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Abstract
A high sensitivity optical fiber gas pressure sensor based on the enhanced Vernier effect is proposed. The sensor is composed of a fiber Fabry-Perot interferometer (FPI) and Mach-Zehnder interferometer (MZI). Since the interference fringes of FPI and MZI drift in the opposite direction with the change of gas pressure, when their free spectral ranges are similar, the enhanced Vernier effect is formed after their cascading. Compared with the traditional Vernier effect gas pressure sensor, the enhanced Vernier effect gas pressure sensor realizes much higher sensitivity gas pressure measurement without complex manufacturing process or desensitized reference interferometer. The experimental results show that the sensitivity of the enhanced Vernier effect sensor is 241.87 nm/MPa. In the two traditional Vernier effect gas pressure sensors formed by cascading FPI and MZI, the sensitivity of sensor is 63.02 nm/MPa and 171.26 nm/MPa, respectively. Compared with the two traditional Vernier effect sensors, the sensitivity of the enhanced Vernier effect sensor is increased by 3.8 times and 1.4 times, respectively. The proposed sensor also has the advantages of good repeatability and stability, fast response, low cost and easy manufacture. Our structure also provides a new design scheme for a high sensitivity optical fiber gas pressure sensor.
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1. Introduction
Gas pressure measurement plays an important role in many fields, such as chemical industry, bioengineering, pharmaceutical industry, environmental monitoring, marine engineering and so on. Optical fiber sensor has the advantages of compact structure, high sensitivity, anti-electromagnetic interference, corrosion resistance, field measurement and so on, which has been widely used in the field of gas pressure sensing. A variety of optical fiber gas pressure sensors have been developed based on fiber grating [1,2], anti-resonant reflecting guidance mechanism [3,4], surface plasmon resonance [5] and optical fiber interferometers [6–14]. Among the optical fiber interferometer gas pressure sensors, the sensors based on Mach-Zehnder interferometer (MZI) [7–9] and Fabry-Perot interferometer (FPI) [10–14] are widely used because of their compact structure, easy manufacture and low cost. However, the maximum gas pressure sensitivity of these structures [1–8,12–14] can only reach a few nanometers per megapascal, which limits their applications in some conditions requiring ultra-high sensitivity. In order to improve the sensitivity of the gas pressure sensor, Zhao et al designed a MZI based on tapered fiber coated with polydimethylsiloxane for measuring gas pressure, and an ultra-high gas pressure sensitivity obtained is ‒159.80 nm/MPa [9]. Chen et al. proposed a FPI based on UV curable polymer film for gas pressure measurement, and an ultra-high pressure sensitivity obtained is 396.00 nm/MPa [11]. However, because the sensor structures use tapered optical fiber and polymer film, respectively, their mechanical strengths are poor and easy to be damaged, which limits their applications in high-pressure environment.
Another method to improve the sensitivity of the sensor is to use optical Vernier effect [15]. By measuring the response of the spectral envelope of the sensor, the sensitivity of the sensor can be amplified by an order of magnitude. Some gas pressure sensors based on the Vernier effect have been proposed, the structures including two cascaded FPIs [16–18], two parallel FPIs [19–21], two cascaded MZIs [22,23], Sagnac interferometer (SI) and FPI cascaded [24], etc. In Ref. [16], the maximum sensitivity of the sensor reaches 303.65 nm/MPa by two cascaded FPIs. In Ref. [24], the sensitivity of the sensor also can reach 31.73 nm/MPa by SI and FPI cascaded.
