1. Introduction

Liquid level transmitters are one of the most frequently encountered sensors in industrial process control systems and are often operated under harsh conditions, which, commonly, include broad temperature ranges (including cryogenic temperatures), corrosive or otherwise chemically aggressive conditions and electromagnetically polluted environments. Many applications also require operation in remote locations where exposure to electromagnetic interference and/or geo-electrical events can be of significant concern. Optical solutions, especially fiber optic sensors, are compatible with many of these environmental constraints, and can provide distinctive operational advantages over more conventional level sensing approaches. Thus, significant efforts have been devoted in the past to the design of fiber-optic liquid level transmitters [1]. Optical liquid level transmitters can in general be classified into three categories: Discrete level detectors, quasi-distributed/multiplexed level detectors [2–12], and sensors for continuous level measurements [13–54]. Optical discreet level sensors have already firmly penetrated commercial applications and have become established solutions in many industrial process applications [55,56]. Optical continuous level transmitters, however, remain an optical design challenge. Multiplexing of discrete level sensors can certainly lead to quasi-distributed level gauges and these solutions can certainly address specific groups of applications. Different types of discrete level sensor arrays and ways to address them have thus been successfully proposed in the past [2–12]. Multiplexed sensor arrays, however, offer limited spatial resolution and require often relatively complex sensor designs and/or signal interrogation approaches. Methods are thus often demanded for fully continuous liquid level measurements. There are direct and indirect approaches to the continuous optical liquid level measurements. Indirect approaches utilize optical measurements of a liquid’s weight, buoyant or other forces asserted by the liquid on the sensors [13–21], and optical hydrostatic pressure sensors [22–26]. While indirect approaches might work well in certain applications, these solutions are sensitive to the changes in acceleration, liquid density (and, consequently, temperature and composition), and suffer from geometrical and dynamic limitations. Direct level measurement methods, which provide information on the position of gas-liquid interface, are thus often preferred. By far the most investigated direct fiber-optic continuous level measurement approach is based on evanescent wave coupling between the level measurement fiber/waveguide and the measured surrounding liquid [27–49]. In these approaches, the refractive index change that occurs along the liquid-exposed waveguide modulates the effective indexes of one or more modes or affects the propagation conditions of one or more modes. These changes are measured by very different approaches, including interferometric principles, fiber Bragg gratings (including tilted and long period gratings), tapered structures, by inducing a transmission loss modulation in submerged fiber, and other methods. In some solutions, the measured liquid also acts as a coupling promotor between two fibers [48,49], which yields level dependent coupling between two waveguides. Another known group of fiber-optical level measurement methods includes systems for distance measurements between the fiber end and liquid surface [50–52]. The main limitation of methods for continuous level measurement described above is, however, in their intrinsic sensitivity to the surface contamination, as they all include active optical sensing surfaces that are in direct contact with measured liquid and/or the atmosphere above the liquid, which make them inherently, and often highly sensitive, to contamination. Realistic use of these approaches for industrial liquid level sensing, where residue formation in not unusual, is thus questionable. Furthermore, refractive indexes of measured fluids are often highly dependent on the temperature and fluid composition, and can affect most of the above-described approaches. Many of the above described methods, while providing good resolution, are also frequently limited in achievable measuring ranges.

