System for measuring microbending and arbitrary microdeformation along a three-dimensional space

Abstract

A system for sensing microbends and microstrains in three-dimensional space, the system being based on a distributed length optical fiber formed to include a set of offset cores deployed in a helical configuration along the length of the optical fiber, each core including a fiber Bragg grating exhibiting the same Bragg wavelength. Microscale local deformations of the multicore fiber produce local shifts in the Bragg wavelength, with the use of multiple cores allowing for a complete microscale modeling of the local deformations. Sequential probing of each core allows for an optical frequency domain reflectometry (OFDR) implementation of the reconstruction of a given three-dimensional shape, thereby delineating the location and size of various microbends and microstrains.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional Application No. 62 / 989,117, filed March 13, 2020, which is incorporated by reference herein. TECHNICAL FIELD

[0003] The present invention relates to a fiber-optic based distributed sensor, and more particularly to a multi-core fiber based sensor capable of detecting the presence of microbends along a given fiber’s extent, thereby providing three-dimensional information about the location and size of various deformations within the space surrounding the distributed sensor. BACKGROUND

[0004] Fiber-optic based distributed sensors have become a valuable tool for performing the characterization of arbitrary deformations in three-dimensional space. Potential applications include 3D printing, surgical catheters, smart wearable devices, fuel tank monitoring systems, composite structures, etc. The use of optical fibers for “shape sensing” offers high precision and high speed operation, and can be particularly suitable for characterizing surfaces and environments that are difficult to access due to the built-in shielding of the optical beams used as sensing probes.

[0005] To date, fiber-optic based distributed sensors have only been able to reconstruct arbitrary paths and shapes at the “macroscopic” level (i.e., in terms of measurements, on the centimeter / meter scale). Looking forward, the ability to perform distributed sensing at smaller scales (i.e., sub-millimeter variations / bends) will become increasingly important. For example, the effect of microbends on the attenuation of optical communication signals propagating along a transmission fiber has been of concern for decades. As transmission losses in optical fibers approach the fundamental limit dictated by inherent absorption and scattering in the glass, losses caused by microscopic physical bends in the fiber (and cable) become increasingly important. However, currently available sensors are not capable of directly measuring such microbends. SUMMARY

[0006] The present invention addresses the remaining needs in the art, and relates to a multi-core fiber based sensor capable of detecting the presence of microbends along a given fiber’s extent, thereby providing three-dimensional information about the location and size of various deformations within the space surrounding the distributed sensor.

[0007] In accordance with the principles of the present invention, the ability to “reconstruct” micro-deformations distributed along the length of an optical fiber is provided by a system based on using a twisted multi-core fiber to probe the distributed reflections of light within the multiple waveguide cores. The fiber cores are formed to include successive fiber Bragg gratings (FBGs) that all exhibit the same Bragg wavelength. Micro-scale local deformations of the sensing fiber produce local shifts in the Bragg wavelength, with the use of multiple cores allowing for a complete modeling of the bends at a particular location.

[0008] In one example embodiment, the present application takes the form of a distributed system for sensing and measuring the distribution of microbends and microstrains in three-dimensional (3D) space that utilizes a multicore sensing fiber in combination with an optical backscatter reflectometer. In particular, the multicore sensing fiber is formed to include a plurality of offset cores radially spaced from a center of the multicore sensing fiber by an amount R o and a plurality of contiguous fiber Bragg gratings (FBGs) inscribed in the plurality of offset cores in a one-to-one relationship. The set of FBGs is formed to reflect light at a common Bragg wavelength λ Bragg The optical backscatter reflectometer includes a tunable laser source for generating a swept wavelength output beam spanning a wavelength range around λ Bragg An optical beam splitter / combiner, an optical detector, and a Fourier transform analyzer for performing optical frequency domain reflectometry (OFDR). The optical beam splitter / combiner is used to split the swept wavelength output beam from the tunable laser source into a swept wavelength "probe" beam directed into the multicore sensing fiber and a swept wavelength reference beam directed into a reflector. The optical beam splitter / combiner is also used to combine a swept wavelength return beam from the multicore sensing fiber and the reflected swept wavelength reference beam to create an interfering FBG sensing beam. The optical detector creates an electronic version of the interfering FBG sensing beam in response to the interfering FBG sensing beam, and the Fourier transform analyzer is then used to perform a Fourier transform on the electronic version of the interfering FBG sensing beam to generate measurements of local variations in the Bragg wavelength along the length of the multicore sensing fiber and thereby reconstruct the shape of the three-dimensional space.

