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Abstract
Optical fiber sensing technology plays an important role in the application of the sensing layer of the Internet of Things. The core of this technology is the demodulation of the fiber Bragg grating (FBG) sensing system. Since the FBG sensor utilizes the wavelength change to respond to the measured size, it is of great significance to improve the accuracy of the FBG wavelength demodulation. However, the demodulation performance of the current FBG wavelength demodulation method still has much room for improvement in terms of accuracy and stability. To this end, we propose a composite gas cell demodulation scheme based on spectrum correction and data fusion by using differential photodetectors, fitting extrapolation, data fusion methods, etc. The issue of low demodulation accuracy arising due to noise, temperature drift, spectral distortion, etc., was addressed to improve the demodulation performance of the FBG. In the experiment, four FBGs with different center wavelengths were used to verify their demodulation accuracy in the range of 1510–1590 nm. The maximum repeatability error of the FBG wavelength was measured to be 2.51 pm, and the linearity was as high as 99.9% or more; under the working environment of −20 °C to 60 °C, the maximum full-scale error did not exceed ±1.71 pm, which is improved by 54.3% compared with the traditional method.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The FBG sensor is a wavelength modulated fiber optic sensor [1]. Compared with traditional sensors, FBG sensors are advantageous owing to the anti-electromagnetic interference, their small size and light weight, reusability, adaptability to harsh environments such as high-temperature voltage fluctuations, nuclear radiations, etc., and they can measure and monitor physical parameters such as strain, temperature and vibration [2,3]. The development of optical and other technologies has caused FBG sensors to attract widespread attention in many fields such as structural health monitoring, aerospace detection, power system measurement, and medical device improvement [4,5]. The essence of the sensing system lies in the detection, conversion, and transmission of information. The accurate demodulation of the FBG sensing signal is one of the key factors that affect the performance of the FBG sensing system. Therefore, in recent years, high-precision wavelength demodulation methods have been proposed to address the above-mentioned problems. So far, many demodulation schemes such as the edge filtering methods, optical interferometer methods, tunable laser or tunable Fabry–Pérot (F–P) filtering methods, and spectral analysis methods have been developed [6]. Among them, the fiber grating demodulation system based on a tunable F–P filter has been widely studied and applied owing to its high demodulation accuracy [7]. In practical applications, the temperature sometimes changes significantly. For example, spacecrafts usually work in vacuum and harsh environments. In addition, the optical fiber sensing system used for international oil pipeline monitoring faces severe challenges while operating in sudden temperature and humidity changes [8,9]. The FBG demodulation system based on the combination of the tunable F–P filter and F–P etalon is susceptible to unpredictable temperature changes, which introduces huge errors [10,11]. Therefore, it is particularly important to construct an FBG demodulation system with algorithms suitable for environments with drastic changes in temperature. Because acetylene (${\textrm{C}_2}{\textrm{H}_2}$) and hydrogen cyanide (HCN) are not sensitive to temperature changes [12–14], the absorption spectra of the ${\textrm{C}_2}{\textrm{H}_2}$ gas cell (1510–1540 nm) and HCN gas cell (1525–1565 nm) can be used to calibrate the standard tools, but the additional calibration module can complicate the structure and introduce additional errors. Literature [15] proposed a method of using the absorption spectrum of the ${\textrm{C}_2}{\textrm{H}_2}$ gas cell as the wavelength reference. This method uses a single peak in the gas cell to correct the peaks in the entire wavelength range of the etalon, but the problem of spectral distortion exists in the actual demodulation system. A single peak can only calibrate the wavelength of the local spectrum, increasing the measurement error of the overall spectrum. Literature [16] proposed the HCN gas cell composite multi-wavelength reference method, which changed the single peak of the gas cell to multi-peak calibration to avoid the cumulative error of the etalon wavelength reference position. However, the actual system not only encompasses the nonlinearity of the F–P filter, but also other factors that cause a spectral distortion in the overall system. Literature [8] considered that the transmittance function of the F–P filter would cause a distortion in the HCN absorption peak and used the deconvolution method to restore the spectrum pattern of the gas cell; however, they did not consider the poor flatness of the ASE light source and the limited power, which would produce the uneven baseline of the spectrum and the weak absorption peak of the gas cell affect the accuracy of the peak search. In addition, literatures [15] and [16] used spline interpolation and Gaussian fitting methods to find peaks that have strict requirements on the spectrum type. Among the seek peak–searching algorithms, the spline interpolation algorithm is the most common method, which has better flexibility, high calculation speed, and better stability. The fitting of cubic spline interpolation to the FBG signal is more suitable for the actual sampling waveform, and the fitting of Gaussian fitting to the FBG signal is more in line with the Gaussian function, but the Gaussian fitting cannot fit the F–P etalon. Under the condition that the peak–searching accuracy is basically the same, the computation of the cubic spline interpolation algorithm is faster than that of the Gaussian fitting algorithm. Therefore, the cubic spline interpolation method with higher accuracy and simple operation is selected as the peak-searching algorithm to compare with the X–dB bandwidth method.
