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Abstract
The thermal cycling process experienced by spacecraft during orbital operation would lead to deterioration of the demodulation performance of fiber Bragg grating (FBG). A new demodulation method based on Fabry-Perot (F-P) filter and hydrogen cyanide (HCN) gas is proposed to improve the performance. The method skillfully utilizes the self-marked HCN absorption lines as absolute wavelength references. In the thermal cycling environment whose temperature ranging from 5°Cto 65°C,the fluctuation of demodulation wavelength reduces to ± 2.6 pm, which is improved by 3.1 times compared with traditional method. The proposed method also shows a good robustness in the cases of weak light source intensity and poor signal-to-noise ratio (SNR) of HCN spectrum.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the aerospace field, the spacecraft suffers extremely complex and severe environments in the outer space, such as vacuum, frigid, electrons, space magnetic field, etc. The harsh environment brings forward prodigious challenge to onboard sensors [1]. Compared with the traditional electromechanical and electronic sensors, fiber optic sensors are essentially suited for aerospace sensing due to its advantages of being lightweight, tiny scale, immune to electromagnetic interference and multiplexing capability [2,3]. As a typical fiber optic sensor, fiber Bragg grating (FBG) has been extensively researched in aerospace application such as temperature measurement [4], hydrogen concentration detection [5] and healthy monitoring [6,7] etc.
The key point of FBG sensing is demodulate Bragg wavelength accurately. Many demodulation schemes had been developed, such as optical interferometer method [8,9], tunable laser or tunable Fabry-Perot (F-P) filter method [10–12], edge filtering method [13], coherent ultrashort pulsed light source [14], spectrum analysis method [15], and so on. Among those methods, tunable F-P filter combined with a F-P etalon as wavelength reference have significant advantages, which include fast demodulation speed, wide spectral range, high-resolution, and high-capacity. However, on-board measurement of spacecraft always leads to a large error due to the temperature drift effect of etalon [16]. It is because that spacecraft during orbiting operation would receive radiant thermal energy from incoming solar radiation, reflected solar energy, and outgoing longwave radiation. The three sources make spacecraft in a thermal cycling circumstance [17]. Therefore, it is important to improve the demodulation performance in the thermal cycling process.
The fundamental absorption lines of atoms and molecules are insensitive to the environmental temperature, this characteristic of gas supplies an excellent choice for wavelength reference [18]. Absorption lines of acetylene (C2H2) [19] and hydrogen cyanide (HCN) [20] had been employed to calibrate the temperature drift of etalon wavelength. These methods can improve the demodulation performance in the thermal cycling circumstance. Unfortunately, the extra calibration step needs more complex algorithms and brings larger size of demodulator, which is inapplicable to spacecraft. Although the investigations that only use C2H2 absorption lines as wavelength references had been reported [21], the wavelength range is 3 nm only, which cannot satisfy the requirement of practical applications.
In this paper, we report a novel FBG demodulation method based on self-marked HCN absorption spectrum as absolute frequency reference. The reference wavelength is determined according to the different wavelength interval of the HCN absorption lines. The demodulation accuracy affected by operating temperature and the demodulation precision affected by the inaccuracy inherent in the system are detailed analyzed. Experiment results demonstrate that this method can effectively improve the demodulation performance in thermal cycling process whose temperature ranging from 5°C to 65°C. Compared with traditional method, the error is reduced by 3.1 times. The demodulation precision ranging from ± 1.8 pm to ± 2.5 pm is obtained in experiment at room temperature, and the good robustness of the method is also guaranteed.
2. Principle
According to the Lambert- Beer law, when a laser with an input intensity of is injected into the absorbing gas, the output intensity can be expressed by:
whereis the wavelength, is the number density of the HCN molecule, is the effective absorption optical path, and is the spectral absorption coefficient; and represent the spectral line intensity and function of absorption line shape, respectively.According to HITRAN molecular spectroscopic database [22], the HCN rotational-vibrational combination band contains more than 50 absorption lines in the 1530 nm to 1565 nm region, divided into two absorption bands of R branch and P branch. Figure 1(a) displays the absorption spectrum obtained by scanning a tunable diode laser with 10 MHz linewidth. The line numbers are labeled below the absorption lines. The wavelength intervals between the absorption line and its adjacent absorption line in short wavelength side are displayed in Fig. 1(b). The wavelength interval of 1.3614 nm between R0 and P1 is clearly wider than other line intervals. This characteristic provides self-marked HCN absorption spectrum, the interval between R0 and P1 could be regarded as a “Marker”.
