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Abstract
In this paper, high spatial-resolution distributed temperature sensing has been realized based on a femtosecond laser written ultra-weak Fabry-Perot Array (FPA). 50 identical Fabry-Perot cavities are fabricated in a 10 mm long optical fiber by femtosecond laser point-by-point written technology, and the corresponding spatial resolution is as high as 200 µm. Besides, by employing the total phase demodulation method, the optical path lengths (OPLs) in the ultra-weak FPA are successively demodulated based on the Rayleigh backscattering signal recorded by an optical frequency domain reflectometry (OFDR), and therefore the absolute temperature values instead of the relative ones can be obtained. When compared with the conventional single mode fiber-based OFDR, the proposed ultra-weak FPA presents both higher spatial resolution and lower temperature sensing uncertainty (0.25 °C) benefiting from the periodically enhanced Rayleigh backscattering. Furthermore, the experiments also confirm that the ultra-weak FPA can be applied for absolute temperature field profile sensing with large temperature gradient, which is particularly suitable for high-resolution temperature measurement of miniature devices.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber optic sensors have received widespread attention due to their advantages such as small size, easiness to form the distributed sensing network, immunity to electromagnetic interference, and adaptability to harsh environments etc. The distributed fiber optic sensing breaks through the limitation of single-point fiber optic sensor, which can realize the measurements of a certain range of points instead of a single point. As far as fiber optic distributed sensing is concerned, it can be mainly divided into optical time domain reflection (OTDR) and optical frequency domain reflection (OFDR). When compared with the OTDR, OFDR exhibits the obvious advantages in spatial resolution, which offers as the mainstream solution for distributed sensing systems with millimeter resolution. Due to this feature, it has been widely applied for temperature [1], strain [2], stress [3], refractive index [4,5], vibration sensing [6] with high measurement resolution.
Essentially, limited by the current detection level of photodetector, the obtained intensity of Rayleigh backscattering signal (RBS) per meter in standard telecommunication fiber is extremely weak, which in turn results in the weak spectral correlation quality, large uncertainty in wavelength shifts and further strong measurement noises. Thus, choosing a larger spatial subsection with more data sampling points is necessary to enhance the correlation quality between the measured RBS profile and the reference one, which finally suppress the sensing noise level and improve the sensing accuracy. Therefore, due to the inherent existence of tradeoff between spatial resolution and sensing precision in OFDR, it is difficult to further reduce the spatial resolution less than millimeter level on the premise of ensuring high accuracy. Assuming the sweeping range of the tunable laser source (TLS) in OFDR is fixed, strong RBS with high signal to noise ratio (SNR) is beneficial to improve the spectral demodulation accuracy and the spatial resolution.
Currently, many methods have been proposed to enhance the RBS for OFDR sensing. To randomly enhance the RBS along the fiber, UV exposure on photosensitive fiber [7], femtosecond radiated fiber [8], MgO-doped high scattering Fibers [9,10], thin-core high-NA fiber [11] and random fiber grating [12] have been reported. On the other side, large-scale fiber Bragg gratings (FBG) and Fabry-Perot (FP) have also been inscribed into the fiber core to periodically enhance the reflected power and improve the demodulation accuracy of distributed sensing. In 2017, Gui et al. proposed 1.5 mm spatial resolution over 6680 FBGs along a 10m-long fiber, the temperature measurement accuracy is roughly 1 °C [13]. In 2019, Wang et al. demonstrated a ultra-short FBG-based FP micro-cavity array with the physical cavity length of 1.24 mm and the 440-µm FBG, and a spatial resolution of 880 µm is achieved [14]. Until now, the point-by-point inscription of Bragg gratings array is still a complex process, and the fabricated lengths is around ∼1 mm [15,16]. The spatial resolution of the FBG array requires to calculate the sum of the FBG length and the grating spacing between the two FBGs. Hence, the spatial resolution is difficult to be further decreased due to the occupied space of the FBG itself. In 2015, Chen et al. realized a detection limit of ∼0.1 °C at a spatial resolution of 1 cm by constructing an ultra-weak intrinsic Fabry-Perot cavity array [17]. In 2021, Zhu et al. cascaded three FP sensors for quasi-distributed refractive index sensing, and the root-mean-square error of the demodulated wavelength is 4.6 pm in OFDR system. In those methods, the wavelength-coded demodulation of the individual sensor presents high demodulation precision. However, the spatial resolution in sub-millimeter scale in the promising of ensuring high accuracy is still a great challenge for the distributed fiber optic sensing particularly in advanced biomedical application [18] or absolute temperature measurement of miniature device. It should be noted that the long period fiber grating (LPG), fabricated by the arc-discharge release or femtosecond period holes drilling and scanning, also has greatly periodically enhanced RBS. However, it is mainly used for single-point fiber sensing instead of distributed measurement. The LPG usually has relatively strong RBS, high insertion loss and is characterized by part of power coupling from the core mode to the high-order cladding modes.
