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Noise reduction by Brillouin spectrum reassembly in Brillouin optical time domain sensors
Optics and Lasers in Engineering 125 (2020) 105865
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Noise reduction by Brillouin spectrum reassembly in Brillouin optical time domain sensors Yuyang Zhang a,b, Yuangang Lu a,b,∗, Zelin Zhang a,b, Jiming Wang b, Chongjun He a,b, Tong Wu a,b a b
College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
a r t i c l e KeyWords: Brillouin sensor Image processing Noise reduction
i n f o
a b s t r a c t In this paper, we present a novel image-processing based spectrum reassembly method to handle the noisy Brillouin gain or loss spectrum in Brillouin optical time domain sensors. The principle of the proposed Brillouinspectrum-reassembly (BSR) Filter, is firstly dividing the Brillouin spectrum along the fiber into several segments according to the differences of Brillouin frequency shift (BFS), then shifting the Brillouin spectrum to reassemble a new image with equal BFSs and filtering the image by a conventional filter, finally shifting the Brillouin spectrum of each segment in the opposite direction to obtain the filtered Brillouin spectrum. Since the size of the filter windows in the reassembled image can be reduced greatly, the total processing time is decreased effectively. Furthermore, the BFS measurement accuracy and spatial resolution can be enhanced due to the edge-preserving image filtering strategy of the method. The measurement performance and processing speed improvements are verified by simulation and experiment. Utilizing a Brillouin optical time domain reflectometry (BOTDR) sensor, we achieve a BFS measurement accuracy improvement of 13%, a spatial resolution improvement of 46% and a processing time reduce of 35% in a 5.2 km-length G657 fiber by use of the proposed method, as compared with an excellent spectrum non-reassembly filtering method.
1. Introduction Distributed Brillouin fiber sensors attract many research interests [1– 4], due to their immunity to electromagnetic interference, large sensing range over tens of kilometers, and capabilities of simultaneous temperature and strain measurements. In distributed Brillouin fiber sensors, two time-domain techniques are widely studied: (a) Brillouin optical time-domain analysis (BOTDA) based on stimulated Brillouin scattering (SBS) [5–13]; (b) Brillouin optical time-domain reflectometry (BOTDR) based on spontaneous Brillouin scattering (SpBS) [14–17]. Various techniques have been proposed to improve the performance of Brillouin optical time domain sensors. Among several advanced techniques, methods such as double-sideband probe scheme [18] and optical pulse coding [19] lead better performance than traditional standard configurations in BOTDA. On the other hand, the measurement of Brillouin beat spectrum in BOTDR [20] and using multi-wavelength detection [21,22] can adequately reduce the operating time and enhance the measurement accuracy in the BOTDR systems. Recently techniques based on image processing [23–26] have been proposed to enhance the performance of distributed Brillouin and Rayleigh scattering-based fiber sensors. Two main denoising techniques, wavelet denoising (WD) [27–29] and non-local means (NLM) [30–32], ∗
have been proposed to improve the accuracy, and attracted lots of attention as they would not add any hardware complexity. Although the aforementioned methods are quite effective, these methods are more or less computationally inefficient, and some of them may deteriorate the measurement spatial resolution. Therefore, it is significate to explore more efficient and more robust image processing methods for Brillouin optical time domain sensors. In the paper, we propose a novel Brillouin-spectrum-reassembly (BSR) Filter to remove noise from the data with high quality and efficiency. In this paper the Brillouin spectrum refer not only to Brillouin gain spectrum in BOTDR but also to Brillouin gain or loss spectrum in BOTDA. The principle of the proposed BSR Filter, is firstly dividing the Brillouin spectrum along the fiber into several segments according to the difference of Brillouin frequency shift (BFS), then shifting the Brillouin spectrum to reassemble a new image with equal BFSs and filtering the image by a conventional filter, finally shifting the Brillouin spectrum of each segment in the opposite direction to obtain the filtered Brillouin spectrum. The advantage of the BSR Filter is that filter window size can be reduced greatly, thus decreasing the processing time. Meanwhile, more similar windows with higher similarity participate in the denoising process, which filters noise more effectively and thus improves the BFS measurement accuracy. Besides, the spatial resolution can be
Corresponding author at: College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu 211106, China E-mail address: [email protected] (Y. Lu).
https://doi.org/10.1016/j.optlaseng.2019.105865 Received 7 May 2019; Received in revised form 11 August 2019; Accepted 16 September 2019 0143-8166/© 2019 Elsevier Ltd. All rights reserved.
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Optics and Lasers in Engineering 125 (2020) 105865
Fig. 1. Flowchart of the denoising algorithm. Fig. 2. Flowchart of the region division method.
preserved well due to the edge-preserving image filtering strategy by use of the region division. Simulation and experimental results verify the validity and feasibility of the proposed noise filtering method. To the best of our knowledge, this is the first time that the BFS characteristics of the Brillouin scattering signal are effectively applied to the image filtering algorithm, which can effectively improve the performance of the Brillouin optical time domain sensors. This may open up a new way to improve the performance of Brillouin signal processing methods based on digital image processing. 2. Method In the following sections, we demonstrate how to achieve noisy data reduction, through the proposed BSR Filter. Fig. 1 illustrates the flowchart of the denoising algorithm. Besides the three main steps of the BSR Filter, another two steps, data acquisition and results display, are also shown in the flowchart. (1) Data Acquisition: During the step, a 2D matrix containing the Brillouin frequency spectrum at each sampled location x is obtained by using the acquisition system of the Brillouin optical time domain sensors. If there are n sample points along the fiber and m frequency points at each sampling location, the original data image with n × m pixels and with gray values in the range [0, 255] is generated from the 2D matrix which contains N = n × m data points. (2) Region Division: By using edge detection, the positions where BFS varies dramatically can be detected, and thus the original image is divided into the different regions (subimages) along the x direction. The Brillouin frequency spectrums in each subimage contain nearly the same BFS. (3) Spectrum Reassembly: Shifting the Brillouin spectrum in each subimage to reassemble a new image where all the values of BFSs are equal. In the reassembled image, the image similarity is improved and thus the size of filter window can be decreased. (4) Image Filtering: Filtering the reassembled image by a conventional filter, and shifting the Brillouin spectrum of each subimage in the opposite direction to obtain the filtered Brillouin spectrum. (5) Results Display: Fitting the Brillouin spectrum with a Lorentzian curve, the BFS information along the entire sensing fiber is thus obtained and displayed. 2.1. Region division In the original data image, the position of the BFS change exhibits a change in the gray values, and two boundary lines parallel to the y direction are formed in the image. The larger the BFS change, the longer the boundary lines are formed. By using the edge detection algorithm, the position of the boundary lines can be effectively determined, and the entire data image can be partitioned according to different BFSs. Fig. 2. illustrates the flowchart of the region division. The four steps of region division are as follows: (1) Gaussian Filtering: Applying Gaussian filter to the entire original gray image. Note that the Gaussian filter is only for edge detection.
(2) LoG Edge Detection: Using the Laplacian of Gaussian (LoG) edge detection algorithm [33] to obtain the edges of the regions with appreciably changed BFS. (3) Line Search: The obtained lines are identified by the line search algorithm we will describe below. (4) Location Report: Report the location of edges which indicated the boundary lines between the regions. Fig. 3(a) is an example of noisy Brillouin frequency spectrum along a 150 m length of fiber, and the range of BFS is from 10.5 GHz to 10.7 GHz. The corresponding original data image is shown in Fig. 3(b). In the range from 75 m to 85 m, there is a BFS change. We use Gaussian filter [34] before LoG edge detection, as edge detection methods rely on smoothing filters before processing. The computational complexity of the Gaussian filter is O(Ns2 ), where the N is the total number of points in the image, and s is the size of the filter kernel. In the step of line search, we propose an algorithm to locate the lines which represent the start and end locations of the regions. First, we divide the whole image into several small search windows of u × v (As that shown in the red window in Fig. 3(c), the total number of points within the window is M = u × v), then count the number of white points in the window. After that, the maximum number on each column is record. Finally, the column with the largest number is found. The column with the large number indicates the position of the line (In this example, the number should be larger than 15). The red dotted line in Fig. 3(c) indicates the edge of dramatically varied BFS regions. By this method, it is efficiently find out the position where the straight line, thus the original image can be divided into the different segments along the x direction according to these positions with rapidly changing gray level. The complexity of this method is O(NM), where the N and M are the total number of points within the image and the window, respectively. 2.2. Spectrum reassembly and image filtering After performing region division, we reassemble Brillouin spectrum and filter the reassembled noisy image by a conventional filter. The process of Brillouin spectrum reassembly can effectively reduce the size of the search window while preserving spatial resolution. The main idea is to make the similar frequency spectrum as close as possible by shifting and aligning the Brillouin frequency spectrums within different regions found in region division process. In the following, we describe the process of Spectrum Reassembly and Image Filtering in detail. In Fig. 4 we have drawn a set of diagram to illustrate the steps of Spectrum Reassembly and Image Filtering in BSR filter. The abscissa represents the detection distance, and the ordinate represents the BFS. In this example, there are 5 subimages in the image with n rows and m columns (n = 9 and m = 12 in Fig. 4). The BFSs of the leftmost and rightmost subimages are equal to the averaged BFS of the entire image. The BFSs of the middle three subimages deviate from the averaged BFS of the entire image. Taking the image as an example, the remaining four steps of the BSR Filter is described as following. Spectrum Reassembly
Y. Zhang, Y. Lu and Z. Zhang et al.
Optics and Lasers in Engineering 125 (2020) 105865
Fig. 3. (a) An example of noisy Brillouin frequency spectrum along the fiber, (b) Original data image corresponding to (a), (c) Edge detection result of data image. (For interpretation of the references to color in this figure text, the reader is referred to the web version of this article.)
