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Abstract
A fiber-optic, extrinsic Fabry–Perot interferometric (EFPI), dual-cavity sensor made of sapphire was fabricated and interrogated by a dual-segment, low-coherence Fizeau interferometer to achieve simultaneous pressure and temperature measurements. The fiber-optic EFPI, dual-cavity sensor had an initial basal cavity length of 680 µm and an vacuum cavity length of 80 µm and was experimentally tested based on temperature and pressure measurements. It was demonstrated that simultaneous pressure and temperature measurement could be achieved in the respective pressure and temperature ranges of 0.1–3 MPa and 20–350 °C.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fiber-optic Fabry–Perot (FP) sensors can be used to measure various parameters, such as temperature, pressure, strain/stress, acceleration, acoustic wave/ultrasound, vibration, and others [1–7]. Given their advantages of high-resolution, increased stability, compact size, anti-electromagnetic interference fiber-optic FP sensors have been extensively applied in aerospace, petrochemical, energy, medical, civil engineering, and many other important industrial areas [8–11].
Nowadays, fiber sensors based on a single FP cavity composed of two parallel reflective surfaces have been very mature. Several types of technologies have been developed for their fabrications, such as micro-electromechanical systems (MEMS), chemical etching, micromachining, direct femtosecond (fs) laser writing, and others. However, to-this-date, the commercial fiber FP sensors have been commonly used to measure one parameter at a single location. Furthermore, most of the interrogators of fiber FP sensors can only interrogate one sensor only.
With the development of various industrial technologies, there has been an increasing demand for multisensor or multiparameter measurements based on fiber-optic FP sensing technologies. In fact, it is not very difficult to achieve multiposition, multiparameter sensing using serial or parallel connections of multiple types of fiber FP sensors with different cavity lengths. However, if multiple parameters are desired to be extracted from a single location, the conventional serial or parallel connection configurations of different types of single-cavity fiber-optic FP sensors may not be suitable. The so-called fiber-optic compound FP sensors, which have two or more FP cavities and simultaneously measure several different parameters will be the best choice.
Many different compact, compound fiber-optic FP sensors have been proposed for the simultaneously measurement of two (or even three) different parameters, such as the refractive index and temperature, force and temperature, strain and temperature, refractive index and pressure, etc. [12–16]. One of the most important compound sensors is the type that can simultaneously measure temperature and pressure. This sensor type possesses a tremendous potential for use in the oil, aviation, and ocean industries [17–21]. Furthermore, in any fiber-optic pressure sensors, the cross-sensitivity of temperature on pressure is always an issue; thus, in real pressure sensing at various environmental conditions, the temperature needs to be measured at the same time to achieve pressure compensation. Pevec and Donlagic reported a miniature compound FP sensor for simultaneous and direct measurements of pressure and temperature based on the use of the single-mode fiber (SMF) by a hydrogen fluoride etching and fusion splicing combining method [17]. A compound cavity FP sensor with a basal cavity of 1000 µm and an air-gap cavity of 17 µm was fabricated and tested in a temperature range of 20–80 °C and a pressure range of 0–0.1 MPa. Pang et al. fabricated a silicon microcavity structure based on MEMS, and introduced a polished fiber into it at an orientation of 45° [18]. Using the method, a silicon microcavity with a cavity length of 87.22 µm was fabricated, and an air cavity with a cavity length of 67.03 µm was formed between the inner surface of the silicon film and the fiber’s cladding surface. A maximum sensing error of 5.13% was achieved in the temperature range of 26.1–243.6 °C and the pressure range of 0.1–0.24 MPa. Yin et al. fabricated a silicon–glass–silicon sandwich bonding hybrid structure on a fiber tip, which contained a silicon cavity sensitive to temperature and a vacuum cavity sensitive to pressure [19]. The sensor yielded a pressure sensitivity of 12.82 nm/kPa with a highly linear pressure response over the range of 10–250 kPa, and a temperature sensitivity of 142.02 nm/°C in the range of −20–70 °C. Although both pressures and temperatures were successfully measured simultaneously, in these reports, the measurement ranges seem to be limited.