[0009] While the sensor fiber can be formed of conventional glass materials, other embodiments can utilize a sensor fiber formed of a material that is less elastic, having a smaller Young's modulus, thereby allowing for finer measurement resolution.

[0010] Other and further embodiments and features of the present application will become apparent during the course of the following discussion and by reference to the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0011] Reference is now made to the drawings wherein like reference numerals are used to designate like parts throughout the various views:

[0012] Figure 1 is an isometric view of a section of a twisted multicore fiber for use as a multicore sensing fiber in accordance with the present application;

[0013] Figure 2 is an end view of the multicore sensing fiber of Figure 1 ; and

[0014] Figure 3 is a block diagram of an example system for sensing and measuring strains in a three-dimensional space associated with a location of the multicore sensing fiber; and

[0015] Figure 4 is a magnified cross-sectional view of a bend location along the multicore sensing fiber, illustrating both compression and expansion between the various offset cores;

[0016] Figure 5 is a plot depicting the reduction in standard deviation in fiber shape measurement as the number of measurements taken is reduced; and

[0017] Figure 6 illustrates the improvement in shape reconstruction associated with performing multiple measurements, wherein Figure 6 (a) is a photographic reproduction of a loop of a multicore sensing fiber, Figure 6 (b) is a reconstruction based on a single measurement, and Figure 6 (c) is a reconstruction based on a set of ten independent measurements. DETAILED DESCRIPTION

[0018] Figure 1 is an isometric view of an exemplary twisted multicore fiber 10 according to the principles of the present invention, which can be used to perform sensing of microbends (and, in general, various other micro deformations) in three-dimensional space. Figure 2 is Figure 1 an end view of the fiber 10, specifically illustrating the placement of a set of offset cores within the multicore fiber 10. In this embodiment, the multicore fiber 10 utilizes a set of six cores 121-126, all of which are radially offset from the center C of the fiber 10 by the same amount (R o ). As shown, the cores are equally spaced from one another, with the set of six cores resulting in an angular displacement Θ of 60° between adjacent cores.

[0019] As best shown in Figure 1 , the sensing cores 12 are in a helical pattern along the length of the multicore fiber 10 (hence, the reference to "twisted" in describing the design of the sensing fiber 10). Such a fiber can be formed during the process of drawing an optical preform into a fiber, with the preform being continuously rotated, resulting in the offset cores 12 spiraling around the central axis of the fiber at a constant "twist frequency" that can be characterized as the number of turns per meter. The defined spatial twist period, denoted Λ s in Figure 1 , is thus formed.

[0020] Each offset core 12 i is formed to include a succession of FBGs 14 i , which can be written into the core during the process of drawing the preform into the final fiber. Each FBG 14 i is created to exhibit the same Bragg wavelength λ Braggsuch that they all reflect the same wavelength of light without any local bending or distortion that would otherwise produce a shift in the Bragg wavelength value.

[0021] Figure 3 An example distributed shape sensing system 100 is illustrated that utilizes a multicore sensing fiber 10 Figure 1 and Figure 2 The system 100 includes an optical backscatter reflectometer (OBR) 20 that utilizes optical frequency domain reflectometry (OFDR) measurements in a manner described fully below to ascertain the presence of micro deformations along the multicore sensing fiber 10, providing detailed information about their location and shape. The ability to collect measurements from multiple offset cores 12 at any lateral position along the extent of the multicore sensing fiber 10 provides the resolution necessary for highly accurate sensing of microbends in the fiber.

[0022] The OBR 20 itself includes a tunable laser source 22 configured as a swept wavelength (frequency) source centered on the Bragg wavelength (λ Bragg ) of the FBGs 14. In one example embodiment, the tunable laser source 22 can be configured to provide a narrow linewidth output that sweeps through a wavelength range of ±10 nm on either side of λ Bragg (i.e., a 20 nm wavelength range). For example, if λ Bragg = 1541 nm, then the tunable laser source can be configured to provide an output beam that scans over a 1531 nm to 1551 nm wavelength range. The 20 nm tunable bandwidth is merely exemplary, and there are situations where a greater bandwidth can be desirable, as discussed below.

[0023] The output beam from the tunable laser 22 is then passed through a beamsplitter 24 of the OBR 20 that directs a majority of the beam (sometimes referred to as a "probe beam" or "probe signal") out of the OBR 20 and into a 1xN optical switch 30. The switch 30 is controlled to direct the probe beam to a selected offset core 12 i of the multicore sensing fiber 10 in a manner described in detail below.