In recent years, based on the traditional Vernier effect, the enhanced Vernier effect has been proposed. In the traditional Vernier effect sensor, the reference interferometer is usually insensitive to the measurement parameters or isolated from the measurement environment. The spectral envelope of the sensor mainly amplifies the sensitivity of the sensing interferometer. In the enhanced Vernier effect sensor, two interferometers are all sensitive to the measurement parameters, their spectra will drift in the opposite direction with the change of the measurement parameters, which results in a much higher sensitivity than that of the traditional Vernier effect. In recent years, Zhang et al. proposed an ultra-high sensitivity refractive index (RI) sensor based on the enhance Vernier effect [25]. In addition, several ultra-high sensitivity temperature sensors based on the enhanced Vernier effect have also been proposed [26–28]. In particular, Pan et al. reported an enhanced Vernier effect gas pressure sensor based on two parallel FPIs, and the sensitivity reaches 131.88nm/MPa [29].
In this paper, a high sensitivity gas pressure sensor based on FPI and MZI cascaded forming the enhanced Vernier effect is proposed. FPI is composed of “single mode fiber (SMF)–multimode fiber (MMF) – capillary – SMF” spliced in sequence. MZI consists of “SMF – MMF – capillary – MMF – SMF” spliced in turn. Then, two micro pores were drilled in the capillary walls of two interferometers by using femtosecond laser processing technology to make the two interferometers communicate with the external gas. When the external gas pressure changes, the air RI in the capillaries of the two interferometers will change, so they are sensitive to the change of gas pressure. Moreover, with the change of gas pressure, their interference fringes drift in the opposite direction, so their gas pressure sensitivity symbols are opposite. Therefore, different from the traditional Vernier effect sensor, in our cascaded structure, FPI and MZI are each other's reference interferometer, and they produce Vernier effect and amplify simultaneously the sensor sensitivity. Then, the two amplified sensitivities are superimposed, a much higher sensitivity is obtained, that is the so-called enhanced Vernier effect. The experimental results show that the gas pressure sensitivity of our sensor is as high as 241.87 nm/MPa, and has a good linear fitting relationship.
2. Sensor fabrication and principle
The proposed sensor is shown in Fig. 1. FPI and MZI are cascaded to form a sensing head, which is connected to a broadband light source (BBS) and an optical spectrum analyzer (OSA) through an optical fiber circulator. A gas pressure insensitive fiber Bragg grating (FBG) is cascaded with FPI to compensate the influence of temperature on the gas pressure sensor. In the sensor structure, SMF and MMF are produced by Wuhan Yangtze Fiber and Cable company. SMF is a standard single-mode fiber with a core/cladding diameter of 9/125 µm. MMF includes two graded index fibers (GIF) MMF1 and MMF2, with core/cladding diameters of 62.5/125µm and 105/125 µm, respectively. The quartz capillary is produced by Polymicro Technologies of the United States. The model of capillary is TSP075150, and its inner/outer diameter is 75/150 µm. When the coating of capillary is burned off, its outer diameter becomes about 125 µm.
Figure 2 shows the schematics and light path diagrams of FPI and MZI. Figure 2(a) is the schematic and light path diagram of FPI. In Fig. 2(a), FPI is composed of “SMF – MMF1 – capillary – SMF” spliced in turn. The splicing structure forms two reflecting surfaces, including the reflecting surface 1 between MMF1 and capillary, the reflecting surface 2 between capillary and SMF. Reflecting lights on two reflecting surfaces form a FPI. In the FPI structure, a specific length of MMF1 is connected to the output end of the FPI, mainly to appropriately increase the interference fringes contrast of FPI by utilizing the self-focusing property of MMF1 [30].
Figure 2(b) is the schematic and light path diagram of MZI. In Fig. 2(b), MZI consists of “SMF – MMF2 – capillary – MMF2 – SMF” spliced in turn. The light incident by lead-in SMF excites multiple modes in MMF2, since the core diameter of MMF2 is larger than the inner diameter of the capillary, such configuration can ensure light separate to two paths. When light transmits from MMF2 to capillary, a part of the light propagates along the air-core of capillary and a part of the light propagates along the capillary wall, and combine into one when lights transmit from capillary to another MMF2 subsequently. Finally, they are coupled into lead-out SMF forming a MZI. According to the results in Ref. [31], the multimode interference excited in MMF2 leads to complex intensity distribution (generally referred to as speckle) in different MMF2 cross-sections. It is generally believed that the self-imaging effect occurs in some specific cross-sections [31]. Therefore, the length of MMF2 in MZI must be selected so that the self-imaging effect doesn't happen, so that there is some overlap between the output speckle pattern of MMF2 and the glass wall of the capillary.