The demodulation precision can be enhanced by using a wavelength tunable laser source with an ultranarrow output linewidth, or an optical spectrum analyzer with ultrahigh resolution [17]. For large-scale applications, this type of equipment is obviously too expensive. In this study, a composite gas chamber demodulation system, based on a SLED light source and F–P filter, using a differential photodetector to make preliminary corrections to the collected gas cell spectrum, has been developed. A spectral baseline correction algorithm, for recovering the ${\textrm{C}_2}{\textrm{H}_2}$ absorption spectrum from the distortion caused by the system, is proposed here. The corrected gas cell spectrum has a deeper absorption peak with a flatter baseline, which is conducive to the setting of the subsequent peak-finding threshold. The X–dB bandwidth method was used to find the peaks to avoid the peak noise to a large extent [18], and the distortion characteristics of the system were theoretically analyzed and researched. A composite gas cell multi-wavelength reference demodulation method based on data fusion is proposed here. The experiments prove that compared with the demodulation method based on a SLED or an ASE light source and F–P filter [19,20], the demodulation scheme can effectively improve the demodulation performance of the FBG: the maximum repeatability error of the FBG wavelength was measured to be 2.51 pm, and the linearity was as high as 99.9% or more; under the working environment of −20 °C to 60 °C, the maximum full-scale error did not exceed ±1.71 pm, which was improved by 54.3% compared with the traditional method.
2. Theory and method
2.1 System principle
A schematic of the FBG sensor demodulation system based on the F–P etalon and ${C_2}{H_2}$ gas cell composite reference designed in this study is shown in Fig. 1(a). The broad-spectrum light emitted by the SLED passes through the tunable F–P filter driven by the triangular wave and becomes the scanning light. The scanning light is divided into three parts after passing through the 1 × 4 coupler: the first part passes through the attenuator and the ${\textrm{C}_2}{\textrm{H}_2}$ gas cell and enters the differential photoelectric detector because the actual light source spectrum is not ideal; the spectrum of the obtained gas cell is bent. Subtracting the spectrum of the gas cell and the spectrum of the light source can initially correct the baseline of the gas cell spectrum, as shown in Fig. 1(b). Because the two differential input channels of the differential photodetector cannot be strictly consistent, and the spectrum of the gas cell still has a certain degree of curvature, which requires further processing by software. The ${\textrm{C}_2}{\textrm{H}_2}$ gas cell not only provides an absolute wavelength reference point and corrects the temperature drift of the F–P etalon; however, it characterizes the nonlinear trend of wavelength scanning within the coverage band of the gas cell, and the second part enters the relative wavelength reference channel and the F–P etalon provides multiple relative wavelengths with equal optical frequency intervals; the third part enters the sensor FBG array after passing through the circulator, and the reflected light enters the photodetector through the circulator. Each optical signal is converted into an electrical signal after passing through a photodetector, and the spectrum data are collected by a data acquisition card.
Fig. 1. (a) Schematic of FBG sensing demodulation system based on gas cell. (b) Correction of gas cell spectrum. (c) Original signals detected by DAQ card.
