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All-silica fiber-optic temperature-depth-salinity sensor based on cascaded EFPIs and FBG for deep sea exploration

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Abstract

Using fusion splicing and hydroxide catalysis bonding (HCB) technology, an all-silica inline fiber-optic sensor with high-pressure survivability, high-resolution salinity measurement capability, and corrosion resistance for deep sea explorations is proposed and experimentally demonstrated. Two extrinsic Fabry-Perot interferometers (EFPIs) and a fiber Bragg grating (FBG) are cascaded in one single-mode fiber (SMF), enabling structural integration of single lead-in fiber and versatility of the sensing probe for temperature, depth, and salinity monitoring. The HCB technology offers a polymer adhesive-free assembly of one open-cavity EFPI for refractive index (RI) (salinity) sensing under normal pressure and temperature (NPT) conditions, showing obvious advantages of strong bonding strength, reliable effectiveness, and no corrosive chemicals requirements. The other EFPI formed by a fused structure is designed for pressure (depth) measurement. The cascading of EFPIs, especially the open-cavity EFPI immersed in water, will result in large light transmission loss and bring challenges to signal interrogation. Graded-index fiber (GIF) micro-collimators and reflective films are added to prevent dramatic degradations of signal intensity and fringe visibility underwater. Thereby, a Fabry-Perot (FP) cavity of several hundreds of microns in length and an open cavity of a thousand microns can be cascaded for underwater applications, effectively enhancing sensitivities and underwater signal readout simultaneously. Results show that the proposed sensor can well operate in the deep-sea pressure range of 0∼2039.43 mH2O, RI range of 1.33239∼1.36885 RIU, and temperature range of 23∼80 °C, with resolutions of 0.033 MPa, 4.16×10−7 RIU, and 0.54 °C, respectively. With the multi-parameter measurement capability, all-silica construction, and inline compact structure, the proposed sensor could be a potential candidate for deep sea exploration.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Temperature, depth, and salinity are important parameters and indicators for seawater monitoring and exploration, which are of great significance to oceanography, hydrometeorology, navigation, and ecological balance [1,2]. Nowadays, commercial conductivity-temperature-depth (CTD) system has been widely used in the development and utilization of the ocean and has made remarkable achievements. However, the CTD system mainly depends on electronic components, which makes it suffer from electromagnetic noise, seawater corrosion, high maintenance cost, and difficulty in long-distance transmission [3]. As potential alternatives to those electronic devices, fiber-optic sensors have been the topic of intense researches for seawater monitoring during the recent past, driven by the principle merits of immunity to electromagnetic interference, corrosion resistance, and ease of distribution, networking, and remote sensing [46]. Fiber Bragg grating (FBG) and Fabry-Perot interferometer (FPI) are promising technologies for seawater explorations, due to their stable structure, easy multiplexing, good repeatability, and parametric measurement diversity [511]. V. Vaddadi et al. mounted an FBG sensor on a metal disk to form a closed air-cavity setup and measure seawater column pressure [6]. D. Duraibabu et al. proposed a temperature-depth sensor for underwater application based on a fiber-optic extrinsic FPI (EFPI) combined with an FBG [7]. R. Flores et al. demonstrated a sensor with two sensing arms for salinity and temperature measurement using focused ion beam (FIB) milling and hydrofluoric acid (HF) etching to create Fabry-Perot (FP) micro-cavities inside single-mode fibers (SMFs) [8]. But they are limited to single parameter detection or dual-parameter measurements of temperature in combination with other parameters.

To further allow compact constructions and multi-parameter measurement capabilities, sensors relying on the cascading of EFPIs with a single lead-in fiber are gradually emerging thanks to their unique structural flexibility and versatility. S. Pevec et al. reported several in-fiber sensors consisting of cascaded EFPIs, mainly fabricated by HF etching or laser micro-machining, for multi-parameter measurements of temperature, refractive index (RI), pressure, and other parameters [911]. Although the cascading of EFPIs is very advantageous for the fabrication of multifunctional inline sensors, the large transmission loss caused by the cascading without effective collimation and compensation may result in weaker optical signal intensity and poorer fringe visibility. This affects the signal readout and even deprives the sensor of its functionality. Therefore, it is particularly important to take advantage of multi-parameter measurement capabilities from the cascading of EFPIs while providing optical signal compensation through improved manufacturing schemes. Adding graded-index fiber (GIF) micro-collimators and reflective films of the interferometer are potential for the fabrication of EFPIs-cascade sensors. To compensate the light loss caused by beam divergence in EFPI, GIF of its ¼ transmission cycle has been used as a beam expander/collimator, which is often referred to as a quarter-pitch collimator [12]. With the addition of GIF micro-collimators, the signal quality has proven to be significantly improved, especially for inline sensors that require larger FP cavity length to improve sensitivity and resolution [12,13]. In addition, reflective films may be required to work with collimators to obtain more sufficient back-reflected signals from the EFPIs with longer cavity lengths [14].

Furthermore, since seawater is oxygen-containing, conductive, and high-pressure, it may raise extra requirements on sensor fabrication. The fiber-optic sensors must be durable enough to work under extreme conditions such as high pressure and strong corrosion. To keep the robustness and stability of the sensing structure, researchers try to avoid the use of polymer adhesives in the manufacturing process whenever possible. Because the polymer adhesive easily creeps and decomposes after a long period of work which severely degrading the performance of the sensors [15]. Studies including those mentioned above have utilized FIB milling, wet etching, laser micro-machining, and laser welding [811,16], for the preparation of polymer adhesive-free sensors. Furthermore, based on our prior work [17], hydroxide catalysis bonding (HCB) technology might be another potential candidate. HCB technology is a polymer adhesive-free bonding method developed by NASA, which has been used to assemble astronomical optical silica components, showing great advantages in working under normal pressure and temperature (NPT) conditions, requiring no corrosive chemicals, achieving high-precision alignment, and increasing bonding strength [1820]. The bonding formed between the two surfaces using the HCB technology relies entirely on silicate-like networks which are robust underwater and resistant to high pressure [20,21]. Compared to the above methods, the HCB technology may be more suitable not only for assembling sensing structures without polymer adhesive but also for the construction of all-silica sensors.