Figure 3 displays the manufacturing process of FPI and MZI. Figure 3(a) is the manufacturing process of FPI. Step 1, SMF and MMF1 are spliced together, and MMF1 is cleaved to the desired length. Step 2, a section of capillary is spliced at the end face of MMF1, and the capillary is cleaved to the desired length. Step 3, another SMF is spliced to the end face of capillary to construct an F–P cavity. Step 4, a micro-pore was drilled on the capillary wall with femtosecond laser, and the FPI was cleaned with an ultrasonic cleaner. According to this method, three FPIs (FPI1, FPI2 and FPI3) with different capillary lengths are fabricated. Figure 3(b) is the fabrication process of MZI. Step 1, SMF and MMF2 are spliced together, and MMF2 is cleaved to the desired length. Step 2, a section of capillary is spliced at the end face of MMF2, and the capillary is cleaved to the desired length. Step 3, another MMF2 is spliced to the end face of capillary, and MMF2 is cleaved to the desired length, then another SMF is spliced to the end face of MMF2. Step 4, a micro-pore was drilled on the capillary wall with femtosecond laser, and the MZI was cleaned with an ultrasonic cleaner. The femtosecond laser used in the preparation of FPI and MZI are wavelength 780 nm, pulse width 35 fs, repetition frequency 1 kHz, and maximum output energy 5 mJ.
Here, both FPI and MZI can be equivalent to two-beam interference. According to the interference theory, the peak wavelength of output spectra of FPI and MZI are as follows respectively:
When the external gas pressure acts on FPI and MZI, the air RI in the capillaries of FPI and MZI will change, so both FPI and MZI are sensitive to the ambient gas pressure. From an updated Edlén equation, the air RI is a function of the pressure P and temperature T [32]:
When the external gas pressure changes, the change of air RI in the capillary and the change of capillary length will be caused. According to the results in Ref. [4], the change of capillary length caused by gas pressure change is much smaller than the change of air refractive index caused by gas pressure. Thus, the change of capillary length caused by gas pressure can be ignored. Therefore, according to Eqs. (1) and (2), the gas pressure sensitivities of FPI and MZI at constant temperature can be approximately expressed as follows:
It can be seen from Eqs. (4) and (5) that when the peak wavelengths are the same, the gas pressure sensitivity of MZI is about 2.16 times that of FPI. When T = 25°C and ${\lambda _{FPI}} = {\lambda _{MZI}} = 1550nm$, the theoretical calculation values of gas pressure sensitivity of FPI and MZI are about 4 nm/MPa and -8.6 nm/MPa, respectively.
When the FSRs of FPI and MZI are similar but not equal, the FPI and MZI cascaded structure will form a Vernier effect [15]. The output spectrum of the cascaded structure is the product of MZI and FPI spectrum, which forms a large spectrum envelope. The peak wavelength and FSR of the spectral envelope can be calculated as follows [15–18]:
When the gas pressure changes, the small drifts of MZI and FPI caused by the gas pressure change will lead to a large drift of the spectral envelope of the cascaded structure. Combining equations (1), (2) and (5), the peak wavelength shifts of spectral envelope can be expressed as:
Therefore, the gas pressure sensitivity of the cascaded structure can be obtained as follows:
In our cascaded structure, both MZI and FPI are sensitive to the gas pressure change, and ${S_{FP{I_P}}}$ is positive and ${S_{MZ{I_P}}}$ is negative, therefore, according to Eq. (9), the value of ${S_P}$ is the maximum, which is the enhanced Vernier effect [15,25]. If MZI as a reference unit is not put into the gas chamber, the Eq. (9) becomes ${S_P} = {S_{FP{I_P}}} \cdot {M_{FPI}}$, which is the traditional Vernier effect [15,16]. If FPI as a reference unit is not put into the gas chamber, the Eq. (9) becomes ${S_P} ={-} {S_{MZ{I_P}}} \cdot {M_{MZI}}$, which is also the traditional Vernier effect [15,16]. It can be seen from the above calculation that the sensitivity of enhanced Vernier effect is much higher than that of two traditional Vernier effects. Moreover, the sensitivity of the enhanced Vernier effect is equal to the sum of the absolute values of the sensitivity of the two traditional Vernier effects.
