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Abstract
We proposed a novel temperature-compensated multi-point refractive index (RI) sensing system by the combination of the cascaded Fabry-Perot (FP) sensors and the frequency modulated continuous wave (FMCW) interferometry. The former is used for simultaneous sensing of RI and temperature, and the latter is used for multiplexing a series of the cascaded FP sensors to realize multi-point sensing. By means of Fourier transform-based algorithms, the interference spectra of each sub-FP sensors can be divided and demodulated independently. Experimentally, three cascaded FP sensors are multiplexed to verify multi-point RI and temperature sensing ability. RI sensitivity up to ∼1200 nm/RIU is obtained within RI range from 1.3330 to 1.3410, and temperature sensitivity up to ∼0.17 nm/°C is obtained within temperature range from 20 °C to 80 °C. The RI precision is as high as 10−5 RIU and the temperature precision is as high as 0.05 °C. In addition, the prospective multiplexing number could reach about 4000 estimated by the minimum detectable light power. The proposed sensing system has potential advantages in the practical applications that require a large number sensing points.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Refractive index (RI) measurement plays an important role in the fields of biomedicine, chemistry and environmental monitoring, etc. [1]. In the last two decades, the optical fiber RI sensors attract an increasing attention due to their advantages such as immunity to electromagnetic interference, high sensitivity, compact structure, and online monitoring capability. Many types of optical fiber RI sensors have been proposed, including optical fiber interferometer (OFI) [2], optical fiber grating (OFG) [3], surface plasmon resonance (SPR) [4], whispering gallery mode (WGM) [5], and so on. However, the RI measurement result is always affected by temperature disturbances due to the temperature dependence of RI. With the increasing demand for detection accuracy, it is realized that temperature compensation is essential in RI measurement. So far, many optical fiber sensors for simultaneous measuring RI and temperature have been reported by fabricating various structures. Examples include cascaded fiber Bragg gratings (FBG) [6–8], cascaded Fabry-Perot interferometers (FPI) [9–11], cascaded Mach-Zehnder interferometers (MZI) [12–14], dual-channel SPR sensors [15–17], and arbitrary combination of various fiber structures [18–23]. Generally, most of these sensors requires a wider spectrum span that allows two sub-spectra responded RI and temperature respectively without cross-talk. Exceptionally, the cascaded interferometer-based sensors have low demand of the wider spectrum span. The traditional cascaded interferometer-based sensors are demodulated by the spatial frequency multiplexing method, the sub-spectra can be extracted and separated by fast Fourier transform (FFT) filter. However, it requires a large difference of optical path difference (OPD) between sub-interferometers, which results in a limited multiplexing number [9–11,20,24,25].
Reviewing the development of the optical fiber sensor for simultaneous measuring RI and temperature, many researchers have made significant contributions [6–23]. However, all of the above optical fiber sensors can only realize single point sensing. For multi-point sensing applications, these sensors are powerless. Up to now, there are few reports on the simultaneous measurement of multi-point RI and temperature. Thus, it is urgent to propose a feasible scheme to reduce the sensing cost. Fortunately, frequency-modulated-continuous-wave (FMCW) technique originated from Radar provides us helpful inspiration. The FMCW technique has been developed rapidly since it was applied to optical fiber diagnosis in 1981 [26], also named optical frequency domain reflectometer (OFDR). Afterwards, distributed temperature and strain sensing is also realized thanks to its ability of simultaneous localization and sensing [27]. Nowadays, OFDR has become a common technique for distributed optical fiber sensing, and is widely used in the sensing of temperature, strain, vibration, and shape [28–31], and is also used to multiplex FBG sensor [32]. However, all of the above-mentioned sensing applications need rely on the Rayleigh backscattering (RBS) in the optical fiber for signal demodulation. The RBS is insensitive to the external RI, so the RI sensing is difficult to be achieved by the OFDR system. Recent years, some successful cases for multi-point RI sensing have been demonstrated by combining OFDR with the etched fiber [33], the macrobending fiber [34], and the tapered fiber [35]. However, the sensing point is limited the fiber length or power loss thereby difficult to reach satisfactory number. Moreover, these multi-point RI sensing systems are low-sensitive to sample RI and have not temperature compensation ability.