As an alternative to the above methods, thermo-optic level measurements methods have been also proposed recently. These methods are potentially far less sensitive to surface contamination, can operate well in conditions of small refractive index contrast between fluid and the gas above the fluid (a common problem in cryogenic applications), and are considerably less sensitive to fluid composition change and the fluid’s properties changes due to the temperature. Thermo-optic level sensing methods were realized successfully as a quasi-distributed sensor (multiplexed discrete level detector arrays), where multiple short sections of highly absorbing fibers were inserted locally at multiple locations down the lead fiber, together with FBGs to allow for multipoint FBG heating and temperature detection [9–11]. Alternately, absorbing fibers were also replaced by fibers with an absorbing coating and locally induced coupling events that directed high (heating) optical power from the fiber’s core to the absorbing cladding nearby FBGs located down the sensing fiber [12]. Design of a fully continuous thermo-optic level gauge, however, proved challenging. In [53] an electrical heater resistive wire was used to heat the sensing optical fiber, while the liquid level was obtained from a longitudinal fiber’s temperature profile acquired by a distributed Raman temperature sensing system. The resistive fiber was also replaced by metal coating in [54], while employing high-resolution Ryleigh range OFDR interrogation. The electrical heating of a sensing fiber unfortunately compromises most advantages that are otherwise provided by the optical approach. In [54] electrical heating of the fiber was also replaced by an absorbing fiber; however, the measurement range seems to be limited to a few hundreds of millimeters due to the simultaneous losses of heating and probing optical signals within the absorbing fibers. All reported fully continuous thermo-optic approaches also utilize complex, high resolution interrogation systems that are based on principles encountered in a fully distributed sensor (Raman OTDR and Ryleigh-range OFDR), which limits the application potential of these approaches strongly to specialized and highly-cost tolerant applications.

In this paper, we propose a long-gauge, all-fiber, all-optical, Fabry-Perot thermo-optic continuous level sensor with an extended level measurement range, which utilizes only a few common telecommunication components. A straightforward sensor design and simple signal interrogation scheme provide an opportunity for cost-efficient measurement system implementation that can allow use of the proposed approach in a wide range of process industry applications. The problem of probing signal loss in highly attenuating fibers is solved by the introduction of vanadium doped fibers that exhibit distinctive spectral attenuation characteristics, and where probing and heating optical signals exhibit substantially different optical attenuations. We also demonstrate that fully distributed temperature sensing capability is not needed for the design of a continuous thermo-optic liquid-level transmitter, and that the latter can rather be replaced by a simple dynamic long-gauge temperature sensor. Correspondingly, we provide a supporting analytical description of the proposed thermo-opto-fluidic level gauge, which might also support the design of similar thermo-fluidic-fiber-optic level gauges or devices.

2. All-fiber thermo-optic liquid level gauge

The proposed sensor design is presented in Fig. 1. The sensor is built around a section of Vanadium-Doped optical Fiber (VDF), which defines the fluid level sensitive region. The VDF exhibits high optical absorption at shorter wavelengths (i.e., around 980 nm), while the absorption at longer wavelengths (i.e., at around 1550 nm) remains limited [57]. For example, the VDF used in this research was a single-mode fiber with 5.8 μm core and NA = 0.12, which had optical absorption of 14.51 dB/m (α = 3.34 Np/m) at 980 nm and 0.65 dB/m at 1550 nm. The optical energy absorbed by VDF at 980 nm results in a non-radiative decay process, which leads to the heat release within the VDF’s core. This provides an opportunity for remote heating of the entire VDF section by application of a telecom optical amplifier pump source, while also providing an efficient way to probe the fiber’s (average) temperature over its entire length by illuminating and interrogating the fiber’s optical path length at longer telecom wavelengths. To achieve this, two semi reflective mirrors were introduced at each side of the VDF to create a low-finesse Fabry-Perot Interferometer (FPI) out of the entire VDF section. This VDF FPI was connected further to the excitation and interrogation system through a lead-in SMF as presented in Fig. 1.

 

Fig. 1 All-fiber, thermo-optic liquid level gauge: An experimental setup.

