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Abstract
In this work we demonstrate the fabrication and characterization of a temperature insensitive, two-dimensional curvature sensor using a resin based Fabry-Pérot interferometer, constructed using a multicore fiber (MCF). The fabrication simplicity makes this fiber device very attractive compared to the already reported technologies. Furthermore, the sensitivity reached (>400 pm/m-1), 7 times higher than the one reported for fiber Bragg gratings written on a similar MCF. The reconstruction of the amplitude and curvature has been performed for, showing errors lower than 4%. A numerical study has also been developed, allowing us to understand the sensor response at different fiber sensor geometries.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical fiber sensors (OFS) are known to have advantages over other sensing technologies. One important aspect of fiber optic sensors is related to their lightweight and compact size, which allows them to be easily incorporated in objects or surfaces. Further advantages of OFS include their ability to run long distances, allowing remote operation. Additionally they require low maintenance costs, have negligible ignition risk and are immune to electromagnetic interference. These characteristics led to the implementation of these type of sensors in applications such as aeronautics, robotics, medicine, structural deformation, and so on, [1–4]. One OFS that fits most of these applications is the one capable to measure curvature. Examples of these sensors are fiber gratings, namely: Bragg gratings (FBGs) [1,5–10], long period gratings (LPGs) [11–13], chiral fiber gratings (CFGs) [14] and tilted Bragg gratings (TFBGs) [15]. Fiber optic interferometers, such as: multimode interferometers (MMIs) [16], Mach-Zehnder interferometers [17,18] and Fabry-Pérot interferometers (FPI) [19–21], could also be used.
Despite the wide range of fiber optic technologies, standard single mode fibers (SMFs) are immune to curvature, since the fiber core is located at the central region of the fiber, meaning that it cannot be stretched or elongated during bend conditions. To accomplish the ability to sense bending, the fiber symmetry needs to be broken, and this has been implemented in different ways, such as, shifting the central region of the fiber core [5,13], offsetting fiber splices [17,18], use of multicore fibers (MCFs) [4,6–10,12], packaging multiple SMFs [13], and also, the use of fiber optic technologies that allow asymmetric mode distribution as is the case already explored for LPGs [11], CFGs [14] and TFBGs [15].
Fiber bending sensors can be categorized as one-dimensional or two-dimensional. One-dimensional sensors can only measure positive and negative directions. On the other hand, two-dimensional fiber sensors are able to discriminate the direction in all fiber orientations. Normally these type of sensors are created by placing in series one-dimensional sensors, as is the case found for the use of two orthogonal: TFBGs [15], and LPGs [11]. However, these techniques require precise alignment during the grating inscription and they could be affected by the surrounding refractive index, making them unsuitable to monitor structures that require their embedment. Furthermore, two-dimensional fiber sensors can also be created by placing in-series FBGs, allowing them to be used as a distributed sensor, through the use of optical frequency division reflectometry technology and solving the Frenet-Serret equations [22]. However, the packaging of such FBGs can be challenging and on top of that, the devices normally used to interrogate such sensors are too expensive.
Despite the wide use and opportunities of fiber grating devices, they still require expensive fabrication procedures. On the other hand, fiber optic interferometers are simple to fabricate and have higher sensitivities, keeping other characteristics such as good precision and versatility [23]. One fiber optic sensor found in this category is the FPI. This interferometer is constructed by placing two in-line fiber reflectors separated by a few microns in length. As light travels through the two reflectors, it will suffer multiple reflections, which according to the different phases of each reflected beam, gives rise to an interference spectra, that can be used to measure different parameters through its spectral shift [24,25]. These FPI sensors have been fabricated using a variety of technologies, such as splicing different types of optical fibers, such as, a hollow silica tube between two SMFs [19], formation of hollow cavities by: chemical etching [26], and also by different laser ablation techniques, such as femtosecond lasers and excimer lasers [23]. Depending on each case, these techniques can comprise challenging fabrication process, such as splicing special fibers, the use of dangerous chemicals and finally the use of expensive laser technologies. Recently, we were able to demonstrate an innovative method to fabricate a fiber based FPI sensor using a resin based cold splicing method [24,25,27]. The sensor consists on the use of two 90° cleaved SMF terminals, aligned concentrically through the fiber cladding and longitudinally separated by a cavity length that is filled with a photopolymerizable resin. The technology can be replicated through the use of conventional fusion splicer machines, allowing easier fiber alignment before adding the photopolymerisable resin. The advantages of this fiber sensor are related to its fabrication simplicity, involving low operator skills, its compact size and also its lower cost compared to other fabrication technologies, such as CO2, femtosecond laser and ultraviolet (UV) inscription. These FPI sensors secure enough attractiveness for the monitoring of a variety of parameters, and we have already demonstrated the capability to measure strain, temperature, pressure, humidity and refractive index [24,25,27]. Furthermore, their use has also been recently reported by another group, for bending applications [20]. Despite the interesting results, the sensor is constructed using an SMF, and thus, it can only be used in one-dimensional applications. Moreover, it cannot discriminate between curvature and other parameters and on top of that, the explanation behind the origin of the sensitivity has not yet been described, since the sensor is constructed on the basis of two SMFs concentrically aligned through their claddings.