In this paper, we propose a novel multi-point RI sensing system with temperature compensation function. The sensing system adopts the FMCW-based interferometer, where a tunable laser source (TLS) whose wavelength in linearly sweeping is employed to replace the traditional white light source, and a photodetector is employed as receiver to replace the traditional optical spectrum analyzer. Meanwhile, the cascaded FP sensor with an open cavity is designed and fabricated for simultaneous measurement of RI and temperature. With help of the FMCW interferometry, the OPD of the sub-FP sensors is no longer limited. In other words, the OPD of the sub-FP sensors can either be the same or different, even all of the sub-FP sensors can have the same OPD, which will not only greatly reduce the manufacturing difficulty of the cascaded FP sensors, but also greatly increase the multiplexing number. Three pairs of cascaded FP sensors are connected into the sensing system in parallel for verifying the multi-point sensing capability. By means of FFT algorithm, we can distinguish each-FP sensor in the spatial domain and separate their reflection signals. By means of inverse FFT (IFFT) algorithm, the interference spectra of each sub-FP sensor can be demodulated independently in wavelength domain. Experimentally, we test the abilities of multi-point simultaneous RI and temperature sensing under RI range from 1.3330 RIU to 1.3410 RIU, and temperature range from 20 °C to 80 °C. RI sensitivities up to ∼1200 nm/RIU and temperature sensitivities up to ∼0.17 nm/°C are obtained experimentally. In addition, the prospective multiplexing number is estimated according to the minimum detectable power, reaching about 4000. The proposed sensing system not only inherits advantage of the simultaneous location and sensing capabilities of the traditional distributed sensors, but also overcomes the difficulty of the traditional single-point sensors in multi-point sensing, which is of great significance in practical applications that require a large number sensing points.
2. Multiplexing principle and simulation
2.1 Basic configuration of the multiplexing system
The basic configuration of the proposed FMCW-based multiplexing system for multi-point simultaneous measuring RI and temperature is based on an optical fiber MZ interferometer, as shown in Fig. 1(a). A TLS whose wavelength (or optical frequency) in linearly sweeping is split into reference and measurement arms. In the measurement arm, a series of cascaded FP sensors are connected in parallel by optical couplers. Each cascaded FP sensor consists of two sub-FP sensors, one of which is used for temperature sensing, and the other is used for RI sensing. The structure of the cascaded FP sensors for simultaneous measuring RI and temperature is shown in Fig. 1(b). The sub-FP sensors for RI sensing have open cavity allowing the entry of sample under test, thus they are sensitive to RI and temperature. The sub-FP sensors for temperature sensing have close cavity, thus they are only sensitive to temperature. Due to the different time delay, the reflected light from different sub-sensors would generate beat signals of different beat frequencies. The superposition result of these beat signals is received by a balanced photodetector (BPD) and a data acquisition card (DAQ). The polarization controller (PC) in the reference arm is used for maximizing the beat signal intensity. By means of FFT and IFFT algorithms, the sub-FP sensors can be distinguished in the beat frequency domain, and their interference spectra can be demodulated in the wavelength domain. The detail data processing is described in the next section.
Fig. 1. (a) Basic configuration of the proposed FMCW-based multiplexing method for multi-point simultaneous measuring RI and temperature. A series of cascaded FP sensors are connected in parallel by optical couplers. (b) The structure of the cascaded FP sensor. (c)-(e) The signal demodulation processing of the multiplexing system.
2.2 Signal demodulation process
The signal demodulation processing for the proposed multiplexing method is illustrated in Figs. 1(c)–1(e). The reflected light from different sub-FP sensors have different time delays (τ) relative to the reference light, therefore, the beat signals of different frequencies are generated, as shown in Fig. 1(c). These beat signals are mixed in time domain (or wavelength domain). Applying FFT algorithm, their power spectra can be separated in frequency domain (or spatial domain), as shown in Fig. 1(d). Then, applying IFFT algorithm, the peak of interest is extracted and transformed back to time (wavelength) domain, thereby the interference spectrum of each sub-FP sensor is demodulated, as shown in Fig. 1(e). Noticeably, the time domain and wavelength domain are equivalent according to formula: Δλ=c/(γt), where λ donates wavelength, c is the speed of light in vacuum, γ donates tuning speed of the TLS in frequency unit, and t is time. The frequency domain and spatial domain are also equivalent according to formula: 2L = cfb/γ, where 2L donates optical path difference (OPD) of sub-FP sensor in measurement arm relative to reference arm, fb is beat frequency.
