We present a high-accuracy fiber-optic Fabry-Pérot (F-P) sensor capable of simultaneously measuring the temperature and gas refractive-index (RI). The sensor consists of a silicon F-P cavity for temperature sensing and a glass F-P cavity with a side groove for gas RI sensing. Two F-P cavities are simply fabricated and connected in series by microelectromechanical system (MEMS) techniques. The hybrid F-P sensor produces a superposition of signals. Changes in temperature and RI can be separated and detected by a fast Fourier transform (FFT) and the wavelength-tracing method. The experimental results demonstrate that the sensitivities of the proposed sensor are 80.7 pm/°C from 10 °C to 60 °C and over 1535.8 nm/RIU in the gas RI range of 1.0000248–1.0007681. Furthermore, the gas RI measurement reaches a high accuracy of ± 7.6 × 10−6 RIU, owing to the temperature compensation. In addition, the measured precisions of the temperature and gas RI are 1.07 × 10−3 °C and 2.73 × 10−8 RIU, respectively.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Accurate measurement of the gas refractive-index (RI) [1–5] and temperature are critical for theoretical and practical requirements in biochemical analysis, high-energy physics and laser systems [6–8]. Various types of fiber-optic sensors have been proposed and used for temperature and RI sensing, such as all-silica structure fabricated by etching and fusion splicing [9–15], arc-discharge technique , milling technique , and fiber tip with micropolymer layer [18–22]. Among them, the sensors based on dual Fabry-Pérot (F-P) cavities have attracted intensive studies benefit from their compact size, immunity to electromagnetic interference, and high sensitivity. The highest resolutions of these sensors are 10−3 °C for temperature and 5 × 10−9 RIU for RI [9,10].
Wang et al.  fabricated an in-fiber ellipsoidal cavity by splicing a single-mode fiber (SMF) and a photonic crystal fiber with an arc-discharge technique. The RI was determined by analyzing the fast Fourier transform (FFT) amplitude ratio, and a precision of ± 7.71 × 10−4 RIU was obtained. The sensor also enabled the simultaneous measurement of temperature by tracking the wavelength shift with a sensitivity of 15 pm/°C. André et al.  milled F-P cavities in optical fiber microtips to form a solid silica cavity and a gap cavity by using a focused ion beam. The reflective signal was demultiplexed based on FFT. Then, the researchers were able to measure the temperature and refractive index simultaneously. The sensor presented sensitivities of −15.8 pm/°C and −1316 nm/RIU and a precision of ± 5.1 × 10−4 RIU.
The temperature-sensitive materials of the above two sensors were both silica, and thus the temperature sensitivity was limited by its low thermo-optic coefficient. Zhang et al.  proposed an end-of-fiber polydimethylsiloxane cap-based fiber Fabry-Pérot interferometer (FPI) that could also be used for the simultaneous measurement of RI and temperature. The RI sensitivity of the interferometer was −240.425 dB/RIU by an extinction ratio measurement in the RI range of 1.3625–1.4150 with a precision of ± 5.29 × 10−4 RIU. The temperature sensitivity of the sensor reached 385.46 pm/°C. However, the sensor was not suitable for gas RI sensing since the extinction ratio might be very low under a gas environment.
In this paper, we propose novel fiber-optic dual FPIs for simultaneous and highly accurate gas RI and temperature measurement. The sensor head is fabricated by employing microelectromechanical system (MEMS) techniques. A silicon F-P cavity and a glass F-P cavity with a side groove are serially connected for temperature and gas RI sensing, respectively. The temperature and RI can be determined simultaneously by tracing the interference wavelength shift separated from the superposed reflection spectra. With the relative high-temperature sensitivity of the silicon cavity, the temperature cross-sensitivity caused by the thermal expansion of glass can be overcome to reach a high RI measurement accuracy after temperature compensation.