In this work, an all-silica inline fiber-optic sensor with three sensing units cascaded in one SMF for deep sea exploration is proposed and experimentally demonstrated, which is composed of an FBG for temperature monitoring and dual EFPIs for pressure (depth) and RI (salinity) measurements respectively. Deep sea measurements typically require sensors capable of withstanding high pressures of 2000 mH2O, along with a resolution of at least 0.003 g/kg (∼10−7 RIU) for salinity measurements [22,23]. The two cascaded EFPIs are designed primarily for the requirements of deep sea applications. The 1st fused EFPI for pressure sensing and the 2nd open-cavity EFPI with ∼1000-µm long cavity length for high-resolution RI measurement are fabricated by fusion splicing and HCB technology, thereby providing a corrosion-resistant and high-pressure tolerant all-silica sensing structure. To overcome the challenges to optical signal interrogation brought by the cascading of two EFPIs underwater, especially the open-cavity EFPI immersed in water, several GIF micro-collimators and reflective films are added to compensate the optical signal transmission loss and enhance the fringe visibility. This makes it possible to improve the sensitivity and resolution of pressure and RI measurements by increasing the FP cavity length up to hundreds or even a thousand microns. The response characteristics of the proposed sensor to temperature, high pressure, and RI are then experimentally studied and results show that the feasibility of the sensor for deep sea monitoring is preliminarily verified. The all-silica sensor may be a candidate for deep sea explorations in the future.

2. Sensor description and operating mechanism

2.1 Structure design and fabrication

The configuration of the all-silica inline sensor is shown in Fig. 1(a). It consists of a lead-in SMF, an FBG, two different FP cavities formed by a hollow-core fiber (HCF, inner diameter-ID: 80 µm, outer diameter-OD: 125 µm, FiberHome) and a glass hollow tube (ID: 127 µm, OD: 1.8 mm, length: 6.5 mm, ITECH) respectively, and three GIF (core diameter: 62.5 µm, OD: 125 µm, YOFC) micro-collimators. The two EFPIs and an FBG are cascaded in one SMF, permitting structural integration of a single lead-in fiber and versatility of the sensing probe. The FBG is used for temperature monitoring. The 1st fused EFPI with a shorter cavity length of ∼350 µm is designed for high static pressure (depth) measurement where two GIF micro-collimators are fused at each side of the HCF. One GIF acts as a beam expander/collimator and compensates the signal loss caused by beam divergence, the other couples the output beam from HCF into the cascaded 2nd open-cavity EFPI. Furthermore, a GIF micro-collimator is also added into the 2nd EFPI and different thicknesses of gold films are deposited both on the endfaces of this GIF and SMF. They allow a longer cavity length around 1000 µm for high-sensitivity RI (salinity) sensing and prevent sharp degradation of fringe visibility when the sensor is immersed into liquids. Figures 1(b) and 1(c) show the physical image of the fabricated 1st and 2nd EFPI.

 figure: Fig. 1.

Fig. 1. Configuration of the all-silica inline sensor, (a) the schematic diagram of the sensing probe, (b) image of the fabricated 1st EFPI under an optical microscope, and (c) image of the 2nd EFPI.

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The all-silica inline sensing structure is entirely made of fused silica and is manufactured by a multistep process. The 1st EFPI is fabricated by fusion splicing only. The fabrication process begins with the preparation of an in-fiber micro-collimator. Light beam propagating in a GIF undergoes an approximately sinusoidal path due to the gradient RI distribution of the fiber core, where the period of the sinusoidal path is always defined as a transmission cycle. When the length of the GIF is ¼ transmission cycle, the beam divergence angle from the GIF is minimal and the GIF can be used as a collimator [12]. A lead-in SMF is fusion spliced with a GIF using a fusion splicer (KL-300T, JILONG), and the GIF is precisely flat cleaved to about ¼ transmission cycle in length (∼260 µm [12]) monitored by an optical microscope and a micrometer, as shown in Figs. 2(a) and 2(b). Then the GIF micro-collimator fused on the fiber tip is spliced with an HCF. The arcing power is turned down to 26 bits (‘bit’ is a self-defined unit of the fusion splicer), and arcing duration is reduced to 1000 ms to avoid collapse of the inner hole and to maintain the mechanical strength of the splicing point, as shown in Fig. 2(c). The GIF micro-collimator collimates diverged beam, thus compensating the light loss caused by the air hole in the 1st EFPI. This step is followed by cutting the HCF into a desirable length and splicing another GIF micro-collimator onto the flat endface of the HCF, as shown in Figs. 2(d), 2(e), and 2(f). This micro-collimator couples the output beam from the inner hole of HCF into the SMF and then transmits it into the cascaded 2nd EFPI.

 figure: Fig. 2.

Fig. 2. The multistep fabrication process of the all-silica inline sensor, (a) fusion splice SMF and GIF, (b) cut GIF, (c) fusion splice GIF and HCF, (d) cut HCF, (e) fusion splice HCF and another GIF, (f) structure of the 1st EFPI, (g) deposit gold film, (h) drip bonding solution, (i) curing process, and (j) cascade successively.

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Since the connection established between two silica components using the HCB technology relies exclusively on the formation of silicate-like networks, it allows for an all-silica construction and robustness of the 2nd EFPI underwater [20,21]. Firstly, the bonding solution is prepared by diluting a sodium silicate solution (typically 14% NaOH, 27% SiO2, in aqueous solution) with deionized (DI) water in a volume ratio of 1:4, and then filtered through a 0.22 µm microporous filter. The sidewall of the glass hollow tube is grooved to create an open path for liquid to flow into the FP cavity. Then the grooved hollow tube, an SMF spliced with a GIF micro-collimator, and another SMF, are ultrasonically bathed for five minutes in methanol, acetone, and DI water to keep the bonding surface clean. Via magnetron sputtering, a thin film of gold with about several nanometers thickness is deposited on the cleaned endface of the GIF micro-collimator, allowing 10∼20% light intensity to be reflected. Since the RI of gold is much lower than that of the fiber core [24], small thickness variations in the gold film do not significantly change the optical path. Thereafter, a 100-nm thick layer of gold is deposited on the cleaned endface of the SMF, which provides high reflectance, as shown in Fig. 2(g). The deposition of gold reflective films is to prevent a sharp degradation of optical signal intensity and fringe visibility when the open cavity is immersed in liquid.