3. Experimental results and discussion
3.1 Output spectra
First, we use BBS, OSA and fiber circulator to measure the spectra of FPI, MZI, and the FPI and MZI cascaded structure, respectively. The BBS is the model of FL-ASE produced by Beijing Kangguan company. The light wavelength range emitted by it is 1250–1650 nm. The OSA is the model of AQ6370D manufactured by Yokogawa, Japan. Its minimum wavelength resolution is 0.02 nm and its working wavelength range is 600–1700nm. In our experiment, the resolution of OSA was set to 0.06 nm, and the wavelength range selected for the sensor measurement was 1300–1600 nm in our experiments. The micrographs of FPIs and MZI were taken with the 10× objective lens of Olympus metallurgical microscope (Model: BX51M).
Figure 4 is the reflection spectra and micrographs of FPI1, FPI2 and FPI3. It can be seen from Fig. 4(a) that their FSRs are about 3.48 nm, 2.94 nm and 2.64 nm respectively. Their spectral fringe contrasts are about 8.52 dB, 5.47 dB and 6.26 dB respectively. In Fig. 4(b), the cavity lengths of the three FPIs are about 327 µm, 385 µm, and 420 µm respectively. The lengths of MMF1 in the three FPIs are about 242 µm, 243 µm, and 174 µm, respectively. Figure 5 is the transmission spectrum and micrograph of MZI. It can be seen from Fig. 5(a) that the FSR and spectral fringe contrast of MZI spectrum are 3.06 nm and 11.27 dB respectively. In Fig. 5(b), the capillary length of MZI is about 1595µm, and the lengths of two section of MMF2 in MZI are about 1 mm, respectively. It can be seen from Fig. 4 and 5 that the difference between the FSR of FPI1, FPI2, FPI3 and MZI is 0.42 nm, 0.12 nm, and 0.42 nm, respectively.
From the spectra of FPI and MZI, we can see that they have very similar FSRs, so they can generate Vernier effect after their cascading. Figure 6(a) shows the output spectrum of FPI and MZI cascaded structure. As can be seen from Fig. 6(a), the output spectrum of the cascaded structure is composed of fine comb interference fringes and slowly changing envelopes. Since the envelope of the sensor spectrum is relatively regular, the fitting method in Ref. [15,19] is used to extract the upper envelope, as shown in the red-curve in Fig. 6(a). The FSR of the spectral envelope of the three cascaded structures are 23.34 nm, 59.04 nm and 19.62 nm respectively. As can be seen from Fig. 6(a), because the difference between FSR of FPI2 and MZI is the smallest, the FSR of its spectral envelope is the largest, so its sensitivity will be the highest [15]. Because the differences of FSR of FPI1 and MZI, and FSR of FPI3 and MZI are slightly large, the FSRs of their spectral envelope are slightly small, so their sensitivity is slightly low [15]. Figure 6(b) shows the Fast Fourier Transform (FFT) spectrum of the cascade structure. In Fig. 6(b), the two main frequency of FFT spectrum components correspond to FPI and MZI respectively. The results show that the interference spectrum of the cascaded structure is mainly formed by the spectra of FPI and MZI.