Direct measurement of absolute temperature profile is also essential in temperature sensing. However, the relative value is usually obtained by the comprehensively used cross-correlation method in OFDR-based system [19]. Therefore, in this paper, we propose a femtosecond laser written ultra-weak FPA to realize the distributed absolute temperature measurement with high spatial resolution. By employing the point-by-point technology of femtosecond laser, a single-mode fiber core is punctured and every two adjacent points form an F-P cavity. 51 points, or 50 identical F-P cavities, are formed in 10 mm length fiber, with corresponding sensing spatial resolution of 200 µm. Besides, the cavity lengths of the F-P cavity are temperature sensitive and each of them can be demodulated sequentially with linear regression method for absolute distributed temperature measurements instead of relative values. Beneficial from the enhanced RBS signal, the sensing accuracy is improved effectively compared with the SMF. The fabricated ultra-weak FPA shows great potentials in high-resolution distributed temperature sensing of miniature device in a narrow space.
2. Ultra-weak FPA fabrication and experiment setup
As seen in Fig. 1, the identical ultra-weak FPA is written by the point-by-point method using a femtosecond laser (repetition frequency: 1 kHz, pulse width: 100 fs). A segment of single-mode fiber (SMF) (Corning, SMF28) coating is stripped off and cleaned, and then fixed on a high-precision 3D stage. The femtosecond laser is adjusted to focus on the fiber core by a 50 × microscope objective. The incident pulse energy is set to be 0.5 µJ, and the fiber moves periodically with an increment of 200 µm. At each point, the femtosecond laser emits with a duration of 1 s, and the exposed area is then modified by the ultrafast laser irradiation. By this method, the Rayleigh scattering is enhanced owing to the formation of laser-induced nano-gratings inside the fiber core [8]. The periodically enhanced scattering spectra of identical ultra-weak FPA is observed by an OFDR system in real time. The number of femtosecond laser modified spots is set to be 51 in a 10-mm distance, and the average total reflected light power is measured as 0.1 µW.
An OFDR system is established as shown in Fig. 2. The linear sweep light is emitted by a tunable source laser (Santec, TLS510). The power is around 10 mW, and the sweeping range and speed are set as 1510.0 − 1570.0 nm and 100 nm/s respectively. The spatial resolution is 13.8 µm according to the expression of $\mathrm{\Delta}{z} = \textrm{c}/({2{\textrm{n}_g}\mathrm{\Delta}{f}} )$, where $\textrm{c}$ and ${\textrm{n}_g}$ are the light velocity and the group refractive index, respectively, and $\mathrm{\Delta}{f}$ is the scanning range of the TLS. The emission light is divided into two beams by OC2, and the two beams are injected into an auxiliary interferometer (AI) and a main interferometer (MI) respectively. The AI is a typical Mach-Zehnder type interferometer with two optical 50:50 couplers OC1 and a delay fiber of 26.38 m. The AI generates equal optic-frequency-interval sampling clock signal to correct the nonlinear frequency sweeping of the TLS, and the produced sample frequency is 1.528 MHz. On the other hand, the strong light enters into the MI, and the light is further divided into two parts by another OC2. Among them, 1% of the light enters the polarization controller, and 99% of the light passes through the circulator with the RBS of the fiber under test (FUT). The two parts of light beat with each other in another OC1. In this study, the polarization diversity method is adopted to eliminate the polarization fading. The beating signal is divided into p light and s light by a polarization beam splitter (PBS), and the electrical signals converted by the two photodetectors are then collected by the data acquisition card. The RBS versus location could be calculated from the vector summing of the s and p component, and the spatial distribution of the RBS can be obtained by applying the Fast Fourier Transformation (FFT) to the signal in optical frequency domain (beating signal in time domain). The Fig. 3 shows the final spatial domain RBS spectra of the identical ultra-weak FPA. The inset shows the enlarged spectra located at 2.6 m, and we can observe that the RBS at each point has been averagely enhanced by around 20 dB.