The HCB bonding process is performed under NPT conditions in class 100 ultra-clean working environment. A small amount of bonding solution is dripped on the sidewall of the two fibers by a micropipette, as shown in Fig. 2(h). Thereafter they are inserted into the hollow tube, and the two gold-deposited endfaces form an FP cavity which is aligned with the open path on the hollow tube sidewall. The hydroxide catalysis starts with hydration and etching, where hydroxide ions in the bonding solution act as a catalyst and etch the two surfaces in contact, then release silicate ions [1820]

$$\textrm{Si}{\textrm{O}_\textrm{2}}\textrm{ + O}{\textrm{H}}^{—}\textrm{ + 2}{\textrm{H}_\textrm{2}}\textrm{O} \to \textrm{Si}{({\textrm{OH}} )}_\textrm{5}^{—} $$

During the release of silicate ions, active hydroxide ions are consumed which reducing the pH of the solution. When pH<11, the silicate ions disassociate and form siloxane chains [1820]

$$\textrm{2Si}{({\textrm{OH}} )}_\textrm{5}^{—} \to \textrm{2Si}{({\textrm{OH}} )_\textrm{4}}\textrm{ + 2}{{({\textrm{OH}} )}^{—} } \to {({\textrm{HO}} )_\textrm{3}}\textrm{SiOSi}{({\textrm{OH}} )_\textrm{3}}\textrm{ + }{\textrm{H}_\textrm{2}}\textrm{O + 2}{{({\textrm{OH}} )}^{—} }$$

With the siloxane chains lengthening, they form networks and bond the two surfaces together. The dehydration process is the final step of HCB technology. The bonding is temporarily settled by keeping at room temperature for 5 minutes, as shown in Fig. 2(i). Since the curing time can be shortened by properly increasing the ambient temperature of the bonding process [17,19], the 2nd EFPI is heat-treated at 200 °C for 24 hours. During this time, the bond severely reduces in thickness and increases in strength [18,19]. When the moisture in the bonding interface is completely evaporated, the two fibers are firmly bonded in the hollow tube. Finally, an FBG for temperature monitoring, the 1st EFPI for high-pressure sensing, and the 2nd EFPI for RI measurement are sequentially cascaded on one SMF to form an all-silica inline multi-parameter sensor, as shown in Fig. 2(j).

2.2 Signal interrogation and sensing principle

A typical all-silica inline sensor is fabricated using the above procedure, and the signal interrogation is performed by an optical sensing interrogator (OSI, sm125, Micron Optics) with a wavelength scanning range of 1510∼1590 nm, a spectral resolution of 5 pm, a sampling rate of 2 Hz, and an intensity dynamic range of 60 dB. Figure 3(a) shows the multiplexed spectrum of the sensing probe immersed in water, which can be regarded as the overlap of an FBG reflection peak and two EFPIs interference spectra. Although the fabrication process involves many steps, the fringe visibility of the interference is improved with the addition of collimations and reflective films. The signal of the 2nd EFPI with a large cavity length up to about 1000 µm remains visible even underwater due to the addition of collimations and reflective films, as shown in Fig. 3(a). Temperature information can be achieved by Bragg peak tracking of the FBG directly from the spectrum. The 1st EFPI and the 2nd EFPI have different FP cavity lengths with characteristic free spectral ranges, thus generating distinctive frequency components. Since the FBG has an impact on the demodulation of the two EFPIs, it is necessary to separate this multiplexed spectrum. Because the spectral width of FBG (2 nm) is far less than that of the light source (80 nm) and the cross-correlation signal processing algorithm we employ for demodulating EFPIs is insensitive to small-scale data loss [25,26]. Removing and extracting the wavelength range occupied by the FBG peak from the spectrum will not have an obvious impact on the accuracy of FP cavity length demodulation [2628].

 figure: Fig. 3.

Fig. 3. Signal interrogation process of the all-silica inline sensor, (a) comparison of the multiplexed spectrum with and without collimation and reflective films in the wavelength domain, (b) comparison of FFT results with and without collimation and reflective films in the frequency domain, (c) and (d) normalized interference spectra after FIR bandpass filters and Hilbert transform.

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From the acquisition of OSI, the multiplexed spectral signals of the two cascaded EFPIs belong to the wavelength domain. Generally, each EFPI is regarded as a low-finesse FPI and estimated by a two-beam interferometer model. The interference spectrum can be expressed as an intensity-modulated signal, which is caused by the optical phase difference (OPD) between two reflected beams

$$I = {I_\textrm{1}} + {I_\textrm{2}} + \textrm{2}\sqrt {{I_\textrm{1}}{I_\textrm{2}}} \cos \left( {\frac{{\textrm{4}\mathrm{\pi }nL}}{\lambda } + \mathrm{\pi }} \right)$$
where I is the intensity of the interference spectrum, I1 and I2 are intensities of the reflected beams, n is the RI of the medium filled in FP cavity, L is the FP cavity length in the air, λ is the working wavelength, and π is the additional phase of half-wave loss. Because $\lambda \textrm{ = }{c / \nu }$, c is the speed of light, ν is frequency, the intensity-modulated signal can be converted into the optical frequency domain to facilitate signal processing methods such as fast Fourier transform (FFT) and bandpass filter.

The spectrum in the wavelength domain in Fig. 3(a) (red curve) is first converted into frequency domain after 16384 points of linear interpolation, and then the FFT is performed. Figure 3(b) (red curve) depicts the FFT results of the multiplexed spectrum in the frequency domain, where two distinctive peaks can be identified in addition to DC and low-frequency components. Peak 1 corresponds to the 1st EFPI, and Peak 2 corresponds to the 2nd EFPI, with primary normalized frequency components appearing at 23 and 96 Hz respectively. By comparing the FFT results with/without collimation and reflective films in the frequency domain, the amplitude of Peak 1 is increased by ∼7 times, and Peak 2 can be read out. The simultaneous use of GIFs and reflective films is a prerequisite to ensure that the interference signal from the 2nd open-cavity EFPI is properly transmitted, returned, and detected underwater, as shown in Fig. 3(b). The FP cavity lengths can be calculated based on the normalized frequency and estimated by [29,30]