3.2 Gas pressure experiment of sensor
The experimental setup of gas pressure is shown in Fig. 7. The self-made metal gas chamber is used to measure the gas pressure of the sensor. The sensing head is sealed in the gas chamber. A BBS (FL-ASE) is used as the input light source. An OSA (AQ6370D) is used to record the spectrum of the sensor. A fiber optic circulator is used to connect them. During the gas pressure test, the manual gas pump is used to pressurize and depressurize to the gas chamber, and the pressure gauge (with resolution of 0.01 MPa) is used to record the change of gas pressure in the gas chamber. The variation range of gas pressure is set between 0–0.4 MPa. When the pressure changes by 0.05 MPa each time, we record the sensor spectrum once. At each gas pressure measurement point, keeping the gas pressure of the gas chamber unchanged for 10 min until the spectrum is stable, and then records the spectral data. The gas pressure experiment is carried out at room temperature of 25 °C.
In all gas pressure experiments, we select the wavelength of a certain peak point in the spectrum as the tracking object, observing the shift of the central wavelength of the peak when the pressure changes, and then finding out the relationship between the wavelength shift and the pressure change. Finally, the measured pressure value is obtained by demodulating the shift of the wavelength.
First, we separately investigated the gas pressure response of FPI2 and MZI with and without micro-pores. Figure 8(a) shows the variation of the peak wavelength of FPI2 with gas pressure increasing. From Fig. 8(a), the peak wavelength of FPI2 with micro-pore drifts toward the long wavelength direction with increase of gas pressure, and the peak wavelength of FPI2 without micro-pore basically does not drift with the gas pressure increasing. Figure 8(b) shows the linear fitting of the peak wavelength of FPI2 versus gas pressure change. From Fig. 8(b), the sensitivities of FPI2 with micro-pore are 3.76 nm/MPa and 3.70 nm/MPa when the pressure rises and falls respectively. The sensitivity of FPI2 without micro-pore was almost zero. The experimental results are basically consistent with the theoretical results.
Fig. 8. (a) Variations of the peak wavelength of FPI2 versus gas pressure, (b) Linear fittings of the peak wavelength of FPI2 versus gas pressure.
Figure 9(a) displays the variation of the peak wavelength of MZI versus gas pressure increasing. As can be seen from Fig. 9(a), the peak wavelength of MZI with micro-pore drifts toward the short wavelength direction as the gas pressure increases, and the peak wavelength of MZI without micro-pore basically does not drift with gas pressure increasing. Figure 9(b) shows the linear fitting of the peak wavelength of MZI versus gas pressure change. From Fig. 9(b), the sensitivities of MZI with micro-pore are ‒7.72 nm/MPa and ‒8.12 nm/MPa when the pressure rises and falls respectively. The sensitivity of MZI without micro-pore was almost zero. The experimental results are basically consistent with the theoretical results.
Fig. 9. (a) Variations of the peak wavelength of MZI versus gas pressure, (b) Linear fittings of the peak wavelength of MZI versus gas pressure.
The experimental results show that the barometric sensitivity of MZI is about 2.16 times that of FPI. In addition, the barometric sensitivity of MZI is negative and that of FPI is positive. If there are no micro-pores in FPI and MZI, they are not sensitive to gas pressure. These experimental results are consistent with the theoretical analysis in section 2.
Secondly, the gas pressure sensitivity of the enhanced Vernier effect produced by FPI and MZI cascaded structure was measured using the experimental device in Fig. 7. In the enhanced Vernier effect experiment, both FPI and MZI are placed in the gas chamber. Figure 10 is the experimental results of FPI1 and MZI cascaded structure with gas pressure change. Figure 10(a) shows the upper envelope peak wavelength shifts of the cascaded structure as gas pressure increasing. As can be seen from Fig. 10(a), the peak wavelength drifts toward the short wavelength direction with the increase of gas pressure. Figure 10(b) shows the linear fittings of the upper envelope peak wavelength versus gas pressure. From Fig. 10(b), the sensitivity of boosting and depressurizing were ‒90.43 nm/MPa and ‒90.10 nm/MPa, respectively.
