1. Introduction

Fiber optic strain sensors have been adopted widely in many industries due to unique properties that arise from fully optical, all-dielectric, and compact designs [1]. Among single-point and multipoint fiber optic strain sensors, Fiber Bragg gratings (FBGs) hold an undisputed and leading role, as they provide possibilities for reliable, efficient, and multipoint strain measurement, while relying on an intrinsic all-fiber design [2–6]. Furthermore, FBGs are easy to mount and relatively straightforward for production. The success of FBGs lies in their intrinsic ability to correlate strain (and temperature) directly to optical frequency. The latter is a physical quantity that can be measured with high precision and resolution, and provides different means for reliable transfer of its calibration to the field. This most prominent advantage of FBGs, however, also represents a substantial limitation when it comes to achievable strain resolution and the measurement system cost. FBGs` spectral sensitivity is relatively low, at the order of 1 pm/µɛ within wavelength ranges of interest, which inevitably implies the use of high-complexity, high-resolution spectral interrogation systems [7]. This is true, even in cases when the measured strain ranges are considerable, and when only moderate strain resolution is required. The demand for high spectral resolution interrogation and associated high system cost proved to be one of the major obstacles in the broader introduction of FBGs in a wide field of possible strain sensing applications. Furthermore, reliable strain sensing in the low µɛ, and even the nɛ range, presents a further challenge, as it requires an even higher spectral resolution, and, consequently, more complex interrogation setups [8]. An additional challenge in the sensing of strain in the low µɛ and nɛ ranges arises from the FBGs’ considerable temperature sensitivity [9], which is a consequence of the intrinsic temperature sensitivity of the silica glass refractive index to the temperature, and thus cannot be overcome easily by the FBG or fiber design. Therefore, static or quasistatic FBG based strain measurement systems` performances at low µɛ ranges are, thus, often determined by the performances of the applied temperature compensation schemes [10]. However, temperature compensation schemes are always limited in their efficiencies, for example, due to the inevitable temperature gradients that occur among measurement and compensation sensors in practical systems. Reduction of the sensing system intrinsic temperature sensitivity before any compensation is, therefore, mandatory for successful measurement of strain in low µɛ and nɛ ranges.

In 2011 we presented a new concept of an all-silica, long-gauge, short-cavity Fabry-Perot (FP) strain sensor [11]. Within this paper we present an evolution of this initial sensor concept into a high-performance strain sensing system. The proposed system provides nano-strain sensing resolution with low intrinsic system’s temperature sensitivity, and can be read out spectrally using mid, or even low-resolution spectrometers. While the second characteristic provides an opportunity for a significant reduction of signal interrogation system cost, the ability to conduct relatively straightforward static/quasi-static measurements within the nɛ range presents a potential and significant advancement in relation to a current state-of-the-art, as it opens measurement capabilities that are not within the reach of FBGs or similar systems.

2. Sensor design and operation

The proposed sensor is shown in Fig. 1, and is composed of the lead-in fiber, a central conical pillar with a flat top end, an outer wall surrounding the pillar, and the tail section of the sensor. The lead-in fiber end and the flat top of the pillar form semi-reflective surfaces that further define a low-finesse Fabry-Perot cavity. Exposure of this structure to the longitudinal strain modulates the cavity length L_c, which is readout optically through the lead-in fiber. The entire structure is made of silica glass. The cavity length changes of ΔL_c can be related to the strain as ΔL_c= L₀ɛ, where L₀ presents the sum of the pillar L_p length and initial cavity length L_c.

 

Fig. 1. Strain sensor: (a) 3D scheme, (b) Typical produced sensor under an optical microscope.