consists of steps (1) and (2), while Image Filtering contains steps (3) and (4). (1) Fit the measured Brillouin spectrum: By fitting one of the measured Brillouin spectrum in each subimage with a Lorentzian curve, the peak frequency of each subimage can be obtained. The obtained peak frequencies correspond to the pixels with the highest gray value in the same subimage, which are shown as the red dotted lines in Fig. 4(a). According to the number of Brillouin spectrums in each region, we calculate the average peak frequency of them (In this example, the peak frequency of the middle three subimages are respectively f2 , f3 and f4 , and the peak frequency of two other subimages are f1 . The average peak frequency favg is obtained by computing a weighted average of peak frequency in all regions according to the Brillouin spectrums number and peak frequency of each region). The accuracy of BFS in the transition area is related to the length of the subimage. The transition region is needed to be divided into several subimages that are as small as possible, so that the error in the alignment of the spectrum center can be reduced. The number of divided subimages depends on the accuracy of the subimages detection. To some extent the BFS of the transition area can be regarded as unreliable information. As long as the start and end points of the transition area can be correctly found in subimages detection procedure, the method wouldn’t impact the sensing system performance. (2) Shift the Brillouin spectrum: Subtracting the averaged peak frequency from the respective peak frequency in each subimage, thus the results are the shift values of Brillouin spectrum within each subimage (In this example, the shift values of the middle three subimages are respectively d1 (d1 = favg -f2 ), d2 (d2 = favg -f3 ) and
d3 (d3 = favg -f4 ), and the shift values of two other subimages are 0. The maximum shift value of the upward and downward movement are respectively du and dd , and their sum is dy (In this example, the du and dd are respectively d3 and d1 ). Next, filling the uneven image boundaries (the bule parts in Fig. 4(b)), the gray values of the filled parts are copied from that minimum values in the same column. Finally, we get an image (Fig. 4(c)) that will be used for denoising. Since the values of the expanded parts are almost equal to the noise floor, the denoising of Fig. 4(c) will not affect the BFS information. (3) Entire image denoising by a conventional filter: In this step, any conventional filter can be used to filter the noise in reassembled image. In this paper, we use an excellent conventional non-reassembly filter, Non-Local Means (NLM) Filter [35–37], to filter reassembled image. However, in our algorithm the size of filter windows can be decreased greatly, compared to that in the conventional NLM Filter applied on non-reassembly Brillouin spectrum image. In reassembled image (Fig. 4(c)), due to the distance of different similarity window with high similarity is fairly close, the search window size (p × q) can be set small enough. Specifically, if the conventional NLM filter search window size is w × w, when it is applied on non-reassembly Brillouin spectrum image the p depends on frequency sampling point and can be set less than w, while q depends on measurement accuracy requirement and it needs to be set to a value larger than or equal to w. Meanwhile, the value of p × q is less than w2 . The p and q value are related to the sensing system, and there are different optimal values in different sampling rate systems according to the measurement accuracy requirement. In general, when the frequency sampling interval is larger than 1 MHz, p < 0.7 w, q ≥ 1.1 w, and p × q < 0.75w2 , otherwise p < 0.25 w, q ≥ w, and p × q < 0.3w2 .
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Fig. 4. Process interpretation diagram of Spectrum Reassembly and Image Filtering in BSR filter. (a) Original image with 5 subimages. The peak frequency location in each subimages is shown as red dotted line. The thicker red dotted line denotes averaged peak frequency of the entire image. d1 , d2 and d3 denote the frequency shift value of the subimages. (b) Image after shifting the Brillouin spectrum in subimages. The gray values of blue regions will be set as the minimum values in the same column to fill the uneven image boundaries. (c) Use a conventional filter to denoise the entire image with the search window of p × q.(d) Image after denoising and the some subimages will be shifted back. (e) Resulting image consists of 5 noise filtered subimages. (For interpretation of the references to color in this figure text, the reader is referred to the web version of this article.)
(4) Restore the Brillouin spectrum: The subimages shift in Spectrum Reassembly will be shifted back (Fig. 4(d)), and the resulting image (Fig. 4(e)) can be obtained. The computational complexity of the Spectrum Reassembly is O(Ns2 + M N +em + ndy ), where e is the number of the subimages. Thus the total computational complexity of the BSR Filter is O(Ns2 + MN + em + ndy ) + O(Filter). The computational complexity of Image Filtering depends on the specific denoising method. In the case of NLM filter [35–37], O(Filter) = O((N + ndy )d2 pq), where d2 is similarity window size, pq is the search window size. It should be noted that, if we use the NLM filter in the proposed BSR Filter as the image filter, as it mentioned above, it wouldn’t increase the processing overhead because the total computational complexity of the BSR Filter O(Ns2 + MN + em + ndy )+O((N + ndy )d2 pq) is lower than that of conventional NLM Filter, which is O(Nd2 w2 ). As the values of w2 and its corresponding pq increase, the processing efficiency enhancement of BSR filter increases. Comparing the proposed method with wavelet denoising, we find that the measurement accuracy and experimental spatial resolution will deteriorate if we use wavelet denoising to pursue high denoising effects. This is because the high denoising effects is achieved at the expense of sacrificing the sensing data details [25]. On the contrary, in the proposed BSR Filter, the data details are preserved well without being affected by denoising process.
2.3. Evaluation criteria Three quantitative measures of the image are used to estimate the filtering quality in this paper. They are Structural Similarity index (SSIM) [38], root mean square deviation (RMSD) [39] of BFS and spatial resolution. The spatial resolution is obtained by calculating 10–90% rise time of a transition of BFS [1]. SSIM is a similarity measure between two images and can be expressed as ( )( ) 2𝜇𝑝 𝜇𝑞 + 𝑐1 2𝜎𝑝𝑞 + 𝑐2 𝑆 𝑆 𝐼 𝑀 (𝑝, 𝑞 ) = ( (1) )( ) 𝜇𝑝 2 + 𝜇𝑞 2 + 𝑐 1 𝜎 𝑝 2 + 𝜎 𝑞 2 + 𝑐 2 where 𝜇 p and 𝜇 q are respectively the mean of p and q, 𝜎 p 2 and 𝜎 q 2 are respectively the variance of p and q, and 𝜎 pq is the covariance between p and q. In Eq. (1) 𝑐1 = (𝑘1 𝐿)2 and 𝑐2 = (𝑘2 𝐿)2 where L is the dynamic range of the pixel-values, k1 equals 0.01 and k2 equals 0.03 by default. The resultant SSIM index is a decimal value between 0 and 1, and value 1 is only reachable in the case of two identical sets of data and therefore indicates perfect structural similarity. RMSD of the BFS evaluates the difference of the BFS along the fiber between the filtered and ideal data, which can be given by √ )2 1 ∑𝑛 ( 𝑀𝑆𝐷 𝑜𝑓 𝐵𝐹 𝑆 = (2) 𝑓𝑖 − 𝑓𝑖𝑑𝑒𝑎𝑙 𝑖=1 𝑛 where n is the sampling points of the x-axis in the processed image, fi is the BFS of the ith sampling point of the filtered image, and the fideal is
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Optics and Lasers in Engineering 125 (2020) 105865
Fig. 5. (a)Ideal Brillouin frequency spectrum along 1 km length fiber with single and complex temperature, (b) The corresponding 2-D digital gray image of (a), (c) The Brillouin frequency spectrum which is corresponding to (a) and corrupted by Gaussian noise along the fiber, (d) The corresponding 2-D digital gray image of (c).
the ideal BFS in the same location. RMSD of BFS is always non-negative, and values closer to zero are better. 3. Simulation results and discussion Fig. 5 shows an image of the Brillouin frequency spectrum along the sensing fiber in numerical simulation experiments, which contain a single BFS change section (corresponding to the mark of the single temperature) and a complex BFS change section (corresponding to the mark of complex temperature). The image contains 200 × 2000 data points with 200 scanning frequencies from 10.5 GHz to 10.7 GHz, and with 2000 sample points along 1 km fiber, corresponding to the sampling interval of 0.5 m per point. Fig. 5(a) is the ideal Brillouin frequency spectrum data which served as ideal data, and Fig. 5(b) is the corresponding 2-D digital gray image. Fig. 5(c) is the Brillouin frequency spectrum which is corresponding to (a) and corrupted by Gaussian noise along the fiber, and Fig. 5(d) is its corresponding 2-D digital gray image. Fig. 6 shows the optical power traces along the fiber at two different frequencies of 10.54 GHz and 10.6 GHz. It can be seen from the figure that the noise is large and it is difficult to distinguish the positions where the single and complex temperature change. The purpose of the region with complex temperature change is to evaluate the performance of denoising filter in real application. Numerical simulation experiments were carried out under two simulated experimental conditions. In the case 1, a 5 m fiber section from
347.5 m to 352.5 m under a single temperature will be studied. While in the case 2, a 130 m fiber section from 635 m to 765 m under the complex temperature will be studied. This arrangement imitates practical situations of different temperature at different locations, which compare the difference of filtering performance between BSR Filter and NLM Filter under different conditions. According to [24], for NLM Filter, the size of similarity window is set as 3 × 3, h equals 12 and search window size is 20 × 20, where h is a smoothing control parameter. For BSR Filter, the size of similarity window is set as 3 × 3, h equals 12 and search window size is 4 × 20. Fig. 7 shows the image of the Brillouin frequency spectrum from 275 m to 425 m along the fiber in case 1. The image contains 200 × 300 data points. Fig. 7(a) and (b) are ideal data and noise data, respectively. And Fig. 7(c) and (d) are the filtering results by applying BSR Filter and NLM Filter on Fig. 7(b), respectively. The contrast ratio in Fig. 7(c) is slightly higher than that in Fig. 7(d), so the central portion of the Brillouin frequency spectrum is much cleaner. The two boundary lines of the temperature region are much clearer in the filtered image by BSR Filter than that by NLM Filter. Fig. 8 illustrates BFS distribution from 340 m to 365 m obtained by use of BSR Filter and NLM Filter. It’s clear that the degree of BFS fluctuation by BSR Filter (blue curve) is lower than by NLM Filter (green curve). The spatial resolution is also slightly worse by NLM. Table 1 shows the comparison of filtering effect parameters of the case 1. The SSIM is 0.13 for original noisy data, which is increased to
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Optics and Lasers in Engineering 125 (2020) 105865
Fig. 6. Optical power traces along the fiber at two different frequencies.
