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Abstract
In this paper, we propose and demonstrate a spectral splicing method (SSM) for distributed strain sensing based on optical frequency domain reflectometry (OFDR), which can achieve km level measurement length, µɛ level measurement sensitivity and 104 µɛ level measurement range. Based on the traditional method of cross-correlation demodulation, the SSM replaces the original centralized data processing method with a segmented processing method and achieves precise splicing of the spectrum corresponding to each signal segment by spatial position correction, thus realizing strain demodulation. Segmentation effectively suppresses the phase noise accumulated in the large sweep range over long distances, expands the sweep range that can be processed from the nm level to the 10 nm level, and improves strain sensitivity. Meanwhile, the spatial position correction rectifys the position error in the spatial domain caused by segmentation, which reduces the error from the 10 m level to the mm level, enabling precise splicing of spectra and expanding the spectral range, thus extending the strain range. In our experiments, we achieved a strain sensitivity of ±3.2 µɛ (3σ) over a length of 1 km with a spatial resolution of 1 cm and extended the strain measurement range to 10,000 µɛ. This method provides, what we believe to be, a new solution for achieving high accuracy and wide range OFDR sensing at the km level.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
A sensing system based on an optical frequency domain reflectometer (OFDR) was first proposed by Froggatt in 1998 [1]. It can obtain changes in physical quantities such as strain [2], temperature [3], and birefringence [4] at any position of the fiber by the correlation shift of the Rayleigh scattering spectrum. Especially in the field of strain monitoring, OFDR sensing systems have been applied to small structural health monitoring, 3D shape sensing, and other short-distance health monitoring fields due to their high spatial resolution, large measurement range, no measurement dead zone, and single-end detection [5–7]. However, in some special monitoring situations, including mega bridge deformation monitoring, large building structures, geotechnical movement monitoring, and some specific IoT areas, special requirements for OFDR sensing systems, which usually require km-level test length [8], µɛ-level test sensitivity [9], and thousands of µɛ-level measurement range [10,11], while maintaining cm-level high spatial resolution.
Research on OFDR strain sensing system, the current research hotspots mainly focus on high accuracy and large measurement range. On the one hand, For the accuracy enhancement of OFDR sensing systems, strain accuracy is primarily influenced by spectral accuracy, nonlinear sweep noise, random range of wavelength sweep, and random noise within the system, among other factors. In 2018 Cui et al. used a spectral domain interpolation preprocessing method to improve spectral accuracy in the spectral range of 20 nm and achieve a strain measurement accuracy of 3.0 µɛ at a spatial resolution of 1 cm and 21.4 m test length [12]. Similarly, Feng et al. also used wavelet transform to enrich the spectral accuracy in the 10 nm spectral range, achieving a measurement accuracy of 1 µɛ and maintaining a spatial resolution of 5 mm in a 5 m test length [13]. In 2022, Guo et al. achieved a minimum spatial resolution of 0.5 µɛ at a spatial resolution of 5 mm and a test length of 4 m by preprocessing to suppress nonlinear phase noise and wavelength random offset in the 130 nm sweep range [14]. As for the random noise within the system, various image processing methods are proposed to suppress it. For example, researchers used 2D image processing methods [15], the total variation method, and 2D gaussian filter arithmetic [16] to suppress it, achieving a minimum strain measurement accuracy of 0.4 mm and a maximum test length of 52 m. In 2022 pan et al. successfully achieved a spatial resolution of 5 cm and a measurement accuracy of 2.0 µɛ with a test length of 200 m by using a BM3D-SAPCA image denoising [17]. Although the above methods achieve high accuracy measurements, the limited ability to suppress phase noise such as nonlinear sweeping noise in the system limits the expansion of the length while maintaining high accuracy. Sensing fiber length generally does not exceed hundred meters level.