In this work we will report the fabrication of a two-dimensional curvature sensor based on a resin FPI method. The sensor is built using a 90° cleaved 7-core MCF and SMF terminals, concentrically aligned through the inner core of the MCF, and separated by a 30 µm distance, filled up with a tough photopolymerizable resin. The interrogation is made in reflection through each of the seven cores of the MCF, while the SMF fiber terminal acts only as the second FPI reflector. A numerical modeling of the fiber sensor will be provided, showing that the bend sensitivity is highly dependent on the transversal alignment between the MCF and SMF, as well as on the shape of the resin that composes the FPI cavity. The six outer cores will be characterized to curvature for different fiber orientations, reaching maximum sensitivity values of ∼420 pm/m-1 that were 7 times higher than the values reached for FBG vector bending sensor constructed on a similar fiber type [6]. The bend orientation and curvature amplitude could be reconstructed using the spectral wavelength shifts of any of two off-diagonal outer core FPIs, allowing to average the final bend orientation and curvature amplitude values. Since the central core of the MCF occupies a neutral region it is not affected by the bent imposed on the sensor. Thus, it can be used as a reference for compensation to other unwanted external parameters. To take this parameter into account the temperature response has also been characterized.
2. Working principle
2.1. Fabry-Pérot interferometer sensitivity
The proposed resin based FPI-MCF curvature sensor is composed of an MCF in-series with a SMF. Both fibers were cleaved orthogonally to their lengths and aligned concentrically through their inner cores. The fiber terminals are separated by a distance L, which is filled with a transparent photopolymerizable resin, that is latter hardened with UV light. The schematic of such device is represented in Fig. 1(a), while the cross section of the MCF is shown in (b).
Fig. 1. (a) Schematic of the proposed resin based FPI-MCF directional bend sensor, composed of an MCF on the left, separated by a cavity length L from the SMF terminal at the right, and a photopolymerizable resin with an ellipsoidal shape filling the medium between the two fiber terminals. (b) Cross section of the MCF, showing the curvature vector projected on three diagonal lines, namely for core 1, 2 and 5, for the 1st quadrant.
The Fresnel reflections of the cleaved fiber tip surfaces (I and II), considering normal incidence and a refractive index of ∼1.51 for the photopolymerizable resin and 1.45 for the silica fiber, at the 1.55 µm region, is about 0.04%, being a two-beam interference model suited to mathematically describe the light interactions occurring on the FPI cavity. When a light beam is injected at each of the cores of the MCF shown at the left hand side of Fig. 1, it will be partially reflected at each of the two fiber interfaces, (I) and (II). The two reflections (for each individual core), will be recombined in each core of the MCF, producing an interference reflection spectra showing maxima and minima, that correspond to the constructive and destructive interference. Considering the intensities of the reflected beams as I1 and I2, for the interfaces I and II, respectively, where I1 = I0R1 and I2 = I0-(1-R1)2R2, being I0 the intensity of the initial beam and R1 and R2 the reflection coefficients for the first and the second Fresnel reflections, respectively, the output intensity resultant from the interference can be expressed as [23]:
where (ϕ1 − ϕ2) refers to the optical phase difference between the two beams, and can be described by [23]: where λ is the free-space wavelength and Δ is the optical path difference (OPD), defined as Δ =2nL, being n and L, the refractive index and length of the medium filling the cavity, respectively. The minima intensity in Eq. (1) can thus occur when ϕλ = (2m+1)π, being m = 0, 1, 2…, and thus, the wavelengths correspond to the minima in the interference spectrum will occur when: From this equation, it is clear that the location of the minima in the spectrum, depend on the refractive index and cavity length, and thus, any change in these parameters will lead to a spectral wavelength shift. Considering that the FPI is under an external perturbation (e.g. strain), the phase difference will change, as a result of the induced changes on the refractive index as well as on the physical length of the FPI cavity. As a result, the wavelength shift of an mth dip/peak wavelength can be expressed by differentiating Eq. (3), resulting in [28]:2.2. Strain in a bent optical fiber
To understand the case studied in this work, lets us assume the situation where an optical fiber is fixed in one terminal, while the other is able to move. Initially the fiber is kept straight with a distance L0 separating the fixed and the mobile terminals. Then, the mobile fiber terminal travels a distance Δx in the direction of the fixed fiber terminal. The scenario may be seen on Fig. 2(a) and (b), where the fiber passes from a straight condition to a bent condition, respectively:
Fig. 2. Optical fiber in: (a) straight and, (b) bent condition when the mobile stage moves a distance Δx from its original position. On the right side of the images it is shown an inset of the transversal section of the fiber.
