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Abstract
Based on the theory of the microwave photonic filter (MPF), to our knowledge, a novel fiber Bragg grating (FBG) wavelength demodulation method based on time-domain detection is proposed. The method uses VNA (vector network analyzer) to measure the S21 parameter of the sensor system, and converts them to the time-domain through inverse discrete Fourier transform (IDFT), The wavelength demodulation and positioning of FBG can be realized by measuring the amplitude and position of the time-domain peak. In order to improve the number of FBG multiplexes, a method is proposed to eliminate the effect of spectrum overlap by normalization in the case of two FBGs and three FBGs. The experimental results show that the temperature sensitivity is 0.00503 RAC/°C, the positioning resolution of the system is 1.25 cm, and the limit of the wavelength difference between two FBGs allowed by the system is 0.25 nm. This method has the advantages of high demodulation precision, strong multiplexing ability and high precision positioning, and has broad application prospects.
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1. Introduction
Since the mass production of FBG, it has become a research hotspot in the field of communication and sensing [1]. As a new type of optical fiber sensor, FBG has the characteristics of light weight, small size, high sensitivity, corrosion resistance, electromagnetic interference resistance and easy networking compared with traditional sensors, and is widely used in the safety monitoring of aerospace, petrochemical, civil engineering, etc. [2]. As a wavelength modulation device, how to accurately demodulate the wavelength change is a key problem that needs to be solved when FBG sensors are moving towards practical application [3]. Researchers at home and abroad have done a lot of work and proposed a lot of effective demodulation methods, such as matching filter method [4], tunable F-P filter method [5], tunable laser scanning method [6], optical chirp demodulation method [7]. The above methods usually realize wavelength demodulation by means of devices such as spectrometers, optical filters, tunable lasers and optical interferometers. These methods are affected by the performance of optical devices, which limits the further improvement of measurement accuracy [8].
In recent years, with the rapid development of microwave photonics (MWP), sensing methods based on radio frequency (RF) detection have gradually become a research hotspot [9]. The measurement of optical wavelength drift and optical power change can be converted into the measurement of microwave signal frequency, phase and time delay, which can significantly improve the sensing accuracy. Most sensing methods based on MWP use photoelectric devices to combine light waves with microwave signals, and convert wavelength or power changes of light into phase and delay changes of microwave signals, so as to map the sensing information in the optical domain to changes in the physical parameters of microwave signals [10]. The demodulation methods based on MWP are mainly realized by microwave photonic heterodyne (MPH), optoelectronic oscillator (OEO) [11] and microwave photonic filter [12]. The method using MPH has high demodulation speed, but the dispersion compensation fiber is easily affected by temperature, which affects large-scale multiplexing. When using OEO to achieve wavelength demodulation, the signal-to-noise ratio and stability are high, but the multiplexing capacity is limited. Wavelength demodulation using MPF is realized by detecting microwave signals, which can realize large capacity and quasi-distributed sensing. In 2015, Javier Hervas et al. proposed a sensing method of FBG cascaded sensor based on wavelength-RF delay mapping. By using dispersive fiber to map wavelength change of FBG into RF delay, the experimental resolution of 14 pm was obtained [13]. In 2018, Di Zheng et al proposed a demodulation method for FBG based multi-core optical fiber curvature sensor. The curvature was reflected by the notch frequency of MPF, and the sensitivity reached 92 MHz/m−1[14]. In 2023, Chiranjit Ghosh proposed an FBG wavelength demodulation method combining microwave detection and nonlinear four-wave mixing (FWM), which converted the wavelength offset of FBG into higher-order FWM signals and finally into intensity changes of RF signals to realize wavelength demodulation. The obtained sensitivity was 36.529 µV /µɛ [15]. In 2023, Qiang Liu proposed a MPF sensing method based on fiber ring resonator (FRR). Due to the Fresnel effect of the MPF of parallel FRR, the strain sensitivity of the system was greatly increased. Experimental results showed that the strain sensitivity was -33.862 kHz/µɛ [16]. In 2017, Deming Liu et al. built a quasi-distributed microwave response sensing system based on weak gratings to achieve high-precision quasi-distributed sensing [17]. This method ignored the influence of wavelength change on the reflected optical power caused by weak gratings, and could not demodulate the wavelength of ordinary FBG.