Fig. 7. Image of the Brillouin frequency spectrum from 275 m to 425 m along the fiber in case 1. (a) Image of ideal data, (b) Image of noise data, (c) Image obtained by using BSR Filter, (d) Image obtained by using NLM Filter.
Table 1 Comparison of filtering effect parameters in Case 1.
SSIM RMSD of BFS(MHz) Spatial resolution(m) Processing Time(s)
Ideal data
Original noisy data
Using BSR filter
Using NLM filter
1 0 0.4 –
0.13 0.84 0.4 –
0.59 0.32 0.4 9.75
0.53 0.56 1.5 45.43
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Optics and Lasers in Engineering 125 (2020) 105865
Fig. 8. The BFS distribution from 340 m to 365 m obtained by use of BSR Filter and NLM Filter in case 1. (For interpretation of the references to color in this figure text, the reader is referred to the web version of this article.)
0.59 by BSR Filter and 0.53 by NLM Filter. For RMSD of BFS, the value changed from 0.84 MHz to 0.32 MHz by BSR Filter, and it is changed to 0.56 MHz by NLM filter. The spatial resolution for ideal data and original noisy data is 0.4 m, and it retains 0.4 m by BSR Filter. But the spatial resolution deteriorates to 1.5 m by NLM Filter. The processing time for the entire image with 200 × 2000 data points is 9.75 s by use BSR Filter and 45.43 s by use NLM Filter. We can notice that, in case 1, BSR Filter improve the original noisy data greatly. Furthermore, comparing with the results obtained by NLM
Filter, a BFS measurement accuracy improvement of 43%, a spatial resolution improvement of 275% and a processing time reduce of 78% can be achieved by using the BSR Filter. Fig. 9 shows the image of the Brillouin frequency spectrum from 695 m to 845 m along the fiber in case 2. The image contains 200 × 300 data points. Fig. 9(a) and (b) are ideal data and noise data, respectively. And Fig. 9(c) and (d) are the filtering results by applying BSR Filter and NLM Filter on Fig. 9(b), respectively. The contrast ratio in Fig. 9(c) is slightly higher than that in Fig. 9(d), so the central portion of the
Fig. 9. Image of the Brillouin frequency spectrum as a function of distance in case 2: (a) Image of ideal data, (b) Image of noise data, (c) Image obtained by BSR Filter and (d) Image obtained by NLM Filter.
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Optics and Lasers in Engineering 125 (2020) 105865
Fig. 10. The resulting BFS distribution from 695 m to 840 m obtained by BSR Filter and NLM Filter in case 2. (For interpretation of the references to color in this figure text, the reader is referred to the web version of this article.)
Table 2 Comparison of filtering effect parameters in Case 2.
SSIM RMSD of BFS(MHz) Spatial resolution(m) Processing Time(s)
Ideal data
Original noisy data
Using BSR filter
Using NLM filter
1 0 0.4 –
0.15 0.85 0.4 –
0.68 0.60 0.4 11.76
0.54 1.05 1.5 54.59
Brillouin frequency spectrum is much cleaner. The two boundary lines of the temperature region are much clearer in the filtered image by BSR Filter than that by NLM Filter. Fig. 10 illustrates BFS distribution from 695 m to 845 m obtained by use of BSR Filter and NLM Filter. It’s clear that the degree of BFS fluctuation by BSR Filter (blue curve) is lower than by NLM Filter (green curve). The spatial resolution is also worse by NLM. Table 2 shows the comparison of filtering effect parameters of the case 2. The SSIM is 0.15 for original noisy data, but it effectively increased to 0.68 by BSR Filter and 0.54 by NLM Filter. For RMSD of BFS, the value changed from 0.85 MHz to 0.60 MHz by BSR Filter, and it is changed to 1.05 MHz by NLM filter. The spatial resolution for ideal data and original noisy data is 0.4 m. As it is same as that in case 1, the spatial resolution retains 0.4 m by BSR Filter, but deteriorates to 1.5 m by NLM Filter. The processing time for the entire image with 200 × 2000 data points is 11.76 s by BSR Filter and 54.59 s by NLM Filter. As for the case 2, we therefore achieve a BFS measurement accuracy improvement of 43%, a spatial resolution improvement of 275% and a processing time reduce of 78% by using the proposed filtering method,
as compared with the NLM Filter. The spatial resolution is deteriorated by the use of NLM filter. What impressive is, in a complex situation, the BSR Filter can also maintain the high stability of the RMSD of BFS and achieve significant reduce in the computation time. What interesting is the RMSD of BFS by using NLM Filter is even worse than the noisy data. The reason for that is the NLM Filter is tended to confuse temperature boundaries especially under the complex temperature circumstance. In the two simulation cases, one desktop platform with Intel i3–7100 (3.9 GHz) and 8 GB RAM was used. From the filtering results in the two cases, it’s clear that the proposed method can achieve better results than that of the NLM Filter. 4. Experimental results and discussion We use a BOTDR setup to measure the Brillouin frequency spectrum along a 5.2 km bend-insensitive (G657) fiber. The 50 m fiber section at the location of 4.06 km is heated to 60 °C inside one oven. The experiment setup of the BOTDR system is shown in Fig. 11. A continuouswave (CW) light from a laser, operating at 1549.96 nm with 10 dBm
Fig. 11. Experimental setup of a BOTDR sensor. EDFA: erbium-doped fiber amplifier; AOM: acousto-optic modulator; FBG: fiber Bragg grating; LO: local oscillator; PC: polarization controller; EOM: electro-optic modulator; PS: polarization scrambler; PD: photodiode.
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Fig. 12. (a) Brillouin frequency spectrum with 5000 AVG, (b) Brillouin frequency spectrum with 256 AVG.
output power and 5 kHz linewidth, is split into distinct branches through a 30/70 optical fiber coupler. In the branch used as the pump light, the light is first amplified by an erbium doped fiber amplifier (EDFA), then a high extinction-ratio (>40 dB) AOM driven is used to generate a 60 ns pulse, and launched into the fiber via a circulator to generate the Brillouin backscattered light. A fiber Bragg grating (FBG) with 3.5 GHz bandwidth is then used to filter the ASE noise. In another branch used as the local oscillator, the EOM is driven by a microwave generator with the frequency of about 8.9 GHz, to generate the reference CW light. Finally, the two branches are combined together via a 50/50 optical fiber coupler and send to a 1.6 GHz bandwidth photodetector (PD). The data sampling rates in the measurement is 123 MSample/s, corresponding to the sampling interval of 0.81 m per point. There are 6350 sampling points, and at each point there are 54 scanning frequencies at a step of 3 MHz. It should be noted that we use a wide pulse width of 60 ns to obtain more sampling points at the BFS rising or falling transition section, so as to evaluate the spatial resolution degradation caused by different filtering methods. In this measurement, we obtain two sets of raw data which contains 54 × 6350 data points. As it shown in Fig. 12(a), a measurement data with 5000 averaging (AVG) is served as a reference for comparison. While in Fig. 12(b), another measurement data with 256 AVG is used
Fig. 13. Images of the Brillouin frequency spectrum as a function of distance in the heated section: (a) image of 5000 AVG, (b) images of 256 AVG, (c) image obtained by using BSR Filter, and (d) image obtained by using NLM Filter.
for verifying the filtering effect of the proposed algorithm. For NLM Filter, the size of similarity window is set as 2 × 2, h equals 3 and search window is 5 × 5. While for BSR Filter, the size of similarity window is set as 2 × 2, h equals 3 and search window is 3 × 6. Fig. 13 shows the images which contains 54 × 120 data points from 4040 m to 4135 m along the fiber. Fig. 13(a) and (b) are the images
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Optics and Lasers in Engineering 125 (2020) 105865
Fig. 14. The BFS distribution obtained by BSR Filter and NLM Filter.
Table 3 Comparison of filtering effect parameters in experiment.
SSIM RMSD of BFS (MHz) Spatial resolution(m) Processing Time(s)
5000 AVG data
256 AVG data
Using BSR Filter
Using NLM Filter
1 0.09 6.3 –
0.63 1.72 12.9 –
0.94 0.63 6.9 2.43
0.95 0.71 9.8 3.72
obtained by 5000 and 256 AVG, respectively. The resulting image with noise-filtered by BSR Filter and NLM Filter are shown in Fig. 13(c) and (d), respectively. The contrast ratio in Fig. 13(c) is slightly higher than that in Fig. 13(d), so the central portion of the Brillouin frequency spectrum is much cleaner. The boundary lines of the temperature are much clearer in the filtered image by using BSR Filter than that by using NLM Filter. By using the proposed noise filter method, we can obtain the BFS distribution along the 5.2 km fiber. Fig. 14 demonstrate the results by use of BSR and NLM filters and 5000 and 256 AVG filters. Note that the BFS curve has two dips near 1.8 km and 3.9 km, which is due to residual strain in the two sections of the fiber. Overall, the results of the BSR and NLM filtering are not much different. However, it can be seen from the heated section in the inset figure that the BSR filtering result is better than that of the NLM filter. The inset figure illustrates the results around the 50 m heated section. The BFS uncertainty from 4075 m to 4105 m of the 256 AVG data is 1.72 MHz, and it is reduced to 0.62 MHz by using BSR Filter and 0.71 MHz by using NLM Filter. The main reason for the better accuracy obtained by using BSR Filter is the flexible selection of the search window size. At the same time, the shift of Brillouin frequency spectrum data is also able to reduce the deterioration of spatial resolution. Table 3 shows the comparison of filtering effect parameters of the case 2. The SSIM is 0.63 for original noisy data, which is increased to 0.94 by BSR Filter and 0.95 by NLM Filter. For RMSD of BFS, the value decreases from 1.72 MHz to 0.63 MHz by BSR Filter, and it is changed to 0.71 MHz by NLM filter. The spatial resolution of the BSR Filter is 6.9 m. Although it is slightly worse than the 6.3 m for 5000 AVG, it is better than the 12.9 m for 256 AVG and the 9.8 m for NLM filter. Therefore, the region division doesn’t change the original spatial resolution and preserve it in a large extent. Besides, the processing time for the entire image with 54 × 6350 data points is 2.43 s by BSR Filter and 3.72 s by NLM Filter. It should be note that the processing speed of experiment is faster than that of simulation because of the search windows size of
experiment is smaller than that of simulation. Since the number of frequency sampling point (m = 54) in experimental data is smaller than that (m = 200) in simulation data and the search windows size is limited by the number of frequency sampling point, the degree of time-saving in the experiment (35%) is lower than that in the simulation (78% in the two cases). In Table 3, we can find that the BSR Filter works well in the fiber sensing experiment. The value of SSIM is nearly the same for BSR Filter and NLM Filter. When comparing with the results obtained by NLM Filter, more effective similar windows with higher similarity participate in the denoising process, which filters noise more effectively and thus offers a BFS measurement accuracy improvement of 13% (The value of 0.09 MHz corresponding to 5000 AVG is taken as the reference). Besides, a spatial resolution improvement of 46% can be achieved due to the edge-preserving image filtering strategy by use of the region division (The value of 6.3 m corresponding to 5000 AVG is taken as the reference). Meanwhile, the reassembled image obtained by BSR Filter contains only noise and Brillouin spectrum information, so the edge preservation operation is removed, and the filter window size is reduced from 5 × 5 to 3 × 6. The above two reasons decrease the processing time by 35%. 5. Conclusion In conclusion, we propose and verify a novel image processing based noise reduction method in Brillouin optical time domain sensors. The new BSR filter combines region division, image reassembly and conventional filter. Simulation and experimental results show that the proposed method can be used as an excellent noise filter, to effectively remove noise and thus can enhance the measurement performance of distributed Brillouin fiber sensors with a shorter process time. The experimental results have shown that a BFS measurement accuracy improvement of 13%, a spatial resolution improvement of 46% and a processing time reduce of 35% can be achieved in a 5.2 km length G657 fiber by using