Fig. 10. (a) Envelope shifts and (b) linear fittings of FPI1 and MZI cascaded structure versus gas pressure.
Figure 11 presents the experimental results of FPI2 and MZI cascaded structure with gas pressure change. Figure 11(a) shows the upper envelope peak wavelength shifts of the cascaded structure as gas pressure increasing. As can be seen from Fig. 11(a), the peak wavelength drifts toward the long wavelength direction with the increase of gas pressure. Figure 11(b) shows the linear fittings of the upper envelope peak wavelength versus gas pressure. From Fig. 11(b), the sensitivity of boosting and depressurizing were 241.87 nm/MPa and 242.87 nm/MPa, respectively. Figure 12 shows the experimental results of FPI3 and MZI cascaded structure with gas pressure change. Figure 12(a) shows the upper envelope peak wavelength shifts of the cascaded structures as gas pressure increasing. As can be seen from Fig. 12(a), the peak wavelength drifts toward the long wavelength direction with the increase of gas pressure. Figure 12(b) shows the linear fittings of the upper envelope peak wavelength versus gas pressure. From Fig. 12(b), the sensitivity of boosting and depressurizing were 90.10 nm/MPa and 91.00 nm/MPa, respectively.
Fig. 11. (a) Envelope shifts and (b) linear fittings of FPI2 and MZI cascaded structure versus gas pressure.
Fig. 12. (a) Envelope shifts and (b) linear fittings of FPI3 and MZI cascaded structure versus gas pressure.
From the above experimental results, it can be found that the three cascaded structures have obtained extremely high pressure sensitivity by the enhanced Vernier effect. Because the difference between the FSR of FPI2 and that of MZI is the smallest, the sensitivity of the FPI2 and MZI cascaded structure is the largest, which is consistent with the theoretical analysis. Moreover, because the FSR of FPI1 is larger than that of MZI, its spectral envelop peak wavelengths will shift toward the short wavelength direction with gas pressure increasing. Because the FSRs of FPI2, FPI3 are smaller than that of MZI, their spectral envelope peak wavelengths will shift toward the long wavelength direction with gas pressure increasing. In conclusion, when MZI is fixed, FPI with different FSR can be used to cascade with it to obtain different barometric sensitivity. In addition, in the FPI2 and MZI cascaded structure, considering the resolution of the OSA is 0.06 nm, so the resolution of the cascaded structure is about 0.24 × 10−3 MPa (0.06/247.87 = 0.00024 MPa) under ideal conditions.
In order to verify the difference between the enhanced Vernier effect and the traditional Vernier effect on sensitivity amplification, we configured two traditional Vernier effect sensors using FPI2 and MZI cascaded structure. As a traditional Vernier effect sensor, the reference interferometer is either insensitive to the measurement parameters or isolated from the measurement environment. Therefore, in the first traditional Vernier effect sensor composed of FPI2 and MZI cascaded structure, FPI2 as sensing unit is put into the gas chamber, and MZI as a reference unit is not put into the gas chamber. Figure 13(a) shows the variation of the upper envelope of the cascaded structure as gas pressure increasing. Figure 13(b) displays the linear fittings of the upper envelope peak wavelength versus gas pressure. The sensitivity of boosting and depressurizing obtained by fitting are 63.94 nm/MPa and 63.02 nm/MPa, respectively. Compared with the sensitivity of a single FPI2, the sensitivity of the cascaded structure is enlarged by about 17 times (63.94/3.76 = 17) using the traditional Vernier effect, which is basically consistent with the theoretical magnification $({M_{FPI}} = \frac{{FS{R_{\textrm{e}nvelope}}}}{{FS{R_{FPI}}}} = 20.1).$
Fig. 13. (a) Envelope shifts and (b) linear fittings of the cascaded structure versus gas pressure in the first traditional Vernier effect.