In this paper, we propose a FBG wavelength demodulation method based on time-domain detection, which converts the frequency domain response of the system into time-domain, and realizes wavelength demodulation and positioning of FBG by measuring the amplitude and position of the time-domain peak. The effect of spectrum overlap and power fluctuation on wavelength demodulation accuracy is eliminated by normalization method, so as to increase the number of FBG multiplexes and realize the large-capacity quasi-distributed measurement. This method has the characteristics of high demodulation precision, strong multiplexing ability and high precision positioning.
2. Experimental system and principle
The FBG wavelength demodulation method proposed in this paper regards the sensing system as a transmission system, and realizes wavelength demodulation by measuring the S21 parameters and converting them into time-domain responses. Figure 1 shows the system diagram and waveform of the main positions in the system.
The wide spectrum light emitted by amplified spontaneous emission (ASE) light source in the system is sent to erbium-doped fiber amplifier (EDFA) after intensity modulation by electro-optic modulators (EOM). The EOM is driven by bias controller,the function of which is to provide a bias voltage to the EOM, so that the static operating point of EOM is offset at the quadrature bias point to ensure that the output signal power is large enough and no distortion occurs. The modulated wide spectrum light is amplified by the EDFA and sent to cascaded FBG sensors through the circulator. The reflected light of the FBG enters the optical filter, converting the wavelength change into change in optical power, and which is converted into electrical signal by photo diode detector (PD). The S21 parameters are measured by VNA. The 1 port of the VNA is connected to the EOM, and which outputs the RF signal for amplitude modulation of the ASE light. Port 2 is connected to the output of PD and receives the electrical signal. Personal computer (PC) transforms the S21 parameters by IDFT to obtain the time-domain response. The amplitude and location of the time-domain peak are measured to realize wavelength demodulate and positioning.
In the system shown in Fig. 1, each FBG is connected by a certain length of fiber, resulting in different time delay for the reflected light of each FBG to reach PD. Each FBG in the system is equivalent to a delay unit of the optical filter, so the system essentially constitutes an MPF.
When N FBGs are connected to the system, the frequency response can be represented by Eq. (1) [18]:
In Eq. (1), ω is the angular frequency of the radio frequency signal, Tk represents the time when the modulated light enters PD from EOM through the k-th FBG, N is the number of FBG, λk represents the wavelength of the k-th FBG, pk(λk) is the weight of the k-th FBG, which has a linear relationship with the reflected optical power.
The impulse response of the system is obtained by IDFT on Eq. (1) as shown in Eq. (2):
As can be seen from Eq. (2), each FBG corresponds to a peak in the TR (time-domain response), and the ATDP (amplitude of the time-domain peak) is proportional to the optical power, and the interval between the peaks depends on the optical transmission time between FBGs.
When the central wavelength of the FBG is changed by external environment, the optical power entering the PD will change due to the optical filter, so that the ATDP will change. The wavelength demodulation of FBG can be realized by detecting the change of ATDP.
The time corresponding to the peak in the TR is the time when the light reaches PD after passing through EDFA, FBG and optical filter from EOM. Therefore, using the propagation speed of light in the fiber, the spatial position of the FBG corresponding to each peak can be calculated. From the above analysis, it can be seen that the sequence and spacing of the peaks in the time-domain response represent the spatial placement order and the spatial distant of the FBG in the system. The spatial distant between two FBGs can be expressed as:
In Eq. (3), vcore represents the propagation speed of light in the optical fiber core; t is the transmission time of light traveling back and forth between two FBGs, which can be obtained by the time-domain response after IDFT of S21 parameters.
