1. Introduction

Methods and sensors for characterization of fluids in process, biomedical and environmental systems have recently been the topic of very intense research [1–5]. In these methods, a fluid’s composition is often obtained through the sensing of the fluid’s physical parameters [4, 6, 7]. Among a fluid’s physical parameters, Refractive Index (RI) proves to be one of the most important and frequently utilized parameters [8] for fluid composition monitoring and determination [9–11]. Most reported methods for RI sensing are, however, related and adapted to the RI sensing of liquids. In comparison to liquid RI sensing, the application of RI sensing for gas composition analysis is, however, considerably more limited. Most gases at pressures of interest have similar and relatively low values of Refractive Indexes. For example, at atmospheric pressure and room temperature, a broad range of different gases` RIs will fall within the range between n = 1.002 and n = 1.0002, with a significant number of gases of interest falling in the range between n = 1.0008 and n = 1.00025. Thus, to apply RI sensing usefully to gas composition determination, RI sensing system resolutions of a minimum 10⁻⁵-10⁻⁷ RIU are required, especially in cases when mixtures of gases with similar RIs are sensed. To achieve environmentally stable sensing capabilities within this range, RI sensors must possess intrinsically low temperature dependence with the possibility for effecting in situ temperature and pressure compensation.

In spite of these difficulties, high-resolution gas composition determination through RI sensing provides several important advantages, as it allows for characterization of non-reactive gases and their mixtures, for example, noble gases, fast response time, simple and cost-efficient sensing setups, very compact (microfluidic compatible) sensor designs and possibilities for on-line process control of small gas volumes.

While the work in the field of fiber-optic RI sensors has been very extensive, only a limited number of proposed solutions seem to be able to approach the requirements encountered in high-resolution gas composition sensing applications. Only a limited number of reports [12–18] actually experimentally demonstrate sensors that can perform stable sensing with an RI range close to n = 1. Among this references only few [12–14] anticipate, but do not experimentally demonstrate, the resolutions within or beyond the 10⁻⁶ RIU range. Most reported high-sensitivity fiber-optic RI sensors utilize fluid-to-waveguide interactions, that often limit the highest sensitivity performance of these sensors to the sensing of liquids that have RI indices close to the effective indices of modes propagating within the fibers [19–30] and, thus, cannot be applied efficiently to most gas sensing applications. Currently there are only a few reports available in the literature [19, 31, 32] that anticipate sensors with RI sensing resolution in excess of 10⁻⁷ RIU, but most of these approaches are not suitable for RI sensing with n close to 1. Furthermore, unfortunately, none of these highest-sensitivity RI sensing reports actually demonstrate resolution experimentally within the claimed ranges by experimental change/modulation of measured RI. These reports mostly rather predict sensor’s resolution from sensor’s spectral sensitivity and declared spectral interrogator resolution.

In this paper, we discuss design and interrogation of a miniature all-fiber Fabry-Perot sensor that can provide stable measurements of small changes in gas RI. The sensor’s RI resolution in excess of 5x10⁻⁹ RIU is demonstrated experimentally by controlled variation of gas composition. To achieve resolution within this range, we show that the sensor’s and signal interrogator’s performance need to be aligned carefully, while environmental temperature and pressure influences on the sensor and gas must be correctly compensated.

2. High resolution sensor system description

2.1 Sensor design and fabrication

The proposed sensor design is presented in Fig. 1 and consists of a standard 125 µm single-mode lead-in fiber, a low-reflectance in-fiber mirror, about a 2.5 mm long section of low Numerical Aperture (NA)/large-core single-mode fiber, a short section (about 40 µm long) of coreless fiber with diameter of 200 µm, two parallel silica beams and a thin end-cap (cap thickness < 20 µm). The cap, the two parallel silica beams and the first’s coreless fiber end-face form an open-path, low-finesse Fabry-Perot (FP) cavity. The sensed surrounding gas can thus freely enter/exit this open-path FP cavity. The short section of low NA/large-core single-mode fiber performs two functions: Firstly, it acts as a temperature sensor where two low-reflectance surfaces/mirrors, positioned at each side of the low NA fiber, form a temperature-sensitive, all-fiber, low-finesse FP interferometer. Secondly, a low NA/large core fiber acts as a beam expander/collimator that helps reduce divergence losses in the open-path FP cavity. This allows for manufacturing of open-path FP cavities with longer lengths, while still obtaining sufficient back-reflection from the end-cap that forms the second semi reflective surface of the interferometer.