Considering the fiber curvature scenario shown in Fig. 2(b), the curvature (C) of the fiber may be expressed as [29]:
where R is the radius of curvature and L0 is the optical fiber arc length at the neutral axis, given by: being α the bent angle. Furthermore, the optical fiber arc length at a y distance from the fiber central region, can be written as: From these two last equations, we may express the longitudinal strain (ɛz), i.e. along the length of the fiber, as:Equation (9), shows that the strain is zero at y = 0, specifically at the neutral axis, and changes linearly as the magnitude of y increases. Moreover, if we do not consider the absolute value, then we can have either tensile or compressive strain, depending if y is positive or negative, respectively. From the same equation, we may observe that the longitudinal strain increases when the radius of curvature decreases and, is zero when $R=\infty$, i.e. C = 0 m-1.
Considering an MCF sensor configuration shown in Fig. 1(a), and taking into account its transversal cross section representation shown on Fig. 1(b), where each core (i) is positioned θi degrees from the origin, and considering that the fiber is able to change its angular position (θv) related to the curvature direction, we may rewrite Eq. (9) as:
where d is the core to core distance. Replacing Eq. (10) into Eq. (4), it is possible to express the wavelength shift of an mth dip wavelength of the FPI, for each of the 7-cores as:2.3. Bend orientation and curvature reconstruction
The method used in this work consists in measuring the spectral wavelength shift (Δλ) of one of the dips of the interference spectrum, for each of the cores that compose the MCF.
For the reconstruction of the orientation and amplitude of the curvature vector $\vec{C}$, we decide to implement the model developed in [6], due to its simplicity and the low errors achieved. For the sake of clarity, this model will be briefly described here.
When the FPI sensors is subjected to curvature C, the FPI cavities will be subjected to strain (tensile or compressive), leading to a spectral wavelength shift. The relationship is linear and is described as C = Δλ/S, where S is the maximum bend sensitivity. From that, the vector components of the curvature vector, projected on the six outer cores may be expressed as [6]:
The curvature vector $\vec{C}$, can then be reconstructed from the vector components, using positional relationship between the FPIs formed for each core of the MCF. An example of the curvature vector projected on three diagonal lines corresponding to cores 1, 2 and 5, for the first quadrant, may be seen in Fig. 1(b). From the projections, it is possible to find three combinations, namely, (${\vec{c}_1},{\vec{c}_2}$), (${\vec{c}_1},{\vec{c}_5}$) and (${\vec{c}_2},{\vec{c}_5}$), which allow the calculation of the amplitude as follows [6]: where:Furthermore, the corresponding orientation angle can be determined from [6]:
3. Methods
3.1. Fabry-Pérot cavity fabrication
The fabrication of the FPI cavity followed a similar procedure as described in our previous publications, [24,27]. However, due to the different fiber involved (i.e. MCF), some additional fabrication steps have been implemented to accomplish the construction of the sensor.
The MCF used in this work was obtained from Fibercore (SM-7C1500(6.1/125)). It is composed of seven cores, one at the center, and six others disposed in a hexagonal shape. The fiber has an outer diameter of 125 µm and a core diameter of ∼5.7 µm, being the core to core separation equal to 35 µm. The microscope image of the cross section of the MCF used in this work is displayed in Fig. 3(a).
Fig. 3. (a) Microscope image of the seven core fiber. (b) Near-field image obtained during fiber angular position. (c) Picture of the FPI sensor (2X magnification).