Fig. 1 Normalized absorption spectrum of HCN gas obtained by scanning a tunable diode laser with 10 MHz linewidth(a), and the wavelength intervals between the absorption line and its adjacent absorption line in short wavelength side(b).
The schematic diagram of the demodulation setup is shown in Fig. 2. Amplified spontaneous emission (ASE) light source, isolator and F-P filter compose of scanning light source module. The F-P filter is tuned to interrogate the FBG and HCN gas via voltage modulation of triangle wave. A Faraday rotator mirror (FRM) is connected to the HCN gas cell to increase the effective absorption optical path. The signal module also outputs square wave voltage, whose frequency is same to the triangle voltage. The square wave voltage is used as trigger signal of data acquisition (DAQ). The reflected optical power of the FBG and HCN gas are sampled via photodetectors (PDs) and DAQ. Each frequency sweep of the F-P filter will produce FBG reflection spectrum and HCN absorption spectrum as shown in Fig. 3(a), from which the Bragg wavelength of FBG is calculated.
Fig. 3 The normalized HCN and FBG spectra collected by DAQ(a), and the HCN spectrum after preprocessing(b).
The actual absorption depth of the HCN spectrum in Fig. 3(a) is far smaller than that in Fig. 1. It is because that the bandwidth of the F-P filter is set to ~200 pm in accordance with FBG reflection spectrum, while the HCN gas have an absorption linewidth of ~16 pm. Excessive bandwidth of the scanning light source results in a reduction of actual absorption depth. On the other hand, the HCN absorption spectrum suffers from optical power fluctuation, which results in an obvious baseline wander (BW). The presence of BW severely interferes the extraction of absorption wavelength and should be removed. Since the BW is induced by low frequency component, it can be removed by low-pass filtering. After that, secondary low-pass filtering is used for denoising. The absorption spectrum after preprocessing is shown in Fig. 3(b). A threshold is set to pick up the absorption lines. The threshold is able to distinguish the “Marker” while ensuring stable absorption peaks, as indicate by the blue line. All the absorption lines below the threshold are indexed by curve fitting algorithm, and the wavelengths are obtained by corresponding to the given HCN absorption wavelengths. Finally, the Bragg wavelength of FBG could be accurately obtained by interpolation at each frequency sweep of the F-P filter.
The computation time for the low-pass filtering, Gaussian fitting and spline interpolation are 0.913 ms, 0.262 ms and 0.008 ms with personal computer (CPU: 3.20 GHz, RAM: 8 GB). The complete demodulation time for each frequency sweep of the F-P filter is less than 1.5ms. The demodulation speed can be further improved by using matured specified digital processing hardware, such as DSP or FPGA, for high speed sensing application.
3. Errors analysis in thermal cycling process
The demodulation error of the method in thermal cycling process relates to the demodulation accuracy and demodulation precision. The demodulation accuracy is affected by the change in operating temperature. The demodulation precision is affected by the inherent inaccuracy during the measure process. These factors are analyzed respectively as follows.
Firstly, the change in operating temperature would affects the demodulation accuracy directly. Although fundamental atomic and molecular absorption lines provide wavelength references with high temperature stability, the temperature will also bring wavelength drift to a certain degree. The effects of temperature include two aspects: direct temperature-induced drift of absorption lines by the change in temperature is less than 0.01 pm/°C [20]; indirect drift of absorption lines through the pressure, since the temperature will affect the collision frequency of molecules in the cell and therefore slightly modify the pressure. According to the ideal gas law, the molecule density of the absorber can be given by
where is the volume fraction of the HCN gas, is the number density. is the ideal gas constant, is the Avogadro constant, is the Boltzmann’s constant. For the gas cell in Standard Reference Material (SRM) 2519a with standard pressure of 25 Torr (~3.3 kPa), 1°C temperature change would cause a 0.2% variation of the pressure [23]. The pressure-induced drift varies with line number from + 0.09 pm/kPa to −0.15 pm/kPa corresponds to temperature-induced drift from + 0.59 × 10−3 pm/°C to −0.99 × 10−3 pm/°C. Therefore, the effects of operating temperature, including the direct temperature-induced drift of absorption lines and the indirect drift through pressure, is less than 0.01099 pm/°C. Contrast to etalon, which temperature drift is usually greater than 0.2 pm/°C, the gas absorption line exhibits high temperature stability.Secondly, the absorption line depth of HCN spectrum affects the precision of the reference wavelength, and further determines the demodulation precision. The absorbance is used to indicate the absorption line depth, which is defined as the attenuation of laser intensity induced by gas absorption [24]:
is proportional to the number density and the effective absorption optical path . To increase the absorption line depth of spectrum, an HCN gas cell with long path and high-concentration should be used. In addition, as described in Fig. 3 (a), the actual absorption line depth will be reduced significantly if the bandwidth of F-P filter is far larger than the absorption linewidth of HCN gas. Since the absorption linewidth has a positive correlation with the pressure of gas [25], the gas cell with high-pressure is also preferred.Thirdly, the demodulation precision relates to the computations during the measurement process, including the low-pass filtering for preprocessing of HCN spectrum, peak-detection of FBG reflection peaks and HCN absorption lines, and interpolation. The Butterworth filter is preferred to improve the signal-to-noise ratio (SNR) of the HCN spectrum due to its flat frequency response curve [26]. There are several peak-detection algorithms include the direct peak-located algorithm, the centroid algorithm and the curve fitting algorithm, etc. Generally, the curve fitting algorithm has the least error, but depends on the selected fitting function which needs to correspond to the accurate absorption line. Ideally, the gas absorption line is a geometric line; considering the influence of natural broadening, collision broadening and Doppler broadening, the actual absorption line shape of gas molecule is a Voigt function, which is the convolution of Lorentzian function () and Gaussian function () [27]:
Due to the complexity of numerical calculation, it is difficult to get an analytical expression for Voigt function. Instead, when the pressure is greater than 100 Torr, the Voigt shape can be well approximated by the Lorentzian shape; when the pressure is relatively low, the Gaussian function is usually used as an alternative. The interpolation method affects the demodulation precision directly. The length of optical cavity of F-P filter is tuned by piezoelectric transducer (PZT). Due to thermal expansion and contraction of PZT, the thermal cycling process will lead to the change of cavity length and poor linearity and repeatability in scanning. Hence, the spline interpolation is used instead of linear interpolation to improve the demodulation precision.4. Experiment and discussion
During the demonstrational experiments, the FBG (MOI) with center wavelength of 1537.13 nm is placed in a metrology well calibrator (Fluke 9170). The sensitivity of the FBG is ~10 pm/°C, the temperature in the calibrator is kept at 25°C, the temperature fluctuation is less than ± 0.005°C, so the wavelength drift caused by the calibrator is less than ± 0.05 pm. The scanning frequency of the F-P filter (Micron Optics, FSR: 108 nm, Bandwidth: 100 GHz) is 100 Hz, so the corresponding demodulation frequency is 100Hz. The data sampling rate of the DAQ (NI6120) is 10 MHz. The light source (Hoyatek), F-P filter, HCN gas cell (Wavelength References) and a F-P etalon (Prinanex) are put into the constant temperature drying oven (Espec). The HCN gas cell contains a fused silica absorption cell, which is filled by HCN gas with a pressure of 25 Torr. The F-P etalon is used for comparison experiment. The operating temperature inside oven is real-time recorded by a reference thermometer (Fluke1524).
Taking into account the cabin temperature of the spacecraft during orbiting operation [17], the demodulation performance in thermal cycling process with a range of 5-65°C is researched. The experiment takes about 400mins. The operating temperature controlled by the constant temperature drying oven is shown in Fig. 4(a). The temperature increase from 10% to 90% takes 24.9 minutes, with an average heating rate of 2.4 °C/min; correspondingly, the cooling rate is 1.0 °C/min. The results of traditional method which based on etalon as reference are indicated by blue curve in Fig. 4(b). The demodulation wavelength fluctuates obviously correspond to the operating temperature. The maximum error is up to ± 8.1 pm and the standard deviation is 3.33 pm. The results based on HCN as reference are indicated by red curve. Intuitively, the demodulation results are more accurate and stable. The wavelength fluctuates within ± 2.6 pm, the standard deviation is 0.798 pm. Compared with etalon-based results, the demodulation error is reduced by 3.1 times and the standard deviation is reduced by 76%. The proposed method effectively improves the demodulation performance in thermal cycling process. It is worth noting that even though the wavelength fluctuation of HCN-based results is agreed with the errors analyzed above, the fluctuation strength is larger than the theoretical value. The authors conjecture that this is due to the uncertainty of the deviation direction of absorption lines during changing in temperature.
Fig. 4 Experiment in thermal cycling process: Operating temperature(a), and demodulation results(b).