On the other hand, for large-range measurements of the OFDR sensing system, the strain expansion is affected by the correlation degradation of the scattering spectrum caused by the actual position deviation. Therefore, the current research is mainly focused on preprocessing the scattering signal. In 2018, Feng et al. used local intercorrelation to improve correlation in the presence of overall correlation degradation, achieving a spatial resolution of 3 mm and a strain measurement range of 3000 µɛ over a sweep of 20 nm, but with a test length of only 3 m. [18]. Zhao et al. used a spectrum registration method further to extend the strain measurement range to 7000 µɛ and maintain a spatial resolution of 5 mm. However, the test length was less than 1 m. [19]. Li et al. then used a combination of distance compensation and wavelet denoising to achieve a strain measurement range of 2000 µɛ at a spatial resolution of 2.56 mm [20]. In 2022, Qu and Zhang et al. achieved a maximum strain measurement range of 10,000 µɛ using a demodulation recursive compensation algorithm [21–23] and a preprocessing method based on local search and Kalman prediction [24] in the 40 nm sweep range, respectively, and has a maximum test length of 47 m. However, since large-range measurements theoretically require a large sweep range, a large sweep at long distances can lead to a sharp accumulation of phase noise that makes demodulation impossible. Sensing fiber generally does not exceed 50 meters. Zhang et al. subsequently extended the strain measurement range to 25 km using an external debugging scheme. But due to the limitation of the modulator performance of the external modulation scheme, the sweep range was only at the GHz level, which resulted in a strain measurement range of only ten µɛ level and a spatial resolution of only 2.5 m [25].
Therefore, although some of the above methods for accuracy enhancement and range enhancement can maintain a sweeping range of several tens of nm and achieve high accuracy and a wide range of strain measurement, the maximum testing distance does not exceed a hundred meters level. And the methods that can achieve km-level test lengths have a sweeping range of only the GHz level, resulting in severe limitations in spatial resolution and strain measurement range. The main reason for this contradiction is the inability to effectively handle the accumulated phase noise over long distances and large sweep ranges. Therefore, it is not yet possible to achieve test lengths in the km level and strain measurement ranges in the thousands of µɛ level.
In this paper, a spectral splicing method (SSM) based OFDR sensing system is proposed to realize long-distance, high accuracy, and wide-range strain measurements. When the conventional method causes strain demodulation deterioration or even failure due to the effect of accumulated phase noise, the SSM can split the long-range, large-range signal into multiple small-range signal sequences. The phase noise in a single signal sequence is significantly reduced and can be handled efficiently. At this point, the effect of phase noise on strain demodulation is significantly reduced. After the phase noise is removed, the individual segments are spatially position corrected to accurately obtain the corresponding spectral signal for each segment. Strain demodulation is then achieved by splicing the recovered wide range of the spectrum. In the segmentation and then splicing process, the accumulated phase noise is removed, and a wide range of spectra is obtained. The accuracy and range of strain measurements are improved. Using this method, we can achieve a measurement range of several thousand µɛ over a test length of km level and maintain a spatial resolution of cm level and a high strain sensitivity.
2. Principle and method
2.1 Strain demodulation principle
In the OFDR sensing system, As shown in Fig. 1(a), the interference light received at fiber locations a∼b can be expressed as:
Fig. 1. (a) Simple OFDR experimental setup. TLS: tunable laser source; OC: optical coupler; BPD: balanced photodetector; FUT: fiber under test; DAQ: data acquisition; (b) Flow chart of traditional cross-correlation demodulation method.