The fabrication process started by stripping the acrylate protective cover (∼15 cm) at the far end of the MCF pigtail, and performing a 90° cleavage with a Fujikura CT30A fiber cleaver. The flat fiber terminal will act as the first mirror to each of the cores that compose the MCF-FPI cavity. The fiber end is then positioned in a 2.5° resolution fiber rotator (HFR007 from Thorlabs, Inc.), with its tip located 13.3 cm far from the fiber rotator. Then, the fiber near-field is observed by placing a 50 X objective lens in front of the fiber tip and collecting the output light with a laser beam profiler (Beam On IR1550 from Duma Optronics, Ltd.). With this step, it was possible to rotate the MCF and establish a reference fiber angular position as is shown in Fig. 3(b).
In order to simplify the sensor fabrication process, the second half of the FPI sensor is based on a standard single mode fiber (SMF-28) pigtail, having 8.2 µm core and 125 µm cladding. The acrylate protective coating of the fiber is removed (∼15 cm), and its terminal is cleaved perpendicularly to its longitudinal length with the Fujikura CT30A cleaver. This fiber terminal will act as the second mirror of each of the 7-core FPIs. The terminals of the MCF and SMF are placed in v-grooves that sit on top of a 1 µm resolution xyz translation stage (MBT616D/M from Thorlabs, Inc.). The fibers are aligned through the cladding with the help of two orthogonal cameras that allow real time visualization of the fabrication process. Next, the FPI cavity length is adjusted by performing a longitudinal 30 ± 1 µm displacement related to the MCF. This distance allows to obtain a free spectral range suited to track the dips/peaks of the FPI interference fringes with good resolution. Furthermore, it is small enough to maintain the robustness of the sensor. The fine transversal alignment of the fibers is performed by injecting laser light at the central core of the MCF and measuring the output power at the SMF far end. This allowed to precisely align the fibers based on the optimization of the maximum power transmitted through the fibers. Finally, a drop of a UV clear liquid resin is carefully placed un between the fibers. The liquid resin takes an ellipsoidal shape due to the surface tension that acts between the resin and the silica fibers. The photopolymerizable resin is later UV hardened with the help of an Opticure LED200 from Norland Products. A microscope image of the cavity, measuring ∼330 µm and 600 µm for the transversal and longitudinal axes, respectively, is shown in Fig. 3(c).To finalize, the far end of the SMF is cleaved with a ILSINTECH CI-08 fiber angled cleaver, with an 8° angle, at a distance of ∼15 cm from the FPI cavity, allowing to prevent Fresnel reflections that may deteriorate the interference signal of the FPI cavity. This, gives also enough fiber length to perform the characterizations.
The measurement was done in reflection, using a four port interrogator (SM-125 from Micron Optics). To easily measure each of the 7-cores of the MCF, each In/Out port of the interrogator was connected to a (1 × 2) optical switch, that is linked to the output ports of an MCF fan In/Out, as is represented on the scheme shown in Fig. 4(a). For each curvature, it is required the acquisition of two data files, one corresponding to the reflection spectra of core 1, 2, and 3 and the other one corresponding to the reflection spectra of core 5, 6 and 7, being core 4 acquired in both files. An example of the FPI reflection spectra collected for the first set of cores (namely, 1, 2 and 3), after the cavity fabrication may be seen in Fig. 4(b).
Fig. 4. (a) Schematic of the MCF-FPI interrogation system. (b) Reflection spectra obtained for the FPIs formed in core 1, 2 and 3.
3.2. Vector bending characterization
The bend characterization was done by placing the fiber rotator containing the MCF, (now attached to the SMF through the photopolymerizable resin), in a setup designed to perform the bend characterizations. For that, the SMF terminal was clamped on another fiber rotator, at a distance 26.6 cm from the MCF clamped terminal. During the characterization, one fiber terminal is kept fixed, while the other is mounted on a 0.1 µm resolution motorized linear stage (MFA-CC, from Newport). The schematic of the vector bend characterization setup is displayed in Fig. 5.
Fig. 5. Directional bend characterization setup of the MCF-SMF resin based FPI cavity. The inset on top shows how the cores sitting along the same diagonal line, are being compressed or elongated. The inset on the bottom shows the cross section of the fiber with the corresponding curvature vector.
The bend characterizations were made by moving the linear stage in steps of 2 µm, ranging from 0 up to 24 µm, allowing to impose curvatures up to 6.4 m-1. For each curvature step, the reflection spectra were collected. The bend characterization was performed for each fiber orientation, by simultaneously adjusting the rotary fiber holders in steps of 15°, ranging from 0 to 360°.