To further research the effects of the operating temperature, the demodulation setup is operated at 5°C, 20°C, 35°C, 50°C and 65°C, respectively. Each temperature run for 30 minutes. It can be seen from Fig. 5, the demodulation results based on etalon vary greatly at different temperatures. For a temperature difference of 60°C, the wavelength difference reaches to 10 pm. It is because that although the etalon used here is one of the best performing products the authors could get on the market, the temperature drift is still up to 0.15 pm/°C. In contrast, the results based on HCN is relatively stable, the maximum wavelength deviation is 1.8 pm.
Figure 6 shows the demodulation results of different frequencies in thermal cycling process. The operating temperature displayed in Fig. 6(a) is increased from room temperature (24.5°C) to 65°C. Figures 6(b)-6(d) show that the demodulation results are consistent at 10 Hz, 50 Hz and 100 Hz. The error is less than 5 pm. However, when the frequency increases to 200 hz, obvious oscillation is appeared with an error of 13.2 pm in Fig. 6(e). It is because that the increase in temperature causes thermal expansion of the PZT and obvious nonlinearity of high-speed tuning [28]. The phenomenon does not occur during low-speed tuning. This shows that the F-P filter-based method is not applicable to high-frequency demodulation in thermal cycling environment.
Fig. 6 Demodulation results of different frequencies under increase in operating temperature: Operating temperature(a), 10 Hz(b), 50 Hz(c), 100 Hz(d), and 200 Hz(e).
High-performance demodulation of the proposed method relies on high SNR of HCN spectrum. The HCN spectrum with poor SNR may leads to deterioration of the reference wavelength and even failure to locate the “Marker”. Experiments with different SNRs of the HCN spectrum are conducted. The SNR is controlled by adjusting the output power of light source by using an optical attenuator. The power gradually attenuates from 58.4 μW to 6.12 μW. The demodulation precisions under different SNRs are listed in Table 1. It can be seen from the table, the demodulation precision gradually deteriorates along with the decrease of SNR. When the SNR increases to 6.12 dB, the demodulation is failed because the “Marker” cannot be located from the HCN spectrum. That is, as long as the source power is kept above 11.04 μW, corresponding to an attenuation rate of 18.9%, the valid demodulation can be achieved. The results show a good robustness of this method.
Table 1. Demodulation results under different SNRs of HCN absorption spectrum
7 FBGs are connected in series in one channel to verify the precision in wide wavelength range. The result in Fig. 7 shows that the precision of 7 FBGs distribute within ± 1.8 pm to ± 2.5 pm. There is a good correspondence between the demodulation precision and the trend of HCN absorption spectrum. This makes sense, since the reference wavelength would be more accurate and stable if the absorption depth is deeper. In wavelength division multiplexing (WDM) of FBGs, the center wavelength selection of FBG and precision requirements could be balanced according to the demand of applications.
5. Conclusion
To alleviate the deterioration of FBG demodulation in thermal cycling environment, this paper presents the use of HCN gas as wavelength references for F-P filter based FBG demodulation. According to the spectral characteristics of HCN absorption spectrum, the interval between R0 line and P1 line is used as “Marker”. All the absorption lines are indexed by the “Marker”, and the wavelength is obtained by corresponding to the given HCN absorption wavelength. The demodulation errors caused by the change in operating temperature and the inaccuracy inherent in the system are analyzed. The experimental results are consistent with the theoretical analysis. In the thermal cycling process from 5°Cto 65°C, the errors of the conventional method which uses etalon as wavelength reference is up to ± 8.1 pm and the standard deviation is 3.33 pm; the errors of the proposed method is reduced to ± 2.6 pm, the standard deviation is 0.798 pm. Unfortunately, the demodulation frequency is presently limited at 100 Hz due to the poor scan linearity of P-F filter in thermal cycling process. Demodulation precision ranging from ± 1.8 pm to ± 2.5 pm is obtained in experiment at room temperature. The precision is positively related to absorption depth of the corresponding absorption lines. The method also has a good robustness, which shows a good potential in harsh temperature environments of aviation and aerospace environments. In addition, further improvements can be achieved by increasing the absorption depth of HCN spectrum and optimizing the baseline removal algorithm, which can be studied in future work.
Funding
National Natural Science Foundation of China (No. 61735011, 61675152, 61505139, 61775161, 61475114, 61378043 and 61227011); National Instrumentation Program of China (No. 2013YQ030915); Tianjin Natural Science Foundation (16JCQNJC02000); The open project of Key Laboratory of Opto-electronics Information Technology (Grant No. 2018KFKT013), and the open project of Key Laboratory of Micro Opto-electro Mechanical System Technology (Grant No. MOMST2016-3), Ministry of Education; Shenzhen Science and Technology Research Project (No. JCYJ20120831153904083)
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