2.2 Data preprocessing
The frame of the original signal detected during the system scan is shown in Fig. 1(c). The ambient temperature was 25 °C. The original spectrum data obtained from the acquisition card are pre-processed by denoising, baseline correction, logarithm, extraction, and interception to obtain ideal spectrum data; then, the center wavelength of the FBG is finally obtained through the gas cell calibration etalon.
The collected FBG reflection spectrum contains various random noises because of the effect of various factors such as the circuit, optical path, and capture card. Denoising processing is required to determine the center wavelength of the FBG reflection spectrum more accurately. The moving average filter can effectively smooth high-frequency noise, smooth the spectrum, and improve the resolution by selecting an appropriate window size. An average window that is too small cannot smooth high-frequency noise, and a window that is too large will cause signal distortion because of the loss of the high-frequency components of the signal. It is necessary to reasonably estimate the highest frequency of the signal. The frequency of the signal is determined via experiments using a moving average filter with a window size of 32; the comparison chart before and after filtering is shown in Fig. 2. The filtered spectral peak becomes smoother, which helps accurately obtain the spectral peak position in subsequent processing.
The spectral peaks of the gas cell and etalon contain many invalid peaks formed by noise that cannot be completely removed even if a moving average filter is used. Therefore, it is necessary to set a proper threshold when searching for peaks to eliminate invalid peaks that do not meet threshold conditions. The flatness of the spectrum after the optical path differential compensation is corrected only to a certain extent because of the influence of the two differential input terminals of the differential photodetector and the corresponding non-ideal factors of the optical path, which is still not ideal and it cannot be effectively eliminated by setting a single threshold. Therefore, this paper proposes a baseline leveling method that can level the baseline of the transmission spectrum to facilitate the accurate elimination of invalid peaks. Consider the gas cell spectrum as an example. First, simple extreme peak finding processing is performed on the spectrum data to obtain the characteristic sequence of the baseline change in the gas cell spectrum. The extreme points of this sequence are expanded by linear interpolation to make the sample points if the number is the same as that of the gas cell spectrum, and the envelope of the gas cell spectrum baseline can be obtained. The amplitude of each point of the envelope and the maximum value of the envelope sequence were subtracted to obtain the compensation value of the flattening correction; the corresponding compensation value was sequentially subtracted from the gas cell spectrum value to correct the gas cell spectrum. Similarly, the etalon spectrum could also be calibrated. The calibration operation affects the longitudinal amplitude of the spectrum and does not affect the lateral spectrum shape of the spectrum; therefore, it does not affect the peak-finding accuracy. In contrast, the corrected spectrum facilitates the automatic setting of the peak-finding threshold in the next peak-finding process.
The calibrated high dynamic range spectrum data can more accurately locate the peak area of each effective peak and improve the reliability of dense peak searching. The logarithm changes only the amplitude of the spectral data without affecting the coordinates of the sampling point in the subsequent peak finding. Then, the data after logarithmic processing is extracted, and it reduces the sampling rate and improves the efficiency of data processing. By evaluating the labeled peak of the etalon, the range of the target wavelength in all spectral data were estimated; only useful data were intercepted, and ideal spectral data were obtained. The comparison charts before and after baseline correction, logarithm, extraction, and interception of the gas cell and etalon are shown in Fig. 3.
2.3 Composite multiwavelength demodulation algorithm based on F–P etalon and ${C_2}{H_2}$ gas cell
The cavity length of the F–P etalon is easily affected by the temperature. When the temperature changes, the transmission peak drifts and affects the accuracy and stability of the demodulation. The gas cell spectrum was used as the reference spectrum to establish the relationship between the sampling point and the wavelength using the high stability of the transmission peak of the gas cell. The demodulation principle is shown in Fig. 4.