When the strain $\varepsilon$ is applied to the fiber, which causes the fiber to stretch or contract by $\Delta L$ (the total length is $L$), a change in this physical length will cause the wavelength shift ${\lambda _{shf}}$ or frequency shift ${v_{shf}}$ of the Rayleigh scattering spectrum [26]. As shown in Fig. 1(b), after we obtain the signals before and after the strain by two measurements, the frequency shift or wavelength shift is calculated by cross-correlation. Then the strain change acting on the fiber can be calculated. And the strain result can be expressed as follows:
2.2 Effect of phase noise
In actual measurements, strain demodulation can be affected by various factors. On the one hand, as shown in Eq. (1), the random phase term $\varphi (t) - \varphi (t - {\tau _i})$ will affect the interferometric signal. And it will interfere with our demodulation of the minimum frequency shift or the minimum wavelength shift as an additional random frequency shift, thus affecting the accuracy of the strain demodulation. And as the phase noise increases, the demodulation accuracy will deteriorate and even lead to demodulation failure. On the other hand, since the actual strain is calculated by frequency shift or wavelength shift, the maximum wavelength shift (sweep range) will limit the theoretical maximum strain demodulation range. Equation (2) can be further expressed as:
In general, by combining the PNC algorithm [27] or the PPNE-deskew filtering algorithm [28] for phase noise suppression, we can obtain the spatial domain Rayleigh scattering spectrum as shown in Fig. 2(a), and achieve km-level strain demodulation, as shown in Fig. 2(b). In theory, the accuracy and range of strain demodulation increase as the sweep range (spectral range) increases. But as shown in Fig. 2(b), the actual demodulation effect shows an improvement followed by deterioration with the increase of the spectral sweep range, and the best results were achieved in the 2 nm sweep range. This situation is mainly due to the effect of accumulated phase noise, and since $\varphi (t) - \varphi (t - {\tau _i})$ can be expressed as $2\pi [\delta {f_0}(t) + \delta \gamma (t)t]{\tau _i}$ [29] (where $\delta {f_0}(t)$ is the instantaneous frequency noise and $\delta \gamma (t)$ is the swept frequency nonlinear error), it is known that the phase noise (instantaneous frequency noise and swept frequency nonlinear error) will accumulate as the swept frequency range increases. In the case of a small sweep range, although the current method can effectively remove the accumulated small phase noise, the too-low spectral accuracy at high spatial resolution also causes strain accuracy deterioration, and even demodulation errors occur. In the case of too large a sweep range, although the spectra are rich in information, the accumulated phase noise exceeds the processing threshold of the current method, resulting in severe phase noise residuals. The residual phase noise leads to degraded demodulation performance and even demodulation error at the end. Therefore, the inability to effectively handle the accumulated phase noise limits the further improvement of strain accuracy and range.
Fig. 2. (a) Scattering signal under different sweep ranges; (b) Strain demodulation under different sweep ranges.
2.3 Spectral splicing method
For the problem of accumulated phase noise over a long distance with a large sweep range, we propose an SSM. The swept signal over a large range can be cut according to a certain time interval T ($t = \sum\nolimits_0^n {{t_n},nT < {t_n} \le (n + 1)T}$, $T$ corresponding to the wavelength interval ${\lambda _n}$, ${\lambda _{all}} = \sum\nolimits_0^n {{\lambda _n}}$). And each segment of the cut signal ${I_{ab}}({t_n})$ is also a complete small-range sweep process (corresponding to a sweep speed defined as ${\gamma _n}$), and the complete signal can be considered as a succession of n consecutive segments:
And after the signal is cut, the total time can be expressed as $t = nT$. So the total phase noise $\Delta {\varphi _{all}}$ can be expressed as the accumulation of the segments:
First, for the instantaneous frequency noise part $2\pi \delta {f_0}({t_n}){\tau _i}$, it is only related to the measurement length and accumulates with the increase of the test length. And for the swept frequency nonlinear error part $2\pi \delta \gamma ({t_n}){t_n}{\tau _i}$, it will accumulate synchronously with the sweep range (since its positive and negative corresponds to the left and right spread of the beat frequency peak, it will not cancel each other but only keep accumulating left and right. Therefore, it is considered as a process that grows with a sweep range when the measurement length is determined). Therefore, according to Eq. (5), we can know that the phase noise of each segment is much smaller than the whole after the segment due to the time cut (sweep range division) brought by the segmentation, which reduces the processing difficulty and makes the phase noise of a single segment can be processed using the current method. Therefore, the phase noise accumulated by the complete signal is effectively handled by segmentation.
After suppressing the phase noise in each segment, we then need to perform spectral splicing to recover the complete spectral information. During spectral splicing, as shown in Fig. 3, the deviation of the sweep speed during the length conversion in the spatial domain leads to serious length deviations in the spatial domain for each signal segment if no processing is done. This impact the interception of the sliding window ${l_{n,M}}$ (total length ${L_n} = \sum\nolimits_0^M {{l_{n,M}}}$, n and M are the continuity between different signal segments and the spatial positional consistency of different signal segments), which in turn affects the accuracy of the splicing.