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As mentioned in the introduction, we presented the basic concept of this sensor structure in [11], however, the full potential of this structure for high resolution and cost-efficient sensor realization was not established and investigated at that time. To exploit the full potential of this structure, the L₀ shall be extended to its maximum possible length, while adjusting the L_c to a value that supports and maximizes the performance of the selected signal interrogation scheme. The maximum L₀ achieved during the initial reporting on this structure in [11] was at the order of 350 µm, while L_c was restricted to few micrometers. Both restrictions arose from the production process, and, thus, restricted the sensitivity and applicable signal processing approaches. Within this paper we report on a significant extension of L₀ and the possibility to tune L_c, which unlocks the true potential of the structure shown in Fig. 1 for a flexible signal processing and high-resolution strain sensing. The structure shown in Fig. 1 was produced by the selective etching process, and involves manufacturing a structure forming fiber (SFF) with the cross-section refractive index profile shown in Fig. 3(a) . The SFF is composed of a pure silica cladding, a P₂O₅ doped ring (about 10.5 mol% of P₂O₅), another pure silica ring and a central region, which is doped weakly in this case with TiO₂ (i.e. about 3.2 mol% of TiO₂). The doped regions of the fiber etch at higher rates than pure silica when exposed to hydrofluoric acid (HF). The etching rate depends strongly on the concentration and type of the dopant. Among dopants compatible with existing fiber preform manufacturing processes, P₂O₅ increases the etching rate at most in concentrations that are still suitable for incorporation in fiber preforms, while the TiO₂ doping provides only a limited effect on the etching rate and does not reduce glass viscosity significantly, which allows for more extensive thermal treatment of TiO₂ doped structures (a pillar in this particular case). Exposure of the SFF to HF thus induces preferential/selective etching of both doped regions. In the case of etching with a 40% HF water solution at room temperature, the doped P₂O₅ ring etches about 50 times faster than pure silica, and at the given initial fiber dimensions (outer diameter of 140 µm) yields a pillar length of about 270 µm, as reported in [12]. During the current investigation, we explored different possibilities extensively, which would increase the etching selectivity (the ratio between the etching rate of doped and undoped glass), and, thus, allow for pillar length extension. We found that etching temperature reduction and addition of organic solvents, like isopropyl alcohol (IPA), can have synergistic effects on etching selectivity, and can thus significantly increase the preferential removal of the P₂O₅ doped ring. This can yield a substantial increase of the pillar length. Figure 2(a) shows an example of the SFF shown in Fig. 3(a), when etched at −20 °C in HF:IPA:H₂O = 18:225:7 mass ratios. The final pillar length was, in this case, 2.9 mm, while the outer diameter of the fiber was reduced (etched) only by 15 µm. The only drawback of this very low temperature and diluted HF etching approach is in the long etching time, which corresponded in this particular case to 150 days. If required, however, an about 30% shorter pillar can be obtained, for example, by using about 54:175:21 HF:IPA:H₂O solution at -10 °C, which requires only 24 h to complete the etching, as shown in Fig. 2(b). For reference, when the same fiber was etched in 40% HF at room temperature, the etching was completed in 7 min, although the pillar length was only about 270 µm long (Fig. 2(c)).

 

Fig. 2. An SFF etched at different conditions: (a) HF:IPA:H₂O = 18:225:7 at -20 °C, (b) HF:IPA:H₂O = 54:175:21 at -10 °C, and (c) 40% HF at 25 °C.

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Fig. 3. (a) Refractive index profile of an SFF, (b) Selective etching of the SFF, (c) Fusion splicing, (d) Thermal stretching, e) and f) End-capping of the lead in fiber to improve the fringe contrast, mainly when using MMFs (an optional step, used only when sensors were prepared with MMF fibers).

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Modification of the etching conditions, however, does not affect the etching selectivity of the TiO₂ region significantly. The pillar end was thus always retreated relative to the outer wall by about 5 µm, which provided an opportunity to splice the SFF to the lead-in fiber while avoiding contact between the pillar end and surface of the lead-in fiber. The initial retraction of the pillar relative to the outer wall was also measured with a white-light interferometer Sumix SMX 7QS. The comparison was made between an SFF etched in HF:IPA:H₂O = 18:225:7 and an SFF that was etched for 7 min at room temperature in 40% HF, which yielded the same fiber outer diameters after etching. In the first case, retraction of the TiO₂ doped pillar corresponded to 5 µm, while, in the second case, the pillar was only marginally less retracted, i.e. 4.8 µm. Weakly doped TiO₂ doped pillar etching selectivity is, thus, marginal, depending on the used etching conditions.

While higher doping levels of the central region of the SFF could result in further retraction of the pillar end, higher doping levels in the pillar inevitably lead to glass viscosity reduction, which makes the pillar soft during splicing and results in a rounded pillar end that does not form a useful FP cavity.