2.3 Simulation analysis
The theoretical model is established according to the principle of coherence for numerical simulation. The electric field through the MZ interferometer can be expressed by
where ER(t) represents the electric field through the reference arm, EPm(t-τm) represents the electric field of the mth reflected point, rm represents reflectivity of the mth reflected point and τm represents time delay, τm=2Lm/c. The electric field ER(t) can be expressed by where ER0 represents electric field amplitude, φ(t) represents electric field phase. For the linear frequency tuning light source, it can be expressed by where f0 represents initial optical frequency of the light source, f0=c/λ0. Replacing t with t-τm, the electric field EPm(t-τm) can also be calculated. Finally, the beat signal intensity can be calculated byAccording to Eqs. (1)–(4), the original beat signal can be simulated. As an example, three cascaded FP sensors numbered as #1, #2 and #3 are adopt for simulation. Each cascaded FP sensor consists of two sub-FP sensors, one of which is used as temperature sensing channel, and the other is used as RI sensing channel. Besides, each sub-FP sensor has two reflected end-faces, a total of twelve for the whole system. Due to transmission loss, the reflectivity of the second end-face is smaller than that of the first end-face for each sub-FP sensor. These six sub-FP sensors are distributed in different locations of the multiplexing system and their cavities are filled with samples of different RIs. The detailed simulation parameters are shown in Table 1. The wavelength tuning range is from 1525 nm to 1575 nm (f0 = 190.5 THz) with tuning speed of 80 nm/s (γ = 10 THz/s). The sampling time is 0.625 s with sampling rate of 10 MSa/s.
Table 1. Simulation parameters of the multiplexing system
The simulation result of the original beat signal is shown in Fig. 2(a), the data length is 6.25 MSa. Then, the power spectrum can be calculated by FFT, as shown in Fig. 2(b). Six pairs of reflected peaks appear at the preset location clearly. As same as the traditional OFDR sensing system [27], the spatial resolution can be given by Δz = c/(2ΔF), where ΔF is frequency sweeping span in Hz, here Δz = 20 µm. The close view of the reflected peaks generated by temperature sensing channels FP1, FP3 and FP5 are shown in Fig. 2(c), and that generated by RI sensing channels FP2, FP4 and FP6 are shown in Fig. 2(e). For each sub-FP sensor, the reflected peaks generated by the first end-face and the second end-face are both clearly visible, and their intensity ratios are almost equal to the preset value. Then, the reflected peaks of interest are selected by a Hanning window with width of 40 points and transformed back to wavelength domain by IFFT, thus the interference spectrum of the FP sensor of interest can be demodulated. Figure 2(d) shows the interference spectra of the temperature sensing channel FP1, FP3 and FP5, the cavity parameters of these three FP sensors are exactly consistent, resulting their interference spectra to completely overlap. Figure 2(f) shows the interference spectra of the RI sensing channel FP2, FP4 and FP6, the RIs in cavity of these three FP sensors are different, resulting their interference spectra to shift. In addition, the simulation result of the RI sensitivity is 1205 nm/RIU, which is almost consistent with other researches of traditional FP sensors [2,9–11].
Fig. 2. (a) Simulation result of the original beat signal. (b) Power spectrum of the beat signal after applying FFT. The reflected peaks appear at the preset location. (c) Close view of the reflected peaks generated by temperature sensing channels FP1, FP3 and FP5, respectively. (d) The interference spectra of the temperature sensing channels after applying IFFT. (e) Close view of the reflected peaks generated by RI sensing channels FP2, FP4 and FP6, respectively. (f) The interference spectra of the RI sensing channels after applying IFFT.
2.4 Effect of multiplexing number on wavelength accuracy
To investigate the effect of the multiplexing number of the cascaded FP sensors on the wavelength accuracy of an individual interference spectrum, we perform the simulation as follows. The distance between the Temperature sensing channel and the RI sensing channel is 1 mm, the distance between the adjacent cascaded FP sensors is 10 mm. Other simulation conditions are consistent with Section 2.3. Based on the wavelength tuning speed and sampling rate, the maximum sensing distance is calculated to 50 m, thus the maximum multiplexing number is 5000. We simulate the interference spectrum of the RI sensing channel of the first cascaded FP sensor when the multiplexing number are 1, 10, 100, 1000, and 5000 respectively. The simulation results are shown in Fig. 3. The interference spectrum keeps almost consistent at different multiplexing number. When the multiplexing number is 5000, the wavelength error is only 7 pm. The simulation results indicate that the accuracy of an individual sensor element is not significantly impaired even with a large number of superimposed sensors.