4. Results and discussion
4.1. Numerical modeling
The strain observed in a homogeneous symmetric structure under a bend condition can be easily estimated from Eq. (9). However, the occurrence of imperfections during the fabrication process of the MCF-SMF resin based FPI, can lead to asymmetries that inevitably give rise to a non-uniform strain distribution along the FPI cavity region. Examples of these imperfections could be associated to the fiber to fiber transversal misalignments, that could be imposed by the errors of the instruments used to construct the FPI and also due to human errors. Further asymmetries on the fiber sensor may also arise from the cavity shape before the UV hardening process, due to the gravity forces that act on the liquid resin prior to the hardening process (expected for high volume resin droplets), leading to a shift of the ellipsoidal shape resin in the direction of the gravity force. Nonetheless, the FPI used in this work is composed of two different materials, namely silica and photopolymerizable resin which have different mechanical properties. Thus, the strain involved in each part of the sensor can vary, depending on the fiber sensor region. Based on these assumptions, it is our intention to analyze the strain distribution when the fiber sensor is subjected to a bend condition. For that, we perform a numerical study using the structural mechanics module of the COMSOL Multiphysics software.
The model consists of two cylindrical rods positioned along the same longitudinal axis (xx), with a length of 0.5 mm each and a diameter of 125 µm. These rods are intended to reproduce the silica optical fibers, being the distance between the fiber terminals set to 30 µm. The system also includes an ellipsoid, mimicking the photopolymerizable resin that surrounds the two fiber terminals. This has a major and minor axis of 350 µm and 250 µm, respectively and is centered at the middle region of the two fiber terminals. The chosen dimensions were hypothetical for a typical resin based FPI cavity, since the relevant information to take from this simulation is related to the strain distribution along the radial position of the fiber terminals and not on the strain value related to the size of the cavity. The ellipsoid material was defined as acrylate polymer, to simulate the photopolymerizable resin that composes the FPI cavity, while the cylindrical rods were defined as glass. In order to curve the fiber sensor, the left-hand side fiber terminal is kept fixed, while the opposite terminal is only able to move along the longitudinal axis. Furthermore, a force with 1.5 N/m2, is applied perpendicular to the top surface of the fibers and ellipsoid, along the zz direction. After performing the simulation, the FPI sensor acquires a curved shape, with a curvature value equal to C ≈ 3.8 m-1. To analyze asymmetries related to the imperfections, we have considered two other configurations, namely the fiber transversal misalignment: by shifting the silica rod on the right either, upwards and downwards; and offsetting the center of the ellipsoid cavity relative to the concentric aligned fiber terminals, by shifting transversally both rods, upwards and, downwards, mimicking a cavity shape distortion. The fiber transversal displacement was set to 20 µm for all the asymmetric cases. The deformed 2D strain results obtained for the FPI sensor considering the symmetric and the four asymmetric cases, are displayed in Fig. 6(a)-(e), for the longitudinal plane (xz plane) and for the transversal plane (yz plane), located at the center of the cavity. As is observed, the strain is symmetrically distributed when the whole system (fibers and resin based ellipsoid), are symmetrically positioned, while stronger color asymmetries are observed when the fibers suffer transversal misalignments, either for the transversal shift of the right fiber as well as when both fibers are both transversely shifted related to the resin based ellipsoid.
Fig. 6. ((a)-(e)) 2D strain results (absolute value), obtained for the longitudinal plane (xz plane), and for the transversal plane (yz plane). The sensors under study are: (a) fibers concentrically aligned, and, ((b)-(e)) fiber misalignments, namely by performing a 20 µm transversal shift (zz direction) to the: right fiber, either (b) upwards and (c) downwards; and both fibers (d) upwards and (e) downwards. The circle shown on the bottom images represent the left-most fiber (In/Out fiber (MCF)). The results presented in (f), correspond to the strain along a vertical line passing at the middle region of the cavity.
For the symmetric case, the results reveal that the strain is zero at the center of the fibers and increases to its periphery. Thus, the central core of the MCF, will be insensitive to curvature and in theory will not respond to it, contrary to the cores located at the periphery, that can respond to the curvature imposed on the fiber with the same magnitude (considering the cores along the same diagonal line). These results are in agreement with Eq. (9).