The experimental results show that the gas RI measurement accuracy can reach ± 7.6 × 10−6 RIU, and the measured precisions of the temperature and gas RI are 1.07 × 10−3 °C and 2.73 × 10−8 RIU, respectively. In addition, MEMS techniques provide a way toward mass production and greatly increase the yield compared with manual production.
2. Sensor fabrication and operating principle
2.1 Structure and fabrication of the sensor
A schematic diagram of the proposed hybrid optical F-P sensor is illustrated in Fig. 1(a). The sensing head is formed by three layers that connect sequentially. A Pyrex glass layer with structures is sandwiched between the top and bottom silicon layers. The fabrication steps are as follows. First, we use spark-assisted chemical engraving (SACE) technology  to machine the structure of the through hole and groove arrays in a Pyrex glass wafer (BOROFLOAT 33) with 500 ± 20-μm thickness, as shown in Fig. 2(a). The radius of the hole is 2500 μm, and the width of the groove is 200 μm.
Next, the bottom silicon layer, a double-sided polished silicon wafer with 300 ± 10-μm thickness, is connected to the structured Pyrex glass wafer by anodic bonding. Then, the top silicon layer, a single-sided polished silicon wafer with ∼50-μm thickness, is connected to the other side of the structured Pyrex glass wafer in the same way. After that, the bonded wafer consisting of three layers is diced to hundreds of independent sensing heads, as shown in Fig. 2(b). Finally, the side of the bottom silicon layer is connected to an SMF that is fixed by a glass ferrule.
The axial through hole in the Pyrex glass layer constructs a gas cavity, and the groove enables the gas to flow freely into the cavity. The polished surfaces of the silicon layer serve as natural ideal partial reflectors with 30.5% reflectivity in a 1550-nm wavelength band , but the reflectivity of the unpolished surface is greatly reduced. As shown in Fig. 1(b), the light injects into the SMF and is reflected between the outside (R1) and inside (R2) surfaces of the bottom silicon layer and the inside (R3) surface of the top silicon layer.
2.2 Operating principle of the sensor
The hybrid fiber optic sensor contains three cavities: silicon cavity, gas cavity, and a long cavity. The silicon cavity formed between R1 and R2 is named FP1 with a cavity length of L1. The gas cavity formed between R2 and R3 is named FP2 with a cavity length of L2. The long cavity formed between R1 and R3 is a combination of FP1 and FP2 with a cavity length of L1 + L2. The reflected beam can be regarded as a two-wave interference model, and the total intensity can be expressed as
When we extract the interference spectra corresponding to FP1 from the superposition reflection spectra by a filter, the phase shift of FP1 can be given as a function of temperature t according to Eq. (2). That is,
Similarly, when we extract the interference spectra corresponding to FP2 from the superposition reflection spectra by another filter, the phase shift of FP2 can be given as function of gas RI ngas and temperature t, that is,Eq. (5), gas RI sensitivity Sn of FP2 at a constant temperature t0 can be deduced as
Also according to Eq. (5), when gas RI remains unchanged, the temperature cross-sensitivity Stc of FP2 can be deduced as
Note that the sensitivities are constants when we determine the initial wavelengths λi0, λj0, and the initial RIs of silicon nsi0 and gas ngas0. When we adopt the following parameters: K−1, K−1, and K−1 [25,26], the sensitivities are estimated to bepm/°C, nm/RIU, pm/°C (withnm, nm, , and in accordance with the experimental data).
According to Eqs. (4) and (5), when °C, the temperature t and gas RI ngas can be measured and calculated as
It can be seen from Eqs. (8) and (9) that the proposed sensor may be able to measure the temperature and gas RI simultaneously by tracking the interference peak wavelength λi and λj from two independent interference spectra. Furthermore, a high-sensitivity temperature measurement can be used to eliminate the temperature cross-influence and help to achieve a high-accuracy gas RI measurement.