 

Fig. 1 Sensor design.

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The use of micro collimation in all-fiber RI sensor was proposed before by utilizing a short section of special graded index fiber [33]. Fiber-based graded index collimator production, however requires high-quality custom made graded index fiber and very precise collimator length control. In the proposed approach we achieve substantial collimation by a simple section of low NA fiber, which is uncomplicated in design and does not require any precision length adjustment. Furthermore we use this section as temperature sensor as explained above.

Furthermore, the end-cap is sputter-coated by a thin aluminum layer, to enhance reflectance and, thus, mitigate the effects of signal loss caused by beam divergence within the open-path FP microcell. The mode field diameter of the low NA/large-core single-mode fiber was about 16.5 µm at 1550 nm. Initial experiments showed that insertion of this low NA/large core fiber section enhances fringe contrast and back-reflected signal level significantly when the cavity lengths exceeds a few hundreds of µm, which has a positive effect on the signal to noise ratio (during experimental investigation we observed a fringe contrast amplitude rise by a factor of up to 6.5 times when compared to the sensors without the proposed collimator assembly). The all silica design of the cavity provides intrinsically low temperature sensitivity of the FP cavity as the CTE of silica is only about 5x10⁻⁷ K⁻¹.

The fabrication of the proposed sensor is based on the specially designed fiber (Structure Forming Fiber – SFF) with a large elliptical phosphorus doped core. The phosphorus doped region, when exposed to hydrofluoric acid (HF), etches at considerably higher rates than pure silica [34] and can, thus, be removed very selectively by the etching process. The cross-section of fiber used for FP cavity production is shown in Fig. 2(a). This quite efficient technique for manufacturing of fiber microcells was first described in [35]. Furthermore production of sensor required utilization of several short fiber sections. Length adjustments of these short fiber sections were achieved by controlled cleaving under an optical microscope after performing fiber splicing as described in detail in ref [36].

 

Fig. 2 Production process.

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In the present sensor design, we developed this technique further for fabrication of long-cavity Fabry-Perot interferometers. The sensor production was started by fusion-splicing a section of SFF with an outer diameter of 200 µm in-between two core-less 200 µm pure silica fibers (Fig. 2(a)). At one end of this structure the coreless fiber was cleaved away at a distance of less than 50 µm from the splice with the phosphorus-doped fiber (Fig. 2(b)), which formed the first fiber subassembly. Then, the second fiber subassembly was prepared by splicing together a lead-in single-mode fiber and fiber with a low NA/large core, while forming an in-fiber mirror at this splice. This was accomplished by applying the single-mode fiber etching process and controlled fusion-splicing, as described in detail in [37]. Low NA/large core fiber was cleaved further at distance of about 2.5 mm from the last splice, which completed the second fiber subassembly preparation. The first and the second fiber subassemblies were then spliced together as depicted in Fig. 2(c). The remaining coreless fiber was then cleaved away at a distance of about 30 µm from the splice with the phosphorus doped fiber (Fig. 2(d)) to form an end-cap. Finally, the entire assembly was chemically etched in 40% HF acid for about 12 minutes. Since the phosphorus doped region etches at considerably higher rate than pure silica (about 30 times faster in the case of this particular fiber and acid), the phosphorus doped elliptical region was removed selectively, leaving behind an open-path microcell defined by two parallel silica beams. The sensor fabrication process was concluded by sputter-coating the end-cap with a thin layer of aluminum. The short section of coreless fiber between the low NA/large core fiber and SFF fiber was introduced to protect the low NA/large core fiber end-surface during etching (the germanium doped region also etches at a higher rate in HF, and this might degrade the optical quality of the surfaces) and to act as a diameter adapter between the 125 µm low NA/large core fiber and phosphorus doped fiber. The phosphorus doped fiber had a larger diameter than standard fibers to allow for creation of a structure with large spacing between the side beams, which further reduces the effects of light propagating through grazing incidence reflections, which can form additional (temperature sensitive) optical paths within the cavity. This allowed formation of sensors with “clean” optical spectrums, even in the case of longer structures. For the purpose of further investigation, we produced 9 different sensors, with open-path FP cavity lengths spanning from 70 µm to 29400 µm. Figure 3 shows several produced sensors, while Fig. 4 demonstrates a 2.5 mm long sensor under a Scanning Electron Microscope (SEM). For demonstration using the SEM, one of the shorter sensors was chosen to fit the lowest magnification window of the SEM. A typical back-reflected optical spectrum and its Inverse Discrete Fourier Transform (IDFT) for the case of the sensor with 8600 µm long open-path FP cavity is shown in Fig. 5. In spite of the long open-path structure, which is bounded at the sides with two parallel beams, the IDFT of the optical spectrum is composed of only of three well-defined temporal components (the first corresponding to the length of the temperature sensing FP interferometer, the second corresponding to the length of the open path FP cavity, and the third that is the sum of both FP interferometer’s lengths). Some minor spurious modes/paths, probably caused by grazing incidence guidance of the side beams, can be observed, as well as suppressed components in IDFT (Fig. 5(b)) on the right side of the second and the third peaks. For the reference, Fig. 5 also shows spectrum and corresponding its IDFT for a sensor without low NA collimation fiber (here we used standard SMF instead of low NA fiber). A significant degradation of the component belonging to RI measuring cavity is visible in non-collimated version (RI measuring cavity amplitude in IDFT is about 5 times lower as in case of low NA collimation fiber version).