Fig. 3. The effect of the multiplexing number on the wavelength error of an individual interference spectrum. Inset: the interference spectrum of an individual sub-FP sensor when multiplexing number are 1, 10, 100, 1000, and 5000 respectively.
3. Experiment preparation
3.1 Manufacture of cascaded fiber FP sensor
The cascaded FP sensors for experiment are self-made by bonding single-mode fiber (SMF) and glass tube together using UV glue. Simply, the manufacturing operation includes four steps. Firstly, for the temperature sensing channel, an SMF with smooth end-face is put into a glass tube, whose inner diameter is 126 µm, slightly larger than the fiber diameter of 125 µm. A drop of UV glue is put on the contact point between the SMF and the glass tube, and it then is cured for 3 minutes. Secondly, the SMF is connected to the traditional optical fiber sensing system consisting of white light source and optical spectrum analyzer (AQ6370C, Yokogawa). Another SMF is put into the glass tube, the gap between two end-faces, i.e. the cavity length, is adjusted by a micro displacement stage of 10 µm accuracy. Meanwhile, the reflected spectrum is real-time monitored until occurring suitable interference spectrum. Thirdly, the contact point is bonded by UV glue as same as the first step. The optical fiber structure is placed under UV light for a half hour until UV glue completely cured. Similarly, another glass tube with a side hole, which allows sample to flow in and out, is used to make RI sensing channel. Finally, the temperature and RI sensing channels are spliced by optical fiber fusion splicer. This manufacture method is simpler than the femtosecond laser micromachining and the special fiber micromachining [2,9–11]. In addition, due to the larger thermal expansion coefficient of the UV glue, the FP sensor structure will subject more obvious thermal deformation, which can be used as sensitivity enhanced temperature sensors [36]. It is noting that our sensor structure will become unstable after long term use because the UV glue is susceptible to damage. In the practical sensing applications, using the femtosecond laser micromachining is more reliable.
3.2 Experiment set-up of the multiplexing system
Figure 4 shows experiment set-up of the proposed multiplexing system, which includes three parts. Part I: Auxiliary interferometer. Generally, it is difficult to realize the ideal linear frequency sweep with the TLS, the nonlinearity will degrade the reflection peak so that it cannot be distinguished [37]. In order to compensate the nonlinearity noise, the common way is to add an auxiliary interferometer, which can realize sampling with constant frequency interval [38]. Here, we adopt a Michelson interferometer as the auxiliary interferometer, two Faraday rotating mirrors (FRM) are connected terminally to provide end reflection and eliminate polarization-induced fading [35], and a delay fiber of 100 m provides optical path difference. A clock generator is employed to convert the sinusoidal beat signal into TTL clock signal, which is used as the sampling clock of the DAQ. Part II: Absorption gas chamber. Due to ambient temperature disturbance, the wavelength of the TLS often tends to shift, which will affect the accuracy of the sensing spectrum. The absorption gas chamber can used to calibrate wavelength shift because its absorption wavelength is insensitive to temperature change. Here, we adopt acetylene gas, which has a series of absorption peaks around 1510 nm ∼ 1540 nm, to calibrate the wavelength drift of the TLS. Part III: Main interferometer. Three pairs of cascaded FP sensors are connected into the multiplexing system by three optical coupler. The detailed description of this part can be seen in section 2.1. The coupling ratio of each optical coupler is descripted in Fig. 4(a). Figure 4(b) shows the photograph of the cascaded FP sensor, limited by our equipment and fabrication method, there is an addition fiber of about 20 cm between the RI sensing channel and the temperature sensing channel. For temperature compensation, during experiment, the RI sensing channel and the temperature sensing channel are placed closely together by bending the fiber. In addition, the equipment information is as follows: the TLS is from Agilent Technologies (Agilent 81600B), the wavelength sweeping span is from 1520 nm to 1580 nm, and the wavelength sweeping speed is 80 nm/s. The output power of the TLS is 5 mW. The BPD is from Fsphotonics (PDB1008), whose bandwidth is 80 MHz. The DAQ is from ART technology (PCI8514). The sampling length is 8 MSa and the sampling time is 787 ms, so the wavelength sampling span is about 60 nm, corresponding to spatial resolution of 20 µm. Besides, according to Nyquist theory, the maximum measurable length of the main interferometer is 50 m, which can be improved by extending the delay fiber length of the auxiliary interferometer.