Fig. 1. Fabrication schematic of femtosecond laser written identical ultra-weak FPA by the point-by-point method.
Fig. 2. OFDR system for identical ultra-weak FPA-based distributed temperature sensing test. (TLS: tunable laser source, AI: auxiliary interferometer, MI: main interferometer, OC1: 50:50 optical coupler, OC2: 1:99 optical coupler, PC: polarization controller, OC: optical circulator, PBS: polarization beam splitter, PD: PIN photodetector, DAQ: data acquisition unit, and FUT: fiber under test).
3. Demodulation method of the ultra-weak FPA
Absolute temperature profile can be determined by analyzing the variation of optical path length (OPL) of each FP cavity. The demodulation procedure of each OPL in the FPA is shown in Fig. 4(a) and (b). Firstly, the fabricated ultra-weak FPA includes 50 identical FP micro cavities, as shown in Fig. 4(a). Secondly, a slide window including two peaks of RBS along the ultra-weak FPA is successively filtered out to analyze the corresponding OPL. Thirdly, the inverse FFT is applied to the peaks to obtain the wavelength spectrum of each individual FP micro cavity. Figure 4(c) shows the typical spectra for the 1er, the 25er and the 50er FP cavity. Fourthly, by using the linear regression (LR) method and the total phase estimation, all the OPLs in the ultra-weak FPA can be calculated based on their interference spectra [20,21]. Particularly speaking, according to the relationship between the phase and OPL ($\varphi = \textrm{k}{\cdot}L + {\varphi_0}$, where $\varphi_0$ is the initial phase and $\textrm{k}$ is the wavenumber, and is the phase corresponding to each wavenumber), the phase $\varphi$ can be obtained from the Hilbert transformation with the discrete wavenumber of $\textrm{k}$. Then using LR method, the OPL and the variable $\varphi_0$ can be preliminarily estimated, and the total phase of $\Phi_{tot}$ is subsequently calculated based on the expression of $\Phi_{tot} ={\textrm{k}_C}{\cdot}L + \varphi_{0}$ where ${\textrm{k}_C}$ is the central frequency of the $\textrm{k}$. Finally, the OPL is determined according to the expression of $OPL{ = \Phi_{tot}}/{\textrm{k}_\textrm{C}}$. It worth noting that, if the RBS signal for OPL demodulation is relatively weak, phase jump phenomena may occur occasionally, and they can be manually corrected with the right fringe order. Figure 4(d) shows the typical OPLs of the ultra-weak FPA, and they are all around 291 µm, which agrees well with the physical period of 200 µm set in the point-by-point femtosecond laser writing process. Hence, the spatial resolution can be considered as 200 µm for the proposed distributed sensing system.
Fig. 4. (a) Demodulation procedure of the ultra-weak FPA; (b) Slide window applied on RBS; (c) Spectra of the three different FPs obtained by inverse FFT; (d) The OPLs for all the FPs along the ultra-weak FPA.
4. Temperature responses
The ultra-weak FPA and a segment of SMF are bounded together, and both of them are put into an oven for temperature response test. They are separated with a distance of 50 cm, and simultaneously heated from 30.0 °C to 65.0 °C with an increment of 5.0 °C. The temperature responses of the ultra-weak FPA are firstly analyzed. For each temperature point, the OPLs and their shift values of the ultra-weak FPA are calculated from the above demodulation procedure. Obviously, the shift value of the OPLs has strong linear relationship with the temperature due to the thermal expansion effect and thermo-optic effect. With the increase of the temperature, the $\mathrm{\Delta}T$ shift value $\mathrm{\Delta}L$ of OPL could be deduced as:
where the α and ξ are the effective thermo-optic coefficient of $\alpha = ({1/{n_e}} )({\partial {n_e}/\partial T} )$ and the thermal expansion coefficient of $\xi = ({1/L} )({\partial L/\partial T} )$, 6.44 × 10−6 /°C and 0.55 × 10−6 /°C for the SMF28, respectively, and ${n_e}$ is the effective refractive index for the fundamental mode of SMF. The theoretical temperature sensitivity of OPL is 2.01 nm/°C for our FPA. The OPLs is with respective correspondence to the temperature, therefore, the absolute temperature profile could be measured by the demodulation of the OPLs of the FPA. The Fig. 5(a) shows the OPL shifts of ultra-weak FPA with the increasing temperatures. The average OPL sensitivity to temperature is determined to be around 1.94 nm/°C based on the linear fitting for all the sensors of ultra-weak FPA, as illustrated in Fig. 5(b). It should be noted that if this OPL sensitivity of 1.94 nm/°C is converted to wavelength sensitivity, it is equal to be around 10.24 pm/°C. Besides, the averaged standard deviation (SD) of the shift values is 0.3850 nm, and therefore the temperature demodulation uncertainty is determined to be 0.20 °C. The error mainly results from the non-uniformity of sensors during the fabrication process of the ultra-weak FPA, and the inhomogeneous distribution of the temperature along the ultra-weak FPA.Fig. 5. (a) Temperature response of the ultra-weak FPA; (b) OPL shift versus temperature; (c) OPL variation of the sensor array during 10 minutes test; (d) Temperature stability analysis of the sensor array.