The etched SFF was spliced to a lead-in fiber (Fig. 3(c1)). The fiber structure was then heated by a filament fusion splicer (Vytran FFS 2000) across the area containing the pillar while driving the splicer`s linear z-motors in the same direction but at slightly different velocities (Fig. 3(d1)), which stretched the outer wall of the structure surrounding the pillar. This operation did not affect the pillar length, as the pillar is a part of the SFF and is not in contact with the lead-in fiber. This thermal stretching steps allowed for a controlled adjustment/setting of the initial FP cavity length. Any cavity length between about 5 and 200 µm can thus be obtained in a controlled way for a given sensor structure, and without significant reduction of the structurès outer diameter. Successful implementation of this controlled length adjustment requires high viscosity of the glass that forms the pillar. Even very low concentrations of P₂O₅ cause sufficient viscosity reduction, which results in pillar end rounding during splicing and a cavity length adjustment step. This is one of the main reasons for TiO₂ doping of the central section of the SFF (it would, for example, be considerably easier simply to dope the central part of the SFF with a very low concentration of P₂O_5, or some other and more frequently encountered fiber dopant). The proposed structure can be used either with single-mode or multimode lead-in fibers, as the flat top of the pillar was designed to be 50 µm in diameter and can, thus, support multimode fibers with core sizes in this range. When using multimode lead-in fibers with large germanium doped cores, a section of coreless fiber (with the length of about 40 µm) was additionally inserted in-between the SFF and the lead in-fiber, as shown in Fig. 3(d2). The coreless fiber was first fusion spliced to the lead-in fiber (Fig. 3(e)), then cleaved away by about 40 µm (Fig. 3(f)), and then spliced to the etched SFF, as shown in Fig. 3(c2). This additional feature (end-capping of the lead-in fiber) was necessary to maintain the high flatness of the lead-in fiber’s end surface. During heating of an unterminated end of the multimode fiber, the viscosity mismatch between the silica cladding and doped core causes the core to protrude slightly out of the fiber end, and yields a curved surface that degrades the fringe contrast significantly, especially when using longer cavity lengths.

During the experimental investigation, we produced and tested three variants of the proposed sensor. The first variant utilized a standard telecom single-mode lead-in fiber spliced directly to the etched SFF, the second variant used an HI780 short wavelength single-mode lead-in fiber also spliced directly to the etched SFF, while the third variant utilized a 50 µm graded index multimode fiber as the lead-in fiber, and was spliced to the SFF through a section of coreless fiber, as already explained above. The FP cavity lengths in these three types of sensors were set to 64, 62, and 28 µm respectively, to accommodate the different signal interrogation systems described further below.

All the sensors were fixed on a 8.25 × 8.25 mm square cross-section rod made from Super Invar with the length of 110 mm. The rod was fixed on its top and placed in a vertical position, while a thin flexible Kevlar thread was connected to the bottom of the invar rod, and was adapted to accept different weights, as shown in Fig. 4(a).

 

Fig. 4. Experimental setup.

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The cross-section of the rod was chosen in a way to yield a rod strain of 1 µɛ per each 1 kg of vertical load applied to the thread. The relationship between the loaded weight mass and the strain induced within the invar rod can be expressed from the well-known relationship between the strain and stress, i.e. ɛ=δ/E = F/(A*E)=mg/(A*E), where ɛ is the strain induced with the rod, δ represents the stress induced by the weight loading, m is the mass of the calibrated weight, A is the cross-section of the invar rod, g is the gravitational acceleration and E is the Young’s modulus of the invar. For values of parameters used in the experimental system (E = 145 GPa, A = 68,06 mm², g = 9.81 m/s²), the relationship between the induced strain and mass of the loaded weight can be expressed as ɛ= 1*10⁻⁶kg^-1 * m, i.e. each gram of loaded weight induces a change in the rod’s strain of 1 nɛ. The latter relationship between the weight mass and induced strain allowed for “comfortable” and well controlled variation of the test invar rod`s strain within the nɛ range by using calibrated weights. Fixing of the sensors to the invar rod was accomplished by using Vishay M-Bond AE-10 Strain Gage Adhesive. We used two sensor mounting approaches. The first approach is shown in Fig. 5(a), and utilized a shallow (about 70 µm deep) groove with a half-moon cross-section and width of about 130 µm, which was milled at the invar rod surface. The invar rod was then pre-compressed in a way to induce 30-100 µɛ of compressive strain in the rod. The grooves were then filled with the adhesive, the sensors/fibers were depressed into the grooves, while removing the remaining excess adhesive. After initial room temperature curing of the epoxy, thermal curing was also accomplished at 80 °C for at least 60 min. After removing the pretension from the invar rod, the rod, with sensors, was additionally exposed to about 5 temperature cycles between 30 and 80°C. In addition to the above-described sensor fixing procedure, we also fixed an additional strain sensor using a standard single-mode lead-in fiber directly onto the invar rod`s surface, but, in this case, the sensor was fixed with the adhesive at two points that were 3 cm apart (the sensor was placed in between the fixing points), as shown in Fig. 5(b). The mounting/pretension and curing procedure were otherwise the same as already described above for the first mounting variant. This second two-point fixing configuration, increases the sensor’s sensitivity further, as it allows for stress concentration within the thin silica wall that surrounds the sensor’s pillar.