$$L = \frac{\textrm{1}}{\textrm{2}}\frac{{{\lambda _\textrm{1}}{\lambda _\textrm{2}}}}{{{\lambda _\textrm{1}} - {\lambda _\textrm{2}}}} \cdot k$$
where λ1 and λ2 are the upper and lower limits of the working wavelength range, k is the normalized frequency, k = NF, N is sampling points, F is the digital frequency [26]. The cavity lengths of the 1st EFPI and the 2nd EFPI of the sensing probe are simply estimated to be 345 µm and 1440 µm underwater. To more accurately extract the small variations in cavity length of the EFPIs, two Hamming window-based finite impulse response (FIR) bandpass filters are designed to filter the optical frequency domain signals, respectively. Then, to further eliminate the influence of the envelope brought by the light source or the addition of GIF on the filtered signal, the Hilbert transform is used to extract the normalized spectrum, as shown in Figs. 3(c) and 3(d). Using the cross-correlation signal processing algorithm [25,26], each normalized spectrum can be interrogated to obtain two absolute FP cavity lengths which can be expressed as a function of pressure and RI, respectively. The cavity lengths of the 1st EFPI and the 2nd EFPI are demodulated to be 341.439 µm and 1437.357 µm (immersed in water), respectively.

When static pressure is applied, the HCF used for the fabrication of the 1st EFPI will deform by the pressure, thus changing the FP cavity length. By monitoring the FP cavity length variations, the pressure information to be measured can be obtained. The relationship between the changes of the FP cavity length and the applied pressure can be expressed as [31,32]

$$\Delta L = \frac{{d{r_\textrm{o}}^\textrm{2}}}{{E({{r_\textrm{o}}^\textrm{2} - {r_i}^\textrm{2}} )}}({\textrm{1} - \textrm{2}\gamma } )\Delta P$$
where d is the distance between the fixed points of the hollow tube, i.e. gauge distance, ro is the OD of the HCF, ri is its ID, P is the applied pressure, E and γ are Young’s modulus (73 GPa) and Poisson’s ratio (0.17) of fused silica. Based on Eq. (5), the pressure sensitivity caused by the deformation of HCF is linearly proportional to the cavity length of the 1st EFPI, which is estimated to be 5.23 nm/MPa.

According to Eq. (3), when the RI of the medium filled in the 2nd FP cavity varies, the total intensity of the interference spectrum and the OPD will change correspondingly. Using the cross-correlation signal processing algorithm, the optical cavity length of an FPI can be measured. The optical cavity length of the FPI and its cavity length in the air is as follows [33,34]

$${L_\textrm{O}} = n\frac{L}{{{n_{\textrm{air}}}}}$$
where LO is the optical cavity length, nair is the RI of the air (about 1.00029). When the medium in the cavity of the 2nd EFPI is the air and others, L and LO can be interrogated by the cross-correlation signal processing algorithm. And the absolute measurement of the RI can be achieved by a simple division, as described in Eq. (6). The sensitivity of the RI measurement can be expressed as ${{\Delta L} / {\Delta n}}\textrm{ = }{{L / n}_{\textrm{air}}}$, which increases with the physical cavity length and shows a linear relationship. The RI sensitivity of the 2nd EFPI is evaluated as 1080.44 µm/RIU.

3. Experimental results and discussion

We experimentally demonstrate the feasibility of the all-silica inline sensor for applications in deep sea monitoring. The response and crosstalk of the sensor to depth, salinity, and temperature are studied. The performance of the sensing probe for deep-sea pressure measurements is first analyzed and verified by simulating a high-pressure environment with hydraulic calibration equipment (GY7511, Jiangsu State Automation Instrument). Figure 4 shows the experimental setup for high-pressure testing in a pressure range of 0∼20 MPa (0∼2039.43 mH2O) at room temperature (23.0 °C), and the readout of a pressure gauge (GY-YBJ, 0.05% F.S., Jiangsu State Automation Instrument) is as a reference. The sensing probe is encapsulated in a sealed stainless steel tube filled with transformer oil as a reliable working medium for high-pressure generation and delivery. The transformer oil is transparent to light and has a RI of about 1.4677 RIU. The output interference spectrum from the OSI of the sensing probe is then demodulated as described previously to obtain the absolute FP cavity length as a function of applied pressure.

 figure: Fig. 4.

Fig. 4. Experimental setup for the high-pressure tests.

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The sensing probe shows good high-pressure survivability and linearity when the pressure is increased from 0 to 20 MPa with a step size of 1 MPa. Figure 5(a) shows the pressure response of the sensor, the FP cavity length of the 1st EFPI decreases with the increasing pressure, indicating that the HCF is deformed. It exhibits a sensitivity of −6.89 nm/MPa after a pressure increase and decrease cycle, which is similar to the theoretical results described in Eq. (5). The estimation of the pressure resolution is obtained by considering the standard deviation (SD) of FP cavity length variations in 450 seconds at 10 MPa [17,35], yielding a pressure resolution of 0.033 MPa (3.37 mH2O), about 0.17%F.S., as shown in Fig. 5(a). In Fig. 5(b), the error percentage of the sensing probe is evaluated by comparing our measured value with the output of the pressure gauge, yielding the maximal absolute error (MAE) of 0.15 MPa, about 0.75%F.S.. The two linear fitting curves are both within the error bars, indicating no obvious hysteresis and good repeatability. The proposed sensor can operate in conditions with higher pressure which in our lab is limited by the maximum pressure of ∼20 MPa generated by the equipment.

 figure: Fig. 5.

Fig. 5. Pressure response of the all-silica inline sensor from 0 to 20 MPa, (a) relationship between FP cavity length and applied pressure, and SD in 450 seconds time span at 10 MPa, and (b) comparison between the measured pressure and the applied pressure.

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Moreover, the pressure crosstalk of the inline sensor is analyzed in Fig. 6. Over the entire pressure measurement range of 0∼20 MPa, the signal of the 2nd EFPI can be easily read out by the addition of GIF collimators and reflective films. And the sensing structure shows no degradation, indicating that the fibers are tightly bonded to the hollow tube by the HCB technology. The FP cavity length increases with the increasing pressure, causing a RI variation of about 5.65×10−3 RIU with a cross-sensitivity of 2.69×10−4 RIU/MPa, as shown in Fig. 6(a). The photoelastic effect in transformer oil and the deformation of the hollow tube under high pressure may be responsible for the pressure-RI dependence [36,37]. They respectively lead to RI variations of the surrounding medium and the changes in physical cavity length of the 2nd EFPI. Due to the high sensitivity of RI sensing deduced from Eq. (6), the crosstalk brought by the photoelastic effect might play a dominant role, leading to an increase in cavity length, as shown in Fig. 6(a). Since the photoelastic effect leads to an acceptable difference between the total RI changes of water and the transformer oil in the range of 0 to 20 MPa [36,37], we consider the pressure crosstalk results in the oil as an approximation in the deep sea environment. The light propagating through the FBG is mostly confined within the core, resulting in its insensitivity to external RI changes and only cross-sensitivity to pressure variations. Its pressure crosstalk can be evaluated by the Bragg peak shift, exhibiting a linear cross-sensitivity of about −3.68 pm/MPa, as shown in Fig. 6(b).

 figure: Fig. 6.