Y. Zhang, Y. Lu and Z. Zhang et al.
the proposed filtering method, as compared with the Non-Local Means (NLM) Filter. Funding This work was supported by National Natural Science Foundation of China (NSFC) (61875086, 61377086) and Aerospace Science Foundation of China (2016ZD52042). Declaration of Competing Interest None. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.optlaseng.2019.105865. References [1] Bao X, Chen L. Recent progress in distributed fiber optic sensors. Sens (Switz) 2012;12:8601–39. doi:10.3390/s120708601. [2] Motil A, Bergman A, Tur M. State of the art of Brillouin fiber-optic distributed sensing. Opt Laser Technol 2016;78:81–103. doi:10.1016/j.optlastec.2015.09.013. [3] Zhang H, Zhou D, Wang B, Pang C, Xu P, Jiang T, et al. Recent progress in fast distributed Brillouin optical fiber sensing. Appl Sci 2018;8:1820. doi:10.3390/app8101820. [4] Zhang D, Cui H, Shi B. Spatial resolution of DOFS and its calibration methods. Opt Lasers Eng 2013;51:335–40. [5] Horiguchi T, Kurashima T, Tateda M. Tensile strain dependence of Brillouin frequency shift in silica optical fibers. IEEE Photonics Technol Lett 1989;1:107–8. [6] Wylie MT V, Brown AW, Colpitts BG. Distributed hot-wire anemometry based on Brillouin optical time-domain analysis. Opt Express 2012;20:15669–78. doi:10.1364/OE.20.015669. [7] Zhou D, Dong Y, Wang B, Pang C, Ba D, Zhang H, et al. Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement. Light Sci Appl 2018;7:32. [8] Diakaridia S, Pan Y, Xu P, Zhou D, Wang B, Teng L, et al. Detecting cmscale hot spot over 24-km-long single-mode fiber by using differential pulse pair BOTDA based on double-peak spectrum. Opt Express 2017;25:17727–36. doi:10.1364/OE.25.017727. [9] Dong Y, Wang B, Pang C, Zhou D, Ba D, Zhang H, et al. 150km fast BOTDA based on the optical chirp chain probe wave and Brillouin loss scheme. Opt Lett 2018;43:4679–82. doi:10.1364/OL.43.004679. [10] Dong Y, Chen L, Bao X. Time-division multiplexing-based BOTDA over 100km sensing length. Opt Lett 2011;36:277–9. doi:10.1364/OL.36.000277. [11] Li W, Bao X, Li Y, Chen L. Differential pulse-width pair BOTDA for high spatial resolution sensing. Opt Express 2008;16:21616–25. doi:10.1364/OE.16.021616. [12] Li Z, Yan L, Shao L, Pan W, Luo B, Liang J, et al. Precise Brillouin gain and phase spectra measurements in coherent BOTDA sensor with phase fluctuation cancellation. Opt Express 2016;24:4824–33. doi:10.1364/OE.24.004824. [13] Qian X, Wang Z, Wang S, Xue N, Sun W, Zhang L, et al. 157km BOTDA with pulse coding and image processing. In: Sixth eur. work. opt. fibre sensors, 9916. International Society for Optics and Photonics; 2016. p. 99162. [14] Kurashima T, Horiguchi T, Izumita H, Furukawa S, Koyamada Y. Brillouin optical– fiber time domain reflectometry. IEICE Trans Commun 1993;76:382–90. [15] Li M, Jiao W, Liuwu X, Song Y, Chang L. A method for peak seeking of BOTDR based on the incomplete Brillouin spectrum. IEEE Photonics J 2015;7:1–10.
Optics and Lasers in Engineering 125 (2020) 105865 [16] Lu Y, Li C, Zhang X, Yam S. Determination of thermal residual strain in cabled optical fiber with high spatial resolution by Brillouin optical time-domain reflectometry. Opt Lasers Eng 2011;49:1111–17. doi:10.1016/j.optlaseng.2011.05.015. [17] Li M, Jiao W, Zhang X, Song Y, Qian H, Yu J. An algorithm for determining the peak frequency of botdr under the case of transient interference. IEEE J Sel Top Quantum Electron 2017;23:269–73. [18] Luc T, Stella Foaleng M, Jie L. Effect of pulse depletion in a Brillouin optical time– domain analysis system. Opt Express 2013;21:14017–35. [19] Liang H, Li W, Linze N, Chen L, Bao X. High-resolution DPP-BOTDA over 50km leaf using return-to-zero coded pulses. Opt Lett 2010;35:1503–5. [20] Lu Y, Bao X, Chen L, Xie S, Pang M. Distributed birefringence measurement with beat period detection of homodyne Brillouin optical time-domain reflectometry. Opt Lett 2012;37:3936–8. [21] Li C, Lu Y, Zhang X, Wang F. SNR enhancement in Brillouin optical time domain reflectometer using multi-wavelength coherent detection. Electron Lett 2012;48:1139–41. [22] Zhang Z, Lu Y, Zhao Y. Channel capacity of wavelength division multiplexing-based Brillouin optical time domain sensors. IEEE Photonics J 2018;10:1–15. [23] Farahani MA, Castillo-Guerra E, Colpitts BG. A detailed evaluation of the correlationbased method used for estimation of the Brillouin frequency shift in BOTDA sensors. IEEE Sens J 2013;13:4589–98. doi:10.1109/JSEN.2013.2271254. [24] He H, Shao L, Li H, Pan W, Luo B, Zou X, et al. SNR enhancement in phase-sensitive OTDR with adaptive 2-D bilateral filtering algorithm. IEEE Photonics J 2017;9:1–10. doi:10.1109/JPHOT.2017.2700894. [25] Wu H, Wang L, Zhao Z, Guo N, Shu C, Lu C. Brillouin optical time domain analyzer sensors assisted by advanced image denoising techniques. Opt Express 2018;26:5126. doi:10.1364/oe.26.005126. [26] Qin Z, Chen H, Chang J. Detection performance improvement of distributed vibration sensor based on curvelet denoising method. Sens (Switz) 2017;17:1380. doi:10.3390/s17061380. [27] Farahani MA, Wylie MTV, Castillo-Guerra E, Colpitts BG. Reduction in the number of averages required in BOTDA sensors using wavelet denoising techniques. J Light Technol 2012;30:1134–42. doi:10.1109/JLT.2011.2168599. [28] Qin Z, Chen L, Bao X. Wavelet denoising method for improving detection performance of distributed vibration sensor. IEEE Photonics Technol Lett 2012;24:542–4. doi:10.1109/LPT.2011.2182643. [29] Zhao Z, Tang M, Wang L, Fu S, Tong W, Lu C. Enabling simultaneous DAS and DTS measurement through multicore fiber based space-division multiplexing. 2018 Optical Fiber Communications Conference and Exposition (OFC); 2018. W2A.7 https://doi.org/10.1364/ofc.2018.w2a.7 . [30] Soto MA, Ramírez JA, Thévenaz L. Intensifying the response of distributed optical fibre sensors using 2D and 3D image restoration. Nat Commun 2016;7:1–11. doi:10.1038/ncomms10870. [31] Soto MA, Ramirez JA, Thevenaz L. Optimizing image denoising for long-range Brillouin distributed fiber sensing. J Light Technol 2018;36:1168–77. [32] Qian X, Jia X, Wang Z, Zhang B, Xue N, Sun W, et al. Noise level estimation of BOTDA for optimal non-local means denoising. Appl Opt 2017;56:4727. doi:10.1364/ao.56.004727. [33] Maini R, Aggarwal DH. Study and comparison of various image edge detection techniques. Int J Image Process 2009;3:1–11. [34] Deng G, Cahill LW. An adaptive Gaussian filter for noise reduction and edge detection. Nucl. Sci. Symp. Med. Imaging Conf.; 1993. [35] Buades A, Coll B, Morel J-M. A non-local algorithm for image denoising. In: 2005 IEEE Comput Soc Conf Comput Vis Pattern Recognit, 2; 2005. p. 60–5. doi:10.1109/CVPR.2005.38. [36] Brox T, Kleinschmidt O, Cremers D. Efficient nonlocal means for denoising of textural patterns. IEEE Trans Image Process 2008;17:1083–92. doi:10.1109/TIP.2008.924281. [37] Froment J. Parameter-Free fast pixelwise non-local means denoising. Image Process Line 2014;4:300–26. doi:10.5201/ipol.2014.120. [38] Wang Z, Bovik AC, Sheikh HR, Simoncelli EP. Image quality assessment: from error visibility to structural similarity. Image Process IEEE Trans 2004;13:600–12. [39] Lehmann EL, Casella G. Theory of point estimation 2006.