 

Fig. 5. (a) Uniform adhesion of the sensor in shallow groove (b)Two point fixture of the strain sensor to increase sensor strain sensitivity.

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In addition to the strain sensors, we also fixed a fiber optic Fabry-Perot temperature sensor on the surface of the invar rod (the sensor was defined by an in-fiber mirror created within a single-mode fiber, as described, for example, in [13]). The sensor was packaged into a glass capillary with an inner diameter of 250 µm and depressed against the invar rod`s surface. The capillary with the temperature sensor was further covered with thermally conductive paste, to assure good thermal contact between the sensor and the invar rod, while placed in the vicinity of the strain sensors. The invar rod with sensors was enclosed into a Styrofoam box, which was, further, connected through 32 mm pipes to a tubular heater with integrated fan, which provided heating and closed-loop air circulation. This setup provided the means of even and controlled heating of the test invar rod with minimum transfer of the fan`s vibrations to the test rod. The entire experimental setup is shown in Fig. 4(b).

3. Experimental evaluation

All three sensor variants were interrogated spectrally, but using three substantially different interrogation setups, as indicated by Fig. 6. The sensors built with standard single-mode fibers had the longest cavities, and were connected to a commercial spectral interrogator FAZT I4, which is based on a tunable semiconductor laser source and can record a sensor’s back-reflected spectral characteristics within a 40 nm wide range around 1550 nm. The sensor built with the short wavelength single-mode fiber (HI780) was connected through a single-mode fiber coupler to an 820 nm SLED (with an FWHM of about 30 nm and output power of 1 mW), and to a Broadcom QWave VIS spectrometer 350-880 nm. The latter is a general purpose, linear-detector-array, cost-efficient spectrometer with a declared spectral resolution of 0.5 nm. The sensor built with the multimode fiber was connected through a multimode coupler to the same spectrometer and an ordinary LED (Luxeon PC Amber), intended for lightning and automotive applications. The central operating wavelength of the LED was 590 nm, while the FWHM was nearly 80 nm wide. A simple butt-coupling between the MMF and LED was used in this case, which yielded about 14 µW of total coupled optical power to the 50 µm multimode fiber.

 

Fig. 6. Optical setup for all three sensor-interrogation configurations: (a) Sensing system with standard SMF and commercial high performance FAZT I4 interrogator, (b) Sensing system with a short wavelength SMF (HI780), SLED (820 nm) and cost-efficient Broadcom QWave VIS spectrometer, and (c) Sensing system with a standard MMF, automotive LED (590 nm) and cost-efficient Broadcom QWave VIS spectrometer.

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In all three cases the setups used provided the possibility to acquire back-reflected optical spectrums. Examples of all three spectrums are shown in Fig. 7 a-c. The fringe contrasts were nearly 100% in the cases of single-mode variants, while about 15% fringe contrast was achieved in the case of the multimode fiber. Figure 7 a-c also show spectrums of all the sensors when the sensors were loaded with strains corresponding to 22.5 µɛ. The high spectral sensitivities are obvious (87.1 pm/µɛ, 39.9 pm/µɛ and 64.8 pm/µɛ in the cases of 1550 nm, 820 nm and 590 nm excitations respectively). Spectral sensitivity is determined by the overall sensor length L₀, a gauge factor k which is determined by the sensor mounting configuration and sensor geometry, the sensors’ free spectral range FSR and operating wavelength λ.