Zhang et al. fabricated a dual-cavity sensor based on the fusion splicing of SMFs, hollow core fiber and a coreless fiber, and a microchannel was drilled on the side of the hollow-core fiber using a fs laser [21]. An intrinsic Fabry–Perot interferometer (IFPI) sensor was used which was sensitive to temperature. Accordingly, the air cavity formed between the SMF and the coreless fiber in the center of the hollow core fiber was used for the sensing of pressure based on changes of its refractive index induced by direct exposure with the gas which flowed into the cavity through the fabricated microchannel. The sensor exhibited a temperature sensitivity of 29.63 nm/°C within the temperature range of 40–1100 °C, and a pressure sensitivity of 1465.8 nm/MPa within the pressure range of 0–10 MPa at room temperature. The structure can be used at high-temperature and high-pressure conditions; however, pressure sensing was achieved based on refractive index measurements. In real applications, the gas component should be known in advance. Moreover, silica, as a type of amorphous material, its microscopic structure would change at increased temperatures, especially when it becomes > 850 °C. Therefore, at these temperatures, the repeatability and lifetime of the sensor can hardly be guaranteed.
Sapphire, whose melting point is 2040 °C, has excellent optical and mechanical characteristics and may be an ideal material for the manufacturing of fiber-optic, high-temperature or pressure sensors. Several publications exist on temperature or pressure sensing at extreme environments [22–24]. However, the number of reports on the simultaneously measurement of temperature and pressure based on sapphire, dual-cavity FP sensors, has been limited [16].
For the applications of compound-cavity FP sensors, simultaneous interrogation of the two FP cavities is also an important issue and needs to be properly addressed. In the publications on the two-parameter compound cavity FP sensors, the spectrum-based Fourier or fast Fourier transform was commonly used [25–27]. However, it is well known that a Fourier transformation method cannot commonly extract the cavity length or the optical path difference (OPD) at a high resolution. The digital cross-correlation method [16,28,29] can be used to extract two different cavity lengths and has a good resolution. However, if the source spectrum is not wide enough, a “mode jumping” effect may be induced that will cause considerable resolution degradations. By using a low-coherence Fizeau interferometer, the correlation interferometric signal can be used for the extraction of the cavity length at high resolution based on the OPD matching of the FP sensor, and the optical wedge of the Fizeau interferometer [30–34]. The method can be referred to as white-light nonscanning correlation, and has the ability to interrogate multiple FP cavity lengths simultaneously if their OPDs are not shorter than half coherence length of the wideband light source used. However, if the OPDs of the FP cavities differ considerably with respect to each other, the length resolution of the shorter cavity cannot be guaranteed. Provided that the optical wedge of the Fizeau interferometer is split into several segments, of which, tilt angles and measurement ranges are optimized according the corresponding FP cavities, then the problem can be solved.
For the simultaneous measurement of pressure and temperature, a fiber-optic, EFPI, dual-cavity sensor which was made of sapphire, was fabricated for the simultaneous measurement of the two parameters, and a white-light nonscanning correlation interrogation system based on dual-segment, low-coherence Fizeau interferometer was proposed and constructed. Based on theoretical analyses and experimental verifications, it was shown that the dual-cavity EFPI sensor with the proposed interrogation method can successfully achieve the simultaneous measurement of pressure and temperature, even when their optical length or cavity length differences are relatively large.
2. Fiber-optic EFPI sapphire dual-cavity sensor
The structure of the sensor is shown in Fig. 1. The sensor’s head is composed of a pressure sensitive diaphragm, a circular vacuum cavity, basal cavity, glass capillary, and an SMF. The pressure-sensitive diaphragm, vacuum cavity, and the basal cavity, are all made by sapphire crystals based on the use of MEMS. The SMF was vertically cut and was fixed at the rear facet of the sapphire EFPI sensor by a short-length, hollow glass tube with the help of adhesives.