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Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Noise reduction by Brillouin spectrum reassembly in Brillouin optical time domain sensors Yuyang Zhang a,b, Yuangang Lu a,b,∗, Zelin Zhang a,b, Jiming Wang b, Chongjun He a,b, Tong Wu a,b a b
College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
a r t i c l e KeyWords: Brillouin sensor Image processing Noise reduction
i n f o
a b s t r a c t In this paper, we present a novel image-processing based spectrum reassembly method to handle the noisy Brillouin gain or loss spectrum in Brillouin optical time domain sensors. The principle of the proposed Brillouinspectrum-reassembly (BSR) Filter, is firstly dividing the Brillouin spectrum along the fiber into several segments according to the differences of Brillouin frequency shift (BFS), then shifting the Brillouin spectrum to reassemble a new image with equal BFSs and filtering the image by a conventional filter, finally shifting the Brillouin spectrum of each segment in the opposite direction to obtain the filtered Brillouin spectrum. Since the size of the filter windows in the reassembled image can be reduced greatly, the total processing time is decreased effectively. Furthermore, the BFS measurement accuracy and spatial resolution can be enhanced due to the edge-preserving image filtering strategy of the method. The measurement performance and processing speed improvements are verified by simulation and experiment. Utilizing a Brillouin optical time domain reflectometry (BOTDR) sensor, we achieve a BFS measurement accuracy improvement of 13%, a spatial resolution improvement of 46% and a processing time reduce of 35% in a 5.2 km-length G657 fiber by use of the proposed method, as compared with an excellent spectrum non-reassembly filtering method.
1. Introduction Distributed Brillouin fiber sensors attract many research interests [1– 4], due to their immunity to electromagnetic interference, large sensing range over tens of kilometers, and capabilities of simultaneous temperature and strain measurements. In distributed Brillouin fiber sensors, two time-domain techniques are widely studied: (a) Brillouin optical time-domain analysis (BOTDA) based on stimulated Brillouin scattering (SBS) [5–13]; (b) Brillouin optical time-domain reflectometry (BOTDR) based on spontaneous Brillouin scattering (SpBS) [14–17]. Various techniques have been proposed to improve the performance of Brillouin optical time domain sensors. Among several advanced techniques, methods such as double-sideband probe scheme [18] and optical pulse coding [19] lead better performance than traditional standard configurations in BOTDA. On the other hand, the measurement of Brillouin beat spectrum in BOTDR [20] and using multi-wavelength detection [21,22] can adequately reduce the operating time and enhance the measurement accuracy in the BOTDR systems. Recently techniques based on image processing [23–26] have been proposed to enhance the performance of distributed Brillouin and Rayleigh scattering-based fiber sensors. Two main denoising techniques, wavelet denoising (WD) [27–29] and non-local means (NLM) [30–32], ∗
have been proposed to improve the accuracy, and attracted lots of attention as they would not add any hardware complexity. Although the aforementioned methods are quite effective, these methods are more or less computationally inefficient, and some of them may deteriorate the measurement spatial resolution. Therefore, it is significate to explore more efficient and more robust image processing methods for Brillouin optical time domain sensors. In the paper, we propose a novel Brillouin-spectrum-reassembly (BSR) Filter to remove noise from the data with high quality and efficiency. In this paper the Brillouin spectrum refer not only to Brillouin gain spectrum in BOTDR but also to Brillouin gain or loss spectrum in BOTDA. The principle of the proposed BSR Filter, is firstly dividing the Brillouin spectrum along the fiber into several segments according to the difference of Brillouin frequency shift (BFS), then shifting the Brillouin spectrum to reassemble a new image with equal BFSs and filtering the image by a conventional filter, finally shifting the Brillouin spectrum of each segment in the opposite direction to obtain the filtered Brillouin spectrum. The advantage of the BSR Filter is that filter window size can be reduced greatly, thus decreasing the processing time. Meanwhile, more similar windows with higher similarity participate in the denoising process, which filters noise more effectively and thus improves the BFS measurement accuracy. Besides, the spatial resolution can be
Corresponding author at: College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu 211106, China E-mail address: [email protected] (Y. Lu).
https://doi.org/10.1016/j.optlaseng.2019.105865 Received 7 May 2019; Received in revised form 11 August 2019; Accepted 16 September 2019 0143-8166/© 2019 Elsevier Ltd. All rights reserved.
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Optics and Lasers in Engineering 125 (2020) 105865
Fig. 1. Flowchart of the denoising algorithm. Fig. 2. Flowchart of the region division method.
preserved well due to the edge-preserving image filtering strategy by use of the region division. Simulation and experimental results verify the validity and feasibility of the proposed noise filtering method. To the best of our knowledge, this is the first time that the BFS characteristics of the Brillouin scattering signal are effectively applied to the image filtering algorithm, which can effectively improve the performance of the Brillouin optical time domain sensors. This may open up a new way to improve the performance of Brillouin signal processing methods based on digital image processing. 2. Method In the following sections, we demonstrate how to achieve noisy data reduction, through the proposed BSR Filter. Fig. 1 illustrates the flowchart of the denoising algorithm. Besides the three main steps of the BSR Filter, another two steps, data acquisition and results display, are also shown in the flowchart. (1) Data Acquisition: During the step, a 2D matrix containing the Brillouin frequency spectrum at each sampled location x is obtained by using the acquisition system of the Brillouin optical time domain sensors. If there are n sample points along the fiber and m frequency points at each sampling location, the original data image with n × m pixels and with gray values in the range [0, 255] is generated from the 2D matrix which contains N = n × m data points. (2) Region Division: By using edge detection, the positions where BFS varies dramatically can be detected, and thus the original image is divided into the different regions (subimages) along the x direction. The Brillouin frequency spectrums in each subimage contain nearly the same BFS. (3) Spectrum Reassembly: Shifting the Brillouin spectrum in each subimage to reassemble a new image where all the values of BFSs are equal. In the reassembled image, the image similarity is improved and thus the size of filter window can be decreased. (4) Image Filtering: Filtering the reassembled image by a conventional filter, and shifting the Brillouin spectrum of each subimage in the opposite direction to obtain the filtered Brillouin spectrum. (5) Results Display: Fitting the Brillouin spectrum with a Lorentzian curve, the BFS information along the entire sensing fiber is thus obtained and displayed. 2.1. Region division In the original data image, the position of the BFS change exhibits a change in the gray values, and two boundary lines parallel to the y direction are formed in the image. The larger the BFS change, the longer the boundary lines are formed. By using the edge detection algorithm, the position of the boundary lines can be effectively determined, and the entire data image can be partitioned according to different BFSs. Fig. 2. illustrates the flowchart of the region division. The four steps of region division are as follows: (1) Gaussian Filtering: Applying Gaussian filter to the entire original gray image. Note that the Gaussian filter is only for edge detection.
(2) LoG Edge Detection: Using the Laplacian of Gaussian (LoG) edge detection algorithm [33] to obtain the edges of the regions with appreciably changed BFS. (3) Line Search: The obtained lines are identified by the line search algorithm we will describe below. (4) Location Report: Report the location of edges which indicated the boundary lines between the regions. Fig. 3(a) is an example of noisy Brillouin frequency spectrum along a 150 m length of fiber, and the range of BFS is from 10.5 GHz to 10.7 GHz. The corresponding original data image is shown in Fig. 3(b). In the range from 75 m to 85 m, there is a BFS change. We use Gaussian filter [34] before LoG edge detection, as edge detection methods rely on smoothing filters before processing. The computational complexity of the Gaussian filter is O(Ns2 ), where the N is the total number of points in the image, and s is the size of the filter kernel. In the step of line search, we propose an algorithm to locate the lines which represent the start and end locations of the regions. First, we divide the whole image into several small search windows of u × v (As that shown in the red window in Fig. 3(c), the total number of points within the window is M = u × v), then count the number of white points in the window. After that, the maximum number on each column is record. Finally, the column with the largest number is found. The column with the large number indicates the position of the line (In this example, the number should be larger than 15). The red dotted line in Fig. 3(c) indicates the edge of dramatically varied BFS regions. By this method, it is efficiently find out the position where the straight line, thus the original image can be divided into the different segments along the x direction according to these positions with rapidly changing gray level. The complexity of this method is O(NM), where the N and M are the total number of points within the image and the window, respectively. 2.2. Spectrum reassembly and image filtering After performing region division, we reassemble Brillouin spectrum and filter the reassembled noisy image by a conventional filter. The process of Brillouin spectrum reassembly can effectively reduce the size of the search window while preserving spatial resolution. The main idea is to make the similar frequency spectrum as close as possible by shifting and aligning the Brillouin frequency spectrums within different regions found in region division process. In the following, we describe the process of Spectrum Reassembly and Image Filtering in detail. In Fig. 4 we have drawn a set of diagram to illustrate the steps of Spectrum Reassembly and Image Filtering in BSR filter. The abscissa represents the detection distance, and the ordinate represents the BFS. In this example, there are 5 subimages in the image with n rows and m columns (n = 9 and m = 12 in Fig. 4). The BFSs of the leftmost and rightmost subimages are equal to the averaged BFS of the entire image. The BFSs of the middle three subimages deviate from the averaged BFS of the entire image. Taking the image as an example, the remaining four steps of the BSR Filter is described as following. Spectrum Reassembly
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Fig. 3. (a) An example of noisy Brillouin frequency spectrum along the fiber, (b) Original data image corresponding to (a), (c) Edge detection result of data image. (For interpretation of the references to color in this figure text, the reader is referred to the web version of this article.)