The stability of the ultra-weak FPA is essential for temperature sensing precision. The Fig. 5(c) shows the recorded OPLs variation of the ultra-weak FPA during 10 min at room temperature. The OPLs vary from different sensors and scanning time. It shows that the enhancement factor of RBS signal gives strong impact on the stability. For strong RBS peak, it presents small OPL variation, otherwise, the stability becomes relatively worse. Thus, during the fabrication process, the precisely controlled femtosecond laser writing ultra-weak FPA with uniform enhancement of RBS is essential for the improvement of the sensing precision, and if necessary, repeated exposure to the femtosecond pulse at the same position may be needed. On the other side, the instability of the wavelength and power of tunable laser also greatly influence the OPL stability and the sensing resolution, and these factors can be suppressed by optimizing the OFDR system. Figure 5(d) shows the average temperature shift for ultra-weak FPA, the instability of the temperature is determined to be around 0.25 °C.
For comparison, the temperature responses of the bounded SMF are also analyzed. The SMF is similar to a random Bragg grating. The relationship between the temperature variation $\mathrm{\Delta}{T}$ and the Rayleigh frequency shifts $\mathrm{\Delta}{\lambda}$ is expressed as $\mathrm{\Delta}{\lambda} = {\textrm{K}_T}\mathrm{\Delta}{T}$, where ${\textrm{K}_T}$ is the temperature sensitive coefficient. The magnitude of the Rayleigh frequency shift can be obtained by cross-correlation calculation of two groups of Rayleigh scattering spectral signals before/after the temperature variation [19]. Besides, the inverse FFT is also employed in each spatial segment of RBS to obtain the corresponding signal in the wavelength domain. The SMF-based temperature resolution and the spatial resolution in the OFDR system need to be comprehensively discussed in the calculation. The relationship between the sensing spatial resolution and the RBS resolution is expressed as ${D_z} = N{\mathrm{\Delta}}\textrm{z}$ where ${\mathrm{\Delta}}\textrm{z}$= 13.8 µm is the minimum RBS resolution, that is, point-to-point distance in RBS [22]. N is the point number of each spatial segment involved in the cross-correlation calculation. Based on this expression, N should be reduced to achieve high spatial resolution. However, the SNR of the cross-correlation calculation will also decrease and the temperature sensing resolution will deteriorate at the same time. As indicated in Fig. 6(a), when N = 200, the sensing spatial resolution is 2.76 mm, and a high temperature sensing accuracy can be seen. Figure 6(b) and (c) shows the wavelength shifts versus SMF length when N = 100 and N = 50, the spatial resolutions are 1.38 mm and 0.69 mm, respectively, but the temperature sensing accuracy gradually becomes worse. Figure 6(d) shows the average temperature response of the SMF, and the wavelength sensitivity is around 10.37 pm/°C. Figure 6(e) gives an enlarged view of the temperature response with spatial resolution of 0.69 mm, and the average standard deviation is 20.10 pm. Thus, the uncertainty of temperature measurement increases from 0.56 °C (corresponding to spatial resolution of 1.38 mm) to 1.94 °C (corresponding spatial resolution of 0.69 mm). Figure 6(f) shows the temperature sensing uncertainty versus spatial resolution with the cross-correlation demodulation method. The fitted relationship between them can be expressed by x1.3y = 1.2, which could be evaluated by Dz*ΔTu = C for simplicity, where the ΔTu is the sensing uncertainty, and C is a constant. It can be seen that, it is difficult to obtain sub-millimeter spatial resolution with a high demodulation accuracy simultaneously using a conventional SMF as the distributed sensing fiber.