In the second traditional Vernier effect sensor composed of FPI2 and MZI cascaded structure, MZI as a sensing unit is put into the gas chamber, and FPI2 as a reference unit is not put into the gas chamber. Figure 14(a) displays the variation of the upper envelope of the cascaded structure as gas pressure increasing. Figure 14(b) is the linear fittings of the upper envelope peak wavelength versus gas pressure. The sensitivity of boosting and depressurizing obtained by fitting are 171.26 nm/MPa and 170.08 nm/MPa, respectively. Compared with the sensitivity of a single MZI, the sensitivity was amplified by about 22.2 times (171.26/7.72 = 22.2) using the traditional Vernier effect, which is basically consistent with the theoretical magnification $({M_{MZI}} = \frac{{FS{R_{\textrm{e}nvelope}}}}{{FS{R_{MZI}}}} = 19.3).$ The experimental results also show that the sensitivity of the second traditional Vernier effect sensor is larger than that of the first traditional Vernier effect sensor. This is mainly because the sensitivity of a single MZI is larger than that of a single FPI2. This is consistent with the theoretical analysis.
Fig. 14. (a) Envelope shifts and (b) linear fittings of the cascaded structure versus gas pressure in the second traditional Vernier effect.
The comparative experimental results show that in the cascaded structure of FPI2 and MZI, the sensitivity of the enhanced Vernier effect is 3.8 times (241.87/63.94 ≈ 3.8) that of the first traditional Vernier effect, and 1.4 times (241.87/171.26 ≈ 1.4) that of the second traditional Vernier effect. In addition, the sensitivity (241.87) of the enhanced Vernier effect is approximately equal to the sum of the sensitivities of the two traditional Vernier effects (171.26 + 63.94 = 235.20). This result is consistent with the theoretical analysis.
To verify the consistency of the enhanced Vernier effect sensor, we use the FPI2 and MZI cascaded structure to measure the gas pressure for 3 weeks. Figure 15 shows the three experimental results at room temperature of 25 °C. It can be seen from Fig. 15 that the three gas pressure experimental data of the sensor are basically consistent, which proves that the sensor has good consistency and repeatability. The stability of the enhanced Vernier effect sensor is also studied. Firstly, the gas pressures of the gas chamber are set of 0.1 MPa, 0.2 MPa, and 0.3 MPa, respectively, then the sensor is put into the gas chamber and the gas pressure of the gas chamber is kept unchanged for 90 min. The stability test results of the sensor are shown in Fig. 16. It can be seen from Fig. 16 that the sensor has good stability under different gas pressure. Within 90 min, the maximum wavelength drifts of the sensor is only 0.05 nm, 0.05 nm and 0.30 nm at 0.1 MPa, 0.2 MPa and 0.3 MPa, respectively.
The response time of FPI2 and MZI cascade structure to measure gas pressure is also studied. Figure 17 records the rise time of the sensor when the gas pressure increases with step of 0.1 MPa and the fall time of the sensor when the gas pressure decreases with step of 0.1 MPa. In response time experiment, we sampled spectral data every 10 s. It can be seen from Fig. 17 that the average rise time and the average fall time of unit gas pressure are 149 s/MPa and 163 s/MPa, respectively. The experimental results show that the gas pressure sensor has the characteristics of short response time.
3.3 Temperature sensitivity of sensor
We carried out temperature experiments on FPI2, MZI, and the FPI2 and MZI cascaded structure, respectively. Figure 18(a) shows the variations of the peak wavelength of MZI and FPI2 versus temperature. It can be found from Fig. 18(a) that the peak wavelength of MZI drifts toward the long wavelength direction with increase of temperature, and the peak wavelength of FPI2 basically does not drift with the temperature increasing. Figure 18(b) shows the linear fittings of the peak wavelength of MZI and FPI2 versus temperature change. It can be found from Fig. 18(b) that the temperature sensitivity of MZI is 0.03 nm/°C as the temperature increases, and the temperature sensitivity of FPI2 is very small and can be ignored [33].