Figure 4 shows that the number of peaks of the gas cell, F–P etalon, and FBG are m, l + n, and 4, respectively. Among them, the first l peaks of the etalon are within the wavelength range covered by the gas cell; the last n peaks are outside the wavelength range covered by the gas cell. The peak-finding algorithm uses the X-dB bandwidth method [21]. In actual measurements, the top of the spectrum peak contains a considerably amount of noise, and the X-dB bandwidth method excludes the noise at the top of the spectrum peak, which is conducive to peak finding of the actual spectrum. First, we perform X-dB peak-finding processing on the sampling data of the gas chamber, F–P etalon, and FBG in sequence; we obtain multiple peak point coordinate sequences $({x_{\textrm{g}1}},{x_{\textrm{g}2}}, \ldots ,{x_{\textrm{g}m}})$, $({x_{\textrm{p}1}},{x_{\textrm{p}2}}, \ldots ,{x_{\textrm{p}l + n}})$, and $({x_{FBG1}},{x_{FBG2}},{x_{FBG3}},{x_{FBG4}})$. A sequence pair of the coordinate sequence of the gas cell peak point $({x_{\textrm{g}1}},{x_{\textrm{g}2}}, \ldots ,{x_{\textrm{g}m}})$ and specific wavelength sequence of the gas cell peak point $({{\lambda_{\textrm{g}1}},{\lambda_{\textrm{g}2}}, \ldots ,{\lambda_{\textrm{g}m}}} )$ is established, i.e., $\{{({{x_{\textrm{g}1}},{\lambda_{\textrm{g}1}}} ),({{x_{\textrm{g}2}},{\lambda_{\textrm{g}2}}} ), \ldots ,({{x_{\textrm{g}m}},{\lambda_{\textrm{g}m}}} )} \}$. It is possible to approximate the correspondence between sampling points and wavelengths by using high-order polynomials because the sequence pair is of finite length. The least squares fitting is employed for the sequence pair, and the sixth-order polynomial fitting function is obtained to express the relationship between the sampling point and wavelength in this interval. This is expressed as
In Eq. (5), ${\varepsilon _1},{\varepsilon _2}$, and ${\varepsilon _3}$ represent coefficients. For the actual system, the relationship between the peak point number and the peak point coordinates is unknown because the functional relationship between the sampling point and the wavelength is unknown. g represent the function and is expressed as
According to the theory of series expansion, the function can be approximated by a high-order polynomial in a finite interval such that the approximate error meets the requirements. Therefore, polynomial fitting is performed on all peak point coordinate sequences $({x_{\textrm{p}1}},{x_{\textrm{p}2}}, \ldots ,{x_{\textrm{p}l + n}})$ of the etalon and all corresponding peak point number sequences $({{1^{st}},{2^{nd}}, \ldots ,{l^{th}}, \ldots ,{{({l + n} )}^{th}}} )$. Through certain experimental tests, a sixth-order polynomial fit was ideal. This is expressed as
In Eq. (10) $({{\lambda_{\textrm{p}1}},{\lambda_{\textrm{p}2}}, \ldots ,{\lambda_{\textrm{p}l}}, \ldots ,{\lambda_{\textrm{p}l + n}}} )$ denotes the peak point wavelength sequence in the entire wavelength range of the etalon, and the $({{\lambda_{\textrm{p}l + 1}},{\lambda_{\textrm{p}l + 2}}, \ldots ,{\lambda_{\textrm{p}l + n}}} )$ in this sequence is recorded as the measured peak wavelength of the etalon. Substituting the etalon peak number sequence outside the wavelength range covered by the gas cell into Eq. (8),
Data fusion techniques combine data from multiple sensors and related information from associated databases to achieve improved accuracy and more specific inferences than those that can be achieved using a single sensor. When two or more input sources provide information about the same target, they can be fused to obtain better or newer data [22]. In this study, data fusion processing was performed on the measured peak wavelength and predicted peak wavelength of the etalon. The respective gain coefficients are calculated for each peak point of the etalon; this is expressed as
Here, $j({j = \{{l + 1,l + 2, \ldots ,l + n} \}} )$ denotes the peak point number of the etalon outside the coverage of the gas cell, T denotes the number of measurements of the ${j^{th}}$ peak of the etalon, ${\mu _{\textrm{p}j}}$ and ${\sigma _{j1}}$ denote the averages of the T measurement wavelengths of the ${j^{th}}$ peak of the etalon, respectively; values and standard deviations, $\mu _{\textrm{p}j}^{\prime}$ and ${\sigma _{j1}}$ are the average and standard deviation of T T-predicted wavelengths with the ${j^{th}}$ peak of the etalon, respectively. The gain coefficient is obtained using the standard deviation between the measured wavelength and predicted wavelength of the etalon as