[0024] Returning to the description of the OBR 20, the remaining output from the beam splitter 24, sometimes referred to as the "reference beam", is directed along a reflected signal path 26. The reflected reference beam and backscattered reflections from the multicore sensing fibre 10 are combined within the beam splitter 24 (operating as a combiner in this direction) to direct the interference combination of these signals to an optical detector 28 included within the OBR 20. The output from the optical detector 28 is then applied as input to a Fourier analyser 29 which performs a frequency domain analysis to convert the frequency domain measurements from the optical detector 28 into spatial domain measurements of phase and amplitude as a function of length along the multicore sensing fibre 10.

[0025] If the multicore sensing fibre 10 is flat and straight, with no microbends (or other types of micro deformation), then the FBGs 14 will all maintain the reference Bragg wavelength λ Bragg and will always reflect the probe beam light at only that wavelength, allowing the remaining wavelengths to continue to propagate along the multicore sensing fibre 10. Thus, since λ Bragg is unchanged, so too is the frequency component of the output from the optical detector 28. Thus, the Fourier analyser 29 provides a constant linear output signal which is indicative of an "unperturbed" multicore sensing fibre 10. Once there is any microbend / deformation within the fibre 10, the Bragg wavelength of one or more of the offset cores 12 will change (see discussion below of Figure 4 ), and the output from the Fourier analyser 29 will contain a set of peaks associated with the microbends. The output from the Fourier analyser 29 can be considered as the output sensing signal from the OBR system 20.

[0026] Thus, in accordance with the principles of OFDR, by illuminating each of the offset cores 12 i with a probe beam scanned across a defined wavelength range, the deformations / microbends along the multicore sensing fibre 10 will be identified within the interference signal processed by the Fourier analyser 29. That is, by performing a Fourier transform on the interference beam, the spectral information can be used to detect and measure micro deformations along the multicore sensing fibre 10. The Fourier transform converts the spectral information in the received interference signal into spatial (temporal) information, in the form of a distributed Bragg wavelength which varies at locations where there are microbends / deformations.

[0027] The Fourier relationship reverses the wavelength scan range of the tunable laser source 22 with the longitudinal spatial domain measurement of strain (and hence curvature and shape). For example, a 20 nm wavelength scan range translates to a 40 pm measurement resolution. Increasing the wavelength scan range to 80 nm (still centred on the defined Bragg wavelength) translates to a 10 pm resolution in local microbend measurement, although at the cost of requiring a tunable laser source 22 capable of generating such a large swept wavelength range.

[0028] Continuing the description of the components of system 100, as mentioned above, the tunable probe beam exiting OBR 20 is provided as an input to a lxN optical switch 30. Optical switch 30 includes a single input / output port 32 and a plurality N of connection ports 341-34 N , each connection port 34 i is associated with a unique offset core 12 i . The plurality N of outputs from optical switch 30 are coupled into a plurality of separate optical fibers 381-38 N , which are associated in a one-to-one relationship with offset cores 121-12 N . The distal end of multicore sensing fiber 10 is immersed in an index-matching gel 50 to suppress undesired Fresnel reflections at the distal face of fiber 10 from re-entering one or more of the plurality of offset cores 12.

[0029] Figure 3 An exemplary arrangement for coupling the outputs from optical switch 30 to multicore sensing fiber 10 is also illustrated. In particular, Figure 3 the use of a tapered fiber bundle (TFB) 40 is shown to provide efficient optical coupling between fibers 38 (from optical switch 30) and the offset cores 12 of fiber 10. In accordance with the known principles of operation of a given TFB, TFB 40 is used to reduce the overall diameter of the "bundle" of input fibers 38 to match an output taper 42 (as shown in Figure 2 , as described above) of the end face of multicore sensing fiber 10. Output taper 42 is oriented so that the core region of each fiber 38 is aligned with one separate offset core 12. That is, the cross-sectional geometry of the output end face 44 of TFB 40 matches that of the end face of multicore sensing fiber 10, as shown in Figure 2 . The use of TFB 40 allows the probe signal to be launched efficiently into multicore sensing fiber 10 and the backscattered signal from multicore sensing fiber 10 to be collected.