Therefore, we calculated correction coefficients and performed spatial position correction for each signal segment, which reduced the length deviation in the spatial domain to improve the accuracy of spectral splicing. After the spatial position correction, by combining the splicing order of Eq. (4), the spliced spectrum can theoretically be obtained in agreement with the complete spectrum. (consistency is assessed by the correlation coefficient $\rho ({\lambda _{splicing}},{\lambda _{complete}}) = {\mathop{\rm cov}} ({\lambda _{splicing}},{\lambda _{complete}})/{\sigma _{{\lambda _{splicing}}}}{\sigma _{{\lambda _{complete}}}}$, where ${\lambda _{splicing}}$ is the splicing spectral signal; ${\lambda _{complete}}$ is the complete spectral signal; ${\mathop{\rm cov}} ({\lambda _{splicing}},{\lambda _{complete}})$ is the covariance between ${\lambda _{splicing}}$ and ${\lambda _{complete}}$;${\sigma _{{\lambda _{splicing}}}}$ is the standard deviation of ${\lambda _{splicing}}$;${\sigma _{{\lambda _{complete}}}}$ is the standard deviation of ${\lambda _{complete}}$). Therefore, although the spatial resolution of Rayleigh scattering is reduced for each segment leading to the reduction of the spectral information obtained from each segment, the splicing process restores the total amount of information in the spectrum. This allows us to obtain the same amount of spectral information while can maintain the same strain demodulation spatial resolution as the large sweep range. So it also does not bring the limitation of spatial resolution. And the splicing spectrum can be expressed as follows:
After obtaining the spliced spectrum, firstly, since the phase noise of each segment has been processed separately, the overall spectrum spliced together phase noise is also effectively suppressed. Theoretically, its effect on the minimum wavelength shift is significantly reduced and the strain accuracy is improved. Secondly, due to the expansion of the spectral range brought by the spectral splicing, the range of the maximum wavelength shift is increased theoretically, and the strain demodulation range is also expanded. So, Eq. (3) can be re-expressed as:
Based on the above analysis, using SSM can effectively reduce the effect of accumulated phase noise while maintaining a wide range of sweeps, thus enabling long-distance, high-accuracy, wide-range strain measurement. The specific process of the SSM is shown in Fig. 4. First, the first and second measurements were performed before and after the application of strain to obtain two-time domain Rayleigh scattering signals, Ref. signal and Sen. signal, respectively. Second, an equally spaced cut of Ref. and Sen. signal. Third, phase noise correction is performed separately for each signal segment after the Ref. and Sen. signal cuts to eliminate phase noise in each segment. Fourth, calculate the correction coefficients and correct the spatial position of each signal segment of the Ref. and Sen. signal, respectively. Fifth, a fast Fourier transform transforms each signal segment of the Ref. and Sen. signal from the time domain to the spatial domain. And sliding intercepts according to a sliding window, where the width of the sliding window indicates the sensed spatial resolution. Sixth, the signals intercepted on each signal segment of Ref. and Sen. signal is converted from the spatial domain to the spectral domain by inverse Fourier. And spectral splicing is performed separately. Seventh, strain values are obtained by cross-correlation according to splicing spectra.
3. Experimental setup and results
3.1 Experimental setup
To verify the effectiveness of the proposed SSM, we built a strain-sensing experimental setup based on the OFDR test principle. As shown in Fig. 5, the light from a tunable laser (SANTEC, TSL-770) is split by a 99:1 coupler (OC1). 99% of the light is injected into the main interferometer to produce a main interference signal. In the main interferometer, another 99:1 coupler (OC3) is used to ensure that 99% of the light is injected into the arm where the circulator (Circulator2) is located to increase the intensity of backward Rayleigh scattered light. And the fiber under test is connected to the second port of the circulator (Circulator2). 1% of the light is injected into the auxiliary interferometer to generate an auxiliary interference signal for phase noise estimation and compensation. The auxiliary interferometer is set to Michelson type and can reduce the effect of polarization fading on the test. The main and auxiliary interference signals are converted to electrical signals by two balanced photodetectors (Newport, 1817-FC) and acquired via a data acquisition card (Spectrum, M4i.4471-x8 180 MHz/s).
Fig. 5. Experimental setup. TLS: tunable laser source; OC: optical coupler; FRM: faraday rotating mirror; BPD: balanced photodetector; FUT: fiber under test; DAQ: data acquisition.
