivalent sensors. The temperature repeatability of ± 0.9 °C (12.5 pm) is obtained from 50 °C to 500 °C, and the strain accuracy of ± 15 µɛ is also achieved in ± 2500 µɛ. The position-deviation compensation is experimentally proved to be effective, providing a useful method to achieve precise inversion of the temperature, strain, and deformation distribution.