where ${K_j}$ denotes the gain coefficient of the ${j^{th}}$ peak of the etalon. Finally, the optimal estimation of the peak wavelength of the etalon was calculated, and the expression wasThe F–P etalon transmission peaks on the left and right sides of the FBG reflection spectrum peak were linearly interpolated to obtain the center wavelength of the FBG. The expression is
FBG1 is marked as the sensor grating numbered 1, ${x_{\textrm{p}e}}$, and ${x_{\textrm{p}e + 1}}$ denote the peak point coordinates of the adjacent etalons on the left and right of FBG1, ${\hat{\lambda }_{\textrm{p}e}}$ and ${\hat{\lambda }_{\textrm{p}e + 1}}$ denote the best estimates of the peak point wavelengths of the corresponding peaks ${e^{th}}$ and ${({e + 1} )^{th}}$ of the etalon, ${x_{FBG1}}$ denotes the coordination of the peak point of FBG1, and ${\lambda _{FBG1}}$ denotes the wavelength of the peak point of FBG1.
3. Results and discussion
According to Fig. 1(a), the minimum power of the SLED light source is 16 mW, the center wavelength is 1550 nm, and the bandwidth is 80 nm; the wavelength range of the ${\textrm{C}_2}{\textrm{H}_2}$ gas cell is 1510–1540 nm with a temperature drift <0.01 pm/°C; For the F–P standard, the free spectrum range is 100 GHz, thermal stability is ≤±0.8 ∼ GHz in the range of −5°C to 70 °C, and the wavelength range is 1510–1590 nm. The wavelength values of the four FBGs on the sensing channel at 30 °C were 1525.025, 1526.514, 1548.837, and 1562.913 nm.
Considering the influence of the system noise during an actual measurement, the wavelength demodulation resolution of the demodulation system was tested. During the experiment, the grating was placed in a constant temperature water tank that was maintained at 30 °C to ensure that the grating was not affected by temperature and stress. The wavelengths of the four FBGs were measured separately, and the collection lasted 5 min. The wavelength demodulation result of this scheme is shown in Fig. 6(a), and the wavelength measurement resolution of the four gratings are all within ±1.5 pm. For comparison, only the peak-finding algorithm in this scheme was replaced with the spline interpolation peak-finding algorithm. The demodulation result is shown in Fig. 6(b), and the resolution is within ±3.2 pm. Intuitively, the measurement resolution of the same system is definitively related to the peak finding algorithm. Compared with the spline interpolation algorithm, this scheme effectively improves the resolution of the wavelength demodulation and lays a foundation for high-precision wavelength demodulation. We speculate that these noises mainly originate from the analog front-end circuits of the photodetectors and data acquisition cards.
Fig. 6. FBG wavelength demodulation resolution test. (a) X–dB bandwidth method. (b) Spline interpolation method.
The most basic sensing application of the FBG is the sensing of temperature and axial strain, and the need for sensing the temperature is inevitable in the cross-sensitivity problem. We studied the wavelength demodulation performance of the FBG in the temperature range of 20–50 °C. Four FBGs were placed in a constant temperature water tank to perform a temperature-rising and falling experiment for testing the repeatability of the demodulation scheme. The temperature was varied by 5 °C each time and maintained for 30 min. After the temperature stabilized, we recorded the wavelength value once. The entire experimental process was repeated 10 times. After averaging the results of 10 measurements, the average was subtracted from each measurement to calculate the repeatability error. The result is shown in Fig. 7. It marks the point where each FBG fluctuated the most, with a minimum repeatability error of 0.807 pm and maximum of 2.507 pm. The repeatability error of each temperature point of the FBG during the heating and cooling processes was small, and the fluctuation range was narrow, which meets the requirement for practical applications. It is worth noting that FBG4 has individual violent fluctuations at the three temperature points of 30, 35, and 40 °C. We believe that this occurs due to the instability of the device and external interference during the experiment.