Fig. 1. Schematic of the fiber-optic, extrinsic Fabry–Perot interferometric (EFPI), dual-cavity sensor which was made of sapphire.
The EFPI dual-cavity sensor can be used for the simultaneous measurements of pressure and temperature. When a uniform pressure is imposed on the sensor, the front diaphragm of the sensor will be deformed accordingly and will cause the length of the vacuum cavity to change. The thickness variation of the vacuum cavity $\varDelta {L_v}$ in the axial center is linearly related to the change of the imposed pressure, and can be expressed as [35]
where $\nu$ is the Poisson’s ratio, $\Delta p$ is the change of the imposed pressure, E is the elastic modulus, and R and d are the radius and thickness of the pressure sensitive diaphragm, respectively. Based on the linear relationship, pressure can be measured based on the cavity length variation obtained from the measurements of the cavity length of the vacuum FP cavity. The pressure has no obvious effect on the basal cavity. Thus, the cavity length changes of the basal cavity can be neglected at different pressures.When the environmental temperature is changed, the cavity lengths of both the basal cavity and the vacuum cavity will also change because of the thermal expansion effect. Both cavity lengths increase when the temperature increases. For the basal cavity,
where, ${L_b}$ is the cavity length of the basal cavity, $\Delta T$ is the value of the temperature variation, and ${\alpha _T}$ is the coefficient of thermal expansion.Given that the cavity length changes of the vacuum and basal cavities are respectively proportional to pressure and temperature changes, the monitoring of the two cavity lengths, or their simultaneous real-time changes, allow the simultaneous measurements of both pressure and temperature. These measurements can be fulfilled using optical interferometric methods. However, in these types of measurements, it is the optical length, i.e. the multiplication of refractive index and geometrical length, to be directly measured. For the vacuum cavity, the optical length (or thickness)
where, ${n_v}$ and ${L_v}$ are the refractive index and length of the vacuum cavity, respectively. Since the refractive index of the vacuum ${n_v} = 1$, the optical length of the vacuum cavity is directly equal to its geometrical length.For the basal cavity, the optical length can be given by
where, ${n_b}$ is the refractive index of the basal cavity. For a temperature variation of $\Delta T$, the optical length variation is where, ${\beta _T}$ is the thermooptic coefficient. Evidently, both the thermal expansion effect and the thermooptic effect effect contribute to the optical length variation when the temperature is changed.The basal cavity is sensitive to temperature but the responses to the imposed pressure are minor. However, the vacuum cavity also responds to temperature changes. Correspondingly, cross-interference temperature changes affect the pressure measurements. Simultaneous measurements of pressure and temperature allow the compensation of the pressure measurements based on the measured temperature values.
There are three reflective surfaces, namely, the inner surface of the pressure-sensitive diaphragm M3, and the front and rear surfaces of the sapphire base and M2 and M1 exist in the EFPI dual-cavity sensor. The vacuum FP cavity is formed between M2 and M3. Furthermore, the basal cavity was formed between M1 and M2. The front surface of the sapphire diaphragm is sensitive to external pressure. Correspondingly, its surface is roughed to eliminate reflections based on scattering.