The propagation speed of light in the fiber core can be expressed as:
In Eq. (4), n0 is the vacuum refractive index, c0 is the propagation speed of light in vacuum, and ncore is the refractive index of the optical fiber core.
By using Eq. (3) and Eq. (4), the distance between each FBG in the system can be obtained, so as to realize the spatial positioning.
The data of S21 obtained by VNA is discrete, and it remains discrete data after IDFT to time-domain. So, the positioning resolution depends on the time interval between two points of the time-domain response data. According to the principle of Fourier transform, the relationship between the time interval and the sampling frequency is Δts = 1/fs.
According to Nyquist sampling theorem, the relation between sampling frequency and bandwidth is fs = 2B. Therefore, when the sweep bandwidth of VNA is the maximum value of BM, the minimum positioning resolution can be obtained, that is:
According to the principle of discrete Fourier transform (DFT), the spectrum obtained by the time-domain signal after DFT is composed of two symmetrical parts, half of which is the effective spectrum. When the amount of data in the frequency domain is N, the corresponding amount of time-domain data is 2N. Therefore, the maximum positioning range can be expressed by Eq. (6) as follows:
To sum up, the positioning resolution and maximum range can be obtained by Eq. (3) – (6).
3. Experiments and results
3.1 Temperature sensing
In this part, the wavelength demodulation method proposed in this paper will be verified by temperature sensing experiments, and the temperature sensitivity of the system will be obtained. The effect of spectrum overlap and optical power fluctuation on wavelength demodulation is analyzed, and a method to eliminate the above effect is proposed.
3.1.1 Experiment settings
A total of seven temperature sensors, FBG1-FBG7, are connected in the system, and their central wavelengths are different. For the convenience of comparison, the seven FBGs are divided into four groups: FBG1, FBG2, FBG6-FBG7, and FBG3-FBG5. Table 1 shows the details of the FBG grouping. Within the temperature range set in the experiments, the spectra of FBGs in the first and second groups do not overlap, two FBGs in the third group will overlap, and three FBGs in the fourth group will overlap.
Table 1. FBG grouping
A programmable optical filter (Model: FINISAR Waveshaper 1000A) is used to convert the wavelength change to the power change. Since there is no FBG for temperature measurement in the first group, in order to improve the sensing sensitivity, the optical filter only covers the 2-4 groups with a wavelength width of 1.5 nm to ensure that the FBGs can be affected by the optical filter within the range of temperature change. The optical filter settings are shown in Fig. 2. In order to study the effect of filter gain on sensing sensitivity, the minimum gain of the three band-gap parts of the optical filter are 0.316, 0.316 and 0.398 respectively, and the maximum gain is 1.
The S21 parameters and TR curve obtained by the above experimental system are shown in Fig. 3. There are 7 FBGs in the experimental system, so the TR curve contains 7 peaks, and the sequence is consistent with the spatial cascade sequence of the FBGs.
3.1.2 Spectrum overlap effect
When the spectrum of FBGs overlaps, the conventional FBG wavelength demodulation method cannot accurately demodulate the wavelength change, thus affecting the sensing accuracy. In order to prevent spectrum overlap, it is necessary to increase the wavelength interval of FBG. The number of multiplexed FBG will be limited when the bandwidth of the light source is certain. The wavelength demodulation method proposed in this paper can achieve accurate wavelength demodulation in the case of serious spectrum overlap, so that the bandwidth utilization of the light source can be greatly improved, and the large capacity multiplexing of FBG can be realized.
In the following, the wavelength demodulation performance after spectral overlap is studied by experiments and data processing method. The method to eliminate the effect of spectrum overlap is given, and the limit of the overlap degree of two FBG spectra allowed for accurate wavelength demodulation is obtained.