Fig. 4. (a) The sketch diagram of the proposed FMCW-based FP sensors multiplexing system; (b) photograph of the cascaded FP sensors for simultaneous RI and temperature sensing. TLS: tunable laser source; FRM: Faraday rotating mirror; PC: polarization controller; CG: clock generator; BPD: balanced photodetector; DAQ: data acquisition card; SMF: single mode fiber.
In order to execute RI and temperature sensing experiments, a series of liquid samples of different RIs are pre-prepared by mixing glycerol-aqueous solutions with different concentrations. The sample RI is measured and calibrated by Abbe refractometer at 20 °C. Here, the sample RI is from 1.3330 RIU to 1.3410 RIU with the interval of 0.0010 RIU. During the experiments, the cascaded FP sensors (both RI sensing channel and temperature sensing channel) are immersed into the sample under test, meanwhile, the sample is placed into water bath to control the ambient temperature accurately.
4. Experiment results and discussions
The signal demodulation process is the same as described in the previous simulation. The original beat signal by experiment is shown in Fig. 5(a), which is messy due to the mixture of countless beat signals. The power spectrum of the original beat signal is then calculated by applying FFT, as shown in Fig. 5(b). Distinctly, there appears several peaks in the power spectrum. The peaks marked green are generated by the connectors in the optical fiber link, and the peaks marked red are generated by six sub-FP sensors. The close view of the latter (taking FP1 as example) is shown in Fig. 5(c), where two reflected peaks marked R1 and R2, which is generated by two end-face of the FP cavity, is clearly visible. The intensity of the peak R2 is smaller than that of the peak R1 due to the transmission loss of the FP structure. Then, applying IFFT to the selected peaks and the original interference spectrum of the sub-FP sensor can be demodulated, as shown in Fig. 5(d). However, different from the simulation results, the original interference spectrum is irregular in intensity due to polarization and power fluctuation of the light source, hence we employ a baseline filter to normalize the spectrum. Finally, the normalized interference spectrum of the sub-FP sensor is obtained, as shown in Fig. 5(e).
Fig. 5. (a) The original experimental beat signal; (b) power spectrum of the beat signal; (c) close view of the reflection peaks generated by FP1; (d) the original interference spectrum of the FP1 obtained after applying the IFFT process; (e) the normalized interference spectrum of the FP1 obtained after removing the baseline.
Following the above signal demodulation process, the interference spectra of all sub-FP sensors can be demodulated. The close view of their reflected peaks and the corresponding interference spectra are shown in Figs. 6(a)–6(b). It can be seen that the interference spectra of every sub-FP sensors are clearly visible. The dashed lines in the Fig. 6(b) represent the normalized interference spectra measured by the traditional optical spectrum analyzer (AQ6370C). Two curves are almost consistent, verifying the spectral reliability of the FMCW-based multiplexing method. Table 2 shows the location of these six sub-FP sensors and their OPDs. The OPDs are almost the same with each other, verifying that the OPD of the cascaded FP sensors is no longer limited compared to the traditional spatial frequency multiplexing method [9–11,24,25].
Fig. 6. (a) Close view of the reflection peaks generated by six FP sensors from FP1 to FP6, respectively; (b) the normalized interference spectra (solid lines) of six FP sensors from FP1 to FP6 respectively, which are almost consistent with the measurement results by the traditional optical spectrum analyzer (dashed lines).