If the absorption or diffraction of the light beam can be neglected in the case of a compound sensor with two FP cavities, and assuming that the input light has a spectral power density of ${I_0}(\lambda )$ at the optical wavelength of $\lambda$, then the spectral power density of the reflected light can be expressed as
where ${R_{\textrm{FP}}}(\lambda)$ is the reflectivity of the dual-cavity FP sensor. Accordingly, for the existing three reflective surfaces, multiple-rounds of reflections (complete back and forth propagation paths) may occur between them, and the reflectivity ${R_{\textrm{FPr}}}(\lambda)$ has a relative complex form, which can be expressed by whereFor the EFPI sapphire dual-cavity sensor shown in Fig. 1, ${l_1} = {L_b}$ and ${l_2} = {L_v}$. Considering the refractive indices of fused silica (∼1.46), sapphire (∼1.77) and vacuum (1), we have ${R_1},{R_2},{R_3}\;<\;<\;1$ and ${R_2} = {R_3}$. The high-order harmonic terms in $K(\lambda )$ can be neglected, and $D(\lambda )\approx 1$. Correspondingly, ${R_{FP}}(\lambda )$ can be written as
3. Dual-segment low-coherence Fizeau interferometer
To achieve simultaneous measurements of the pressure and temperature from the two cavities of the fiber-optic EFPI dual-cavity sensor, in this study, we proposed white light, nonscanning correlation interrogation based on a dual-segment, low-coherence Fizeau interferometer. The interrogation system is composed of a superluminescent diode (SLD), 2×2 fiber coupler, fiber collimator, Powell lens, two-segment optical wedge, charge coupled device (CCD) linear array, data processing unit, and a computer, as shown in Fig. 2. A wide-band light emitted by the SLD is input into the 2×2 fiber coupler and coupled into the EFPI dual-cavity sensor. By the reflection of its three surfaces and the interference effect between the reflected light, part of the light containing sensor information relevant to optical lengths of the FP cavities is reflected back. The reflected light is coupled in the free space as a collimated beam by the fiber collimator, it is then expanded in one direction by the Powell lens, and passes through the two-segment optical wedge as a line-type beam. After the multibeam interference modulation of the two-segment optical wedge, the light is illuminated on the CCD linear array. Finally, the intensity distribution of the light is converted into an electric signal. Based on the treatment of the data processing unit, the peak positions of the two interferometric correlation signals which correspond to the basal cavity and vacuum cavity are identified for the simultaneous extraction of temperature and pressure.
Fig. 2. Schematic of the dual-segment, low-coherence Fizeau interferometer interrogation system used for fiber-optic EFPI dual-cavity sensor.
The core of the dual-segment, low-coherence Fizeau interferometer is a dual-segment optical wedge which consists of two air-gap optical wedges at different tilt angles and inner separation thickness ranges for the interrogation of the two FP cavities of the EFPI dual-cavity sensor. The thickness of the optical wedge ${d_i}$ at the position ${x_i}$ can be estimated based on
The case at which $i = 1$ represents the first optical wedge segment which has a thickness range which covers the changing range of the vacuum cavity, $i = 2$ represents the second optical wedge segment and has a thickness range which covers the changing range of the basal cavity, and ${d_{0i}}$ is the thickness of the two wedge segments at their shorter ends.The dual segment optical wedge can be constructed using three optical glass plates. Correspondingly, two air-gap optical wedges can be formed between the ground plate and the two plates which are titled at different angles and have different separation ranges. The outer surfaces of the glasses are coated with anti-reflection film to eliminate undesired reflections, and the inner surfaces of the glass plates are coated with a film that causes partial reflections. To achieve different tilt angles and separation ranges, films with different thicknesses were inserted at the two ends of the glass plates. The first segment has a small tilt angle and a thickness range which covers the changing range of the shorter vacuum cavity. The second part has a large thickness range to cover the longer basal cavity.