The wavelength demodulation method proposed in this paper is to convert the wavelength change of FBG into the optical power change through the optical filter, and then demodulate the wavelength through the change of the ATDP of the system. When the wavelength of FBG changes, the degree of spectrum overlap will change, which in turn changes the optical power. Therefore, when spectrum overlap occurs, the optical power is affected not only by the optical filter, but also by the spectrum overlap. Therefore, to eliminate the effect of spectrum overlap on wavelength demodulation, it is necessary to eliminate the change of optical power caused by spectrum overlap and retain the effect of optical filter.
In order to achieve the above purpose, the experiment is divided into two steps: calibration experiment and sensing experiment. The purpose of the calibration experiment is to obtain the influence of the spectrum overlap on the change of optical power. Therefore, when conducting the experiment, the optical filter is removed. The temperature of the water bath is set to rise from 14°C to 80°C, and the relationship between the ATDP and temperature is obtained only in the case of spectrum overlap. In the sensing experiment, the optical filter shown in Fig. 2 is added to the system, and the above process is repeated to obtain the relationship between the ATDP and temperature in the case of the effect of spectrum overlap and the optical filter. By normalizing the two relations obtained from the two experiments, the effect of spectrum overlap can be eliminated, thus the wavelength demodulation in the case of spectrum overlap can be realized.
The spectra obtained through calibration experiment is shown in Fig. 4. It can be seen that the spectrum of FBG2 in Group 2 does not overlap with that of other FBG within the entire temperature range. Therefore, with the increase of temperature, the optical power does not change, but the reflection spectrum moves in the direction of increasing wavelength. The spectrum of FBG7 is close to that of FBG6 in Group 3. When the temperature is low, the spectrum of FBG7 gradually enters from the left side of the spectrum of FBG6, and then gradually moves away from the spectrum of FBG6 as the temperature rises until it is completely separated. The spectrum of FBG5 in Group 4 is initially located in the middle of the FBG3 and FBG4 spectra, and as the temperature increases, it first leaves the spectrum of FBG3, then separates, then overlaps with the spectrum of FBG4, and finally crosses over the spectrum of FBG4.
Figure 5 shows the spectra with filter (sensing experiment) and without filter (calibration experiment) at different temperature. It can be seen that when there is no optical filter, in the temperature range, the reflection spectrum amplitude of FBG2 remains unchanged with the increase of temperature. The spectrum amplitude increases gradually with the increase of temperature after the optical filter is added. Unlike FBG2, FBG5 and FBG7 are simultaneously affected by optical filters and other FBGs in the same group, resulting in a change in spectrum amplitude, but the law of change is not obvious.
The TR of the system is obtained after IDFT is performed on the S21 data of the two experiments measured by VNA. Figure 6 shows the TR of FBG2, FBG5 and FBG7 under the two conditions of calibration experiment and sensing experiment. It can be seen that the ATDP of FBG2 is basically unchanged without filter. When the optical filter is added, the change of the ATDP is consistent with the characteristics of the optical filter. Without the optical filter, the ATDP of FBG5 increases first, then decreases and then increases with the increase of temperature, because the reflection spectrum of FBG5 first overlaps with FBG3, and then overlaps with FBG4 with the increase of temperature, which corresponds to the law of overlap change caused by spectral movement in Fig. 4. After the optical filter is added, the ATDP is attenuated, but the envelope is similar to that without the optical filter. The ATDP corresponding to FBG7 gradually increases with the increase of temperature, which is caused by the reflection spectrum of FBG7 gradually moving away from FBG6, which is also consistent with the rule shown in Fig. 4. After the optical filter is added, the overall envelope appears similar to that without the optical filter.
From the above analysis, it can be seen that the spectrum of FBG2 is not affected by spectrum overlap, so when there is the optical filter, its ATDP gradually increases with the increase of temperature. FBG5 and FBG7 are affected by spectrum overlap, their ATDPs are nonlinear to temperature, and the envelope of ATDPs changing with temperature is roughly the same with and without filters. When the reflection spectra of the two FBGs are seriously overlapped, it can be measured by the spectrometer that the optical power attenuation is greater than 10 dB. When the reflection spectra of the two FBGs are completely overlapped, the reflected optical power of one FBG drops to 0. Overall, the optical power effect caused by spectrum overlap is greater than that of the optical filter, so only by eliminating the effect of spectrum overlap can accurate wavelength demodulation be achieved.