consists of steps (1) and (2), while Image Filtering contains steps (3) and (4). (1) Fit the measured Brillouin spectrum: By fitting one of the measured Brillouin spectrum in each subimage with a Lorentzian curve, the peak frequency of each subimage can be obtained. The obtained peak frequencies correspond to the pixels with the highest gray value in the same subimage, which are shown as the red dotted lines in Fig. 4(a). According to the number of Brillouin spectrums in each region, we calculate the average peak frequency of them (In this example, the peak frequency of the middle three subimages are respectively f2 , f3 and f4 , and the peak frequency of two other subimages are f1 . The average peak frequency favg is obtained by computing a weighted average of peak frequency in all regions according to the Brillouin spectrums number and peak frequency of each region). The accuracy of BFS in the transition area is related to the length of the subimage. The transition region is needed to be divided into several subimages that are as small as possible, so that the error in the alignment of the spectrum center can be reduced. The number of divided subimages depends on the accuracy of the subimages detection. To some extent the BFS of the transition area can be regarded as unreliable information. As long as the start and end points of the transition area can be correctly found in subimages detection procedure, the method wouldn’t impact the sensing system performance. (2) Shift the Brillouin spectrum: Subtracting the averaged peak frequency from the respective peak frequency in each subimage, thus the results are the shift values of Brillouin spectrum within each subimage (In this example, the shift values of the middle three subimages are respectively d1 (d1 = favg -f2 ), d2 (d2 = favg -f3 ) and
d3 (d3 = favg -f4 ), and the shift values of two other subimages are 0. The maximum shift value of the upward and downward movement are respectively du and dd , and their sum is dy (In this example, the du and dd are respectively d3 and d1 ). Next, filling the uneven image boundaries (the bule parts in Fig. 4(b)), the gray values of the filled parts are copied from that minimum values in the same column. Finally, we get an image (Fig. 4(c)) that will be used for denoising. Since the values of the expanded parts are almost equal to the noise floor, the denoising of Fig. 4(c) will not affect the BFS information. (3) Entire image denoising by a conventional filter: In this step, any conventional filter can be used to filter the noise in reassembled image. In this paper, we use an excellent conventional non-reassembly filter, Non-Local Means (NLM) Filter [35–37], to filter reassembled image. However, in our algorithm the size of filter windows can be decreased greatly, compared to that in the conventional NLM Filter applied on non-reassembly Brillouin spectrum image. In reassembled image (Fig. 4(c)), due to the distance of different similarity window with high similarity is fairly close, the search window size (p × q) can be set small enough. Specifically, if the conventional NLM filter search window size is w × w, when it is applied on non-reassembly Brillouin spectrum image the p depends on frequency sampling point and can be set less than w, while q depends on measurement accuracy requirement and it needs to be set to a value larger than or equal to w. Meanwhile, the value of p × q is less than w2 . The p and q value are related to the sensing system, and there are different optimal values in different sampling rate systems according to the measurement accuracy requirement. In general, when the frequency sampling interval is larger than 1 MHz, p < 0.7 w, q ≥ 1.1 w, and p × q < 0.75w2 , otherwise p < 0.25 w, q ≥ w, and p × q < 0.3w2 .
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Fig. 4. Process interpretation diagram of Spectrum Reassembly and Image Filtering in BSR filter. (a) Original image with 5 subimages. The peak frequency location in each subimages is shown as red dotted line. The thicker red dotted line denotes averaged peak frequency of the entire image. d1 , d2 and d3 denote the frequency shift value of the subimages. (b) Image after shifting the Brillouin spectrum in subimages. The gray values of blue regions will be set as the minimum values in the same column to fill the uneven image boundaries. (c) Use a conventional filter to denoise the entire image with the search window of p × q.(d) Image after denoising and the some subimages will be shifted back. (e) Resulting image consists of 5 noise filtered subimages. (For interpretation of the references to color in this figure text, the reader is referred to the web version of this article.)
(4) Restore the Brillouin spectrum: The subimages shift in Spectrum Reassembly will be shifted back (Fig. 4(d)), and the resulting image (Fig. 4(e)) can be obtained. The computational complexity of the Spectrum Reassembly is O(Ns2 + M N +em + ndy ), where e is the number of the subimages. Thus the total computational complexity of the BSR Filter is O(Ns2 + MN + em + ndy ) + O(Filter). The computational complexity of Image Filtering depends on the specific denoising method. In the case of NLM filter [35–37], O(Filter) = O((N + ndy )d2 pq), where d2 is similarity window size, pq is the search window size. It should be noted that, if we use the NLM filter in the proposed BSR Filter as the image filter, as it mentioned above, it wouldn’t increase the processing overhead because the total computational complexity of the BSR Filter O(Ns2 + MN + em + ndy )+O((N + ndy )d2 pq) is lower than that of conventional NLM Filter, which is O(Nd2 w2 ). As the values of w2 and its corresponding pq increase, the processing efficiency enhancement of BSR filter increases. Comparing the proposed method with wavelet denoising, we find that the measurement accuracy and experimental spatial resolution will deteriorate if we use wavelet denoising to pursue high denoising effects. This is because the high denoising effects is achieved at the expense of sacrificing the sensing data details [25]. On the contrary, in the proposed BSR Filter, the data details are preserved well without being affected by denoising process.
2.3. Evaluation criteria Three quantitative measures of the image are used to estimate the filtering quality in this paper. They are Structural Similarity index (SSIM) [38], root mean square deviation (RMSD) [39] of BFS and spatial resolution. The spatial resolution is obtained by calculating 10–90% rise time of a transition of BFS [1]. SSIM is a similarity measure between two images and can be expressed as ( )( ) 2𝜇𝑝 𝜇𝑞 + 𝑐1 2𝜎𝑝𝑞 + 𝑐2 𝑆 𝑆 𝐼 𝑀 (𝑝, 𝑞 ) = ( (1) )( ) 𝜇𝑝 2 + 𝜇𝑞 2 + 𝑐 1 𝜎 𝑝 2 + 𝜎 𝑞 2 + 𝑐 2 where 𝜇 p and 𝜇 q are respectively the mean of p and q, 𝜎 p 2 and 𝜎 q 2 are respectively the variance of p and q, and 𝜎 pq is the covariance between p and q. In Eq. (1) 𝑐1 = (𝑘1 𝐿)2 and 𝑐2 = (𝑘2 𝐿)2 where L is the dynamic range of the pixel-values, k1 equals 0.01 and k2 equals 0.03 by default. The resultant SSIM index is a decimal value between 0 and 1, and value 1 is only reachable in the case of two identical sets of data and therefore indicates perfect structural similarity. RMSD of the BFS evaluates the difference of the BFS along the fiber between the filtered and ideal data, which can be given by √ )2 1 ∑𝑛 ( 𝑀𝑆𝐷 𝑜𝑓 𝐵𝐹 𝑆 = (2) 𝑓𝑖 − 𝑓𝑖𝑑𝑒𝑎𝑙 𝑖=1 𝑛 where n is the sampling points of the x-axis in the processed image, fi is the BFS of the ith sampling point of the filtered image, and the fideal is
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Fig. 5. (a)Ideal Brillouin frequency spectrum along 1 km length fiber with single and complex temperature, (b) The corresponding 2-D digital gray image of (a), (c) The Brillouin frequency spectrum which is corresponding to (a) and corrupted by Gaussian noise along the fiber, (d) The corresponding 2-D digital gray image of (c).
the ideal BFS in the same location. RMSD of BFS is always non-negative, and values closer to zero are better. 3. Simulation results and discussion Fig. 5 shows an image of the Brillouin frequency spectrum along the sensing fiber in numerical simulation experiments, which contain a single BFS change section (corresponding to the mark of the single temperature) and a complex BFS change section (corresponding to the mark of complex temperature). The image contains 200 × 2000 data points with 200 scanning frequencies from 10.5 GHz to 10.7 GHz, and with 2000 sample points along 1 km fiber, corresponding to the sampling interval of 0.5 m per point. Fig. 5(a) is the ideal Brillouin frequency spectrum data which served as ideal data, and Fig. 5(b) is the corresponding 2-D digital gray image. Fig. 5(c) is the Brillouin frequency spectrum which is corresponding to (a) and corrupted by Gaussian noise along the fiber, and Fig. 5(d) is its corresponding 2-D digital gray image. Fig. 6 shows the optical power traces along the fiber at two different frequencies of 10.54 GHz and 10.6 GHz. It can be seen from the figure that the noise is large and it is difficult to distinguish the positions where the single and complex temperature change. The purpose of the region with complex temperature change is to evaluate the performance of denoising filter in real application. Numerical simulation experiments were carried out under two simulated experimental conditions. In the case 1, a 5 m fiber section from
347.5 m to 352.5 m under a single temperature will be studied. While in the case 2, a 130 m fiber section from 635 m to 765 m under the complex temperature will be studied. This arrangement imitates practical situations of different temperature at different locations, which compare the difference of filtering performance between BSR Filter and NLM Filter under different conditions. According to [24], for NLM Filter, the size of similarity window is set as 3 × 3, h equals 12 and search window size is 20 × 20, where h is a smoothing control parameter. For BSR Filter, the size of similarity window is set as 3 × 3, h equals 12 and search window size is 4 × 20. Fig. 7 shows the image of the Brillouin frequency spectrum from 275 m to 425 m along the fiber in case 1. The image contains 200 × 300 data points. Fig. 7(a) and (b) are ideal data and noise data, respectively. And Fig. 7(c) and (d) are the filtering results by applying BSR Filter and NLM Filter on Fig. 7(b), respectively. The contrast ratio in Fig. 7(c) is slightly higher than that in Fig. 7(d), so the central portion of the Brillouin frequency spectrum is much cleaner. The two boundary lines of the temperature region are much clearer in the filtered image by BSR Filter than that by NLM Filter. Fig. 8 illustrates BFS distribution from 340 m to 365 m obtained by use of BSR Filter and NLM Filter. It’s clear that the degree of BFS fluctuation by BSR Filter (blue curve) is lower than by NLM Filter (green curve). The spatial resolution is also slightly worse by NLM. Table 1 shows the comparison of filtering effect parameters of the case 1. The SSIM is 0.13 for original noisy data, which is increased to
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Optics and Lasers in Engineering 125 (2020) 105865
Fig. 6. Optical power traces along the fiber at two different frequencies.