Fig. 6. The pressure crosstalk of the all-silica inline sensor from 0 to 20 MPa, (a) relationship of cavity length of the 2nd EFPI and RI reading versus applied pressure, and (b) relationship between Bragg peak shift and applied pressure.

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Then the performance of the all-silica inline sensor for salinity measurements is studied, which exhibits high sensitivity and resolution. The sensing probe is immersed in NaCl solutions with different salinity from 6.18 to 234.02 g/kg at normal pressure and room temperature. Salinity can be obtained from RI measurements due to their linear relationship [38]. The RI of the solutions is calibrated by an Abbe refractometer (WYA-3S, Shanghai INESA Physico-Optical Instrument) as a reference (over 1.33239∼1.36885 RIU range). The sensor remains connected to the OSI as in Fig. 4 and is successively immersed in each NaCl solution to record the response. Then we remove the sensing probe and pipette out the remaining liquid before immersing it in the next solution. Similar to FBG, the light beam transmitted in the HCF is mostly confined within the inner hole, thus the 1st EFPI is unaffected by RI changes as well. The optical length of the 2nd FP cavity increases sharply when immersed in solutions, denoting that the solutions fill the FP cavity, as shown in column diagrams in Fig. 7(a). The results of the measured FP cavity length are shown in scatter diagrams in Fig. 7(a), and the variations of the cavity lengths versus RI for the two cascaded EFPIs are shown in Fig. 7(b). The 2nd EFPI exhibits a RI sensitivity of 1080.46 µm/RIU or a salinity sensitivity of 173.69 nm/(g/kg). The sensitivity is similar to the theoretical values from Eq. (6). The absolute RI measurement can be realized by Eq. (6), and the measured RI is compared with the reference one from the Abbe refractometer, as shown in Fig. 7(c). The red lines are linear fit curves of the sensor to the RI response, and the blue guideline represents the case when the measured RI is the same as the reference one. The MAE between the measured RI and the reference one is 5.48×10−5 RIU (0.34 g/kg), about 0.15% F.S.. The RI resolution is obtained by evaluating the SD of FP cavity length variations in 450 seconds at 1.34692 RIU [17,35], yielding 4.16×10−7 RIU (∼2.59×10−3 g/kg), about 0.0011% F.S., as shown in Fig. 7(d). This meets the resolution requirements for deep sea salinity measurements (∼3×10−3 g/kg [22,23]). The all-silica inline sensor is robust over the entire underwater testing without any disintegration, indicating that the polymer adhesive-free assembly provided by the HCB technology is water-resistant.

 figure: Fig. 7.

Fig. 7. RI response, error percentage, and resolution of the all-silica inline sensor in the range of 1.33239∼1.36885 RIU, (a) the increase value and measured cavity length of the 2nd EFPI, (b) relationship between FP cavity length and reference RI, (c) comparison of the measured RI and the reference one, and (d) SD in 450 seconds time span at 1.34692 RIU.

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The temperature characteristics of the cascaded FBG and the temperature crosstalk of the inline sensor are analyzed. The sensing probe is immersed in a water bath calibrated by a thermocouple. The temperature is varied in the range from 23 to 80 °C. The variations can be determined by the Bragg peak shift of the FBG, exhibiting a sensitivity of 9.22 pm/°C, as shown in Fig. 8(a). Since the spectral resolution of the OSI is 5 pm, the temperature resolution is obtained as 0.54 °C. The MAE between the measured temperature and the applied one is 0.44 °C, about 0.77%F.S., as shown in Fig. 8(b).

 figure: Fig. 8.

Fig. 8. Temperature response of the all-silica inline sensor, (a) temperature response of the cascaded FBG and Bragg peak shift, and (b) comparison of the measured temperature and the applied temperature.

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Meanwhile, the temperature crosstalk is evaluated over the entire range while observing the variations in pressure and RI reading, as shown in Figs. 9(a) and 9(b). In theory, the increase temperature can both lead to thermal expansion of the HCF and the glass hollow tube used for EFPIs fabrication. The relationship between FP cavity length variations and temperature changes can be approximated as [39]

$$\Delta L = L{\alpha _\textrm{c}}\Delta T$$
where T is the applied temperature, αc is the thermal expansion coefficient of the materials, which are 5.5×10−7/°C for HCF and 3.3×10−6/°C for the glass hollow tube, respectively. And the temperature cross-sensitivity of the 1st EFPI of the sensing probe can be evaluated as 0.19 nm/°C. For the 2nd EFPI, it is about 3.57 nm/°C.

 figure: Fig. 9.

Fig. 9. The temperature crosstalk of the all-silica inline sensor from 23 to 80 °C, (a) relationship of FP cavity length of the 1st EFPI and pressure reading versus applied temperature, and (b) relationship of FP cavity length of the 2nd EFPI and RI reading versus applied temperature.

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As shown in Fig. 9(a), the cavity length of the 1st EFPI increases with the increasing temperature, which is induced by the thermal expansion of the HCF. It causes a total pressure reading to change by around 1.74 MPa with a temperature cross-sensitivity of 0.21 nm/°C, similar to the theoretical results above, leading to a temperature-pressure dependence of −0.0305 MPa/°C. Since an increase in temperature always leads to a decrease in the RI of liquid [37,40] and then causes a decrease in FP cavity length. This might significantly exceed the theoretical increase value in the cavity length caused by the thermal expansion of the glass hollow tube, thereby only showing a decrease in the FP cavity length of the 2nd EFPI. The change in total RI reading corresponds to −6.67×10−3 RIU with a temperature-RI dependence of −1.19×10−4 RIU/°C, as shown in Fig. 9(b).