3.1.3 Method of eliminating spectrum overlap effect
The key to achieve accurate wavelength demodulation is to eliminate the influence of spectrum overlap on optical power. Therefore, this part will propose a normalized data processing method to process the data of calibration experiment and sensing experiment.
Figure 7 shows the temperature-wavelength relationships of the three FBGs obtained by calibration, and it can be seen that the wavelengths of the three FBGs exhibit a linear relationship with temperature. Suppose that the temperature-wavelength relationship is:
In Eq. (7), λ is the central wavelength of FBG, k1 is the temperature-wavelength coefficient of FBG, and C1 is a constant.
After the reflected light of FBG passes through the optical filter, the power of reflected light can be expressed as:
In Eq. (8), P is the reflected optical power of FBG, P0 is the incident optical power of FBG, k2 is the slope of the band-gap part of the optical filter, H(λ) is the characteristic function reflecting the influence of spectrum overlap on the reflected optical power of FBG, and C2 and C3 are constants. In Eq. (8), k2 > 0 indicates that there is an optical filter; k2 = 0 means that the gain of the optical filter is 1, that is, there is no optical filter. According to Eq. (8), when the temperature changes, the degree of spectral overlap will also change, and the reflected optical power will also change accordingly. In this way, both the filter and spectral overlap will affect ATDP, resulting in large errors in the demodulation results.
Because there is a linear relationship between the ATDP and the reflected optical power, and when the optical power is 0, the ATDP is also 0, so the relationship between the two can be expressed as:
In Eq. (9), k3 is a constant. For the case that there is no filter in the system, that is, when k2 = 0, substituting Eq. (9) into Eq. (8) can obtain the ATDP without the optical filter, as shown in Eq. (10).
When the optical filter is added to the system, that is, k2 > 0, the ATDP can be obtained similarly, as shown in Eq. (11).
By dividing Eq. (11) and Eq. (10), we can obtain:
In Eq. (12), k = (k1·k2)/C3, C = (k2·C1 + C2)/C3, which are constants. I1/I0 is defined as relative amplitude change (RAC). According to Eq. (12), the RAC obtained by the above method shows a linear relationship with temperature, eliminating the influence of spectrum overlap.
3.1.4 Experimental results and analysis
According to the above analysis, using Eq. (12) can eliminate the influence of spectrum overlap and obtain the relationship between RAC and temperature. Figure 8 shows the relationship curves of RAC and temperature of FBG2, FBG5 and FBG7, as well as spectrum at different temperature.
The reflection spectrum of FBG2 does not overlap with that of other FBGs within the entire temperature range, and its reflected optical power is only affected by the optical filter, so the RAC increases linearly with temperature. In Fig. 8(a), the relationship curve between temperature and RAC of FBG2 is shown on the left, and the reflection spectrum of FBG2 at 20°C, 44°C and 80°C is shown on the right. It can be seen that the R2 reaches 0.9969. As can be seen from the spectrum in Fig. 8(b), the reflection spectrum of FBG5 is in the middle of that of FBG3 and FBG4. With the change of temperature, its reflection spectrum overlaps with that of FBG3 and FBG4 successively. The spatial position of FBG5 is behind FBG3 and FBG4, so when the overlap degree is relatively large, the reflected power of FBG5 is very low, resulting in a small ATDP and a large measurement error. Only in the range of 30 °C-44 °C, the linear relationship between the RAC and temperature is good, and the R2 reaches 0.9986. When the temperature is too low or too high, the linear relationship is also poor due to the large error. Figure 8(c) shows the temperature sensing characteristics of FBG7. It can be seen that when the temperature is low, the reflection spectrum of FBG7 overlaps with that of FBG6. With the increase of temperature, the reflection spectra of the two gradually separated. When the temperature is 42°C, there is a good linear relationship between the RAC and temperature, and the R2 is 0.9584. When the temperature is low, similar to FBG5, the data deviate more due to the larger errors.