In the experiment, we set the sweep range of the tunable laser TLS to 20 nm (wavelength sweep range 1540-1560 nm) and the sweep speed $\gamma$= 20 nm/s. Therefore, the sweep time of the corresponding laser is 1 s. The auxiliary interferometer delay fiber length is set to 50 m, and the overall arm length difference is 100 m because it is of Michelson type. The strain generation device is fixed at the end of the 1170 m fiber to be measured to apply strain, and the acquisition card sampling rate is set to 90 MHz/s.
3.2 Signal segmentation and position correction
First, we need to segment the signal. According to the theoretical part above, we know that the best demodulation sensitivity and the absence of demodulation bad points in the 2 nm wavelength band suggest that we can effectively handle phase noise and recover spectral information in this band. Therefore, we segmented the signal at 2 nm intervals during the experiment. Figure 6 shows the cut of the main interferometric signal for the first measurement. We can see that the 20 nm swept signal is uniformly cut into ten parts according to the equal cut interval $T = 0.1\textrm{ }s$ (corresponding to the wavelength cut interval ${\lambda _n} = 2\textrm{ }nm$). Each part can be treated as a separate sweep process in this case. And both main and auxiliary interferometric signals in the first and second measurements need to be cut according to the interval T. And thanks to the segmentation process, the phase noise of each segment is effectively reduced, and we can easily remove the phase noise of each segment using current phase noise suppression methods. In addition, the phase noise suppression method used in this experiment is the PPNE-deskew filtering algorithm [28].
After segmentation and phase noise suppression, we further observed each signal segment in the spatial domain. Figure 7(a) shows the spatial domain of each signal segment of the main interference signal of the first measurement after phase noise correction. It can be seen that there is a serious spatial position deviation between the signals of different segments. By calculating the triple standard deviation of the end peak position between different segments, we know that the position deviation reaches 29.4536 m. It is caused by the deviation of the scanning speed from the actual when length conversion is performed in the spatial domain. Therefore, we need to obtain the actual sweep speed information according to the signal segment of the corresponding auxiliary interference signal and calculate the ratio between it and the set sweep speed to obtain the correction coefficients and perform the spatial position correction, respectively. Figure 7(b) shows the correction effect of each signal segment after the spatial position correction. It can be seen that the position deviation is significantly corrected compared to the test result in Fig. 7(a). And by calculation, we can know that the position deviation of the end peak after correction is reduced to 1.0 mm. Similarly, we need to do the same for the second measurement. Through position correction, we significantly reduce the position deviation of spatial domain signals in different spectral bands and improve the consistency of position properties in the spectral splicing process.
Fig. 7. (a) Spatial domain scattering signal before spatial position correction; (b) Spatial domain scattering signal after spatial position correction.
3.3 Spectral and strain demodulation consistency
In the subsequent experiments, we evaluated the effect of spatial position correction on spectral recovery. Due to the effect of accumulated phase noise, we could not compare the 20 nm complete spectrum with its corresponding spliced spectrum. So as shown in Fig. 8, we chose five spectral ranges, 1540-1544 nm, 1544-1548 nm, 1548-1552 nm, 1552-1556 nm, and 1556-1560 nm, and compared the spliced spectra before and after the spatial position correction with complete spectra, respectively.
Fig. 8. Comparison of the 4 nm spliced spectrum with the 4 nm complete spectrum in the spectral range 1540-1544 nm, 1544-1548 nm, 1548-1552 nm, 1552-1556 nm, and 1556-1560 nm before and after spatial position correction. (a) Spectral range 1540-1544 nm before spatial position correction; (b) Spectral range 1540-1544 nm after spatial position correction; (c) Spectral range 1544-1548 nm before spatial position correction; (d) Spectral range 1544-1548 nm after spatial position correction; (e) Spectral range 1548-1552 nm before spatial position correction; (f) Spectral range 1548-1552 nm after spatial position correction; (g) Spectral range 1552-1556 nm before spatial position correction; (h) Spectral range 1552-1556 nm after spatial position correction; (j) Spectral range 1556-1560 nm before spatial position correction; (k) Spectral range 1556-1560 nm after spatial position correction.