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The sensor fabrication is simple and straightforward and includes a few fiber length adjustment and splice steps: Firstly, a section of VDF was cut at the length that defined the sensor’s measurement range. Both ends of the VDF were then cleaved and coated by a thin layer (about 200 nm thick) of TiO₂ using magnetron sputtering. A Single-Mode Fiber (HI1060) (SMF) was then spliced to both ends of the coated VDF using low-power pulsed arc-fusion splicing. This resulted in the creation of about 2% reflectance in-fiber mirrors at each splice between SMF and VDF. In-fiber mirror creation through TiO2 deposition is a well-known technique described for example in [58]. The SMF at the one end of the VDF was further angle cleaved about 5 mm away from the splice to couple out of the fiber all remaining optical power. The SMF on the other end of the VDF was used to connect the sensor to the excitation and interrogation system. Both semi reflective mirrors thus defined an all-VDF, low-finesse, long-gauge, Fabry-Perot Interferometer (FPI). The VDF fiber had an outer diameter of 92 μm and did not contain any primary coating (primary acrylate coating was removed after completion of the splices between the VDF and SMF by soaking the VDF in acetone for 30 min and peeling off the coating). The sensor (an FPI made out of the VDF section) was further packed in an aluminum U-profile with dimensions of 30x30 mm to provide mechanical protection of the fiber, limit potential fluid velocity at the surface of the VDF to (nearly) zero, and to keep the distance between the fiber and any solid objects in the vicinity (measured liquid freely entered/exited the U-profile containing the VDF). The VDF was also slightly pre-strained in a U-profile, while the holders at the top and bottom sides of the profile keep the distance between the U-profile and the fiber at a minimum distance of 10 mm. The fiber was fixed into the U-profile by two holders made of short aluminum plates with thickens of 10 mm and length of 5 mm. These two plates were fixed into the U-profile by two small screws, while the fiber sensor itself was spot-glued to these two holders near splices with VDF (in all cases SMF sections were glued to the holder by an epoxy adhesive; the length of glued section was about 2-3 mm), as shown by inserts in Fig. 1.

The excitation and interrogation system consisted of a few simple and widely available components: A 400 mW telecom amplifier pump diode, Wavelength Division Multiplexer (WDM), two fused bi-conically tapered fiber couplers (FBTs), an isolated telecom 1550 nm distributed feedback diode (DFB), two detectors, an analog-to digital interface (including two transimpedance amplifiers and two laser diode drivers, one of them was fully digitally programmable), and a Personal Computer (PC), as shown in Fig. 1. The PC ran interrogation algorithms written in LabView interfaced with MatLab. The lead-in SMF end located at the side opposite to the sensor was connected to a Wavelength Division Multiplexer (WDM), which merged/separated 980 nm and 1550 nm light signals. The 980 nm pump LD was connected to a programmable current generator to allow full digital control of the diode’s output power. An FBT with split ratio of 99:1 and monitoring detector were added to the system in order to control the output power of the 980 nm LD precisely.

The 980 nm LD output power was modulated periodically over time, which caused time dependent temperature changes of the VDF. These time dependent temperature changes of the VDF caused Optical Path-Length variation (OPL) within the VDF’s core. Since the VDF was configured as an FPI, OPL time variations generated time dependent variations (interference fringes) in the back-reflected optical signal, originally emitted by the 1550 nm telecom DFB diode. This time varying, back-reflected signal at 1550 nm was guided to the detector (Det 1). The signal acquired by the detector was amplified, digitized and sent for on-line processing to the PC. The PC extracted OPL variations from the acquired signal during each heating cycle (this process is described in detail later in the text). The extracted OPL variations were then correlated directly to the amplitude of the fiber’s average temperature change. The amplitude of the average VDF’s temperature (total OPL change), when exposed to cyclical heat excitation, depends strongly on the fluid’s level. This is because fluids exhibit, in general, considerably higher heat conductivities than most gases, and the part of the fiber that is immersed into the liquid experiences considerably stronger transfer of the generated heat into the fiber’s surrounding in comparison to the part of the VDF that is located in the dry area (i.e., in gas). Thus, the OPL amplitude variations in cyclically heated VDF correlate directly to the fluid’s level. The exact correlation between the VDF’s OPL change, the heating optical power P and the liquid level, can be obtained by a proper thermo-opto-fluidic analysis:

When an absorbing fiber with the length L is exposed to the heating power P, the steady-state change of OPL can be expressed as [57]:

The sensor’s active section (the VDF section) always consists of two parts: The part that is dry and the part that is immersed into the measured liquid. By applying heating optical power P to the sensor and taking into account Eq. (1), the optical path length change within the VDF due to the heating optical power application to the upper dry part (ΔOPL_D) can be expressed as:

Similarly, by taking into account Eq. (1), the optical path length change in the wet (bottom) section of the VDF (ΔOPL_w) is given by:

The total optical path-length change in the measurement FPI caused by the exposure of the sensor to the heating optical power P is given by:

Furthermore, to avoid the relatively complex and uncertain determination of constants q_D and q_W in the above expressions (which depend on fluido-mechanical parameters, like the Nusselt number), the need for knowledge of exact initial heating power and optical losses in the system, a simple initial calibration procedure can be carried out, which simplifies the use of the proposed sensor considerably. This can be accomplished by taking two reference measurements, the first when the sensor is fully immersed into the liquid, and the second when the sensor is fully dry. When the sensor is completely dry (fully out of the liquid), the path-length change of dry sensor ΔOPL_dry becomes directly correlated to the contestant q_D:

The above expression is valid for steady state conditions. In order to use these results, the excitation period (duration of heating source on + off time) shall be considerably longer than the thermal time constant of the fiber in the gas.

Thus, measurement of OPL variation during cyclic heating exaction has to be accomplished to measure liquid level L_w. To measure OPL variation precisely, we adopted the following approach: The heating optical power was increased from 0 to maximum value (to about 360 mW) over time in a way to induce a nearly linear over time OPL change. Since the fiber-fluid system can be reasonably-well approximated as a first-order linear system [57], the linear increase in heating optical power over time also causes a nearly time-linear increase in the fiber’s temperature and, consequently, OPL over time. Some minor correction of the heating laser diode drive current from the linear shape was, however, required to linearize OPL variation in the VDF. Thus, we corrected the linear-over-time LD’s drive current curve by adding another square root coefficient to the linear equation for current calculation, i.e., diode drive current was shaped/determined as I_d = k₀ + k₁*t + k₂*t^1/2 as shown in Fig. 2 (k₀ = 159.3 mA, k₁ = 0.2562 mA/ms and k₂ = 7.358 mA/ms^1/2 were chosen heuristically in a way that the peak current reached about 80% of the nominal drive current set by the diode specification, k_o was chosen to be slightly larger than the diode’s threshold current). This yielded an almost fully linear temperature/phase/ΔOPL variation over time during excitation of the VDF fiber with a 980 nm heating diode. The heating power ramp-up duration corresponded to 1000 ms and was chosen to be about three times larger than time constant of the fiber in the air, which was approximately 300 ms (for bare 90 μm fiber) [57]. After completion of each heating cycle, a pause of 1000 ms was introduced to allow for the fiber’s temperature to return to its initial steady state value. During this cool-down period interference fringes were also generated. Fringes generated during the cool-down period are chirped due the exponential decay of the fiber’s temperature (heating diode is in off-state) and were ignored in further level calculations. However, it would be possible to use OPL changes during cool-down periods in the further development of the sensor, which might further improve resolution of the sensor. Figure 2 shows several examples of back-reflected signal variation at 1550 nm at the different fluid level positions (using a sensor with a length of 45 cm) when we applied optical heating optical power that caused a nearly linear increase in the fiber’s temperature.

 

Fig. 2 Typical diode drive current and signals at detector 1 during continuous, uninterrupted operation of the sensor. The recordings are taken over 2.5 s intervals and at different liquid levels (one full, 2 s long, temperature cycle is shown together with ending and starting parts of a proceeding (N-1) and a succeeding (N + 1) temperature cycles). Section with the duration between 0 and 0.25s shows the end of the cool-down sequence of the preceding (N-1) fiber’s temperature cycle, section between 0.25s-1.25 s represent a full fiber’s heat-up sequence, section between 1.25s-2.25 s represents a full fiber’s cool-down sequence, and section between 2.25s and 2.5s depicts the starting part of the heat-up sequence of the succeeding (N + 1) temperature cycle: a) Current applied to the laser diode as a function of time b) Optical power recorded at detector 1 when the test vessel is empty, c) Optical power recorded at detector 1 when the test vessel is 50% filled with water, d) Optical power recorded at detector 1 when the test vessel is fully filled with water (total OPL change here is less than half of the wavelength meaning that not even a full interference fringe is generated over full heat-up/cool down cycle).