Fig. 18. (a) Variations of the peak wavelengths of FPI2 and MZI versus temperature, (b) Linear fittings of the peak wavelengths of FPI2 and MZI versus temperature.
Figure 19 shows the upper envelope peak wavelength shifts and linear fitting of FPI2 and MZI cascaded structure as the temperature changes. It can be seen from Fig. 19 that the temperature sensitivity is ‒0.81 nm/°C with the increase and decrease of temperature. Therefore, the cascade structure can also be regarded as a traditional vernier effect temperature sensor, with a sensitivity about 27 times that of a single MZI (0.81/0.03 = 27). In addition, according to the measured gas pressure and temperature sensitivity, the temperature cross sensitivity of the gas pressure sensor is estimated to be 3.3 kPa/°C (0.81/241.87 = 0.0033 MPa/°C). This value is smaller than that in the Refs. [9,19,29].
Fig. 19. (a) Envelope shifts and (b) linear fittings of FPI2 and MZI cascaded structure versus temperature.
3.4 Compensation of temperature cross-sensitivity of the sensor
Because the sensor is sensitive to temperature, when the sensor measures the gas pressure if the ambient temperature also changes, it will also cause a drift of the spectral envelope and affect the gas pressure measurement results. In here, we use a FBG to compensate the influence of temperature on the gas pressure sensor [34]. Figure 20 is the output spectrum of FBG, FPI2 and MZI cascaded structure. Figure 21 shows the wavelength shifts and linear fitting of FBG versus gas pressure and temperature respectively. It can be seen from Fig. 21 that FBG is sensitive to temperature and the temperature sensitivity is 10.9 pm/°C, and FBG is insensitive to gas pressure and the gas pressure sensitivity is approximately zero. The influence of the sensor spectral envelope drift caused by temperature on the sensor gas pressure measurement can be offset by the following mathematical formula [34]:
3.5 Comparison with other studies
Our experimental results are compared with those of some high-sensitivity gas pressure sensors, as shown in Table 1. From the comparison in Table 1, it can be found that the sensitivity of our proposed sensor is only lower than that of Refs. [11] and [16], and higher than that of other references. In Ref. [11], although ultra-high sensitivity is obtained, the measurement range is small and the film thickness is difficult to control. In Ref. [16], the measurement range is also small. Although the enhanced Vernier effect is also used in literature [29], its gas pressure sensitivity is only about half that of our sensor. In addition, our sensor has the advantages of simple structure, good robustness and easy manufacture.
Table 1. Comparison of high sensitivity gas pressure sensors
4. Conclusion
In summary, We fabricated FPI and MZI with quartz capillary, and then used FPI and MZI cascade to form a gas pressure sensor with enhanced Vernier effect. In the sensor structure, both FPI and MZI are sensitive to air pressure, and their spectral wavelengths drift in the opposite direction when the gas pressure changes. Therefore, when their FSRs are similar, they will form an enhanced Vernier effect sensor after their cascading, which can obtain extremely high sensitivity. We fabricated three FPIs with similar FSR, and they were cascaded with MZI forming three enhanced Vernier effect sensors. Their sensitivities were -90.43 nm/MPa, 241.87 nm/MPa and 90.1 nm/MPa, respectively. In addition, the sensor has good repeatability and stability, short response time and high sensitivity, so it is suitable for gas pressure sensitive measurement of low-pressure gas tanks in the chemical industry, biological engineering and pharmaceutical industry.
Funding
the Fund of Graduate Innovation Research of Hubei Normal University (20220498); the Scientific Research Funding Project for Young Teachers of Hubei Normal University (20210037); The Middle-aged and Youth Science and Technology Innovation Team of Hubei Province University (T2020014).
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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