From Fig. 8(b) and Fig. 8(c), it can be seen that there is a linear relationship between the RAC and temperature only within a certain temperature range. In Fig. 8(b), precise wavelength demodulation cannot be accomplished at temperatures below 30 ° C or above 44 ° C due to the excessive overlap of FBG reflection spectra. In Fig. 8(c), the same situation occurs when the temperature is below 42 ° C. The wavelength of FBG at this time can be calculated according to the temperature point and the temperature sensitivity of FBG, and the wavelength difference of overlapping FBG can be calculated, that is, the minimum wavelength difference allowed by the system, which is about 0.25 nm. Since the temperature points selected in the test are discrete, the minimum wavelength difference calculated according to the above method is approximate. If the temperature step is smaller, the calculated minimum wavelength difference is closer to the exact value. As shown in Fig. (7), the temperature-wavelength coefficients of FBG2, FBG5 and FBG7 are 0.01067 nm/°C, 0.01077 nm/°C and 0.01072 nm/°C respectively.
The slope of the linear fitting curve shown in Fig. 8 is the temperature sensitivity measured by the experimental system, which are 0.00447 RAC/°C, 0.00503 RAC/°C and 0.00397 RAC/°C respectively. As can be seen from Fig. 7, the relationship between temperature and wavelength of FBG2, FBG5 and FBG7 is different, and the slopes of optical filter corresponding to the three FBGs are also different. Therefore, under the current experimental conditions, the temperature sensitivity of the three FBGs is different. According to the parameters of the optical filter and the temperature-wavelength relationship of the three FBGs, the temperature sensitivity of FBG can be calculated, as shown in Eq. (13):
In Eq. (13), A is the minimum gain of the band-gap of the optical filter, which are 0.316, 0.316 and 0.398 respectively. TFBG is the temperature change of FBG corresponding to the optical filter bandwidth, which can be expressed as:
In Eq. (14), kt is the temperature-wavelength coefficient of FBG; Bf is the bandwidth of the band-gap of the optical filter, which is set to 1.5 nm in the experiment.
The temperature sensitivity calculated using Eqs. (13) and (14) and the temperature sensitivity measured experimentally are shown in Table 2.
Table 2. Comparison of calculated and measured values for temperature sensitivity
By comparing the calculated and measured values, it can be seen that the two are basically consistent, indicating that the method proposed in this paper is effective to eliminate the influence of spectrum overlap.
Due to the different temperature-wavelength relationships between FBG2 and FBG5, the temperature sensitivity of FBG5 is slightly higher than that of FBG2 when the minimum filter gain is both 0.316. When the temperature-wavelength relationship of FBG2, FBG5 and FBG7 are close, the temperature sensitivity of FBG2 and FBG5 is higher than that of FBG7, because the minimum gain of the optical filter of the former is smaller than that of the latter. It can be seen that the temperature sensitivity is related to the temperature-wavelength relationship of FBG and the gain of the optical filter, which is consistent with the rules embodied in Eq. (13) and Eq. (14).
3.2 Effect of optical power fluctuation
The stability of optical devices, flange looseness, and fiber bending in the system can all affect the optical power, thus affecting the ATDP. This results in the fluctuation of P0 in Eq. (8), If the temperature change is reflected directly by the ATDP, additional errors will be brought. According to Eq. (12), RAC is independent of P0, therefore, the normalization method proposed above can not only eliminate the influence of spectrum overlap, but also reduce the influence caused by optical power fluctuations, which will be verified by changing the power of the light source in this part.