Since each single sensing unit of the inline sensor is sensitive to temperature, pressure, or RI almost simultaneously, all crosstalk signals should be excluded from the measured values, and then the target ones can be obtained. By building a transfer matrix with these linearly fitted slopes of sensitivity and cross-sensitivity above, the target temperature, pressure, and RI variations can be extracted [41,42]

$$\left[ {\begin{array}{{ccc}} {{S_{\textrm{FBG - T}}}}&{{C_{\textrm{FBG - P}}}}&{{C_{\textrm{FBG - n}}}}\\ {{C_{{\textrm{1}^{\textrm{st}}}\textrm{ EFPI - T}}}}&{{S_{{\textrm{1}^{\textrm{st}}}\textrm{ EFPI - P}}}}&{{C_{{\textrm{1}^{\textrm{st}}}\textrm{ EFPI - n}}}}\\ {{C_{{\textrm{2}^{\textrm{nd}}}\textrm{ EFPI - T}}}}&{{C_{{\textrm{2}^{\textrm{nd}}}\textrm{ EFPI - P}}}}&{{S_{{\textrm{2}^{\textrm{nd}}}\textrm{ EFPI - n}}}} \end{array}} \right]\left[ {\begin{array}{{c}} {\Delta T}\\ {\Delta P}\\ {\Delta n} \end{array}} \right] = \left[ {\begin{array}{{c}} {\Delta {\lambda_\textrm{T}}}\\ {\Delta {L_\textrm{P}}}\\ {\Delta {L_\textrm{n}}} \end{array}} \right]$$
where S is sensitivity, C is cross-sensitivity, λT is Bragg’s center wavelength of the FBG. The parameter units of each column of the matrix are nm/°C, nm/MPa, and nm/RIU. When the Bragg center wavelength and FP cavity length are demodulated without obvious errors, and the sensitivity and crosstalk characteristics of each parameter are stable and linear, this approach can well decouple the interdependence between the three parameters according to Eq. (8). Even if the sensor brings some error, the demodulation error and linearity of sensitivity characteristics for each parameter are still within acceptable limits. Multiple experiments will yield more accurate matrix parameters to reduce those errors if needed. When applied to the testing in this work, the change values of the parameters are obtained by mapping their inverse matrices. Then, the target variations of temperature, pressure, and RI can be deduced by
$$\Delta T\textrm{ = 109}\textrm{.80}\Delta {\lambda _\textrm{T}} - \textrm{0}\textrm{.059}\Delta {L_\textrm{P}}$$
$$\Delta P\textrm{ = 3}\textrm{.35}\Delta{\lambda _\textrm{T}} - \textrm{0}\textrm{.15}\Delta {L_\textrm{P}}$$
$$\Delta n\textrm{ = 0}\textrm{.012}\Delta {\lambda _\textrm{T}} + \textrm{0}\textrm{.000033}\Delta {L_\textrm{P}}\textrm{ + 0}\textrm{.000001}\Delta {L_\textrm{n}}$$

Via the above scheme, the temperature, pressure (depth), and RI (salinity) of the deep sea can be obtained simultaneously by tracking the Bragg peak of the FBG and demodulating the variations of the two EFPIs. Besides, the proposed sensor shows no noticeable degradation or malfunction through the entire testing, indicating that fusion splicing and HCB technology can effectively ensure the high-pressure survivability and robustness of the all-silica sensing structure for deep sea applications. Meanwhile, the addition of GIF collimators and reflective films well compensate the signal loss and enhances the fringe visibility, allowing the signal to be read out and demodulated. Furthermore, specific analysis of the real deep sea environment is also required before applying the sensing probe to practical ocean explorations in the future, such as varying sensitivity by adjusting the FP cavity length, analyzing the measurement curves based on real seawater parameters, and designing the sensor package, etc.

4. Conclusion

An all-silica inline fiber-optic sensor with two EFPIs and an FBG cascaded in one SMF is proposed and experimentally demonstrated. The sensing probe designed for temperature, depth, and salinity measurement in a deep sea environment is fabricated using fusion splicing and HCB technology. The HCB technology provides polymer adhesive-free assembly under NPT conditions with high bonding strength, no corrosive chemicals requirements, and reliable effectiveness. And the all-silica sensing structure of the sensor is very beneficial to the high-pressure survivability and corrosion resistance requirements in deep sea explorations. The sensing probe utilizes several GIF micro-collimators to compensate the light loss and enables cascading of two EFPIs with cavity lengths of hundreds and even a thousand microns in an underwater environment, thereby improving the sensitivities and resolutions of pressure and RI measurements to meet the requirements of deep sea applications. Temperature, pressure, and RI sensitivity characteristics of the sensor and the crosstalk between the three parameters are studied in the range of 23∼80 °C, 0∼20 MPa, and 1.33239∼1.36885 RIU, respectively. A transfer matrix is employed to minimize the effect of crosstalk for more accurate demodulation. The feasibility of the sensor for deep sea environmental monitoring is experimentally verified. With further optimization of the sensor and specific analysis of the real ocean environment, the proposed sensor with compact inline structure, high-pressure tolerance, high-resolution RI measurement capability, and corrosion resistance may become an option for deep sea explorations in the future.

Funding

National Natural Science Foundation of China (61727816, 61520106013); Fundamental Research Funds for the Central Universities (DUT21ZD212).

Disclosures

The authors have no relevant financial interests in this article and no potential conflicts of interest to disclose.

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.