Table 2. Experiment parameters of the multiplexed sub-FP sensors
Subsequently, the experiments of simultaneous measurement of RI and temperature are carried out. Firstly, the cascaded FP sensors are successively immersed into pre-prepared samples with different RIs. In order to ensure the accuracy of the experiment results, these sensors are cleaned and dried every time when the sample is changed. Meanwhile, it is especially necessary to keep the temperature constant during the experiment. Figure 7 shows the experiment results under a series of RIs ranging from 1.3330 RIU to 1.3410 RIU with the interval of 0.0010 RIU and the constant temperature of 20 °C. The spectrum evolution (taking the cascaded FP sensor #1 as example) is shown in Figs. 7(a)–7(b). Here, only one spectrum period are plotted out for clarity. The interference spectrum of the FP1 (temperature sensing channel) remains unchanged with RI of sample because the FP cavity is isolated from the external environment. The interference spectrum of FP2 (RI sensing channel) red-shifts with increasing of RI of sample, which is consistent with the research results of traditional FP-based RI sensors. The sensing curves of the total six sub-FP sensors are shown in Fig. 7(c). The sensitivities of three sub-FP sensors as RI sensing channel are 1203.9 nm/RIU, 1279.8 nm/RIU and 1230.3 nm/RIU, respectively, and the other three sub-FP sensors as temperature sensing are all insensitive to RI change. The experiment results also verify there is no cross-talk between the sub-FP sensors.
Fig. 7. The interference spectra shift of (a) the temperature sensing channel FP1 and (b) the RI sensing channel FP2 as a function of RI of the sample under test, from 1.3330 RIU to 1.3410 RIU with the interval of 0.0010 RIU; (c) the RI sensing curves of six FP sensors from FP1 to FP6, correspondingly.
Next, the cascaded FP sensors are immersed into one sample that keeps unchanged, and the ambient temperature is accurately controlled by the water bath. Figure 8 shows the experiment results under a series of temperature ranging from 20 °C to 80 °C with the interval of 10 °C. The spectrum evolution (taking the cascaded FP sensor #1 as example) is shown in Fig. 8(a) and Fig. 8(b). The interference spectra of both FP1 and FP2 red-shift with increasing of temperature. The spectrum shift is caused by the combination of the thermal refractive index change of the sample and the thermal expansion of the FP cavity. Generally, the thermo-optical coefficient of the sample is negative while the thermal expansion coefficient is positive, thus the direction of spectrum shift depends on the value of the two coefficients. For our FP cavity structure, there is a large thermal expansion coefficient because of the use of UV glue, resulting to red-shift of the spectrum. In addition, the sensitivity of the FP1 (temperature sensing channel) is larger than that of the FP2 (RI sensing channel), which is resulted from the larger thermo-optical coefficient of liquid sample than that of the air cavity. The sensing curves of the total six sub-FP sensors are shown in Fig. 8(c). The sensitivities of three sub-FP sensors as RI sensing channel are 0.042 nm/°C, 0.041 nm/°C, and 0.046 nm/°C, respectively, and the other three sub-FP sensors as temperature sensing are 0.185 nm/°C, 0.158 nm/°C, and 0.176 nm/°C, respectively.
Fig. 8. The interference spectra shift of (a) the temperature sensing channel FP1 and (b) the RI sensing channel FP2 as a function of temperature, from 20 °C to 80 °C with the interval of 10 °C; (c) the temperature sensing curves of six FP sensors from FP1 to FP6, correspondingly.
Finally, the RI and temperature change ΔRIi and ΔTi of the cascaded FP sensor #i (i=1,2,3……) can be demodulated by the sensing matrix, which can be described as:
In order to evaluate the detection accuracy of the multi-point RI sensing system, we repeat the experiment under the same conditions for 20 times. The interference spectra of 20 experiments are demodulated successively, as shown in Fig. 9(a), in which every interference spectra are all almost overlapped. Figure 9(b) shows the close view of the second interference dip at 1542.25 nm, presenting a tiny wavelength shift about 50 pm between 20 experiment results. The wavelength shift of the interference spectrum is mainly produced by the electric noise of receivers and the wavelength drift of the TLS. The former is difficult to avoid while the latter can be compensated by the acetylene gas absorption spectrum. Figure 9(c) shows the evolution of the acetylene gas absorption spectrum during 20 experiments, presenting a tiny wavelength shift about 30 pm. The wavelength shift of the acetylene gas absorption spectrum indicates the wavelength drift of the TLS, thus the interference spectrum of the FP sensors can be calibrated by subtracting the wavelength shift of the acetylene gas absorption spectrum. Figure 9(d) shows the wavelength shift of the interference spectrum before and after calibration, the standard deviation (SD) of the interference spectra is reduced from 11.6 pm to 6.6 pm. Finally, the detection precision can be obtained by substituting SD and sensitivities into Eq. (5). Table 3 shows the sensitivities and wavelength SD of three cascaded FP sensors, and the calculated results show the high temperature precision about 0.05 °C and high RI precision better than 10−5 RIU.