2.3 Demodulation method of the superposition reflection spectra
To demodulate the superposition reflection spectra, we combine the FFT and wavelength-tracing method. We first use the cubic spline interpolation method to ensure equal frequency sampling intervals, and then adopt the FFT to convert the reflection spectra from the wavelength domain to the frequency domain. After that two proper band-pass filters are used to retrieve the interference spectra corresponding to the distinctive frequency component of FP1 and FP2, respectively. Hence, the wavelength shifts of the two interference spectra can be traced separately. In order to avoid the phase ambiguity issue of the wavelength-tracing method, we first obtain the rough optical path difference (OPD) of each F-P cavity, given as, where N refers to the sample point number of the FFT, k refers to the abscissa corresponding to the peak of the frequency component . After that, we calculate the interference order of a certain interference peak wavelength λm as , where m is the interference order. This method ensures that the traced wavelength is always under the same interference order, and combines the advantages of high-precision measurement and large measured range.
3. Experiment result and discussion
3.1 Experimental setup
The experimental setup for the temperature and air RI measurement is shown in Fig. 3. Through a circulator, we directed the output of a superluminescent diode (SLD) light source into the sensor head. After that, an optical spectrum analyzer (YOKOGAWA AQ 6370) received the reflected signal from the sensor. We put the proposed sensor at the mean time in an air-pressure chamber. We chose a high-accuracy controller that allowed us to adjust the pressure precisely within 0.02 kPa. A dryer was connected before the air compressor. The chamber was placed in a thermostat with a precision of 0.5 °C.
3.2 Sensor characteristic
The recorded reflection spectra at room temperature and the atmospheric pressure are shown in Fig. 4(a), and the subfigure shows the magnified observation result. Figure 4(b) shows the FFT result. We can see three distinguishable frequency peaks marked separately as peaks 1, 2, and 3, which correspond to the cavities of FP2, FP1, and the long cavity, respectively. Figures 4(c) and 4(d) show the independent interference spectra corresponding to FP1 and FP2 after filtering, respectively.
In order to demonstrate the characteristics of the silicon cavity FP1 and the glass cavity FP2, we changed the temperature from 10 °C to 60 °C in steps of 5 °C under 100 kPa and then traced the peak wavelength λi of FP1 and λj of FP2, respectively.
3.2.1 Characteristic of FP1
Figure 5(a) shows the extracted interference spectra corresponding to FP1. With an increase in temperature, the peaks of the interference pattern gradually shifted toward longer wavelengths. The relationship between the temperature and peak wavelength is shown in Fig. 5(b). The variation of the wavelength with temperature is linear, and the temperature sensitivityof the proposed sensor is 80.7 pm/°C, which is in good agreement with the design value of 87.0 pm/°C. Therefore, temperature t can be calculated as the function
3.2.2 Characteristic of FP2
Edlén equation for the RI of air  gives an accurate way to calculate the air RI from temperature and pressure:
Figure 6(a) shows the extracted interference spectra corresponding to FP2. It can be seen that the peaks of the interference pattern still shifted toward longer wavelengths with a decrease in RI, which is caused by the temperature-cross sensing. We can calculate the parameter B(t) as according to Eq. (9). The relationship between measurement results of B(t) and temperature are shown in Fig. 6(b). A linear response and sensitivity of 5.48 pm/°C was found, which agrees with the design value of 5.1 pm/°C.
Therefore, gas RI ngas can be calculated as Eq. (13).
The temperature-cross sensitivity St-n on the RI measurement can be deduced from Eq. (13) as
Therefore the proposed sensor can be used to measure the temperature and RI simultaneously, and the temperature cross-sensitivity on RI measurement can be compensated by the temperature measurement owing to the silicon cavity.