 

Fig. 3 Several produced sensors with different open path FP cavity lengths under an optical microscope.

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Fig. 4 Scanning Electron Microscopic image of a typical sensor.

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Fig. 5 (a) Back reflected optical spectrum with applied Gaussian window, (b) Inverse Discrete Fourier Transform with corresponding time axis and axis converted in optical path length (multiplied by c/2). Fig. also shows comparison between collimated and non-collimated sensor.

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2.2 Sensor operation

A small change in Refractive Index of the gas that fills a low-finesse FP cavity results in a shift of the cavity’s cosines` spectral characteristic, which can be described as:

where S_RI represents the spectral sensitivity of the RI sensing interferometer, and Δλ_RI presents the spectral shift of the cavity’s cosines` characteristics. The spectral sensitivity of an open-path Fabry-Perot interferometer can be obtained by differentiating an expression for local spectral peak positions λ_m in the back reflected optical spectrum of an FPI:

By substituting (1 + 2m) with 4nL/λ_m, we obtain:

where L represents FPI length and n the Refractive Index of the material that defines/fills the FPI resonator or cavity. A gas-filled cavity with n close to 1 will thus yield a spectral sensitivity of about 1550 nm/RIU at wavelengths around 1550 nm, regardless of the RI measurement cavity length. Even the spectral sensitivity is independent of the cavity length, but this does not necessarily apply for the system’s measurement resolution, as will be shown in the Experimental section. For example, longer FPIs provide narrower free spectral ranges, which makes spectral peaks narrower/sharper and, in the presence of noise, their localization might be more accurate, as in the case of shorter cavities.

The RI of gases is also affected strongly by the temperature and pressure. For example, a change in temperature of only 1 K in the case of nitrogen gas will already cause gas RI change by about −4x10⁻⁷ RIU. An RI sensor used in gas composition analysis and with useful resolution within the range of 10⁻⁷ or higher, thus requires a fine-tuned, high resolution temperature compensation. The temperature of the RI sensing cavity shall be measured with an accuracy, or at least repeatability, that is better than a few tens of mK. Due to the potential presence of minute temperature gradients, this can only be achieved efficiently by a compact dual-parameter sensor that provides accurate temperature information on the RI sensing cavity [38]. The sensor described in this paper satisfies this condition, as the temperature sensing part (temperature sensing FPI) is compact and in a direct thermal contact with the RI sensing cavity as described above.

The proposed sensor’s temperature can be obtained by tracking of the spectral interference fringe shift, which is generated by the temperature sensing FPI:

Where S_T represents the spectral sensitivity of the temperature sensing interferometer, and Δλ_T represents the shift of the temperature sensing FPI spectral fringe. The temperature sensing FPI’s spectral sensitivity can be described (using the same approach as above) as:

By assuming dn/dT for silica to be 9.5 x 10⁻⁶/°C, the spectral sensitivity of an FPI made out of SiO₂ fiber is, thus, about 0.01 nm/°C.