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The determination of OPL variation within each heating cycle includes measurement of total phase change ϕ within the recorded interference fringe in the back-reflected optical signal at 1550 nm during application of a single optical heating ramp-up sequence:

Since the frequency of the interference fringe generated at the detector’s input is nearly constant at the particular fluid level, an efficient phase change and, consequently, OPL retrieval is possible by an appropriate signal processing algorithm. Thus, the fringe obtained during application of the optical heating ramp-up sequence was recorded into the computer’s memory and then processed in real-time. A phase extraction algorithm is depicted in Fig. 3. The amplitude of the input signal was scaled between [-1, 1] and the bias was removed before processing. An input signal is shown in Fig. 4(a) (and also in Fig. 2, marked by *) and was considered as a quasi-cos function. The frequency range of signals of interests was between 1 and 25 Hz. The sampling time of a signal was set to 0.33 ms, and signal was represented using 3000 samples. The acoustic noise from the environment was filtered-out using a FIR filter of the 150th order. Three different cut-off frequencies were used, because one filter was not able to cover all the frequency range. The base frequency of the signal was estimated using a Fast Fourier Transform (FFT) and appropriate normalized cut off frequency (ω_N = ω_c/(ω_s/2)) of 0.014, 0.01 and 0.05 were selected for different frequency ranges between 0 and 5 Hz, 4-16 Hz and above 16 Hz, respectively. A periodic part of the signal, shown in Fig. 4(a), was extracted using peak detection. Peaks were estimated by finding zeros of a gradient function. Figure 4(b) shows a new signal constructed using the remaining part of signal shown in Fig. 4(a). The extracted phase of the signal, shown in Fig. 4(b), is a function of time and angle and is depicted in Fig. 4(c).

 

Fig. 3 Block diagram of the phase estimation algorithm.

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Fig. 4 An example of interference fringe processing, which was generated during fiber’s heat-up sequence (a sequence marked with “(*)” in Fig. 2(b).): a) Experimentally acquired quasi periodic cos function during fiber heat-up sequence. b) Construction of non-periodic signal. c) Reconstructed angle function.

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The algorithm depicted in Fig. 3 thus estimates the phase value of the periodic and non-periodic parts of the signal. For example, the phase of the signal depicted in Fig. 4(a) was 4729°, because the signal had 12 periods; therefore, the phase of the periodic signal was 360°*12 = 4320° and the phase of non-periodic part was 409 degrees. The proposed approach is, in principle, an improved fringe counting technique that also takes into account the residue, while also employing a highly efficient adaptive filtering that eliminates the noise that is caused by potential acoustical events in the sensor’s surroundings.

Finally, the measured OPL variation was converted into the liquid level by application of Eq. (9). To utilize this equation, initial calibration was performed by measuring the sensor’s responses (OPL changes) with full and empty test tanks, as already described above.

In addition to the sensor shown in Fig. 1, we also investigated the design of the sensor with two lead fibers and dual-side heating power delivery to the sensing FPI as shown in Fig. 5. Dual side power delivery linearizes the static characteristics of the sensor (due to the more evenly absorbed heating optical power over the entire length of the VDF) and extends the operational range of the gauge while employing the VDF with the same absorption coefficient. Thus, this sensor had an active length of 1 m while using the same VDF as in the version of the sensor described above (i.e., in Fig. 1). Dual side power delivery was achieved by an additional 50:50 FBT coupler, which split the power from the 980 nm source and delivered it from both sides to the VDF.

 

Fig. 5 Thermo-optic level gauge with dual side optical heating power delivery.