Fig. 9. (a) The interference spectra of 20 times repetitive experiments before wavelength calibration; (b) close view of the interference dip at 1542.25 nm; (c) acetylene gas absorption spectra during 20 experiments; (d) the wavelength shift of interference spectrum before and after wavelength calibration.
Table 3. Detection precision of three cascaded FP sensors
Although only three cascaded FP sensors are multiplexed for demonstration in this work, we can also increase the sensors number by connecting one coupler after another. The prospective multiplexing number is determined by the minimum detectable light power. In order to estimate the prospective multiplexing number, we research the minimum detectable light power. We place a variable optical attenuator (VOA) in the measurement arm to change the input light power. For the Nth cascaded FP sensor, the reflection light power can be calculated by
where Pin represents the input light power of the measurement arm, rFP represents the reflectivity of the FP cavity (rFP ≈ 0.4% for liquid cavity), and rn represents the coupling ratio of the nth optical fiber coupler (rn = 5% in the experiment). When Pin decreases from 1 mW to 100 nW, the reflection peak of the sub-FP sensor also decreases from 12 dBm to −9 dBm, as shown in Fig. 10(a). However, the normalized interference spectrum keeps unchanged at different input light power, as shown in Fig. 10(b). According to Eq. (6), when Pin = 100 nW, Pout = 250rFP pW = 1 pW. In other words, the minimum detectable light power is smaller than 1 pW. Assuming the reflection light power of every sub-FP sensors are all 1 pW, and the light source power is 4 mW, then the maximum multiplexing number can be estimated to Nmax=[(4rFP mW)/(250rFP pW)]0.5 = 4000, which is much large than the paper [34]. In addition, the multiplexing number can be further improved by enlarging the light source power.Fig. 10. (a) The reflection peaks at different input light power of the measurement arm. (b) The normalized interference spectra correspondingly.
Table 4 shows the performance comparison among different multi-point RI sensing systems. Compared to other multi-point RI sensing system, our sensing system has higher sensitivity, which results higher RI resolution. The sensing system has also the ability of temperature compensation, which is very important in RI measurement. Most important, the sensing points’ number of the sensing system is easy to be extended by connecting one coupler after another. The only limitation is that the RI detectable range is narrow (0.008 RIU), but it can also be enlarged by reducing the cavity length of the sub-FP sensors. Noting that the shortest cavity length should larger than twice the spatial resolution of the sensing system for demodulating the interference spectrum. Concretely, the shortest cavity length should larger than 40 µm, thus the maximum RI detectable range is 0.019 RIU (Δnmax = λ/(2LFP)).
Table 4. Performance comparison among different multi-point RI sensing systemsa
5. Conclusion
In summary, we proposed and demonstrated a novel multi-point RI sensing system with temperature compensation, by the combination of the cascaded FP sensors and the multiplexing method based FMCW technique. The theoretical model of the sensing system is established and the signal demodulation algorithm is built up correspondingly. The blended original signal is divided in spatial domain by FFT, and then the interference spectrum is demodulated independently in wavelength domain by IFFT. Experimentally, the multi-point RI and temperature simultaneous sensing experiments is performed and the well sensing capabilities is realized. The RI sensitivities of the three multiplexed cascaded FP sensors are high up to 1203.9 nm/RIU, 1279.8 nm/RIU and 1230.3 nm/RIU respectively, under RI range from 1.3330 RIU to 1.3410 RIU. Meanwhile, the temperature sensitivities of the three multiplexed cascaded FP sensors are high up to 0.185 nm/°C, 0.158 nm/°C, and 0.176 nm/°C respectively, under temperature range from 20 °C to 80 °C. The RI precision is as high as 10−5 RIU and the temperature precision is as high as 0.05 °C. In addition, the prospective multiplexing number is estimated according to the minimum detectable power, reaching about 4000. The proposed sensing system has potential advantages in several practical applications that require a large number sensing points.
Funding
National Key Scientific Instrument and Equipment Development Projects of China (2017YFF0108700); National Natural Science Foundation of China (61975045); Natural Science Foundation of Heilongjiang Province (LH2020F014).
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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