3.3 Test results and discussion
The RI measurement accuracy of the proposed sensor was tested experimentally. We altered the pressure from 10 kPa to 280 kPa in steps of 10 kPa at 10 °C, 20 °C, 30 °C, and 40 °C, corresponding to the air RI changing from 1.0000248 to 1.0007681. We traced the interference peak wavelength λi and λj from two independent interference spectra. The relationships between λi, λj and pressure P are shown in Fig. 7 and Fig. 8(a), respectively. Figure 8(b) shows the relationship between the wavelength shift and corresponding gas RI change, which exhibits excellent linearity. The RI sensitivities are all around 1540 nm/RIU, as shown in Table 1.
We substituted the measured value of λi into Eq. (10) to determine the current temperature t, and then substituted t and λj into Eq. (13) to determine the air RI. We take the difference between the RI measured result and the theoretical value (according to Eq. (11)) as measurement accuracy . The measurement differences are within ± 7.6 × 10−6 RIU, as shown in Fig. 9, indicating an RI accuracy of ± 7.6 × 10−6 RIU.
From the discussion above, we successfully measured the temperature and air RI simultaneously with the help of the dual-cavity structure, and eliminated the temperature cross-influence on the RI measurement.
The precisions of the proposed sensor were also evaluated experimentally. We placed the sensor at a room temperature of 25 °C and 100 kPa for 1 h and sampled at intervals of 30 s. As shown in Fig. 10, it was found that the standard deviations of wavelength variation corresponding to λi and λj were ∼0.029 pm and ~0.014 pm, respectively, which resulted in a temperature precision (corresponding to a three-time standard deviation) of 1.07 × 10−3 °C at a temperature sensitivity of 80.7 pm/°C and the RI precision of 2.73 × 10−8 RIU at an RI sensitivity of 1540 nm/RIU.
Finally, we investigated the temperature and RI repeatability of the proposed sensor. We placed the sensor at atmospheric and altered temperature increased from 10 °C to 60°C and then decreased to 10 °C for 2 cycles. The response of FP1 is shown in Fig. 11(a), from which we can see that the sensor exhibits a good temperature repeatability. The maximum deviation between the measured wavelength λi and the four-time averaged wavelength was ± 17.2 pm. Thus, the sensor has a repeatability of ± 0.21 °C at a temperature sensitivity of 80.7 pm/°C.
We placed the sensor at 25 °C and altered pressure increased from 10 kPa to 280 kPa and then decreased to 10 kPa for 2 cycles. The response of FP2 is shown in Fig. 11(b). The sensor also exhibits a good RI repeatability. The maximum deviation between the measured wavelength λj and the four-time averaged wavelength was ± 10.4 pm. Thus, the sensor has a repeatability of ± 6.75 × 10−6 RIU at a RI sensitivity of 1540 nm/RIU.
Table 2 compares the previously proposed optical fiber RI FPI in terms of precision and repeatability. Such test results indicate high precision and repeatability of the proposed sensor. Therefore, this sensor can be used for high-precision gas concentration analysis applications. We also expect that the sensor has potential in liquid RI measurements.
A hybrid FPI was proposed and demonstrated for simultaneous gas RI and temperature sensing in this paper. The sensor consisted of a silicon-glass-silicon structure fabricated by MEMS techniques that provide the possibility of batch production. The principle of the sensor was theoretically analyzed. The characteristics of the two F-P cavities were verified and calibrated experimentally. The temperature sensitivity of our proposed sensor was 80.7 pm/°C, and the gas RI sensitivity was higher than 1535.8 nm/RIU. The experiment demonstrated that the temperature and gas RI can be simultaneously determined by using FFT and tracing the wavelength shift from the extracted interference spectra. The silicon cavity played an important role in compensating the temperature cross-sensitivity of a glass cavity, which contributed to a high gas RI accuracy of ± 7.6 × 10−6 RIU. Test results showed the precisions of the proposed sensor were 1.07 × 10−3 °C and 2.73 × 10−8 RIU. The high sensitivity and high gas RI measurement accuracy of the device make it promising for high-precision gas concentration analysis applications.
National Natural Science Foundation of China (61735011).
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