Linear fitting was performed on the data of 10 temperature rises and falls; the change trend of the wavelength during heating and cooling was compared, and the linearity and hysteresis characteristics of the wavelength change with temperature were observed. A randomly selected test result and fitting curve are illustrated in Fig. 8. The R2 of the four sets of fitting curves are all greater than 0.999, which indicates that the linearity of the sensor demodulation system is good. Besides FBG2, the other three heating and cooling curves of the sensor almost coincide, which imply that the hysteresis characteristics of the sensor demodulation system are better. The wavelength difference at the same temperature point of FBG2 is slightly different, which implies the hysteresis characteristics are poor, and this is attributed to the problem of the FBG2 packaging structure.
Considering the working environment of a spacecraft in orbit, i.e., extreme temperature measurements and chemical reagent storage, etc. [23,24], the demodulation performance during the heating process from −20 to 60 °C was studied. During the experiment, we first put the FBG in a constant temperature water tank and kept it at 30°C to ensure that the wavelength of the FBG did not drift. Then we put the entire demodulation system (including gas cell and F–P etalon) in a constant temperature box, and controlled the temperature from −20°C to 60°C in steps of 10°C. It was increased every 10°C and data collection lasted for 5 minutes. In order to compare the function of the test gas cell, two methods were used to process the test data. One involved using the method described in this article to calculate the wavelength of the FBG using the transmission spectrum of the gas cell and the F–P etalon, and the other involved using just the transmission spectrum of the F–P etalon to calculate the wavelength of the FBG, and the data processing result is shown in Fig. 9. The data represented by the red line indicates the demodulation result when only the etalon is used and the gas cell is not used, the data represented by the blue line represents the demodulation result when both the gas cell and the etalon are used as the composite wavelength reference. During the heating process of the demodulation system from −20 to 60°C, the red line trend representing the etalon is consistent with the temperature change trend represented by the black dashed line, which verifies the overall rightward drift of the etalon as the temperature increases. However, the blue line is basically unaffected by the change of the black dashed line and remains level. The result showed that when the etalon is used as the wavelength standard and the gas cell is not used, the maximum error ±4.86 pm, and the standard deviation σ was 2.70 pm. When the gas cell and etalon were used as composite reference, the maximum error was within ±1.71 pm, and the standard deviation σ was 0.66 pm. Compared with the demodulation method that only the etalon reference is used, the gas cell composite reference method improved the accuracy by 54.3% and the standard deviation reduced by 75.6%. Therefore, the demodulation method based on the composite reference of the gas cell has a higher temperature stability in a variable temperature environment.
Fig. 9. Comparison of FBG wavelength demodulation results with and without the gas cell as a reference during the heating process from −20 to 60 degrees.
In the FBG wavelength demodulation method proposed in this paper, a precise determination of the spectral peak positions of the gas cell, F–P etalon, and FBG has a great influence on the accuracy of wavelength demodulation. Therefore, this article compares the wavelength demodulation error and the standard deviation when using an X–dB peak finding and a spline interpolation peak finding. The comparison results are shown in Table 1.
Table 1. Demodulation performance of X-dB and spline interpolation method.
It can be seen from Table 1 that the wavelength demodulation error and standard deviation of the X–dB peak-finding method are significantly lower than the values obtained when spline interpolation was used, indicating that the wavelength solution proposed in this paper using X–dB peak-finding and data fusion can effectively improve the accuracy of wavelength demodulation.
It can be seen from the above three experimental results that the various performances of FBG3 and FBG4 were worse than FBG1 and FBG2. This is because the wavelengths of FBG1 and FBG2 were directly calculated by the gas cell and etalon, while the wavelengths of FBG3 and FBG4 were outside the wavelength range covered by the transmission spectrum of the gas cell, and their wavelengths were derived from the system's fitting extrapolation function and data fusion. Although it has a great advantage in terms of accuracy compared with the previous demodulation method, a certain cumulative error still exists.