Fig. 7. Image of the Brillouin frequency spectrum from 275 m to 425 m along the fiber in case 1. (a) Image of ideal data, (b) Image of noise data, (c) Image obtained by using BSR Filter, (d) Image obtained by using NLM Filter.
Table 1 Comparison of filtering effect parameters in Case 1.
SSIM RMSD of BFS(MHz) Spatial resolution(m) Processing Time(s)
Ideal data
Original noisy data
Using BSR filter
Using NLM filter
1 0 0.4 –
0.13 0.84 0.4 –
0.59 0.32 0.4 9.75
0.53 0.56 1.5 45.43
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Fig. 8. The BFS distribution from 340 m to 365 m obtained by use of BSR Filter and NLM Filter in case 1. (For interpretation of the references to color in this figure text, the reader is referred to the web version of this article.)
0.59 by BSR Filter and 0.53 by NLM Filter. For RMSD of BFS, the value changed from 0.84 MHz to 0.32 MHz by BSR Filter, and it is changed to 0.56 MHz by NLM filter. The spatial resolution for ideal data and original noisy data is 0.4 m, and it retains 0.4 m by BSR Filter. But the spatial resolution deteriorates to 1.5 m by NLM Filter. The processing time for the entire image with 200 × 2000 data points is 9.75 s by use BSR Filter and 45.43 s by use NLM Filter. We can notice that, in case 1, BSR Filter improve the original noisy data greatly. Furthermore, comparing with the results obtained by NLM
Filter, a BFS measurement accuracy improvement of 43%, a spatial resolution improvement of 275% and a processing time reduce of 78% can be achieved by using the BSR Filter. Fig. 9 shows the image of the Brillouin frequency spectrum from 695 m to 845 m along the fiber in case 2. The image contains 200 × 300 data points. Fig. 9(a) and (b) are ideal data and noise data, respectively. And Fig. 9(c) and (d) are the filtering results by applying BSR Filter and NLM Filter on Fig. 9(b), respectively. The contrast ratio in Fig. 9(c) is slightly higher than that in Fig. 9(d), so the central portion of the
Fig. 9. Image of the Brillouin frequency spectrum as a function of distance in case 2: (a) Image of ideal data, (b) Image of noise data, (c) Image obtained by BSR Filter and (d) Image obtained by NLM Filter.
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Fig. 10. The resulting BFS distribution from 695 m to 840 m obtained by BSR Filter and NLM Filter in case 2. (For interpretation of the references to color in this figure text, the reader is referred to the web version of this article.)
Table 2 Comparison of filtering effect parameters in Case 2.
SSIM RMSD of BFS(MHz) Spatial resolution(m) Processing Time(s)
Ideal data
Original noisy data
Using BSR filter
Using NLM filter
1 0 0.4 –
0.15 0.85 0.4 –
0.68 0.60 0.4 11.76
0.54 1.05 1.5 54.59
Brillouin frequency spectrum is much cleaner. The two boundary lines of the temperature region are much clearer in the filtered image by BSR Filter than that by NLM Filter. Fig. 10 illustrates BFS distribution from 695 m to 845 m obtained by use of BSR Filter and NLM Filter. It’s clear that the degree of BFS fluctuation by BSR Filter (blue curve) is lower than by NLM Filter (green curve). The spatial resolution is also worse by NLM. Table 2 shows the comparison of filtering effect parameters of the case 2. The SSIM is 0.15 for original noisy data, but it effectively increased to 0.68 by BSR Filter and 0.54 by NLM Filter. For RMSD of BFS, the value changed from 0.85 MHz to 0.60 MHz by BSR Filter, and it is changed to 1.05 MHz by NLM filter. The spatial resolution for ideal data and original noisy data is 0.4 m. As it is same as that in case 1, the spatial resolution retains 0.4 m by BSR Filter, but deteriorates to 1.5 m by NLM Filter. The processing time for the entire image with 200 × 2000 data points is 11.76 s by BSR Filter and 54.59 s by NLM Filter. As for the case 2, we therefore achieve a BFS measurement accuracy improvement of 43%, a spatial resolution improvement of 275% and a processing time reduce of 78% by using the proposed filtering method,
as compared with the NLM Filter. The spatial resolution is deteriorated by the use of NLM filter. What impressive is, in a complex situation, the BSR Filter can also maintain the high stability of the RMSD of BFS and achieve significant reduce in the computation time. What interesting is the RMSD of BFS by using NLM Filter is even worse than the noisy data. The reason for that is the NLM Filter is tended to confuse temperature boundaries especially under the complex temperature circumstance. In the two simulation cases, one desktop platform with Intel i3–7100 (3.9 GHz) and 8 GB RAM was used. From the filtering results in the two cases, it’s clear that the proposed method can achieve better results than that of the NLM Filter. 4. Experimental results and discussion We use a BOTDR setup to measure the Brillouin frequency spectrum along a 5.2 km bend-insensitive (G657) fiber. The 50 m fiber section at the location of 4.06 km is heated to 60 °C inside one oven. The experiment setup of the BOTDR system is shown in Fig. 11. A continuouswave (CW) light from a laser, operating at 1549.96 nm with 10 dBm
Fig. 11. Experimental setup of a BOTDR sensor. EDFA: erbium-doped fiber amplifier; AOM: acousto-optic modulator; FBG: fiber Bragg grating; LO: local oscillator; PC: polarization controller; EOM: electro-optic modulator; PS: polarization scrambler; PD: photodiode.
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Fig. 12. (a) Brillouin frequency spectrum with 5000 AVG, (b) Brillouin frequency spectrum with 256 AVG.
output power and 5 kHz linewidth, is split into distinct branches through a 30/70 optical fiber coupler. In the branch used as the pump light, the light is first amplified by an erbium doped fiber amplifier (EDFA), then a high extinction-ratio (>40 dB) AOM driven is used to generate a 60 ns pulse, and launched into the fiber via a circulator to generate the Brillouin backscattered light. A fiber Bragg grating (FBG) with 3.5 GHz bandwidth is then used to filter the ASE noise. In another branch used as the local oscillator, the EOM is driven by a microwave generator with the frequency of about 8.9 GHz, to generate the reference CW light. Finally, the two branches are combined together via a 50/50 optical fiber coupler and send to a 1.6 GHz bandwidth photodetector (PD). The data sampling rates in the measurement is 123 MSample/s, corresponding to the sampling interval of 0.81 m per point. There are 6350 sampling points, and at each point there are 54 scanning frequencies at a step of 3 MHz. It should be noted that we use a wide pulse width of 60 ns to obtain more sampling points at the BFS rising or falling transition section, so as to evaluate the spatial resolution degradation caused by different filtering methods. In this measurement, we obtain two sets of raw data which contains 54 × 6350 data points. As it shown in Fig. 12(a), a measurement data with 5000 averaging (AVG) is served as a reference for comparison. While in Fig. 12(b), another measurement data with 256 AVG is used
Fig. 13. Images of the Brillouin frequency spectrum as a function of distance in the heated section: (a) image of 5000 AVG, (b) images of 256 AVG, (c) image obtained by using BSR Filter, and (d) image obtained by using NLM Filter.
for verifying the filtering effect of the proposed algorithm. For NLM Filter, the size of similarity window is set as 2 × 2, h equals 3 and search window is 5 × 5. While for BSR Filter, the size of similarity window is set as 2 × 2, h equals 3 and search window is 3 × 6. Fig. 13 shows the images which contains 54 × 120 data points from 4040 m to 4135 m along the fiber. Fig. 13(a) and (b) are the images
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Fig. 14. The BFS distribution obtained by BSR Filter and NLM Filter.
Table 3 Comparison of filtering effect parameters in experiment.