[0030] System 100, as shown in Figure 3 , is used to identify microbends along multicore sensing fiber 10 by the local asymmetric stress induced within the fiber cross-section at a given location of microbend B. Figure 4 is a magnified cutaway isometric view of multicore sensing fiber 10 at a particular location B where it is experiencing deformation. This particular bend causes core 122 to be compressed and thus reduce the spacing between adjacent gratings in FBG 142. In accordance with the known properties of Bragg gratings, this reduction in grating period also reduces the Bragg wavelength experienced by FBG 142. Core 123 is not affected by this bend because it is located at the neutral plane of fiber 10 (as shown in Figure 4As shown in the diagram, the Bragg wavelength of FBG 143 remains constant. The core 124 undergoes expansion at this bend, which widens the space between adjacent gratings forming FBG 144, thereby reducing the grating period and Bragg wavelength of FBG 144.

[0031] By using optical switch 30, a swept wavelength probe beam sequentially illuminates each individual offset fiber core 12. i The variation in the Bragg wavelength associated with a specific fiber core at a given lateral position thus allows for the reconstructing of the type of shape deformation. That is, including switching capabilities within system 100 allows data to be collected sequentially from multiple offset fiber cores 12 to obtain the cross-sectional deformation at selected locations along fiber 10. Repeating this process along the range of the multi-core sensing fiber 10 allows for the complete reconstruction of various microbending (and other types of deformation) occurring along its span.

[0032] Once the Fourier analyzer 29 has completed all measurements, the associated distributed curvature and shape of the three-dimensional space can be determined by, for example... Figure 3 The reconstruction module 27, coupled to the output of the Fourier analyzer 29, is created as shown. The distributed curvature of the multi-core sensing fiber 10 is a vector κ(z), whose phase provides information about the direction of local microbending, which helps to reconstruct the distributed shape of the multi-core sensing fiber 10. Generally, the space-dependent curvature κ(z) depends on the local strain and the geometry of the offset core 12, where

[0033]

[0034] Where R o It is the center of fiber 10 and the offset core 12 u The radial offset between the centers, u defines the individual fiber core, ρ u (z) is the corresponding fiber core 12 u The unit vector, and ε u (z) is in the corresponding fiber core 12 u The strain induced in the glass. The strain optical coefficient η (~0.78) of the silicon glass and the Bragg wavelength Δλ recorded using a Fourier analyzer 29. Bragg The measured local changes, and the corresponding local strain ε experienced by the fiber core u. u (z) can be defined by refactoring module 29 as follows:

[0035]

[0036] By using optical switch 30, each offset fiber core 121-12 is illuminated sequentially. NStrain information from the plurality N (e.g., N = 6) offset cores 12 is added within the reconstruction module 29 in a manner shown in the definition of the spatially dependent curvature K(z) to develop both the magnitude and phase of the distributed fiber curvature. The bend direction along each curve of the multicore sensing fiber 10 is represented by the phase portion of the curvature. It should be appreciated that the number of individual offset cores 12 included within the multicore sensing fiber 10 directly impacts the accuracy of the calculated distributed curvature, with an increased number of offset cores increasing the amount of data captured and recorded by the Fourier analyzer 29.

[0037] Finally, the distributed shape S of the deformed fiber can also be provided as an output from the reconstruction module 27. In particular, the distributed shape is reconstructed from the calculated spatially dependent curvature K(z) using the Frenet-Serret equations, which are a set of differential equations that describe a three-dimensional (3D) curve, to provide the distributed shape output from the module 27. Specifically, the Frenet-Serret equations relate the local shape parameters including tangent T(x,y,z), normal N(x,y,z), and binormal B(x,y,z) vectors to the fiber curvature and torsion measured at closely spaced locations. Mathematically, this is expressed as:

[0038]

[0039] where S≡ [T(x,y,z); N(x,y,z); B(x,y,z)], and the torsion τ(z) quantifies how quickly the bend direction changes along the length of the curved fiber. In practice, the spatial derivative of the phase component of the distributed curvature vector leads to the torsion quantity τ(z) (= dθ b (z) / dz) produced along the length of the multicore sensing fiber 10. By repeatedly solving this expression for the eigenvalues and eigenvectors of the set S along the length (z-axis) of the multicore sensing fiber 10, the distributed shape of the fiber can be estimated.

[0040] It is important to note that the initial conditions for solving the above expression assume that there is no curvature and torsion at the location z = 0, i.e., K(0) = τ(0) = 0 at the input end of the multicore sensing fiber 10. Furthermore, the tangent T(x,y,z), normal N(x,y,z), and binormal B(x,y,z) vectors at z = 0 are defined as three orthogonal unit vectors in an arbitrarily chosen three-dimensional spatial reference frame. The tangent vectors at arbitrary locations are assumed to "point" in the direction of the fiber length increase and indicate the local fiber direction. Thus, the concatenation of tangent vectors at closely spaced locations along the length of the multicore sensing fiber 10 represents the distributed shape of the fiber.