At position ${x_i}$, the spectral power density at the wavelength $\lambda$ after the optical wedge can be expressed as
When the fiber-optic EFPI sensor is illuminated by the wide-band light emitted by the SLD, the spatial distribution of the reflected light received by the CCD linear array after it passes the optical wedge can be written as,
The air-gap optical wedge is the key device for the correlation operation, and it is used to achieve a spatial scanning of the correlation operation with the optical thickness of each FP cavity of the compound FP sensor. For the mixing effect of Eq. (13), there are three optical lengths, namely, ${L_v}$, ${n_b}{L_b}$, and ${n_b}{L_b} + {L_v}$, for correlation with ${d_i}$. When the inner separation ${d_i} = {d_{i0}} + {x_i}\tan {\theta _i}$ of the optical wedge at a position ${x_i}$ is equal to one of the three optical lengths, the correlation interferometric signal will attain a maximum light intensity. Given that the vacuum cavity length ${L_v}$ is covered by the first optical segment, the maximum value of the correlation interferometric signal corresponding to the pressure signal will occur within the first optical wedge segment. If the optical length ${n_b}{L_b}$ of the basal cavity is covered within the range of the second optical wedge segment, the maximum value of the correlation signal corresponding to the basal cavity will occur within the second optical wedge segment. By properly designing the optical wedge, i.e., by choosing ${n_b}{L_b}$ and ${n_b}{L_b} + {L_v}$ to take values outside the thickness range of the first optical wedge segment, and by choosing ${L_v}$ and ${n_b}{L_b} + {L_v}$ values to be outside the thickness range of the second optical wedge segment, then only the two correlation interferometric signals corresponding to the vacuum and basal cavities will appear in each of the segments, and pressure and temperature can be interrogated independently from the vacuum and basal cavities based on the simultaneous selection of the peak positions of the two signals of the dual-segment, low-coherence Fizeau interferometer.
4. Experiments and analyses
4.1 Sensor and optical wedge fabrication
For the fabrication of the dual-cavity EFPI sensor, three layers of single-crystal sapphires were used. One layer was directly used as the basal cavity. A hole was firstly drilled through the entire thickness of the middle layer, and it was then connected with the first layer by direct bonding at high temperatures. After thermal treatment, the thickness of the middle layer with the hole was adjusted to the required thickness using mechanical polishing. The third layer was attached to the middle layer with the hole using the high-temperature, direct bonding method under a vacuum condition in a commercial vacuum bonding system, and also was thinned by mechanical polishing to form the pressure sensitive diaphragm. The sensitive structure was then cut out with the use of an intense fs laser. Additionally, a single mode fiber was attached and fixed to the rear end of the EFPI sensor based on the use of a glass capillary through an ultraviolet-curable epoxy. Finally, the entire structure was inserted into a ceramic tube structure and was fixed in it. Because the temperature- and pressure-sensitive parts of the EFPI sensor were composed of single sapphire crystals, and given that no other adhesives or materials were used in the pressure sensitive structure, the sensor has a good response to pressure and temperature. The tested fiber-optic dual-cavity sapphire EFPI sensor has a basal cavity length of 680 µm, and an initial vacuum cavity length of 80 µm, as shown in Fig. 3(a). Its reflection spectrum in a wavelength range of 840–860 nm has a waveform of a fast oscillating signal modulated by a slowly varying envelope, seen in Fig. 3(b).
Fig. 3. (a) Photograph of the fabricated fiber-optic, dual-cavity, EFPI sensor and (b) its reflection spectrum in a spectral range of 840-860 nm.
For the extraction of pressure and temperature from the two FP cavities of the fiber-optic EFPI sensor, a dual-segment, optical wedge with an air-gap was fabricated, as shown in Fig. 4. Given that the basal cavity length and the vacuum cavity length of the fabricated compound FP sensor were 680 µm and 80 µm, respectively, and given that both cavity lengths will change within a certain range at different pressures and temperatures, the two segments of the optical wedge should correspondingly cover the changing ranges of the two cavity lengths. Given that the peak of the correlation interferometric signal appears at the position at which the OPDs of the FP cavity and the inner separation of the optical wedge match each other, the refractive index of the sapphire should also be considered for the basal cavity measurements. We used an optical glass plate as the base and placed two optical glass plates on it. To ensure that the two segments of the optical wedges have different thickness ranges, polyimide films with different thicknesses were used as the spacers. At each spacer, the polyimide film and the glass plate were fixed with UV-curable adhesives. The first segment was fabricated with an inner separation range of 20–100 µm, and the second segment was fabricated to have an inner separation range of 1260–1180 µm (which corresponds to a sapphire basal cavity length of 712–667 µm).