Fig. 6. OFDR-based SMF temperature sensing with spatial resolution of 2.76(a), 1.38(b) and 0.69 mm(c); (d) Average temperature response of SMF from 2.100 m to 2.110 m; (e) Enlarged temperature response in a 10 mm range with spatial resolution of 0.69 mm; (f) Temperature sensing uncertainty versus spatial resolution.
Hence, by comparing the temperature sensing performance of the proposed ultra-weak FPA and the conventional OFDR based on SMF, we can find that the ultra-weak FPA exhibits relatively high spatial resolution and temperature sensing precision. Moreover, relying on the total phase demodulation, the proposed ultra-weak FPA can realize the absolute temperature measurement instead of the relative value by using the cross-correlation method in SMF, this also shows the obvious advantage.
Furthermore, the ability of the ultra-weak FPA for absolute temperature sensing with high spatial resolution is examined. A small section of resistance wire (4 Ω/m) with a diameter of 0.2 mm is employed, and its length is around 7.5 cm. Both the resistance wire and the ultra-weak FPA sensor are respectively placed into two silica tubes with inner diameter of around 0.3 mm. The resistance wire is suspended vertically onto the sensing fiber with a certain distance Y, and gradually approaches the latter with a step of 0.1 mm during sensing process. Hence, one side of spatial distribution of temperature field around the resistance wire could be measured by this way. The results are shown in the Fig. 7. The tested area is 10.0 mm × 3.0 mm. The room temperature is 27.2 °C, and the core temperature of the heated resistance wire is around 108.7 °C. It worth noting that each pixel in Fig. 7 corresponds to a FP sensor, and the absolute temperature distribution with large temperature gradient from the core to the edge is successfully illustrated based on the proposed ultra-weak FPA owing to its ultra-high resolution.
Fig. 7. Distributed temperature profile of a heated resistance wire in an area of 10.0 mm × 3.0 mm measured by the ultra-weak FPA.
Finally, Table 1 summarizes the performance comparison of OFDR-based distributed sensing in the recent years. The upper panel lists the types of OFDR sensing systems with randomly RBS-enhanced fiber, and most of them used the cross-correlation method. For a certain demodulation system with fixed sensitivity, the other spatial resolution could be evaluated by the expression of Dz*ΔTu = C for simplicity. Therefore, Dz*ΔTu can represent the sensing accuracy per millimeter in a similar TLS scan range. Among them, the fiber with enhanced RBS, especially with the random fiber grating, show great improvement of sensing performance. The lower panel shows the periodically RBS-enhanced OFDR sensing type, in which the spatial resolution strongly depends on the physical period. Among them, the presented FPA sensor shows significantly improved spatial resolution and sensing accuracy, which offering an alternative method for high spatial resolution temperature sensing.
Table 1. Performance comparison of OFDR-based distributed sensing with high spatial resolution
5. Conclusion
In this paper, the high-resolution distributed temperature sensing has been realized based on a femtosecond laser written ultra-weak FPA. 50 identical FP cavities are fabricated in a 10 mm long fiber and the corresponding spatial resolution is as high as 200 µm. Based on the total phase demodulation method, the OPLs in the ultra-weak FPA are successively demodulated with the Rayleigh backscattering signal recorded by an optical frequency domain reflectometry. The experimental results demonstrate that the average temperature response sensitivity of the OPLs is 1.94 nm/°C. When compared with the conventional SMF-based OFDR sensing, the ultra-weak FPA exhibits both higher spatial resolution and lower temperature sensing uncertainty benefiting from the periodically enhanced Rayleigh backscattering. In addition, based on total phase demodulation, the absolute temperature values instead of the relative ones can be obtained with the corresponding OPLs of the ultra-weak FPA. Moreover, with optimized demodulation process, the spatial resolution is expected to be further improved if using smaller point-to-point period in the ultra-weak FPA fabrication. Finally, considering the total reflected light power is around only 0.1 µW, the multiplexing number of the FP micro cavity in the ultra-weak FPA can be increased further for large-scale distributed temperature sensing in the applications of absolute temperature field sensing of miniature devices.
Funding
Stabilization Support Program for Higher Education Institutions of Shenzhen (20200811232156001); National Natural Science Foundation of China (51808347); Shenzhen Basic Research Project (JCYJ20220531103007016).
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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