[0041] The measurement sensitivity of the inventive system can be increased by increasing the signal-to-noise ratio (SNR) of the OBR 20 or widening the tuning wavelength range of the tunable laser 22 to increase the measurement resolution (as mentioned above). The SNR depends on the spectral beating signal generated in the OBR 20 by interfering the reference beam with the backscattered signal . That is, Therefore, the SNR can be increased, for example, by a factor of two by increasing the intensity of the tunable laser source 22 or by simply increasing the amplitude of the refractive index modulation Δη ac of the Bragg grating 14 by a factor of two, because Decreasing the background noise (e.g., shot noise, dark current noise, frequency measurement noise, etc.) present in the instrument itself of the OBR 20 also increases the SNR of the OBR 20, thus improving the measurement sensitivity of the system.

[0042] Increasing the measurement sensitivity in the transverse plane of the multicore sensing fiber 10 can also be provided by increasing the radial offset R o between the fiber core 12 and the central axis of the fiber 10 while maintaining the same outer diameter of the fiber. The amount of Bragg wavelength shift (Δλ Bragg ) in the presence of bending-induced fiber strain is directly related to the value of R o as shown in the following relation:

[0043]

[0044] where η is a fixed quantity representing the strain-optical coefficient of the silica glass, y0is the fiber displacement in the transverse plane with respect to the straight (flat) neutral plane, and k d is the period of the deformation applied along the length of the fiber. Obviously, the amount of detected wavelength shift can be increased by proportionally increasing the radial offset (i.e., R o ) of the fiber core 12. This results in a linear increase of the SNR of the system, thus ultimately improving the sensitivity of the measurement.

[0045] Another alternative method to improve the measurement sensitivity is to reduce the overall diameter of the multicore sensing fiber 10. Since the fiber is cylindrical, reducing the diameter helps to reduce the moment of inertia I (I = π / 4 * R 4 ), where R is the radius of the fiber 10. Thus, by reducing the moment of inertia, the flexibility (and thus the bending) of the multicore sensing fiber 10 itself is increased, thus providing a greater Bragg wavelength shift in the FBG 14. The increase in I can improve the sensitivity of the local strain, the local curvature, and ultimately the distributed shape measurement. In particular, by reducing the fiber diameter by 50%, I 50％the value of y0is reduced to approximately 0.0625 I, and the resulting bend amplitude y0and associated Bragg wavelength shift Δλ Bragg are both increased by a factor of 16.

[0046] Fabrication of multicore sensing fiber 10 with optical materials having a Young's modulus (E) less than that of conventional silica glass (E = -70 GPa) also results in an increase in SNR. Soft glasses, such as chalcogenide and fluoride glasses, provide a suitable platform for the reduced Young's modulus of multicore sensing fiber 10. On the other hand, by increasing the precision of the estimated group delay for the distributed backscatter signal, the longitudinal sensitivity of the shape sensing measurement can be proportionally increased. A collection of distributed measurements of the refractive index of fiber 10 can be used to determine the estimated group delay.

[0047] It is also found that performing repeated measurements for each offset core allows for a reduction in the noise present in the average. For example, switch 30 can be controlled to perform multiple switching from port 341 to port 34 N , thereby forming multiple measurement scans of multicore sensing fiber 10. That is, by performing multiple scans for each offset 12, the noise contribution associated with a single scan is reduced by averaging over the multiple scans. That is, the result of the repeated measurements is a suppression of the noise present in the measurement data by averaging over the data of the multiple scans, effectively enhancing the SNR and improving the accuracy of the fiber shape measurement. Figure 5 The reduction in the standard deviation of the strain measurement as a function of the number of averaged scans is illustrated. When the data of 10 separate measurements is averaged, a suppression of the standard deviation of greater than 3 dB is observed. The effect of this multiple scan noise suppression is also analyzed in terms of the accuracy of the shape reconstruction.

[0048] Figure 6 (a) is a photographic reproduction of an exemplary multicore sensing fiber bent into a circular loop, the diameter of the loop being approximately 40 cm. Figure 6 (b) is a reconstruction formed in accordance with the teachings of the present application when only a single set of measurements is obtained (i.e., a single scan), while Figure 6 (c) the reconstruction shown is obtained by averaging the results of 10 separate scans. It is found that when the measurements of the multiple scans are not averaged, the reconstructed shape of the fiber exhibits a rather high error with respect to the actual layout of the fiber, clearly indicating the influence of noise. This is particularly true in the case of a light bend and small curvature setup, where the strain signal is not significantly larger than the noise.