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The relations between OPL variations and liquid level for this dual side heating power supply configuration can be derived in a similar way as Eqs. (8) and (9), and can be expressed as (assuming half of the heating power is delivered to each end of the absorbing fiber):

Photography of experimentally built sensors are shown in Fig. 6.

 

Fig. 6 (a) 45 cm long liquid level sensor in the test vessel (b) 45 cm and 100 cm long liquid level sensors.

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3. Experimental results

Figure 7 shows the measured phase/OPL variations versus liquid level in the test tank when the liquid level was increased gradually from zero to a maximum level for both versions of proposed level sensors. The non-linear relation between level and measured OPL was expected and is predicted by expressions Eqs. (8) and (11). By inserting OPL variations for a full and empty vessel, and fiber’s absorption data (14.51 dB/m or α = 3.34 Np/m@980 nm) into Eqs. (8) and (11), we also calculated and displayed the relation between the set liquid level and, by the theoretical model, the predicted OPL change. Figure 7 indicates excellent correlation between the predicted and measured OPL-level relations.

 

Fig. 7 (a) 45 cm long gauge with single side heating power supply: Blue dots represent measured OPL variation at different liquid levels; the red curve is the calculated OPL variation (using Eq. (8) and initial calibration) as a function of liquid level; b) The same as a), but for 1 m long gauge with dual-side heating power supply (expected/calculated OPL variation was obtained according to Eq. (10)).

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To determine the liquid level position from the measured variations of OPL, the measured OPL variations were inserted directly into Eqs. (9) and (12). Figure 8 shows the measured level positions (using back-reflected signal variation, OPL extraction algorithm and Eqs. (9) and (12)) versus experimentally set level positions for both versions of sensors. Linear relations, with R²>0.998 were obtained, which confirms that Eq. (9) and (12) provide high-fidelity correlation between OPL change and level. Thus, no additional linearization is required when processing the results.

 

Fig. 8 Measured level versus experimentally set level: a) 45 cm long gauge with single side heating power supply b) 100 cm long sensor with dual-side heating power supply.

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The total change of OPL within each interrogation cycle was between about 0.9 μm and 24.9 μm for short level gauge, and between 1.74 μm and 37.6 μm for the long (dual side supplied) level gauge, which corresponds to the maximum average temperature variation of VDF of 3.8 °C in the case of 1 m and about 5.5 °C in the case of a 45 cm sensor.

Figure 9 shows the experimental system resolution demonstration, where we increased and decreased the water level in small steps, while observing sensor responses over a longer time period (60 min). Figure 9 indicates a system resulting of about 2 mm in the case of a 45 cm long sensor and 3 mm in the case of a 1 m sensor, which is equivalent to around 0.44% and 0.3% for 45cm and 1 m sensor, respectively. The long duration test, shown if Fig. 9, also indicates that the long-term stability is better than 0.45% and 0.3% of the full scale ranges, which indicates that absolute accuracy in the same range shall be feasible with the proposed system.

 

Fig. 9 shows the response of a 45 cm long sensor (a) and 1 m long sensors (b) when the level was raised and lowered in small consecutive steps (2 mm, 5 mm, 10 mm and 20 mm) over 60 min time interval (in this test we averaged 5 raw measured values). Measurements were complete with hall full test vessels.