4.2 Interrogation system
As shown in Fig. 5, an experimental interrogation system was established based on the fabricated dual-segment air-gap optical wedge for the simultaneous interrogation of the pressure and temperature of the fiber-optic EFPI sensor according to Fig. 2. The SLD used has a center wavelength of 850 nm, a 3 dB bandwidth of 60 nm, and a typical output power of 15 mW. The 2×2 fiber coupler is a wide-band type, and has a splitting ratio of 50:50. In addition, the insertion loss in the wavelength range of 850${\pm}$100 nm did not exceed 0.3 dB. The optical isolator was embedded in the box of the SLD, which had an isolation of 32 dB in the wavelength range of 850${\pm}$50 nm. The collimated beam output from the fiber collimator had a beam spot diameter of 0.3 mm, and was reshaped into a beam with a line-type profile by the Powell lens with a big fan angle of 60°. The linear array of the CCD was placed at a distance of 50 mm from the Powell lens. The dual-segment optical wedge was attached to the front surface of the CCD linear array. To avoid background-light disturbance on the linear array of the CCD and protect the surfaces of the optical device from contamination owing to dust, the fiber collimator, Powell lens, dual-segment, air-gap optical wedge, and the CCD linear array, were all assembled and sealed in a metal cassette, as observed in the inset of Fig. 5.
Fig. 5. Experimental system of the dual-segment Fizeau interferometric interrogation system for fiber-optic, dual-cavity, FP sensors. The inner structure of the cassette is shown in the inset.
A self-designed signal processing circuit with an FPGA as the central processing chip was used for driving the CCD linear array, and a peak positioning algorithm was used for the pressure and temperature measurements obtained from the two correlation interferometric signals.
4.3 Peak positioning of the correlation interferometric signal
After the fiber-optic EFPI sensor is connected to the Fiezeau interrogation system, two correlation interferometric signals are obtained on the linear array of the CCD, that is, an original signal for the sensor at room temperature, and a standard atmospheric pressure signal, as shown in Fig. 6(a). One of the interferometric signals corresponds to the pressure sensitive vacuum cavity, and the other corresponds to the basal cavity which is sensitive to temperature. It can be observed that the two correlation interferometric signals are both fast oscillating and are modulated by a slowly varying envelope. There is also a varying background in the detected signal. Based on the theory described previously, the peak position of the correlation interferometric signal directly corresponds to the OPD matching of the FP cavity and the inner separation of the optical wedge. Thus, the main issue of the signal processing unit is the peak positioning of the correlation signal.
Fig. 6. Peak detections of the correlation interferometric signals. (a) Complete signal trace obtained by the linear CCD array, and (b) magnified views of the two correlation interferometric signals of the vacuum and basal cavities.
To process the signal, the main task is to precisely identify the peak position of the correlation interferometric signal. However, as serious disturbances arise from the low-frequency background signal and the high-frequency noise, the peak position of the correlation interferometric signal cannot be accurately determined directly by peak searching. To solve this problem, we proposed an algorithmic procedure which was composed of Fourier transform, bandpass filtering in the frequency domain, inverse Fourier transform back to the time domain, envelope fitting, and zero fringe detection operations, based on a gravity center method. Details of the algorithm are similar to those listed in Ref. [34]. The main difference of the previously published algorithm with the one proposed in this study is that two correlation interferometric signals are present that need to be treated simultaneously.