[0049] It will be apparent to those skilled in the art that various modifications and variations can be made to the present application without departing from the spirit or scope of the application. Thus, it is intended that the present application cover the modifications and variations of the example implementations described herein, all of which are considered to be within the spirit and scope of the present application.

Claims

1. A distributed system for sensing and measuring micro-bends and micro-strains in three-dimensional (3D) space, comprising: a multicore sensing fiber comprising a plurality of offset cores spaced radially from a center of the multicore sensing fiber by R o where R o is selected to provide a desired change in Bragg wavelength Δλ Bragg in the presence of a deformation, where and where η is a fixed quantity representing the strain-optic coefficient of the material forming the multicore sensing fiber, yo is a quantity of local displacement of the deformation in the transverse plane with respect to the straight neutral plane, and k d is the period of the deformation applied along the length of the multicore sensing fiber; and a plurality of successive Fiber Bragg Gratings FBG are inscribed in said plurality of offset cores in a one-to-one relationship, each FBG being formed to reflect light at a common Bragg wavelength λ Bragg ; and an optical backscatter reflectometer comprising Tunable laser source for generating a swept wavelength output beam across a wavelength range of λ Bragg surrounding wavelengths. an optical beamsplitter / combiner for splitting a swept-wavelength output beam into a swept-wavelength probe beam directed into the multicore sensing fiber and a swept-wavelength reference beam directed into a reflector, the optical beamsplitter / combiner also for combining a swept-wavelength return beam from the multicore sensing fiber and the reflected swept-wavelength reference beam to create an interferometric FBG sensing beam; an optical detector responsive to the interferometric FBG sensing beam for creating an electronic version of the interferometric FBG sensing beam; and a Fourier transform analyzer coupled to the optical detector and used to perform a Fourier transform on the electronic version of the interferometric FBG sensing beam to generate measurements of local variations in Bragg wavelength along the length of the multicore sensing fiber and from which to reconstruct the shape of the three-dimensional space.

2. The distributed system of claim 1, wherein the plurality of cores are disposed in a helical pattern along an axial length of the multicore sensing optical fiber, the helical pattern being periodic with a defined period Λ s .

3. The distributed system of claim 1, further comprising an optical switch arrangement deployed along the path of the swept-wavelength probe beam for controlling the coupling of the swept-wavelength probe beam and between the plurality of offset cores within the multicore sensing fiber.

4. The distributed system of claim 3, wherein the optical switch arrangement comprises a l x N optical switch and the plurality of offset cores comprises a complex number N of offset cores, the l x N optical switch configured to provide a one-to-one relationship coupling a complex number N of switch ports and the complex number N of offset cores.

5. The distributed system of claim 4, wherein the l x N optical switch is controlled to sequentially couple the swept-wavelength probe beam to individual ones of the complex number N of switch ports, thereby sequentially coupling the swept-wavelength probe beam to individual offset cores in turn, performing a scan sequence of the multicore sensing fiber over a period of time.

6. The distributed system of claim 5, wherein a plurality of scans of individual offset cores are performed to reduce the signal-to-noise ratio in the measurements generated by the Fourier transform analyzer.

7. The distributed system of claim 4, further comprising a tapered fiber bundle deployed between the output of the l x N optical switch and the input face of the multicore sensing fiber, the tapered fiber bundle reducing the physical size of a plurality of output fibers exiting the l x N optical switch to a diameter substantially equal to the diameter of the multicore sensing fiber.

8. The distributed system of claim 1, further comprising A reconstruction processor for determining a distributed curvature in a three-dimensional space The distributed curvature is a vector whose phase provides information about the direction of the local microbending and is defined as: where R o is the radial offset between the center of the multicore sensing fiber and the center of the offset core, u defines the individual core, is the unit vector of the associated offset core, and is the strain induced in the associated offset core and is defined as follows: wherein is the strain-optic coefficient associated with the composition of the multicore sensing fiber.

9. The distributed system of claim 8, wherein the reconfiguration processor is further configured to determine a distributed shape S of the three-dimensional space based on the determined distributed curvature vector and is defined as follows: wherein is the tangent of the distributed curvature vector, is the normal of the distributed curvature vector, is the binormal of the distributed curvature vector, demonstrating and quantifying how quickly the direction of bending varies along the length of the multicore sensing fiber.

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