From the results in Fig. 8(a), (c), (e), (g), and (j), before spatial position correction, the degree of consistency between the spliced spectra and the complete spectral signals of the corresponding spectral bands is low. The spliced spectra do not recover the information of the original spectra well. This situation is due to the deviation of the spatial position at the time of interception. However, as shown in Fig. 8(b), (d), (f), (h), and (k), the consistency of the spliced spectrum with the complete spectrum is significantly improved after the correction of the spatial position of each segment. The spliced spectrum can effectively recover the original spectrum information. This situation also illustrates the remarkable effect of spatial position correction on spectrum recovery. We also quantified the degree of consistency by calculating the correlation coefficient $\rho ({\lambda _{splicing}},{\lambda _{complete}})$. Before the spatial position correction, the correlation coefficients of the five complete spectra and the splicing spectrum were 0.02, 0.06, 0.04, 0.05, and 0.03, respectively. And after the spatial position correction, they were increased to 0.93, 0.93, 0.95, 0.91, and 0.93, respectively. The improved correlation indicates that the original spectral signal is effectively recovered, and most of the effective information of the spectrum is retained. And since each segment can maintain high consistency, it can be known that as the splice range (the number of splice segments) increases, the splice spectrum can still maintain high consistency with the original spectrum.
Based on the consistency of the spectra, we also compared the strain demodulation result of the complete and splicing spectra at 1548 nm-1552 nm. Figure 9 shows a comparison of the strain demodulation effect at 200 µɛ. The calculation shows that the maximum strain error does not exceed 0.5 µɛ, which also shows a high degree of agreement.
Fig. 9. Comparison of strain demodulation effect of 1548 nm-1552 nm splicing spectrum and 1548 nm-1552 nm complete spectrum.
3.4 Improvement of strain sensitivity and strain range
Based on spectral consistency and strain test consistency, the spliced spectrum can effectively recover the information of the original spectrum and bring a consistent demodulation effect. In subsequent experiments, we evaluated the improvement of SSM on strain demodulation results compared with the traditional cross-correlation demodulation methods. Since the best demodulation strain sensitivity can be achieved at a sweeping range of 2 nm by the traditional cross-correlation demodulation methods, so we compared the strain demodulation effect of the 20 nm splicing spectrum and 2 nm spectrum.
Firstly, we compared the strain sensitivity improvement at end loading 200 µɛ. The length of the intercepted spatial domain Rayleigh scattering signal when performing single-point strain demodulation is 1 cm (demodulation spatial resolution is 1 cm). It can be seen from Fig. 10(a) that the improvement in strain demodulation sensitivity at 1170 m length is huge for the 20 nm splicing spectrum compared to the 2 nm spectrum. This situation is because SSM achieves the suppression of accumulated phase noise over a large range and the expansion of the spectral range. We evaluated the degree of improvement in strain sensitivity by calculating the triple standard deviation of the minimum strain demodulation value. The results show strain sensitivity improved from ±7.8 µɛ (3σ) to ±3.2 µɛ (3σ) at 1 cm demodulated spatial resolution, which brings almost a 2.5 times improvement in strain sensitivity. Secondly, as shown in Fig. 10(b), we can see that thanks to the improved strain sensitivity. The strain demodulation uncertainty is significantly reduced in the strain region, and the accuracy of the system test is improved. We continuously tested five groups of strain data while keeping the strain unchanged and calculated the error bars for each strain value in the strain region. The error bars fluctuated by a factor of three standard deviations. The calculated error bars allow us to obtain the mean values of the five measurements at each demodulation position in the strain region and the magnitude of the fluctuations. We can consider this mean value as the actual strain value and the fluctuation size as the range of deviation of each demodulated value from the actual value. The corresponding error bar results are shown in Fig. 10(c). It can be seen that in the strain-applied region, the deviation of the strain value from the actual value for demodulation is significantly reduced by the SSM method, and the uncertainty of the strain demodulation is reduced by more than two times as a whole. The reduction of uncertainty indicates the improvement of demodulation repeatability. This shows that the reproducibility of strain demodulation has been improved thanks to the improved spectral processing capability of SSM.
Fig. 10. (a) Comparison of strain demodulation sensitivity between 2 nm spectra and 20 nm splicing spectra; (b) Comparison of 2 nm spectra and 20 nm splicing spectral strain regions;(c) Comparison of error bars under five measurements in the strain region for 2 nm spectra and 20 nm splicing spectra.