4. Conclusion
A gas cell composite reference demodulation system with a differential photodetector was designed, and the gas cell spectrum was corrected to a large extent by using the differential idea; for the actual collected spectrum data, the noise and unevenness of the light source spectrum were considered. A more comprehensive preprocessing method, including moving average, baseline correction, logarithm, etc., can be used to obtain a more ideal spectral data. The fitting extrapolation method was used to deal with the problem of lateral distortion of the spectrum, and a data fusion algorithm was introduced to obtain the optimal estimated wavelength value of the etalon, which improved the wavelength resolution and demodulation accuracy of the FBG. The demodulation scheme has a high demodulation accuracy and good application prospects in harsh temperature environments such as aerospace. In addition, it is necessary to carry out an in-depth research on the corresponding circuit and specifically design a low-noise and high-sensitivity photodetector and an analog front-end circuit of the data acquisition card that meet the requirements of this system to further reduce the noise. It is also necessary to increase the non-linearity of the algorithm developed for extraction before acquisition to further address the problem of spectral distortion, which can be studied in future works.
Future high-precision wavelength demodulation schemes may be more inclined to a combination of multiple demodulation methods. For example, the combination of the hardware's composite reference method and the intelligent algorithm merges into a new high-precision wavelength demodulation method. They can greatly overcome the problems of noise, spectral distortion, and spectrum overlap, while ensuring the temperature stability of wavelength demodulation.
Funding
Fundamental Research Funds for the Central Universities (2018MS097); National Natural Science Foundation of China (61775057).
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.
References
1. L. Mohanty, S. C. Tjin, D. T. Lie, S. E. Panganiban, and P. K. Chow, “Fiber grating sensor for pressure mapping during total knee arthroplasty,” Sens. Actuators, A 135(2), 323–328 (2007). [CrossRef]
2. A. Othonos, K. Kalli, and G. E. Kohnke, “Fiber Bragg gratings: Fundamentals and applications in telecommunications and sensing,” Phys. Today 53(5), 61–62 (2000). [CrossRef]
3. M. Mieloszyk, L. Skarbek, M. Krawczuk, W. Ostachowicz, and A. Zak, “Application of fibre Bragg grating sensors for structural health monitoring of an adaptive wing,” Smart Mater. Struct. 20(12), 125014 (2011). [CrossRef]
4. L. Dziuda, F. W. Skibniewski, M. Krej, and J. Lewandowski, “Monitoring respiration and cardiac activity using fiber Bragg grating-based sensor,” IEEE Trans. Biomed. Eng. 59(7), 1934–1942 (2012). [CrossRef]
5. J. W. Arkwright, N. G. Blenman, I. D. Underhill, S. A. Maunder, N. J. Spencer, M. Costa, S. J. Brookes, M. M. Szczesniak, and P. G. Dinning, “Measurement of muscular activity associated with peristalsis in the human gut using fiber Bragg grating arrays,” IEEE Sensors J. 12(1), 113–117 (2012). [CrossRef]
6. J. Wu, H. P. Wu, J. B. Huang, and H. C. Gu, “Research progress in signal demodulation technology of fiber Bragg grating sensors,” Chin. Opt. 7(4), 519–531 (2014). [CrossRef]
7. Z. Xu, X. Shu, and H. Fu, “Fiber Bragg grating sensor interrogation system based on an optoelectronic oscillator loop,” Opt. Express 27(16), 23274–23281 (2019). [CrossRef]
8. X. Z. Zhang, Y. Q. Li, H. F. Hu, J. F. Jiang, K. Liu, X. J. Fan, M. Feng, and T. F. Liu, “Recovered HCN absorption spectrum based FBG demodulation method covering the whole C-band for temperature changing environment,” IEEE Access. 8(1), 15039–15046 (2020). [CrossRef]
9. X. Qiao and M. A. Fiddy, “Distributed optical fiber Bragg grating sensor for simultaneous measurement of pressure and temperature in the oil and gas downhole,” Proc SPIE. 4870(6), 554–558 (2002). [CrossRef]
10. B. de Assumpcao Ribeiro, M. M. Werneck, and J. L. da Silva-Neto, “Novel optimization algorithm to demodulate a PZT-FBG sensor in AC high voltage measurements,” IEEE Sensors J. 13(4), 1259–1264 (2013). [CrossRef]
11. Z. Y. Li, Z. D. Zhou, X. L. Tong, T. Xiong, Z. H. Tang, L. J. Cai, and M. Zhao, “Research on high speed and large capacity fiber grating demodulator,” Acta Opt. Sin. 32(3), 52–57 (2012).