References

1. Y. Qian, Y. Zhao, Q. Wu, and Y. Yang, “Review of salinity measurement technology based on optical fiber sensor,” Sens. Actuators, B 260, 86–105 (2018). [CrossRef]  

2. M.R. Brininstool, “Oceanic Applications of Fiber Optics,” Proc. IEEE OCEANS 91 (1991).

3. G. I. Roden and J. D. Irish, “Electronic Digitization and Sensor Response Effects on Salinity Computation from CTD Field Measurements,” J. Phys. Oceanogr. 5(1), 195–199 (1975). [CrossRef]  

4. D. B. Duraibabu, S. Poeggel, E. Omerdic, R. Capocci, E. Lewis, T. Newe, G. Leen, D. Toal, and G. Dooly, “An Optical Fibre Depth (Pressure) Sensor for Remote Operated Vehicles in Underwater Applications,” Sensors 17(2), 406 (2017). [CrossRef]  

5. Y. Liu, X. Liu, T. Zhang, and W. Zhang, “Integrated FPI-FBG composite all-fiber sensor for simultaneous measurement of liquid refractive index and temperature,” Opt. Lasers Eng. 111, 167–171 (2018). [CrossRef]  

6. V. Vaddadi, S. Parne, S. Afzulpurkar, S. Desai, and V. Parambil, “Design and development of pressure sensor based on Fiber Bragg Grating (FBG) for ocean applications,” Eur. Phys. J. Appl. Phys. 90(3), 30501 (2020). [CrossRef]  

7. D. B. Duraibabu, G. Leen, D. Toal, T. Newe, E. Lewis, and G. Dooly, “Underwater Depth and Temperature Sensing Based on Fiber Optic Technology for Marine and Fresh Water Applications,” Sensors 17(6), 1228 (2017). [CrossRef]  

8. R. Flores, R. Janeiro, and J. Viegas, “Optical fibre Fabry-Pérot interferometer based on inline microcavities for salinity and temperature sensing,” Sci. Rep. 9(1), 9556 (2019). [CrossRef]  

9. S. Pevec and D. Donlagic, “Miniature fiber-optic sensor for simultaneous measurement of pressure and refractive index,” Opt. Lett. 39(21), 6221–6224 (2014). [CrossRef]  

10. S. Pevec and D. Donlagic, “MultiParameter Fiber-Optic Sensor for Simultaneous Measurement of Thermal Conductivity, Pressure, Refractive Index, and Temperature,” IEEE Photon. J. 9(1), 1–14 (2017). [CrossRef]  

11. S. Pevec and D. Donlagic, “Miniature Fiber-Optic Pitot Tube Sensor,” IEEE Sens. J. 20(9), 4732–4739 (2020). [CrossRef]  

12. R. Wang, Z. Liu, and X. Qiao, “Fringe visibility enhanced Fabry-Perot interferometer and its application as gas refractometer,” Sens. Actuators, B 234, 498–502 (2016). [CrossRef]  

13. Y. Zhang, Y. Li, T. Wei, X. Lan, Y. Huang, G. Chen, and H. Xiao, “Fringe Visibility Enhanced Extrinsic Fabry–Perot Interferometer Using a Graded Index Fiber Collimator,” IEEE Photon. J. 2(3), 469–481 (2010). [CrossRef]  

14. S. Pevec and D. Donlagic, “Miniature fiber-optic Fabry-Perot refractive index sensor for gas sensing with a resolution of 5 × 10−9 RIU,” Opt. Express 26(18), 23868–23882 (2018). [CrossRef]  

15. D. Luo, P. Li, Y. Yue, J. Ma, and H. Yang, “In-Fiber Optic Salinity Sensing: A Potential Application for Offshore Concrete Structure Protection,” Sensors 17(5), 962 (2017). [CrossRef]  

16. L. Wang, Y. Wang, J. Wang, and F. Li, “A High Spatial Resolution FBG Sensor Array for Measuring Ocean Temperature and Depth,” Photonic Sens. 10(1), 57–66 (2020). [CrossRef]  

17. Y. Liu, Z. Jing, R. Li, Y. Zhang, Q. Liu, A. Li, C. Zhang, and W. Peng, “Miniature fiber-optic tip pressure sensor assembled by hydroxide catalysis bonding technology,” Opt. Express 28(2), 948–958 (2020). [CrossRef]  

18. D. Gwo, “Hydroxide-catalyzed bonding,” U.S. Patent 6, 548 (2003).

19. S. Sinha, K. E. Urbanek, A. Krzywicki, and R. L. Byer, “Investigation of the suitability of silicate bonding for facet termination in active fiber devices,” Opt. Express 15(20), 13003–13022 (2007). [CrossRef]  

20. A. A. Van Veggel and C. J. Killow, “Hydroxide catalysis bonding for astronomical instruments,” Adv. Opt. Techn. 3(3), 293–307 (2014). [CrossRef]  

21. P. Li, J. Zhang, J. Li, X. Lei, Y. Liu, and J. Wang, “Low Temperature Bonding of Quartz Glass for Vacuum Chamber Made of Glass,” Chinese Journal of Vacuum Science and Technology 34(3), 230–234 (2014). [CrossRef]  

22. P. Grosso, D. Malardé, M. Menn, Z. Wu, and J. Tocnaye, “Refractometer resolution limits for measuring seawater refractive index,” Opt. Eng. 49(10), 103603 (2010). [CrossRef]  

23. P. Grosso, M. Menn, J. Tocnaye, Z. Wu, and D. Malardé, “Practical versus absolute salinity measurements: New advances in high performance seawater salinity sensors,” Deep-Sea Res. Pt. I: Oceanographic Research Papers 57(1), 151–156 (2010). [CrossRef]  

24. W. Zhou, D. Mandia, S. Barry, and J. Albert, “Anisotropic effective permittivity of an ultrathin gold coating on optical fiber in air, water and saline solutions,” Opt. Express 22(26), 31665–31676 (2014). [CrossRef]  

25. Z. Jing and Q. Yu, “White light optical fiber EFPI sensor based on cross-correlation signal processing method,” in Proceedings of 6th International Symposium on Test and Measurement. (Academic2005), pp.3509–3511.

26. Z. Jing, “Study on White Light Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor and its Application,” Doctoral dissertation, Dalian University of Technology (2006).

27. Q. Wang, L. Zhang, C. Sun, and Q. Yu, “Multiplexed Fiber-Optic Pressure and Temperature Sensor System for Down-Hole Measurement,” IEEE Sens. J. 8(11), 1879–1883 (2008). [CrossRef]  

28. L. Zhang and Q. Yu, “An improved demodulation method for F-P and FBG multiplexing system,” J. Optoelect. Laser. 20(8), 1008–1011 (2009).

29. T. Liu and G. F. Fernando, “A frequency division multiplexed low-finesse fiber optic Fabry-Perot sensor system for strain and displacement measurements,” Rev. Sci. Instrum. 71(3), 1275–1278 (2000). [CrossRef]  

30. S. Musa, “Real-Time Signal Processing and Hardware Development for a Wavelength Modulated Optical Fiber Sensor System,” Doctoral dissertation, Virginia polytechnic institute and state university (1997).