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The system also exhibited relatively good acoustical noise immunity, which might be of concern when using long interferometers. This immunity can be attributed to the use of adaptive band-pass filtering of back-reflected signals employed during OPL variation calculation, as described above. It should be also stressed that the system is not measuring absolute temperature, but rather temperature change that occurs during period of active heating of the fiber with limited duration (1 s). After completion of the fiber’s heating sequence, the fiber temperature drops to its steady state temperature. The cycle is then repeated. The temperature changes during heating cycle, as shown theoretically and confirmed experimentally, depend only on the delivered heating power, Nusselt numbers of measured fluids and actual liquid level. Thus, absolute temperature fluctuations do not affect measurement results. In order to experimentally verify this, we enclosed the proposed level sensor (version with single-side lead fiber connection) together with a compact test water tank into a climatic chamber. We filled the test tank with water to a level, which corresponded to about a one-half of the sensor operational level range. Then we varied sensor’s ambient temperature between 30 C° and 60 C° in 10 C° steps (there were 2 h intervals between measurements to allow for a full heat-up of the system under test). Results are shown in Fig. 10 and demonstrate measurement system temperature dependence, which was about 0.1 cm over the test temperature range and within measurement system’s noise range. Since the proposed sensor is made of a short and straight section of SM fiber, which can reasonably well preserve polarization [59], we were not able to observe any significant polarization dependence nor fading effects in the proposed sensor configuration.

 

Fig. 10 Measured level as a function of sensor’s ambient temperature. Water level during the test was constant, about 22.4 cm.

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Finally, the system can be improved further by adopting different signal interrogation approaches. For example, overall VDF thermal time consistency depends on the fluid surrounding the fiber, and measurement of the time constant might yield an even more stable and accurate system in a similar way as was done in [60]. More sensitive approaches to VDF change measurements can also lower the required heating power.

4. Conclusion

This paper proposed an all-fiber, thermo-optic fluid level sensor for continuous level measurements that can be used in vessels with larger vertical dimensions, while utilizing fully optical and dielectric design of the sensor and connection between the sensor and measurement site. The sensor design includes an optical absorbing fiber that is configured into a long FPI. The absorbing fiber is heated cyclically by application of a remote medium power 980 nm optical source. Since the intensity of heat conduction from the heated fiber depends on the immersion depth of the fiber into the liquid, the heated fiber’s temperature variations correlate directly to the liquid level. The temperature variations along the cyclically heated sensing optical fiber were obtained by observing the interference pattern generated by the FPI that was defined by the same heated fiber. The interrogation system consisted of only a few telecommunication optoelectronics components, signal conditioning with an analog-to-digital interface and a PC running appropriate algorithms (the latter could easily be replaced by a proper microcontroller). We also provided an analytical description of the proposed thermo-opto-fluidic level gauge, which might also support the design of similar thermo-fluidic-fiber-optic level gauges or devices. Application of VDF also provides an opportunity to separate the heating and probing optical signals, which allows for effective use of heating power while enabling simple and efficient sensor interrogation. The proposed simple two-point calibration procedure also eliminated the need for any knowledge of relatively complex fluido-dynamic parameters that are otherwise required to describe a sensor’s characteristics. Besides measuring OPL variation with full and empty test vessels, the only partner that needs to be known for accurate prediction of a sensor’s static characteristic is the fiber’s absorption coefficient and wavelength of the heating optical source. Furthermore, two possible sensor configurations were proposed: The first configuration uses a single lead-in fiber, which is simpler and more practical for potential field use but yields more pronounced nonlinear characteristics and shorter measurement span, and the second configuration, which utilizes two lead fibers and dual-side heating power delivery, which yields more linear static characteristic and larger measurement spans.

Unlike in most currently proposed optical fiber-based sensor systems for continuous level measurements, the proposed approach does not involve any direct contact of any active/sensitive optical surface with the measured liquid, which provides opportunities to use this principle in many industrial applications that involve liquids that are prone to formation or residues or contaminations. Furthermore, the system does not rely on a distributed temperature measurement system and allows for a very simple and efficient signal interrogation that is based entirely on widely used standard telecommunication components. This provides opportunities for cost-effective realization of a measurement system, which is essential for the great majority of process industry applications.

The achieved level resolution is in the range of 0.3%-0.45% of full measurement range and could probably be improved further. Different level measurement ranges can be addressed by choosing fibers with different absorbing coefficients. In this work, we demonstrated 0.45 m and 1 m measurement range level gauges by using a fiber with optical absorption of 14.51 dB/m. Heating optical power could be likely further and considerably reduced, but this might require a more sensitive and more complex interrogation system.