The temperature obtained from the temperature sensing FPI is then used to correct the RI measurement result. The temperature sensitivity of the proposed gas filed open-path FP cavity arises from two factors: Thermal expansion of the silica beams and temperature sensitivity of the gas that is present within the cell. The optical path-length change due to the temperature change can thus be described as:

Where CTE represents the coefficient of linear thermal expansion of SiO₂ (CTE = 5.5x10⁻⁷ K⁻¹ at 300 K) and dn/dT is the thermo-optic coefficient of the measured gas. The change in measured/output RI due to the change in temperature Δn_T can be expressed from the above expression as:

Both parts of coefficient K_T have opposite signs, however, for most gases at atmospheric pressure the part with dn/dT will prevail. Furthermore, the dn/dT in gases is not constant, but it rather exhibits a fairly significant dependence on the temperature. In fact, in the first approximation, the Refractive Index of the gas is inversely proportional to the absolute temperature [13]. For some gases, like air [39], these relationships have been studied in detail and proved to be non-trivial. In the implementation of the proposed sensor, we therefore rather used polynomial based RI correction with the form of:

The coefficients k₀ to k₄ were obtained by the initial calibration process, where all parameters (gas composition and pressure) were constant except the temperature, that was varied deliberately with the expected temperature operational range from 19 to 26 °C.

Pressure is another factor that must be considered in high resolution RI measurements of gases, as the gas RI is considerably dependent on the pressure. In comparison to the temperature effects, the pressure sensing required for the RI measurement compensation can be carried out by a separate high-resolution pressure sensor, which does not need to be in immediate vicinity of the RI sensor. Thus, for this purpose, we used an external electrical sensor. The correlation between the pressure and RI can be estimated by calculation of gas density ρ. The relation between ρ and RI for gases is presented by the Gladstone – Dale relationship [40]:

If we consider that pressure is proportional to gas density, the expression can be rewritten in:

Where K_P presents the constant, which can be determined by a proper calibration process. Finally, the measured and compensated RI change can be expressed as:

2.3 Sensor interrogation

Shifts in multiple sinusoidal interferometers’ spectral characteristics were separated and tracked by utilization of IDFT) [38, 41, 42]. In this approach, the IDFT is performed on the optical spectral data that were acquired by an optical spectral signal interrogator. Prior to the IDFT, spectral data were converted from the optical wavelength domain into the optical frequency domain. The complex IDFT data contain local peaks in their absolute values, which correspond to round trip time-of-flights of individual low-fines FP interferometers (as already shown in Fig. 5). Phases of these complex peak values (ϕ = ArcTan(Im/Re)) further correspond to the relative positions of spectral components (spectral fringes) of individual FP interferometers in the optical frequency spectrum. Thus, by calculating the phases of complex values that otherwise correspond to the local absolute peaks in IDFT data, one can track small changes in an individual interferometer’s length changes reliably:

This IDFT based technique allows for a very efficient and cross-talk-free separation of individual spectral components within an acquired optical spectrum that contains multiple frequency components, generated by more than one FPI. Another important property of this method is that the method utilizes the entire set of acquired spectral data points to calculate the interference fringe position in the optical frequency domain. Unlike the commonly used methods for spectral shift tracking of sensors` characteristics, which rely on a single local peak (or dip) tracking, and which take advantage of only a limited set of local spectral data points around the tracked peak, IDFT utilizes in full the entire available spectral data acquired by the signal interrogator. This is reflected in a low output measurement noise, which is especially beneficial in high-resolution measurement systems.

Finally, the RI and temperature measurement was performed by utilizing IDFT on spectral data acquired by the signal interrogator as described above. These data were complemented by the pressure data obtained from a separate electrical high-resolution pressure sensor (unlike temperature sensors, a pressure sensor does not need to be in the vicinity of the RI sensor). Data from both FPIs and pressure sensor were then used to calculate the compensated Refractive Index change according to expression (11).

3. Experimental results

The experimental demonstration of the proposed sensor’s operation and performance was accomplished by inserting the sensor under test into an aluminum gas cylinder with a total volume of 2 liters. The cylinder was equipped with several valves, as shown in Fig. 6, to allow cylinder evacuation, pressure equalization with atmospheric pressure, and controlled filling with reference and test gases. The pressure equalization line was always accomplished through a 3 cm long capillary tube, to prevent gas exchange between the surroundings and the cylinder. The cylinder was also equipped with a semiconductor high-resolution pressure sensor MS5611 [43], a small fan for gas mixing, and resistive heating wire wound around the cylinder, which allowed heating of the entire test vessel.