31. B. B. Muvdi and J. W. McNabb, Engineering Mechanics Materials (Macmillian Publishing Company, 1984).

32. E. J. Hearn, Mechanics of Materials (Pergamon, 1977).

33. Y. Liu, Z. Jing, A. Li, Q. Liu, P. Song, R. Li, and W. Peng, “An open-cavity fiber Fabry-Perot interferometer fabricated by femtosecond laser micromachining for refractive index sensing,” Proc. SPIE 11209, Eleventh International Conference on Information Optics and Photonics, 1120902 (2019).

34. P. Song, Z. Jing, A. Li, C. Guo, and W. Peng, “Refractive Index Measurement of Liquid Based on Open Fiber Fabry-Perot Interferometer,” Chinese Journal of Lasers 44(12), 191–197 (2017). [CrossRef]  

35. W. Wang, W. Wu, S. Wu, Y. Li, C. Huang, X. Tian, X. Fei, and J. Huang, “Adhesive-free bonding homogenous fused-silica Fabry-Perot optical fiber low pressure sensor in harsh environments by CO2 laser welding,” Opt. Commun. 435, 97–101 (2019). [CrossRef]  

36. K. Vedam and P. Limsuwan, “Piezo- and elasto-optic properties of liquids under high pressure. II. Refractive index vs density,” J. Chem. Phys. 69(11), 4772–4778 (1978). [CrossRef]  

37. R. M. Waxler and C. E. Weir, “Effect of Pressure and Temperature on the Refractive Indices of Benzene, Carbon Tetrachloride, and Water,” Journal of Research of the National Bureau of Standards 67A(2), 163–171 (1963). [CrossRef]  

38. H. Minato, Y. Kakui, A. Nishimoto, and M. Nanjo, “Remote refractive index difference meter for salinity sensor,” IEEE Trans. Instrum. Meas. 38(2), 608–612 (1989). [CrossRef]  

39. H. Xiao. “Self-calibrated interferometric/ntensity based fiber optic pressure sensors,” Doctor dissertation, Virginia Polytechnic Institute and State University (2000).

40. M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl. Opt. 46(18), 3811–3820 (2007). [CrossRef]  

41. Y. Zhao, Q. Wu, and Y. Zhang, “Simultaneous measurement of salinity, temperature and pressure in seawater using optical fiber SPR sensor,” Measurement 148, 106792 (2019). [CrossRef]  

42. S. Wang, H. Yang, Y. Liao, X. Wang, and J. Wang, “High-Sensitivity Salinity and Temperature Sensing in Seawater Based on a Microfiber Directional Coupler,” IEEE Photon. J. 8(4), 6804209 (2016). [CrossRef]  

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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Figures (9)

Fig. 1.
Fig. 1. Configuration of the all-silica inline sensor, (a) the schematic diagram of the sensing probe, (b) image of the fabricated 1st EFPI under an optical microscope, and (c) image of the 2nd EFPI.
Fig. 2.
Fig. 2. The multistep fabrication process of the all-silica inline sensor, (a) fusion splice SMF and GIF, (b) cut GIF, (c) fusion splice GIF and HCF, (d) cut HCF, (e) fusion splice HCF and another GIF, (f) structure of the 1st EFPI, (g) deposit gold film, (h) drip bonding solution, (i) curing process, and (j) cascade successively.
Fig. 3.
Fig. 3. Signal interrogation process of the all-silica inline sensor, (a) comparison of the multiplexed spectrum with and without collimation and reflective films in the wavelength domain, (b) comparison of FFT results with and without collimation and reflective films in the frequency domain, (c) and (d) normalized interference spectra after FIR bandpass filters and Hilbert transform.
Fig. 4.
Fig. 4. Experimental setup for the high-pressure tests.
Fig. 5.
Fig. 5. Pressure response of the all-silica inline sensor from 0 to 20 MPa, (a) relationship between FP cavity length and applied pressure, and SD in 450 seconds time span at 10 MPa, and (b) comparison between the measured pressure and the applied pressure.
Fig. 6.
Fig. 6. The pressure crosstalk of the all-silica inline sensor from 0 to 20 MPa, (a) relationship of cavity length of the 2nd EFPI and RI reading versus applied pressure, and (b) relationship between Bragg peak shift and applied pressure.
Fig. 7.
Fig. 7. RI response, error percentage, and resolution of the all-silica inline sensor in the range of 1.33239∼1.36885 RIU, (a) the increase value and measured cavity length of the 2nd EFPI, (b) relationship between FP cavity length and reference RI, (c) comparison of the measured RI and the reference one, and (d) SD in 450 seconds time span at 1.34692 RIU.
Fig. 8.
Fig. 8. Temperature response of the all-silica inline sensor, (a) temperature response of the cascaded FBG and Bragg peak shift, and (b) comparison of the measured temperature and the applied temperature.
Fig. 9.
Fig. 9. The temperature crosstalk of the all-silica inline sensor from 23 to 80 °C, (a) relationship of FP cavity length of the 1st EFPI and pressure reading versus applied temperature, and (b) relationship of FP cavity length of the 2nd EFPI and RI reading versus applied temperature.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

Si O 2  + O H  + 2 H 2 O Si ( OH ) 5
2Si ( OH ) 5 2Si ( OH ) 4  + 2 ( OH ) ( HO ) 3 SiOSi ( OH ) 3  +  H 2 O + 2 ( OH )
I = I 1 + I 2 + 2 I 1 I 2 cos ( 4 π n L λ + π )
L = 1 2 λ 1 λ 2 λ 1 λ 2 k
Δ L = d r o 2 E ( r o 2 r i 2 ) ( 1 2 γ ) Δ P
L O = n L n air
Δ L = L α c Δ T
[ S FBG - T C FBG - P C FBG - n C 1 st  EFPI - T S 1 st  EFPI - P C 1 st  EFPI - n C 2 nd  EFPI - T C 2 nd  EFPI - P S 2 nd  EFPI - n ] [ Δ T Δ P Δ n ] = [ Δ λ T Δ L P Δ L n ]
Δ T  = 109 .80 Δ λ T 0 .059 Δ L P
Δ P  = 3 .35 Δ λ T 0 .15 Δ L P
Δ n  = 0 .012 Δ λ T + 0 .000033 Δ L P  + 0 .000001 Δ L n
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