In the first step of the experiment, the gain coefficient of the optical filter is set to 1, the power of the light source is set to increase from 20 mW to 32 mW with the step of 2 mW, and the ATDP of the three FBGs is recorded. In the second step, other experimental conditions are kept unchanged, only the optical filter gain coefficient is changed to 0.5, and the above process is repeated. The results obtained are shown in Fig. 9. It can be seen that the ATDP increases linearly with the increase of optical power, and the ratio of the ATDP is basically consistent with the ratio of the optical filter gain coefficient set in the two steps of the experiments, which further indicates that the optical power fluctuation of the system has little influence on the experimental results after processing with the algorithm proposed in this paper, and only the effect of the optical filter is retained.
3.3 Positioning function
The TR can be obtained after IDFT of the S21 parameters, and the distance between FBGs can be obtained after the time corresponding to the ATDP is transformed, so as to realize the positioning of the sensor. This part will test the positioning function.
In the positioning experiment, the wavelength range of the ASE (Model: CONQUER KG-ASE-CL) is 1520-1570 nm. 7 FBGs are connected in the system, and the 3 dB bandwidth is about 0.3 nm. The sweep frequency range of the VNA (Model: KEYSIGHT N9923A) is set to 2 M-4 GHz, and the sampling number is 10001. As can be seen from Eq. (5) and Eq. (6), under the above settings, the maximum range of the measured distance of the system is 250 m, and the positioning resolution is 1.25 cm.
Because the optical fiber is thin and flexible, and there is a residual length inside the armored optical cable, it is difficult to accurately measure the length of the optical fiber. Aiming at the above reasons, the length of the optical fiber between the 7 FBGs is roughly measured with a meter stick with an index value of 1 mm, so as to preliminarily verify the positioning function of the system. Then, the optical fiber delay line is added to the system to simulate the change of optical fiber length, and the positioning resolution and error of the system are accurately measured.
To make a rough measurement with a meter stick, straighten the optical cable and lay it flat on the ground, then use the meter stick to measure the distance between the middle of the two FBG sensors. The optical fiber lengths between FBGs measured by meter stick and experimental system are shown in Table 3. It can be seen that the lengths obtained by the two methods are basically the same, indicating that the positioning is basically accurate. At the same time, there are errors, and the optical fiber length measured by the meter stick is smaller than that measured by the experimental system, because the residual length of the fiber in the cable cannot be measured with the meter stick, and the exact position of FBG in the sensor package structure can not be obtained accurately.
Table 3. Optical fiber length between FBGs measured by meter stick and experimental system
In order to accurately measure the positioning resolution of the system, a fiber delay line (Model: General Photonics MDL-002) is added between FBG1 and FBG2 to simulate the change in fiber length by varying the transmission time of light between the two FBGs. According to the VNA parameter settings, the positioning resolution of the system is 1.25 cm. As can be seen from Eq. (5), the corresponding transmission time is 125 ps. Therefore, the delay time of the optical fiber delay line is set to vary from 125 - 1000 ps with the step of 125 ps.
Figure 10(a) shows the distance change of the time-domain peak when the step is 125 ps. It can be seen that the position of the peak corresponding to FBG1 basically does not change, and the position of the peak corresponding to FBG2 to FBG7 moves to the right at a step of 1.25 cm, which is consistent with the theoretical analysis. The length of the optical fiber corresponding to the step of the delay time set in the above experiment is exactly the positioning resolution of the system, so there is no error between the measured value and theoretical analysis. When the delay time step is not an integral multiple of 125 ps, the measurement error will be introduced. Figure 10(b) shows the distance change measured when the delay time step is less than or greater than 125 ps. It can be seen that when the delay time changes less than 125 ps, such as from 500 ps to 600 ps, theoretically, the peak corresponding to FBG2 should move 1 cm, while the horizontal coordinate of the peak corresponding to FBG2 moves to the right at 1.25 cm. When the delay time changes by more than 125 ps, for example from 100 to 500 ps, the moving distance of the peak corresponding to FBG2 should be 4 cm theoretically, while the experimental result is 3.75 cm, resulting in an error. The above experimental data show that the measured results are all integral multiples of 1.25 cm, indicating that the positioning resolution of the system is 1.25 cm.