 

Fig. 6 Experimental setup.

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Before making any measurements with the proposed system, we investigated the impact of the spectral signal interrogator performance and FP cavity length on the measurement systems` output noise (RI resolution). As already mentioned in the sensor manufacturing section, we prepared a range of, otherwise identical, sensors with different open-path FP cavity lengths. These sensors were exposed to the nitrogen atmosphere at atmospheric pressure and temperature-stabilized laboratory conditions. All sensors were spectrally interrogated by two different commercial but, according to the manufacturer’s data, similar spectral interrogators: NI PXIe-4844 and FAZT I4. Both interrogators have very similar declared spectral resolutions (NI PXIe-4844: 1 pm, FAZT I4: +/− 1 pm) and full spectrum sampling rate (NI PXIe-4844: 10 Hz, FAZT I4: 16 Hz). Both interrogators differed in spectral bandwidth, which was 80 nm in the case of the NI PXIe-4844 and 39.2 nm in the case of the FAZT I4. An identical IDFT based algorithm was used to process spectral data from both interrogators. The calculated phase change (spectral shift of interference fringe) of the component that belongs to the open-path RI measurement interferometer was filter/averaged further in a way to equalize the sampling rate at the outputs of both interrogation systems (five calculated values were averaged in the case of NI PXIe-4844 and eight in the case of FAZT I4). This equalized the sample rate for both interrogator systems, while bringing the bandwidth of both systems to 2 Hz. Then, each of the produced sensors was exposed to the controlled test atmosphere and pressure while being interrogated by both interrogators within 2 minutes long intervals. The data acquired during these test intervals were stored into the computer memory and used for calculation of the signal’s (RIU’s) effective noise by applying the Root Mean Square (RMS) calculation algorithm. Results obtained on the entire set of produced sensors and for both interrogators are shown in Fig. 7.

 

Fig. 7 Calculated RMS of RIU noise: (a) Comparison between NI PXIe and FAZT I4, estimation was made using 9 sensors with different open path cavity lengths (log axis), (b) Zoom-in of FAZT I4 results shown for sensors longer than 250 μm (linear axis).

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Figure 7 offers a few interesting observations and possible conclusions:

The remaining set of experiments was devoted to the demonstration of the proposed sensing system performance. In all further experiments we selected the sensor with an 8.6 mm long open-path-cavity and FAZT I4 interrogator (this shall be approximately a nearly optimum combination according to the results from Fig. 7). The sensor was first calibrated (by varying temperature and pressure) in a pure N₂ atmosphere to determine all coefficients required for further temperature and pressure compensation. The coefficients for temperature compensation calculated by polynomial fitting (as defined by Eq. (8)) were: k₀ = 7.5232*10⁻⁵, k₁ = −1.1411*10⁻⁵/C, k₂ = 6.88*10⁻⁷/C², k₃ = −1.94*10⁻⁸/C³ and k₄ = 2.07 x10⁻¹⁰/C⁴. The pressure compensation constant corresponded to K_P = 2.668*10⁻⁷/mbar.

The first set of tests was devoted to demonstration of the system’s measurement resolution. In these tests we injected small, but well defined, volumes of CO₂ and H₂ into the N₂ gas filled test cylinder to induce small and controlled changes in the RI of the test gas. CO₂ was used to raise RI, while H₂ has lower RI than N₂ and was used to return the gas mixture to the base level in order to be able to show the rectangular response of the sensor to gas RI changes. All experiments were carried out at atmospheric pressure. The measurement data from the electrical pressure sensor was averaged, firstly by using sensors’ internal averaging (1024 samples) and then externally (averaged samples from the sensor were further averaged 1600 times by the measurement algorithm), which provided pressure sensor resolution of 0.004 mbar, which corresponds to pressure uncertainty of about 1x10-9 RIU. Obtained resolution is consistent with sensors’ manufacturer specifications [43]. RI change was always compensated (calculated) according to Eq. (11).