As an example, the peak positioning process for a correlation interferometric signal is shown in Fig. 6. An original correlation signal modulated by a background signal and high-frequency noise is transformed into the frequency domain by the Fourier transform. After bandpass filtering, the signal is transformed back to the time domain. It can be observed that the background signal and high-frequency noise have been filtered out, and the envelope is identified based on an instantaneous, effective value extraction process. Accordingly, the center of the signal is positioned by using of the gravity center method, and the nearest peak of the fast oscillation signal is precisely determined to a subpixel level as the main peak of the correlation interferometric signal. The two peaks of the two correlation interferometric signals corresponding to the vacuum and basal cavities were detected at the pixel positions of 1248.36 and 2801.48 respectively, as shown in Fig. 6(b). As the pressures and temperatures change, the pixel number of the main peak of the two correlation interferometric signals will shift to different positions. Setting of the pixel number positions of the two main peaks allows the extraction of temperature and pressure.
4.4 Pressure and temperature outcomes
Pressure and temperature experiments were carried out to investigate the performance of the proposed interrogation system for dual-cavity FP sensors. The experimental setup is shown in Fig. 7. The fabricated fiber-optic EFPI sensor was placed into a pressure controlled gas chamber which can also be heated by a high-temperature furnace (KSL-1200X, temperature control accuracy: ±1 °C). The pressure of the gas chamber was controlled by a precision pressure controller (Druck, PACE-5000), which has a full measurement range of 21.1 MPa, and a resolution of 0.003% at full scale (FS). High-purity nitrogen stored in a gas cylinder was used for the pressure test.
The dual-cavity FP sensor was tested at four different temperatures of 50 °C, 150 °C, 250 °C, and 350 °C, respectively. At each temperature, different sensor pressures were used which ranged from 0.2 MPa to 3 MPa at steps of 0.4 MPa. At each pressure setting, the pressure value was controlled and was maintained for 3 min at the same state to reach static equilibrium. At the same time, the correlation interfererometric signals of the two FP cavities were monitored by the proposed dual-segment, low-coherence, Fizeau-interferometer-based interrogation system. The relationships of a) the main peak position of the correlation interference signal of the vacuum cavity and the pressure obtained by the first optical wedge segment, and b) the main peak position of the correlation interfering signal of the basal cavity and the temperature obtained by the second optical wedge segment of the interferometer are shown in Figs. 8 and 9, respectively.
In Fig. 8, it can be observed that at the same temperature and at increasing pressures, the peak of the correlation interferometric signal gradually moves to the direction at which the air-gap thickness of the first wedge segment is reduced. This is attributed to the fact that the vacuum cavity length is gradually reduced as the pressure is increased. As the temperature is increased, the peak of the correlation interferometric signal moves by a few pixels. The length of the vacuum cavity used for pressure sensing was also affected by the temperature, whereby pressure increases as the temperature increases. The relation between the peak position of the correlation interferometric signal and temperature under one atmospheric pressure is plotted in Fig. 9. It can be noted that as the temperature increases, the peak moves to the direction associated with smaller pixel numbers, i.e., toward the direction of larger thickness values in the case of the second optical wedge. This is attributed to the fact that when the temperature is increased, the optical length of the basal cavity gradually becomes longer. The coefficient of determination R2 for the pixel versus temperature is approximately equal to 99.84%, which shows a good linearity.
The experiment shows that based on the use of the fiber-optic EFPI sensor, both the temperature and pressure can be measured simultaneously. The sensor can be directly used in high-temperature pressure sensing if the epoxy used can be replaced by some high-temperature adhesives.