In all cases, the back reflected spectrums were processed in the same way: The acquired spectrum of each sensor was firstly converted from the wavelength to a frequency domain. Then, the (inverse) Fast Fourier Transform (IFFT) was performed on the acquired spectrum, while searching out the component within the IFFT with the maximum absolute value. A phase Φ of this component with the largest absolute value in the IFFT represents the phase of the sinusoidal spectral fringe within the acquired optical spectrum, and can be correlated to the FP cavity length ΔL_C change as:

 

Fig. 7. Sensor's back reflected optical spectrums for different sensors` setups: (a) Standard SMF with commercial high price FAZT I4 interrogator, (b) SMF around 780 nm with cost-efficient Broadcom QWave VIS spectrometer, and (c) Standard MMF with low-cost Broadcom QWave VIS spectrometer.

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The static characteristics and resolutions of all the experimentally produced strain measurement systems were then measured by applying calibrated weights to the end of the thread that was connected to the invar rod, as shown in Fig. 4(a). For a direct comparison, the bandwidth of all measurement systems was limited to a 1 Hz sampling rate, by applying averaging of the results obtained from the IFFT. All tests were done at stable room temperature.

Figure 8 shows the static characteristics for all four systems when applying strain from 0-1000 nɛ to the invar rod. The strain can be calculated from the measured cavity length change ΔL_C as:

 

Fig. 8. Static characteristics for four different sensors in different interrogation configurations: (a) Sensor using standard SMF lead-in fiber and commercial FAZT I4 interrogator around 1550 nm, (b) Sensor using SMF, SLED at 820 nm and Broadcom QWave VIS spectrometer, (c) Sensor using 50 µm MMF, automotive LED around 590 nm and Broadcom QWave VIS spectrometer, and (d) The same sensor configuration as in a) except using a two point fixture to enhance strain sensitivity.

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The system`s strain resolutions were determined by cyclical loading of the invar road (through the Kevlar thread) by different small weights. The system`s resolution was then estimated as the strain required to produce the output signal with an amplitude which was about equal to the root-mean-square of the system’s output noise amplitude. The results for all tested sensor systems are shown in Fig. 9 and indicate the following resolutions: A resolution of better than 1 nɛ was achieved by the application of a two-point fixing of the proposed strain sensor and application of a tunable laser based FBG interrogator (FAZT I4); about a 2 nɛ resolution was achieved by application of the same sensor and interrogator, but with firm fixation of the sensor into the shallow groove in the test rod (those results are consistent, as the two point fixation yielded about 2.6 times higher sensitivity due to the strain concentration effect as described above). A resolution of about 20 nɛ was demonstrated clearly by the combination of a single-mode fiber coupled SLED and general-purpose Broadcom QWave VIS spectrometer. Surprisingly, the resolution of a system using an illumination/automotive grade VIS-LED, butt-coupled to a multimode fiber, and the general-purpose Broadcom QWave VIS spectrometer, yielded a system strain resolution of better than 70 nɛ. Even the latter system outperformed significantly almost any commercial high-end FBG based strain measurement system, while the application of the FAZT I4 yielded a strain measurement system, which can perform strain sensing confidently within the 0-1 µɛ range.

 

Fig. 9. Estimation of different sensing systems` strain resolutions using consecutive loading and unloading of an invar road with calibrated weights. The weight sizes were increased until the change in the output signal did not exceed the average noise level at the system output (averaging of raw data was used to provide a uniform 1 Hz sampling rate in all test cases): a) Sensor with two point fixation, standard SMF and FAZT I4 interrogator (estimated resolution better than 1 nɛ); b) Uniformly adhered sensor using standard SMF and FAZT I4 interrogator (estimated resolution 2 nɛ); c) Uniformly adhered sensor using 820 nm SLED, SMF for 780 nm Broadcom QWave VIS spectrometer (estimated resolution 20 nɛ); d) Uniformly adhered sensor using a butt-coupled automotive VIS LED, 50 µm MMF and Broadcom QWave VIS spectrometer (estimated resolution 50 nɛ).