For the cases where the symmetry is broken, the results show that the strain is asymmetrically distributed, leading to have non-zero strain values at the central region of the In/Out fiber. These results show that an FPI cavity constructed on the basis of two SMF terminals can in fact respond to curvature if asymmetries (i.e. from imperfections or intentionally introduced) are present on the fiber sensor. These results explain why the sensors reported in Refs. [20,21], are able to measure curvature. Furthermore, these results also show that an FPI sensor constructed on a basis of an MCF-SMF (as is the case in this study), will have a central core able to respond to curvature. However, this could be a disadvantage for applications where this core is intended to be used as a reference for the discrimination of unwanted parameters, such as temperature [6]. For such particular case it is mandatory that all the parts involved on the fiber sensor are symmetrically arranged.
In order to better understand the results presented in the 2D strain results, shown in Fig. 6, the strain was measured along a line parallel to the zz axis and coincident with the cavity middle region. The results are shown Fig. 6(f).
As is shown in Fig. 6(f), the strain obtained for the symmetric FPI sensor, is zero at the central axis of the In/Out fiber and increases to the periphery. Regarding the asymmetric cases, the center of symmetry is shifted related to the In/Out fiber, and because of that, the strain reaches non-zero values at the center of the In/Out fiber. Furthermore, this also leads to have strain intensities unequally distributed, creating strain more pronounced in one region compared to the one diametrically opposed (see the discrepancy between the strain values for the ±35 µm region, at the dashed grey line, (corresponding to the distance of the cores in the MCF)). Because of this, and taking into account Eq. (9), the wavelength shifts observed for each of the diagonal cores will be highly dependent on the fiber transversal misalignments as well as on the cavity shape. Thus, careful preparation of the sensors needs to be given in order to get a sensor with similar responses along the same diagonal line. However, we stress out that even if discrepancies between the responses occur, the sensors ability to reconstruct the curvature amplitude and orientation is not compromised, as far as the temperature compensation is ensured by other means.
4.2. Curvature characterization
The reflection spectra of all the 7-core FPI cavities were collected for each curvature step. As an example, we show the spectra results collected for three cores siting along the same diagonal line, namely for core 1, 4 and 7, regarding the curvatures of 0.0 m-1 and 6.4 m-1, and for θv = 0°. The results may be seen in Fig. 7(a), (b) and (c), respectively.
Fig. 7. (a) Reflection spectra of the 7-core FPI sensor for the cores sitting along one of the diagonal lines of the MCF, namely, (a) core 1, (b) core 4 and (c), core 7. The spectra were taken for θv = 0° and C = 0.0 m-1 and 6.6 m-1.
As is shown in Fig. 7(a) and (c), the spectra of core 1 and core 7 are blue- and red-shifted with increasing curvature, respectively. The results indicate that the FPI cavities corresponding to each of the cores are being compressed and elongated, respectively. However, the spectra shown in Fig. 7(b), obtained for core 4, (i.e. the core at the central region), does not show any wavelength shift. The results are in accordance with the numerical analysis and in agreement with Eq. (10), since core 4 is at the neutral region, while core 1 and core 7 are shifted +35 µm and -35 µm from that region, respectively.
In order to verify the dependence of the FPI wavelength shifts with the applied curvature, we measured the wavelength shift of the central dip of each spectrum at the region between 1530 nm and 1550 nm, for all the cores, at each curvature and fiber orientation. In Fig. 8(a)-(f), we show the wavelength shifts as function of curvature for all the 7-core FPI cavities, for four different fiber orientations, namely for: θv = 0°, θv = 15°, θv = 45°and θv = 60°, respectively.
Fig. 8. Dip wavelength shift as function of curvature for all the 7-core FPIs, regarding the fiber orientations of (a) 0°, (b), 15°, (c) 45° and (d) 60°. A linear fitting for the results of each FPI-core and the correspondent calculated sensitivities is also presented.