Then, the spectral range expansion by SSM also brings a significant expansion of the strain measurement range. We first loaded strains of 200 µɛ, 400 µɛ, 600 µɛ, 800 µɛ and 1000 µɛ sequentially at 1170 m. Figure 11(a) shows the effect of strain demodulation using 2 nm spectra at strains ranging from 200 to 1000 µɛ. We can see that the demodulation error rate tends to increase incrementally as the strain increases. The reason for this is in two ways. On the one hand, it is due to the low signal-to-noise ratio of the spectra in the sweep range of 2 nm. On the other hand, it is due to the severe decrease in the correlation of the spectra with increasing strain in the small spectral range. Therefore, it leads to significant demodulation errors as the strain increases. The strain information can no longer be recovered at 1000 µɛ. However, as shown in Fig. 11(b), the demodulation error is suppressed in the case of 20 nm spliced spectra. And we can fully demodulate the strain information, and the strain demodulation range is expanded. This situation is due to the expansion of the spectral range, and the spectral correlation also is significantly improved.
Fig. 11. (a) Strain demodulation of the 2 nm spectrum; (b) Strain demodulation of 20 nm splicing spectra.
Finally, we further enlarge the loading strain value, loading the strain of 2000 µɛ, 4000 µɛ, 6000 µɛ, 8000 µɛ, and 10000 µɛ at the length of 1170 m, respectively (which is well beyond the theoretical test limit of the 2 nm spectral range). As can be seen in Fig. 12(a), thanks to the expansion of the spectral range, we successfully demodulate the 10000 µɛ at a length of 1170 m (the existing method of position offset correction [23] was used to correct the position deviation due to the large strain). As shown in Fig. 12(b), we also calculated the functional relationship between the measured strain and the applied strain at 2000 µɛ to 10000 µɛ. The calculated slope and ${R^2}$ are 0.98 and 0.99, respectively, which indicates that the measured and applied strains are essentially equal. The same illustrates the effectiveness of SSM.
Fig. 12. (a) Measured strain at 2000 µɛ∼10000 µɛ; (b) Measured strain as a function of applied strain at 2000 µɛ∼10000 µɛ.
In addition, we also evaluated the processing time of the SSM method and compared it with the conventional cross-correlation demodulation method. While keeping the test platform (processor AMD 3955WX and 256 G RAM) and data volume consistent (sweep range 1540-1560 nm, sweep speed 20 nm/s, sampling rate 90 MHz/s), the overall time spent by the traditional cross-correlation demodulation method is 461.5 s while that of the SSM method is 336.1 s. Thanks to the segmented data processing process in the SSM method, which consumes less processing resources for each segment of the signal processing and therefore improves the data processing time to some extent.
4. Summary
In summary, an SSM for OFDR sensing systems is proposed to achieve long-range, high-accuracy, and wide-range strain measurements. The method controls the phase noise accumulated in each segment by signal cutting to within the threshold that the current phase noise suppression method can handle, so it can be processed separately. Therefore, the effect of accumulated phase noise over long distances and large ranges on strain demodulation is effectively reduced. In order to correct the spatial position deviation caused by segmentation, we use spatial position correction to correct the deviations that exist in the spatial domain for each segment, thus achieving accurate recovery of large-range spectra. By the SSM, we can obtain a wide range of spectra that are less affected by phase noise. Therefore, the strain accuracy is significantly improved, and the strain range also is extended. We experimentally demonstrated that we achieved a strain sensitivity of ±3.2 µɛ (3σ) on an 1170 m sensing fiber with a spatial resolution of 1 cm using a 20 nm splicing spectrum, which brings a 2.5 times improvement over the strain sensitivity of the 2 nm spectral segment, and the strain measurement range is extended to 10,000 µɛ. Therefore, this method provides support for the realization of km-level high-precision large-range structure monitoring, shape sensing, etc.
Funding
National Science Fund for Distinguished Young Scholars (61925501); National Natural Science Foundation of China (62127815); Guangdong Introducing Innovative and Entrepreneurial Teams (2019ZT08X340); Introducing Leading Talents of "The Pearl River Talent Recruitment Program" of Guangdong Province (2019CX01X010).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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