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The applied IFFT demodulation algorithm extracts the position (phase) of the periodic interference fringe position within the acquired optical spectrum. The total output noise of the extracted phases determines the total systems’ resolution. The output phase noise depends on many factors, including light source characteristics, total system optical losses, the sensors’ FSRs, fringe contrast, and interrogator/spectrometer properties, and cannot be anticipated directly, for example, from the declared spectral resolution of the spectrometer or interrogator. From Fig. 9 we can estimate that the noise of the extracted fringe position phases corresponded to 0.0028, 0.043 and 0.185 degrees for cases of systems using an SMF based FAZT I4 interrogator, an SMF/SLED based Broadcom QWave VIS spectrometer, and an MMF/LED based Broadcom QWave VIS spectrometer respectively. These phase noises further correspond to wavelength noises, and, consequently, spectral resolutions of about 0.14, 0.64 and 3.2 pm, which further correspond to strain resolutions of about 0.8 (two-point sensor fixture), 1.6, 17 and 50 nɛ. The strain resolution is higher in the case of the SMF FAZT I4 interrogator using a two-point fixture, as the two-point fixture provides double sensitivity.

Further tests and analysis were devoted to the evaluation of possibilities for static absolute strain measurements within the low µɛ and nɛ ranges, where mitigation of the temperature effects becomes of essential importance. The intrinsic temperature sensitivity of the proposed sensor depends on the difference between the thermal expansion of the pure silica outer wall and the pillar. The cavity length changes due to the change in temperature can be expressed as:

 

Fig. 10. Intrinsic temperature sensitivity of typical unmounted strain sensors.

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All three sensors exhibited nearly the same temperature coefficient of about 2.4 × 10⁻⁷K^-1, which is in good agreement with the above estimated value for k_T. This value is more than 40 times lower than in the case of FBGs [9] at 1550 nm.

Temperature induced errors in systems using the proposed structure will, thus, arise mainly from the thermal expansion of the material that is measured, and the ability to compensate for those effects. Low thermal expansion materials, like the Super Invar used in the current tests, are, therefore, usually required in the design of systems aimed for high resolution static strain measurements. In addition, accurate temperature compensation using reference temperature sensors or reference strains sensors are also required, to achieve zero-point stability in the nɛ range. Figure 11 shows the measured virtual strain induced by a temperature change of 14°C for the first sensor mounted on the invar rod by the two point fixture, and the second sensor attached to the invar rod, as presented in Fig. 5(a) (in this and further tests we were using the single-mode fiber sensors` version interrogated by the FAZT I4 interrogator). The virtual strain temperature coefficient for the first and second sensors corresponded to 0.42 µɛ/°C and 0.45 µɛ/°C respectively, which is about consistent with Super Invar CTE (0.07-1.24 µɛ/°C) [17]. To mitigate this effect, we added (as described above) another FP temperature sensor in a close vicinity of the strain sensor. An initial calibration was carried out, where we slowly heated the sensor setup while recording the virtual strain and temperature at the sensor. The recorded virtual strain vs. temperature characteristics (which is nearly linear as shown in Fig. 11) was approximated further with a linear function.

 

Fig. 11. Temperature characteristic of strain sensors attached to the invar surface.

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The coefficients of linear function were stored and used in further measurements to calculate and compensate (subtract) temperature induced virtual strain from the measured strain values.

Figure 12 shows an example when the temperature of the invar sensing rod was heated from 29°C to 39°C while using the above-described compensation scheme. For reference, the invar rod was also loaded and off-loaded periodically by weight, which induced multiple strain changes with an amplitude of 20 nɛ during the duration of the tests. As shown by Fig. 12, the zero-point between both temperature extremes remained within about 25 nɛ limits.

 

Fig. 12. Strain measurements in the nano strain range while the temperature was varied from 29 to 39 °C.