The results observed in Fig. 8, indicate that depending on the fiber orientation, both positive and negative wavelength shifts are observed for each of the 6 outer cores of the MCF-SMF resin based FPI sensor. Considering for instance the case when θv = 0°, found in Fig. 8(a), the FPIs corresponding to core 5, 6 and 7 are in compression, while the ones for core 1, 2 and 3 are being stretched, showing thus, a negative and positive wavelength shifts, respectively. From theory and considering that the FPI cavity is perfectly symmetric, core 1 and core 7 are at 35 µm from the neutral region, so, they should have the highest sensitivities and at the same time be equal in magnitude. The obtained values were 420 ± 4 pm/m-1 and -418 ± 3 pm/m-1, respectively, which are similar in magnitude. Furthermore, these sensitivities are 7 times higher than the ones reached for two dimensional vector bending sensor based on FBGs [6], and is 6 times higher than the ones reached for one dimensional sensors using FPIs fabricated with a silica capillary tube [21]. Considering now other cores along other diagonal lines, as is the case for core 2 and core 3 as well as core 5 and 6, the sensitivities achieved were equal to 214 ± 4, 203 ± 3, -215 ± 3 and -218 ± 6 pm/m-1, respectively, which were lower in magnitude than the ones obtained for core 1 and core 7 as expected, since they are located at a distance: d.cos(60°) < d. Furthermore, their magnitudes were all similar with few discrepancies, proving that the fiber sensor response is in agreement with theory. Finally, the remaining core, i.e. core 4, which sits at the neutral region, presents an insensitive response upon curvature. As can be seen in Fig. 8, when the fiber orientation θv changes, the response of each core also changes according to the strain at each core radial position (see Eq. ((10)). Looking to Fig. 8(d), where θv = 60°, we may observe that this fiber orientation corresponds exactly to the one found in Fig. 8(a), but, with the core numbering at different positions. Thus, taking the same logic described before, core 3 and 5 should have similar amplitudes, and based on the assumption that the whole sensor is symmetric, their sensitivities should be similar to the ones found for core 1 and 7 (θv = 0°). The results revealed values of 423 ± 6 pm/m-1 and -407 ± 5 pm/m-1 for core 3 and 5, respectively, which reveals slight differences between both and also between core 1 and 7. This small differences could be related to fiber misalignments as reported on the numerical section results.
In order to better visualize the FPIs response we represent the curvature sensitivities reached for all the seven cores as function of the fiber orientation, either in polar and cartesian coordinates. The results are shown in Fig. 9(a) and (b), respectively.
Fig. 9. Curvature sensitivity as function of the fiber orientation in, (a) polar and, (b) Cartesian coordinates. The results presented in these graphs had a 4° correction due to the low precision reached through the near-field alignment. The lines passing through the markers in (a) are used as a guide, while the lines in (b) represent the fitting curves.
As is shown in Fig. 9(a), the angular dependence of the bend sensitivities for the six outer core FPI cavities, show an “8”-shaped pattern with low drifts, which are associated to the fine measurement errors taken during the characterizations. It is worth to mention that the results presented on Fig. 9 had a 4° correction in order to compensate for the errors taken during the near-field alignment process performed in the fabrication step. As it is observed in polar and cartesian coordinates, each core reaches its maximum curvature sensitivity at every 180°, presenting all of them similar absolute sensitivity values. Furthermore, at every 60° two cores sitting along the same diagonal line, present maximum amplitude sensitivities due their alignment with the curvature vector. Moreover, they also reach sensitivities close to zero, when they are orthogonal to the bending vector.
In order to know the maximum bend sensitivities Si, taking into account the 4° correction, we fitted sine curves to the experimental data points found in Fig. 9(b), achieving values of: 421.0, 409.3, 432.6, 426.6 and 422.2 pm/m-1, for core 1, 2, 3, 5, 6 and 7, respectively.
In order to test the performance of the system, we collect a set of spectra for different curvature and fiber orientations. The reconstruction of the curvature amplitude and direction was tested based on the wavelength shifts attained for all the cores sitting on the periphery of the MCF and using Eq. (12) to Eq. (21) Note that the calculated values are averaged over a total of 12 combinations. The actual values and reconstructed values are shown in Fig. 10(a) and (b), respectively.
Fig. 10. Reconstructed and actual values for different fiber orientations (a) and curvature amplitudes (b).
Figure 10(a) and (b) show that the reconstructed curvature amplitude and direction values are close to each other. The percentage error reached for both parameters was lower than 4%, showing high accuracy and good reliability of the method for the reconstruction of the directional curvature and amplitude. Furthermore, the values were similar to the ones found for 7-core FBG fiber sensor technology [6] and lower than the errors found for other technologies using 7-core fibers, namely, Brillouin [31].
In order to know the maximum curvature amplitude that the sensor could reach we did a theoretical calculation based on the maximum strain (ɛtot) that the sensor can sustain. To do that, and taking into account that the sensor is composed of two materials, and thus, different strain distributions (see Fig. 6(a)-(e)), we have used the equation deduced in [32], which can be written as:
Considering the maximum sensitivity reached experimentally by the sensor (∼420 pm/m-1), and taking into account the estimate taken for the maximum curvature (∼20 m-1), we were able to calculate a maximum dip wavelength shift of ∼8.4 nm. This value is well below the free spectral range of the sensor (∼20 nm, see Fig. 7(a-c)). Therefore, the sensor is able to operate without concerns related to spectral overlap.