Figure 8(a) demonstrates the smallest change of CO₂ concentration in N₂ that caused change in the system`s output larger than the average noise amplitude. This change in CO<sub>2</sub> concentration corresponded to 35 ppmv, which further corresponds to the RI change of about 5x10<sup>−9</sup> RIU. The system`s bandwidth (using a digital averaging filter) was set to 0.025 Hz in this test. The test included injection of 0.07 ml of CO₂ into the cylinder with 2 liters of pure N₂. For lowering of the RI by the same value, we inserted 0.065 ml of H₂ gas in the same cylinder. Figure 8(b) shows the same experiment, but with slightly increased gas concentrations (50 ppmV of CO₂ and 45 ppmV of H₂, which corresponds to an RI change of 7.5x10⁻⁹ RIU). Spikes in characteristics are due to local jumps in concentration that occur right after injection and before full mixing of the injected gases. These measured changes in RI are in good agreement with the expected/calculated changes in RI. For the example described above and in Fig. 8, the RI of the gas mixture can be described as n = n₁φ₁ + n₂φ₂ (φ₁ is a volume fraction of the pure component 1, φ₂ is a volume fraction of the pure component 2) [44]. By inserting typical values for the case of a mixture containing 99.9965% of N₂ (n_N2 = 1.00029442) and 0.0035% of CO₂ (n_CO2 = 1.00043822), we obtained gas mixtures n = 1.000294425, which represents a change of 5x10⁻⁹ RIU with respect to the pure N₂ RI. By further inserting 0.0032% of H₂ (n_H2 = 1.00013617), the recalculated value for n is 1.00029442, which is about 5x10⁻⁹ lower than the previous mixture and matches initial value of pure N₂ approximately.

 

Fig. 8 (a) Experimental demonstration of the system’s measurement resolution using gas injections that cause RI changes of 5x10⁻⁹ RIU at a bandwidth of 0.025 Hz (averaging of 650 samples), (b) Same as a) but using gas injections that cause RI changes of 7.5x10⁻⁹ RIU at a bandwidth of 0.1 Hz (averaging of 160 samples).

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The sensor operation in response to the larger gas composition changes is shown in Fig. 9(a). Figure 9(a) shows the sensor’s responses when we injected 15 ml of CO₂ repetitively into the 2 liter test cylinder with pure nitrogen in 6 consecutive steps. Figure 9(b) shows the responses to smaller, 0.42 ml injections of CO₂ into the same cylinder. The later injections corresponded to step increases of RI by about 3x10⁻⁸ RIU in each step. Figure 9 also demonstrates the stable longer-term operation of the sensing system within the 10⁻⁸ RIU range. Measured RI changes are consistent with the expected/calculated changes based on injected volume/concentration changes.

 

Fig. 9 Response of the produced sensor to RI change by insertion of CO₂ in pure N₂: (a) Measurements taken at a broad range of RI change, (b) Measurements of low concentration changes equal to 210 ppmv of CO₂.

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Finally, we deliberately varied the gas mixture’s temperature and pressure to estimate the robustness of the entire sensor system to environmental changes. In the first experiment, we increased the pressure by 2.8 mBar in three consecutive steps by adding the N₂ to the N₂ atmosphere. In the last (fourth) step, we added 1 ml of CO₂. Since we needed to exchange the gas line in this last step, partial pressure release occurred during line exchange, which caused intermediate and partial pressure drop. As presented in Fig. 10(b), this dynamic pressure variation was well compensated by the proposed system, thus no pressure fluctuation effect is observable in Fig. 10(c). Figure 10 also indicates that induced pressure changes caused uncompensated RI changes as large as 2 x10-6 RIU, while the compensated RI showed completely flat response during N₂ injections and an expected RI increase in the case of CO₂ injection. Pressure, raw and compensated RI signals are shown for the entire test in Fig. 10.

 

Fig. 10 Efficiency of pressure compensation: (a) Comparison between compensated and not compensated RI change, (b) Variation of the pressure during the experiment at room temperature (temperature varied by less than 0.02 °C during the experiment).

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Figure 11 shows the responses of raw and compensated RI signals to the temperature changes. As shown in Figs. 10 and 11, moderate changes in temperature and pressure cause considerable changes in the RI readout. Measured change in the uncompensated RI signal due to the temperature change by 1 K already caused an RI readout change of about −5x10⁻⁷ RIU, and the change in pressure by only 1 mBar corresponded to an RI readout change of about 2.7x10⁻⁷ RIU. Comparison of compensated (Fig. 10(c) and Fig. 11(c)) and uncompensated output (Fig. 10(a) and Fig. 11(a)) demonstrate clearly the necessity for temperature and pressure compensation, even in the case of relatively small changes in pressures and temperature. These compensations shall actually be introduced in RI sensing of gases as soon as the required resolutions approach the 10⁻⁶ RIU range, even when only moderate pressure and temperature variations are expected. Figures 10 and 11 also demonstrate that the introduced compensations reduced influences of pressure and temperature variations on the RI measurement efficiently within a reasonable range of both influential parameters down to nearly RI system noise level.