In the case of the vacuum cavity, the main peak position of the correlation interferometric signal yields linear relationships with respect to both the pressure and temperature according to
where ${T_0}$ and ${P_0}$ are the initial temperature and pressure, respectively, $N({{P_0},{T_0}} )$ is the corresponding pixel position of the peak of the correlation interferometric signal, and ${k_P}$ and ${k_T}$ are the pressure and temperature sensitivities which can be estimated based on the fitted experimental data. The four curves of pressure as a function of pixel number at different temperature were fitted to have slopes of −22.028, −21.98, −22.06, −22.028 /MPa, respectively. The average value was used as the value of the pressure sensitivity ${k_P}$, i.e., ${k_P} ={-} 22.024\textrm{ /MPa}$. From the experimental data, the changing rate of the pixel number against temperature, i.e., temperature sensitivity, can also be estimated to ${k_T} = 0.0197 /{}^\textrm{o}\textrm{C}$. Based on the fitting of the experimental data, $N({{P_0},{T_0}} )= 1248.3$ and corresponds to a pixel position for which the curve cross the vertical axis at a temperature of 0 °C. The temperature can be extracted directly from the pixel position of the basal cavity’s correlation interferometric signal from the second optical wedge of the Fizeau interferometer.For the basal cavity, the following relationship applies
where ${N_b}({{T_0}} )$ is the corresponding pixel position of the peak of the correlation interferometric signal on the second optical wedge at an initial temperature ${T_0}$, and ${k_{bT}}$ is the shift ratio of the pixel number against temperature. Use of the experimental data obtained from the basal cavity under a pressure of one atmosphere at various temperatures (Fig. 9), yields the fitted relation of ${N_b}(T )= 2805.52364 - 0.22689T$. Thus, the temperature surrounding the sensor can be directly obtained from the peak positioning of the basal cavity’s correlation interferometric signal.Based on the parameters listed above, from any pixel number $N({P, T} )$ associated with the correlation interferometric signal of the vacuum cavity, the pressure can be extracted from
Based on the extracted temperature from the basal cavity, correspondingly, the temperature cross-effect on the pressure can be eliminated effectively, as shown in Fig. 10. This figure shows the calibration relationship between the interrogated pressure and the reference pressure read from the precision pressure controller. The maximum pressure error was less than 0.02 MPa. The position shift of the correlation interferometric signal caused by temperature change has been successfully eliminated.Fig. 10. Corrected pressure estimated based on the consideration of the temperature extracted from the basal cavity.
5. Conclusions
A fiber-optic, EFPI, dual-cavity sensor made of sapphire was fabricated and interrogated by a dual-segment, low-coherence Fizeau interferometer to achieve simultaneous measurements of pressure and temperature. The pressure-sensitive vacuum cavity and the temperature-sensitive basal cavity of the sapphire dual-cavity sensor were simultaneously interrogated based on the peak positioning of the two correlation interferometric signals, which corresponded to the two FP cavities on the two different optical wedge segments of the dual-segment Fizeau interferometer. A fiber-optic EFPI sensor with an initial basal cavity length of 680 µm and a vacuum cavity length of 80 µm was tested and interrogated based on simultaneous temperature and pressure measurements, for pressures in the range of 0.1–3 MPa and temperatures in a range of 20–350 °C. Although the fiber-optic EFPI sapphire dual-cavity sensor under its current form can only work under a limited temperature range caused by the upper temperature limits of the UV epoxy, the glass capillary, and the glass fiber, however, if they can be properly replaced by the high-temperature inorganic glue, the ceramic capillary and the sapphire fiber respectively, then the sensor has the potential to be used in extremely high temperature environments above 1000 °C. Furthermore, the proposed dual-cavity length interrogation method can be generalized for the interrogation of other types of dual-cavity sensors to achieve the simultaneous measurements of the two parameters. If a compound Fizeau interferometer with three (or more) segments can be designed and optimized, the method can also be generalized for the simultaneous measurements of three or more parameters based on compound sensor measurements from three or more cavities.
Funding
National Natural Science Foundation of China (51475384, 61905187); Xi'an Key Laboratory of Intelligent Detection and Perception (201805061ZD12CG45); Foundation of Shaanxi Key Laboratory of Integrated and Intelligent Navigation (SKLIIN-20180210).
Disclosures
The authors declare no conflicts of interest.
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