4.3. Temperature characterization
Since the central core FPI sensor shows an almost insensitive response when subjected to curvature, as is observed in Fig. 8 and Fig. 9, this brings the opportunity to make the sensor insensitive to unwanted external parameters, such as temperature. To do that, one possibility could be by simply subtracting the wavelength shift of the cores found in the periphery (that respond to both curvature and temperature), to the wavelength shift observed for the central core. Yet, this can only be performed if the temperature response of all the FPI-MCF cores is equal. In order to check this, we decide to perform a temperature characterization. For that, we placed the sensor in a climatic chamber (Angelantoni CH340), with 0.3 C accuracy. The characterization was swept from 22 to 30 °C, in steps of 2 °C, giving 30 minutes’ stabilization between steps, before signal acquisition. The results of the dip wavelength shift for all the FPIs are shown in Fig. 11.
Fig. 11. Dip wavelength shift as function of temperature for all the 7-core FPIs. The lines are the linear fits of each FPI-core. The corresponding linear sensitivities are also presented.
As is seen in Fig. 11, the dip wavelength shift of each of the 7-core FPIs, follows a linear tendency with the temperature, and is similar to all of them, reaching values ranging between 176 ± 4 pm/°C and 134 ± 4 pm/°C for core 2 and 6, respectively and155 ± 4 pm/°C for the central core. The maximum difference in sensitivities related to the central core is about 21 pm/°C, which considering the proposed methodology (subtracting the wavelength shifts of the periphery to the one of the central core), could introduce errors on the reconstruction of the curvature amplitude and direction, mainly for large temperature variations. To avoid this issue, we proposed to calculate the temperature using the sensitivity of the central core, and then, the sensitivities of the cores found in the periphery, should be used to calculate their corresponding temperature wavelength shift needed to be discounted to each of the FPI-MCF cores. Using this approach, the sensor could operate insensitive to temperature enabling to reconstruct the orientation and amplitude of the curvature, and keeping the opportunity to simultaneously measure temperature.
5. Conclusion
In this work we have developed a two-dimensional vector bending sensor based on a resin based Fabry-Pérot cavity formed between the tip of a 7-core MCF and a SMF. Theoretical results reveal that the sensor response is dependent on the symmetry of the parts involved in the fiber sensor, showing that for a symmetric structure, a symmetric strain response over the cores siting in the periphery is expected, together with an insensitive response for the central core, which allow the sensor to operate free of external unwanted parameters. Experimental results reveal that the sensor behaves as predicted, showing a negligible response by the central core and curvature sensitivities for the outer cores close to each other and higher than 400 pm/m-1, which were 7 times higher than the ones found for FBGs in similar MCFs. The reconstruction of the orientation and amplitude of the curvature vector were tested for a set of values for all the four quadrants, showing percentage errors lower than 4%, which demonstrates the accuracy the reliability of the method. This achievement is related to the multiple reconstructions (12 combinations), allowed by the 6 outer cores present in the fiber. This allows to average the values and reach good performances. The errors showed in this work are similar to the ones found in [6], however, the technology needed to fabricate the proposed FPI cavities is much simpler than FBG fabrication. Finally, we have also shown the possibility to use the sensor insensitive to external parameters, such as temperature.
The results presented in this work could find potential applications in two-dimensional vector bend sensing applications, such as the ones found in robotic arms. We believe that this work could be also interesting for the development of fiber shape sensors, namely by using in series FPI cavities and reconstructing the shape through the use of the phase shifts associated to each cavity of the cores of the MCF [33]. In such scenario, the number of sensors would be limited by the available power of the optical source, the sensitivity of the receptor and the losses associated to each FPI cavity. For the last, and considering negligible loss due to the Fresnel reflections, we just consider the fiber to fiber displacement losses [34] (UV resin as the filling medium), which for the present case is less than 1 dB for cavities with L ≤ 30 µm. Thus, for such configuration, a reasonable number of sensors, would be to consider less than 10 concatenated FPI cavities. Therefore, this makes a convincing technology for short range fiber shape sensing applications.
Funding
Fundação para a Ciência e a Tecnologia (contract program 1337, FOPEComSens (PTDC/EEI-TEL/1511/20), MCTechs (POCI-01-0145-FEDER-029282), UIDB/50008/2020-UIDP/50008/2020).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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