SSIM RMSD of BFS (MHz) Spatial resolution(m) Processing Time(s)
5000 AVG data
256 AVG data
Using BSR Filter
Using NLM Filter
1 0.09 6.3 –
0.63 1.72 12.9 –
0.94 0.63 6.9 2.43
0.95 0.71 9.8 3.72
obtained by 5000 and 256 AVG, respectively. The resulting image with noise-filtered by BSR Filter and NLM Filter are shown in Fig. 13(c) and (d), respectively. The contrast ratio in Fig. 13(c) is slightly higher than that in Fig. 13(d), so the central portion of the Brillouin frequency spectrum is much cleaner. The boundary lines of the temperature are much clearer in the filtered image by using BSR Filter than that by using NLM Filter. By using the proposed noise filter method, we can obtain the BFS distribution along the 5.2 km fiber. Fig. 14 demonstrate the results by use of BSR and NLM filters and 5000 and 256 AVG filters. Note that the BFS curve has two dips near 1.8 km and 3.9 km, which is due to residual strain in the two sections of the fiber. Overall, the results of the BSR and NLM filtering are not much different. However, it can be seen from the heated section in the inset figure that the BSR filtering result is better than that of the NLM filter. The inset figure illustrates the results around the 50 m heated section. The BFS uncertainty from 4075 m to 4105 m of the 256 AVG data is 1.72 MHz, and it is reduced to 0.62 MHz by using BSR Filter and 0.71 MHz by using NLM Filter. The main reason for the better accuracy obtained by using BSR Filter is the flexible selection of the search window size. At the same time, the shift of Brillouin frequency spectrum data is also able to reduce the deterioration of spatial resolution. Table 3 shows the comparison of filtering effect parameters of the case 2. The SSIM is 0.63 for original noisy data, which is increased to 0.94 by BSR Filter and 0.95 by NLM Filter. For RMSD of BFS, the value decreases from 1.72 MHz to 0.63 MHz by BSR Filter, and it is changed to 0.71 MHz by NLM filter. The spatial resolution of the BSR Filter is 6.9 m. Although it is slightly worse than the 6.3 m for 5000 AVG, it is better than the 12.9 m for 256 AVG and the 9.8 m for NLM filter. Therefore, the region division doesn’t change the original spatial resolution and preserve it in a large extent. Besides, the processing time for the entire image with 54 × 6350 data points is 2.43 s by BSR Filter and 3.72 s by NLM Filter. It should be note that the processing speed of experiment is faster than that of simulation because of the search windows size of
experiment is smaller than that of simulation. Since the number of frequency sampling point (m = 54) in experimental data is smaller than that (m = 200) in simulation data and the search windows size is limited by the number of frequency sampling point, the degree of time-saving in the experiment (35%) is lower than that in the simulation (78% in the two cases). In Table 3, we can find that the BSR Filter works well in the fiber sensing experiment. The value of SSIM is nearly the same for BSR Filter and NLM Filter. When comparing with the results obtained by NLM Filter, more effective similar windows with higher similarity participate in the denoising process, which filters noise more effectively and thus offers a BFS measurement accuracy improvement of 13% (The value of 0.09 MHz corresponding to 5000 AVG is taken as the reference). Besides, a spatial resolution improvement of 46% can be achieved due to the edge-preserving image filtering strategy by use of the region division (The value of 6.3 m corresponding to 5000 AVG is taken as the reference). Meanwhile, the reassembled image obtained by BSR Filter contains only noise and Brillouin spectrum information, so the edge preservation operation is removed, and the filter window size is reduced from 5 × 5 to 3 × 6. The above two reasons decrease the processing time by 35%. 5. Conclusion In conclusion, we propose and verify a novel image processing based noise reduction method in Brillouin optical time domain sensors. The new BSR filter combines region division, image reassembly and conventional filter. Simulation and experimental results show that the proposed method can be used as an excellent noise filter, to effectively remove noise and thus can enhance the measurement performance of distributed Brillouin fiber sensors with a shorter process time. The experimental results have shown that a BFS measurement accuracy improvement of 13%, a spatial resolution improvement of 46% and a processing time reduce of 35% can be achieved in a 5.2 km length G657 fiber by using
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the proposed filtering method, as compared with the Non-Local Means (NLM) Filter. Funding This work was supported by National Natural Science Foundation of China (NSFC) (61875086, 61377086) and Aerospace Science Foundation of China (2016ZD52042). Declaration of Competing Interest None. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.optlaseng.2019.105865. References [1] Bao X, Chen L. Recent progress in distributed fiber optic sensors. Sens (Switz) 2012;12:8601–39. doi:10.3390/s120708601. [2] Motil A, Bergman A, Tur M. State of the art of Brillouin fiber-optic distributed sensing. Opt Laser Technol 2016;78:81–103. doi:10.1016/j.optlastec.2015.09.013. [3] Zhang H, Zhou D, Wang B, Pang C, Xu P, Jiang T, et al. Recent progress in fast distributed Brillouin optical fiber sensing. Appl Sci 2018;8:1820. doi:10.3390/app8101820. [4] Zhang D, Cui H, Shi B. Spatial resolution of DOFS and its calibration methods. Opt Lasers Eng 2013;51:335–40. [5] Horiguchi T, Kurashima T, Tateda M. Tensile strain dependence of Brillouin frequency shift in silica optical fibers. IEEE Photonics Technol Lett 1989;1:107–8. [6] Wylie MT V, Brown AW, Colpitts BG. Distributed hot-wire anemometry based on Brillouin optical time-domain analysis. Opt Express 2012;20:15669–78. doi:10.1364/OE.20.015669. [7] Zhou D, Dong Y, Wang B, Pang C, Ba D, Zhang H, et al. Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement. Light Sci Appl 2018;7:32. [8] Diakaridia S, Pan Y, Xu P, Zhou D, Wang B, Teng L, et al. Detecting cmscale hot spot over 24-km-long single-mode fiber by using differential pulse pair BOTDA based on double-peak spectrum. Opt Express 2017;25:17727–36. doi:10.1364/OE.25.017727. [9] Dong Y, Wang B, Pang C, Zhou D, Ba D, Zhang H, et al. 150km fast BOTDA based on the optical chirp chain probe wave and Brillouin loss scheme. Opt Lett 2018;43:4679–82. doi:10.1364/OL.43.004679. [10] Dong Y, Chen L, Bao X. Time-division multiplexing-based BOTDA over 100km sensing length. Opt Lett 2011;36:277–9. doi:10.1364/OL.36.000277. [11] Li W, Bao X, Li Y, Chen L. Differential pulse-width pair BOTDA for high spatial resolution sensing. Opt Express 2008;16:21616–25. doi:10.1364/OE.16.021616. [12] Li Z, Yan L, Shao L, Pan W, Luo B, Liang J, et al. Precise Brillouin gain and phase spectra measurements in coherent BOTDA sensor with phase fluctuation cancellation. Opt Express 2016;24:4824–33. doi:10.1364/OE.24.004824. [13] Qian X, Wang Z, Wang S, Xue N, Sun W, Zhang L, et al. 157km BOTDA with pulse coding and image processing. In: Sixth eur. work. opt. fibre sensors, 9916. International Society for Optics and Photonics; 2016. p. 99162. [14] Kurashima T, Horiguchi T, Izumita H, Furukawa S, Koyamada Y. Brillouin optical– fiber time domain reflectometry. IEICE Trans Commun 1993;76:382–90. [15] Li M, Jiao W, Liuwu X, Song Y, Chang L. A method for peak seeking of BOTDR based on the incomplete Brillouin spectrum. IEEE Photonics J 2015;7:1–10.
Optics and Lasers in Engineering 125 (2020) 105865 [16] Lu Y, Li C, Zhang X, Yam S. Determination of thermal residual strain in cabled optical fiber with high spatial resolution by Brillouin optical time-domain reflectometry. Opt Lasers Eng 2011;49:1111–17. doi:10.1016/j.optlaseng.2011.05.015. [17] Li M, Jiao W, Zhang X, Song Y, Qian H, Yu J. An algorithm for determining the peak frequency of botdr under the case of transient interference. IEEE J Sel Top Quantum Electron 2017;23:269–73. [18] Luc T, Stella Foaleng M, Jie L. Effect of pulse depletion in a Brillouin optical time– domain analysis system. Opt Express 2013;21:14017–35. [19] Liang H, Li W, Linze N, Chen L, Bao X. High-resolution DPP-BOTDA over 50km leaf using return-to-zero coded pulses. Opt Lett 2010;35:1503–5. [20] Lu Y, Bao X, Chen L, Xie S, Pang M. Distributed birefringence measurement with beat period detection of homodyne Brillouin optical time-domain reflectometry. Opt Lett 2012;37:3936–8. [21] Li C, Lu Y, Zhang X, Wang F. SNR enhancement in Brillouin optical time domain reflectometer using multi-wavelength coherent detection. Electron Lett 2012;48:1139–41. [22] Zhang Z, Lu Y, Zhao Y. Channel capacity of wavelength division multiplexing-based Brillouin optical time domain sensors. IEEE Photonics J 2018;10:1–15. [23] Farahani MA, Castillo-Guerra E, Colpitts BG. A detailed evaluation of the correlationbased method used for estimation of the Brillouin frequency shift in BOTDA sensors. IEEE Sens J 2013;13:4589–98. doi:10.1109/JSEN.2013.2271254. [24] He H, Shao L, Li H, Pan W, Luo B, Zou X, et al. SNR enhancement in phase-sensitive OTDR with adaptive 2-D bilateral filtering algorithm. IEEE Photonics J 2017;9:1–10. doi:10.1109/JPHOT.2017.2700894. [25] Wu H, Wang L, Zhao Z, Guo N, Shu C, Lu C. Brillouin optical time domain analyzer sensors assisted by advanced image denoising techniques. Opt Express 2018;26:5126. doi:10.1364/oe.26.005126. [26] Qin Z, Chen H, Chang J. Detection performance improvement of distributed vibration sensor based on curvelet denoising method. Sens (Switz) 2017;17:1380. doi:10.3390/s17061380. [27] Farahani MA, Wylie MTV, Castillo-Guerra E, Colpitts BG. Reduction in the number of averages required in BOTDA sensors using wavelet denoising techniques. J Light Technol 2012;30:1134–42. doi:10.1109/JLT.2011.2168599. [28] Qin Z, Chen L, Bao X. Wavelet denoising method for improving detection performance of distributed vibration sensor. IEEE Photonics Technol Lett 2012;24:542–4. doi:10.1109/LPT.2011.2182643. [29] Zhao Z, Tang M, Wang L, Fu S, Tong W, Lu C. Enabling simultaneous DAS and DTS measurement through multicore fiber based space-division multiplexing. 2018 Optical Fiber Communications Conference and Exposition (OFC); 2018. W2A.7 https://doi.org/10.1364/ofc.2018.w2a.7 . [30] Soto MA, Ramírez JA, Thévenaz L. Intensifying the response of distributed optical fibre sensors using 2D and 3D image restoration. Nat Commun 2016;7:1–11. doi:10.1038/ncomms10870. [31] Soto MA, Ramirez JA, Thevenaz L. Optimizing image denoising for long-range Brillouin distributed fiber sensing. J Light Technol 2018;36:1168–77. [32] Qian X, Jia X, Wang Z, Zhang B, Xue N, Sun W, et al. Noise level estimation of BOTDA for optimal non-local means denoising. Appl Opt 2017;56:4727. doi:10.1364/ao.56.004727. [33] Maini R, Aggarwal DH. Study and comparison of various image edge detection techniques. Int J Image Process 2009;3:1–11. [34] Deng G, Cahill LW. An adaptive Gaussian filter for noise reduction and edge detection. Nucl. Sci. Symp. Med. Imaging Conf.; 1993. [35] Buades A, Coll B, Morel J-M. A non-local algorithm for image denoising. In: 2005 IEEE Comput Soc Conf Comput Vis Pattern Recognit, 2; 2005. p. 60–5. doi:10.1109/CVPR.2005.38. [36] Brox T, Kleinschmidt O, Cremers D. Efficient nonlocal means for denoising of textural patterns. IEEE Trans Image Process 2008;17:1083–92. doi:10.1109/TIP.2008.924281. [37] Froment J. Parameter-Free fast pixelwise non-local means denoising. Image Process Line 2014;4:300–26. doi:10.5201/ipol.2014.120. [38] Wang Z, Bovik AC, Sheikh HR, Simoncelli EP. Image quality assessment: from error visibility to structural similarity. Image Process IEEE Trans 2004;13:600–12. [39] Lehmann EL, Casella G. Theory of point estimation 2006.