12. X. J. Fan, J. J. Jiang, X. Z. Zhang, K. Liu, S. Wang, Y. N. Yang, F. Sun, J. Zhang, C. H. Guo, J. S. Shen, S. C. Wu, and T. G. Liu, “Self-marked HCN gas based FBG demodulation in thermal cycling process for aerospace environment,” Opt. Express 26(18), 22944–22953 (2018). [CrossRef]
13. G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Fiber Bragg-grating strain sensor interrogation using laser radio-frequency modulation,” Opt. Express 13(7), 2377–2384 (2005). [CrossRef]
14. E. Rivera and D. J. Thomson, “Accurate strain measurements with fiber Bragg sensors and wavelength references,” Smart Mater Struct. 15(2), 250 (2010). [CrossRef]
15. J. F. Jiang, P. He, T. G. Liu, K. Liu, S. Wang, Y. H. Pan, L. Yu, and J. L. Yan, “Demodulation of temperature stabilized fiber Bragg grating sensor based on composite wavelength reference,” Acta Optica Sinica. 35(10), 82–87 (2015).
16. J. F. Jiang, C. J. Zang, S. Wang, X. Z. Zhang, K. Liu, Y. N. Yang, R. W. Xie, X. J. Fan, and T. G. Liu, “Study on composite multi wavelength reference stabilization method of FBG demodulator in variable temperature environment,” Journal of Optoelectronics • Laser. 276(6), 575–581 (2018).
17. S.D. Dyer, P.A. Williams, R.J. Espejo, J.D. Kofler, and S.M. Etzel, “Fundamental limits in fiber Bragg grating peak wavelength measurements,” Proc. SPIE. 5855(5), 88–93 (2005). [CrossRef]
18. M. S. Djurhuus, S. Werzinger, B. Schmauss, A. T. Clausen, and D. Zibar, “Machine learning assisted fiber bragg grating-based temperature sensing,” IEEE Photonics Technol. Lett. 31(12), 939–942 (2019). [CrossRef]
19. W. Sheng, G. D. Peng, Y. Liu, and N. Yang, “An optimized strain demodulation method for PZT driven fiber Fabry–Perot tunable filter,” Opt. Commun. 349, 31–35 (2015). [CrossRef]
20. D. S. Ivan, K. Ana, S. Marko, B. Marko, and S. Zvonimir, “Portable FBG based optical sensor array,” IEEE Sensors Applications Symposium (SAS 10(6), 1–5 (2015). [CrossRef]
21. D. Tosi, “Review and analysis of peak tracking techniques for fiber Bragg grating sensors,” Sensors 17(10), 2368 (2017). [CrossRef]
22. A. Alofi, A. Alghamdi, R. Alahmadi, N. Aljuaid, and M. Hemalatha, “A review of data fusion techniques,” The Scientific World Journal 167(7), 1–19 (2013). [CrossRef]
23. G. Batts, “Thermal environment in space for engineering applications,” In 32nd Aerospace Sciences Meeting and Exhibit. (Academic, 1994), p. 593.
24. B. W. Li, Y. G. Liu, X. Y. Song, H. W. Fu, Z. A. Jia, and H. Gao, “Research on Low Temperature Sensing Characteristics of Fiber Bragg Grating,” Chin. Piezoelectrics & Acoustooptics. 42(6), 787–790 (2020).