Fig. 10. The distance change of the time-domain peak when the delay time is different. (a) The step is 125 ps. (b) The step is less than or greater than 125 ps
In order to test the positioning error as a whole, the delay time range of the optical fiber delay line is set to be 0-1000 ps with the step of 100 ps. The theoretical values, experimental values and deviations obtained are shown in Fig. 11. It can be seen that the maximum error is 0.5 cm.
In general, the length of the bare FBG is greater than 1 cm, and after packaging, the length of the FBG sensor is about 10-20 cm. Therefore, in practical application, the distance between the two FBG sensors is greater than the minimum positioning resolution of the system, so that high-precision positioning can be achieved.
4. Discussion
The sweep bandwidth of the VNA used in the experiment system is 2 MHz-4 GHz, and the sampling number is 10001. If high performance VNA is used, the positioning range and resolution can be further improved. In addition, the increase of sweep bandwidth and sampling number will also lead to a longer measurement time, affecting the real-time performance of the system. For example, if a VNA with a maximum sweep bandwidth of 26.5 GHz and a sampling number of 200001 is used, the positioning range and resolution can reach 928 m and 1.88 mm.
In order to verify the feasibility of the proposed scheme, a mature VNA is used. During data processing, the S21 data collected by VNA is exported to PC for further processing. Therefore, the measurement time of the demodulation system consists of the collection time of S21 data and the data processing time, among which the collection time is the main part. In the follow-up study, a microprocessor-based S21 acquisition and processing module will be developed to realize real-time data processing and further obtain the measurement time of the demodulation system.
The minimum gain coefficient of the optical filter used in this experiment is 0.316. If the gain coefficient is further decreased, the sensing sensitivity can be increased. However, if the attenuation is too large, the optical power will be reduced, and the ATDP will be reduced, resulting in large measurement errors.
The bandwidth of the light source and the bandwidth of the FBG will affect the multiplexing capability of the system. In the experiment, the bandwidth of the light source is 1520-1570 nm. If the bandwidth is increased, the multiplexing capability can be further improved. The bandwidth of the FBG used in the experiment is 0.3 nm, and the limit of the wavelength difference measured between two FBGs is 0.25 nm. If the FBG with smaller bandwidth is used, the wavelength difference limit can be further reduced, thus improving the multiplexing capability, but it will affect the dynamic range of temperature measurement.
5. Conclusion
In this paper, a novel wavelength demodulation method of FBG based on time-domain detection is proposed. The method realizes wavelength demodulation and positioning of FBG by measuring the amplitude and position of the peak in TR. The influence of spectrum overlap and positioning resolution are studied, and a normalization method is proposed to eliminate the influence of spectrum overlap and optical power fluctuation on wavelength demodulation. The calculation method of positioning resolution is given and verified by experiments. The experimental results show that when the sweep bandwidth of the VNA is 2 MHz - 4 GHz and the sampling number is 10001, the minimum positioning resolution is 1.25 cm. When the minimum gain coefficient of the optical filter is 0.316, the maximum sensitivity is 0.00503 RAC/°C. When the FBG bandwidth is 0.3 nm, the limit of the wavelength difference between two FBGs is 0.25 nm under the premise of ensuring the system sensing accuracy. This method allows the reflection spectrum of FBG to overlap to some extent. Therefore, compared with the traditional wavelength demodulation method, this scheme can make full use of the bandwidth of the light source and improve the multiplexing capability of FBG. This method is applicable not only to temperature sensing, but also to the sensing of physical quantities such as strain, refractive index and pressure. This method has the advantages of high demodulation precision, strong multiplexing ability, high precision positioning and so on.
Funding
National Natural Science Foundation of China (62205105); S&T Program of Hebei (SZX2020034).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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