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While better and more sophisticated temperature compensation schemes could also be applied (for example, using multiple strain and/or temperature sensors), the results in Fig. 12 indicate that the presented sensor with its low intrinsic temperature sensitivity can provide not only high resolution, but also configurations that might provide possibilities for stable static and absolute strain measurements with the nɛ range. The remaining drifts of zero-point in static and quasi static strain measurement can be attributed mainly to the appearance of temperature gradients between the strain and the temperature (or compensation) sensors. This was due to the very good contact of the strain sensor with the invar rod, which was fixed through a metallic support structure with the test table at room temperature. On the other hand, the temperature sensor was not in direct contact with the invar rod, to assure selective temperature measurements, which lead to a gradient appearance between the strain and temperature sensor when the room temperature and sensor’s structure were at considerably different temperatures (the invar rod was in thermal contact with the room environment through its mechanical fixture). Thus, in the used setup, strong heating of the sensor leads to the creation of a non-negligible gradient between the sensor, invar rod and the temperature sensor, which limited the efficiency of temperature compensation at higher temperatures. Thus, if the system would need to be designed for operation over a wide range of temperatures, more efficient thermal management would be required (for example, at least good thermal insulation of the measurement rod from the surrounding would need to be realized).

Figure 13 shows a medium duration stability test for the highest resolution variant of the proposed sensing system (using a two-point fixture of the sensor and FAZT-I4 interrogator). The test was conducted at stable room temperature conditions over a period of 1 hour. During this test, we additionally insulated the sensor thermally (including the invar pillar and its mechanical connection with the surroundings), to minimize the effects of any temperature fluctuations on the sensor`s performance. The total drift of the baseline remained within + - 0.5 nɛ limits during the entire test, indicating the potential of the proposed sensor not only for very high resolution, but also potentially high absolute accuracy strain measurements. For reference, during the duration of the test, the sensor was loaded and unloaded with calibrated wight for three times, which induced change in strain for 1 nɛ.

 

Fig. 13. Medium term (1 hour long) stability test at room temperature conditions (ΔT ∼ 0.5 °C) using a two-point fixture of the sensor and FAZT-I4 interrogator. Separate temperature sensor was used to provide temperature compensation. Red line shows temperature of the room in the vicinity of the experimental setup using separate high resolution temperature sensor. During the duration of the test, the sensor was loaded and unloaded with calibrated wight for three times, which induced change in strain for 1 nɛ.

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Low intrinsic sensor’s temperature sensitivity in combination with low thermal expansion of the base material are, thus, factors that govern viable static strain sensor performances.

4. Conclusion

In conclusion, we presented a deeply etched, long active length, short FP cavity strain sensor structure. The proposed sensor structure yields high strain sensitivity (the spectral sensitivity of the FP interference fringe can exceed 85 pm/µɛ) and low temperature sensitivity. It provides the opportunity to adopt the sensor’s spectral characteristics (free spectral range and operating wavelength range) to a broad variety of spectrally resolved signal interrogation configurations.

When a high-end commercial FBG signal interrogator was used, a strain sensing resolution of 1 nɛ was demonstrated experimentally. The proposed sensor structure can, however, also be interrogated efficiently by general purpose and cost-efficient VIS-NIR linear detector array-based spectrometers, while still providing strain sensing resolutions within the range of a few 10 nɛ. Furthermore, the structure can be combined with multimode telecom lead-in fibers and low-cost broadband LEDs intended for automotive/lightning applications. This can all lead to a considerable cost reduction of the entire strain measuring system, which is currently one of the main obstacles in introducing fiber optic strain sensing systems in a broader variety of industrial and similar applications. This is especially true in view of the recent commercial success and ongoing efforts to reduce the cost and size of compact UV-VIS-NIR spectrometers.

The very low intrinsic temperature sensitivity of the proposed sensors (about 40 times lower than in the case of an FBG) simplifies measurement system design, and provides realistic opportunities, not only for building systems with dynamic nɛ resolution, but also for the design of systems that can achieve absolute static strain measurements in the nɛ range. It should be stressed that comparable temperature sensitivity cannot be achieved with FBGs, as the FBG temperature sensitivity arises from the temperature sensitivity of the fiber’s core refractive index. Thus, even there are reports on nɛ resolution demonstration with FBGs [8,18]. These FBG systems would be very difficult to implement and operate in micro and sub-micro strain static and quasi static measurement configurations (the virtual strain caused by a 1 K temperature change in an FBG system corresponds to more than 10 µɛ, which would require temperature compensation at the sub mK level when measuring static strains in the nɛ range).