 

Fig. 11 Temperature – pressure compensation, when varying temperature at atmospheric pressure: (a) Comparison between compensated and not compensated RI change, (b) Variation of temperature and pressure during the experiment, (c) Fully compensated RI response (@ 0.08 Hz interrogation system bandwidth – averaging of 200 samples).

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4. Discussion

Over the past decade, fiber optic Refractive Index sensors have been attracting significant attention from the sensor research community. High resolution RI sensing is of high interest, as it provides opportunities directly to build a range of industrial, chemical and/or biochemical process sensors. In these applications, RI sensors are typically used to detect changes in the composition of the material that surrounds or is deposited onto the RI sensors. Thus, the proposed RI sensors shall be able to provide temperature independent RI measurement related purely to the composition of the measured material. This temperature effects free operation shall be provided within a reasonably wide temperature range (for example within a few K wide range) – if minute temperature fluctuations cannot be distinguished from compositional changes, the sensor’s useful resolution will be limited to the ability to stabilize the temperature, and this requirement can easily fall within the mK range for the highest resolution sensors. Among available recent reports on high resolution RI sensors, claims for very different ranges of achievable RIU resolutions can be found; some of these reports claim resolutions with 10⁻⁸ to even 10⁻¹⁰ RIU range. Surprisingly, these claimed resolution ranges are, however, mostly unconfirmed experimentally. For example, instead of measuring an actual system’s resolution, the sensor’s resolution was estimated from a declared signal interrogator’s spectral resolution and spectral sensitivity of the particular peak in the sensor’s spectrum. Furthermore, often temperature and other influential effects are not taken into account adequately in many reports claiming high resolution or high sensitivity RI sensors. As shown by this investigation, an RI sensing system resolution is often a complex function of different system parameters (a sensor’s spectral sensitivity, which, if often claimed as important and often a sole achievement, is just one of many). Therefore, we believe that reporting on any RI sensor with resolutions in excess of 10⁻⁵ RIU should always be accompanied by experimental demonstration of the presented resolution and a sufficiently in-depth analysis of all parameters that influence the system`s performance (temperature, pressure, interrogation system parameters, sensor`s spectrum quality, etc.). Without direct experimental verification of RI resolution, also under varying temperature and pressures in cases of gases, claims on sensitivities better than 10⁻⁵ RIU probably cannot be made reliably.

5. Conclusion

Within this paper we presented a Fabry-Perot sensor for high resolution RI sensing of gases. We were able to demonstrate RI measurement resolution of about 5x10⁻⁹ RIU experimentally by using controlled changes of a test gas composition. High-resolution and in situ temperature and pressure compensations were introduced to achieve this RIU resolution range. Since mK range temperature gradients among the temperature measurement site and of the RI sensor can already compromise measurement results` integrity, the proposed sensor includes a temperature sensing part that can achieve sufficiently high temperature resolution while being miniature and in direct contact with the RI sensing cavity. Pressure compensation was introduced by a separate high-resolution electrical sensor. It has been shown experimentally that the FP RI sensor’s resolution depended on the sensor’s length, in spite of the fact that the spectral sensitivity of the Fabry-Perot RI sensing cavity is independent of its length. Substantially different measurement resolutions were obtained when using two different spectral signal interrogators that have the nearly the same declared spectral resolutions. The difference can likely be related to the spectral linewidths and related laser phase noises in both interrogators. Furthermore, it appears that there is an optimal range of FP sensors’s cavity lengths for each interrogator type that yields the maximum achievable system RIU resolution.

Unlike some waveguide/modal interface based sensors [21] that have good potential for making very high resolution RI sensors, but are unfortunately limited to measurement of fluids with Refractive Indexes close to the material that constitutes the waveguide, the present sensor can operate over an almost arbitrary RI range, including the range of Refractive Index near n = 1, which is of particular interest for high resolution gas sensing applications.