A system for measuring microbends and arbitrary small deformations along three-dimensional space

Abstract

A system for sensing microbends and microdeformations in three-dimensional space based on the distributed length of an optical fiber is formed to include a group of offset cores arranged in a helical configuration along the length of the fiber, with each core containing a fiber Bragg grating exhibiting the same Bragg wavelength. Microscale local deformations in a multicore fiber result in local shifts in the Bragg wavelength, and the use of multiple cores allows for complete microscale modeling of the local deformations. Sequential probing of each core enables optical frequency-domain reflectometry (OFDR), allowing for reconstruction of a given three-dimensional shape and depicting the location and size of various microbends and microdeformations.

Description

[Technical field]

[0001] [CROSS REFERENCE TO RELATED APPLICATIONS] This application claims priority to U.S. Provisional Patent Application No. 62 / 989,117, filed March 13, 2020, which is incorporated herein by reference. The present invention relates to optical fiber based distributed sensors, and more particularly to multicore fiber based sensors that can detect the presence of microbends along a given fiber span, providing three-dimensional information regarding the location and size of various deformations in the space surrounding the distributed sensor. [Background technology]

[0002] Optical fiber-based distributed sensors have emerged as a valuable tool in performing characterization of arbitrary deformations in three-dimensional space. Potential applications include 3D printing, surgical catheters, smart wearables, fuel tank monitoring systems, composite structures, etc. The use of optical fibers for "shape sensing" offers high accuracy and high speed operation and may be particularly applicable to characterize difficult-to-access surfaces and environments as a result of the innate shielding nature of the light beam used as the sensing probe.

[0003] Until now, fiber-based distributed sensors have been able to reconstruct arbitrary paths and shapes only at the "macro" level (i.e., at the centimeter / meter scale in terms of measurements). Pushing ahead, the ability to perform distributed sensing at smaller scales (i.e., sub-millimeter changes / bends) becomes more important. For example, the effect of microbends on the attenuation of optical communication signals propagating along transmission fibers has been of interest for several years. As transmission losses in optical fibers approach fundamental limits dictated by intrinsic absorption and scattering in glass, losses induced by microscopic physical bends in optical fibers (and cables) become increasingly relevant. However, such microbends cannot be directly measured with currently available sensors. Summary of the Invention

[0004] The problems remaining in the prior art are addressed by the present invention, which is directed to a multicore fiber-based sensor that is capable of detecting the presence of microbends along a given fiber span and provides three-dimensional information regarding the location and size of various deformations in the space surrounding the distributed sensor.

[0005] In accordance with the principles of the present invention, the ability to "reconstruct" small deformations distributed along the length of an optical fiber is provided by a system based on the use of a twisted multi-core optical fiber to probe the distributed reflection of light in multiple waveguiding cores. The cores are formed to contain continuous fiber Bragg gratings (FBGs) that all exhibit the same Bragg wavelength. Microscale local deformations of the sensing fiber produce local shifts in the Bragg wavelength, and the use of multiple cores allows for complete modeling of bending at specific locations.

[0006] In one exemplary embodiment, the invention takes the form of a distributed system for sensing and measuring microbends and small deformations in three-dimensional (3D) space that utilizes a multicore sensing fiber in combination with an optical backscattering reflectometer. In particular, the multicore sensing fiber is configured to measure a quantity R in a radial direction from the center of the multicore sensing fiber. 0The optical backscattering reflectometer is formed to include a plurality of offset cores spaced apart by 100 .mu.m and a plurality of continuous fiber Bragg gratings (FBGs) inscribed in a one-to-one relationship on the plurality of offset cores. The set of FBGs is formed to reflect light at a common Bragg wavelength .lambda.Bragg. The optical backscattering reflectometer includes a tunable laser source for generating a swept-wavelength output beam spanning a wavelength range encompassing .lambda.Bragg, an optical beam splitter / combiner, a photodetector, and a Fourier transform analyzer for performing optical frequency domain reflectometry (OFDR). The optical beam splitter / combiner functions to split the swept-wavelength output beam from the tunable laser source into a swept-wavelength "probe" beam that is directed to the multicore sensing fiber and a swept-wavelength reference beam that is directed to the reflector. The optical beam splitter / combiner is also used to combine the swept-wavelength return beam from the multicore sensing fiber and the reflected swept-wavelength reference beam to generate an interferometric FBG sensing beam. The photodetector responds to the interferometric FBG sensing beam to generate an electronic version of the interferometric beam, and the Fourier transform analyzer then performs a Fourier transform on the electronic version of the interferometric FBG sensing beam to generate a measurement of the local change in Bragg wavelength along the length of the multicore sensing fiber, which is then used to reconstruct the shape of the three-dimensional space.

[0007] The sensor fiber may be formed from a conventional glass material, although other embodiments may utilize sensor fibers formed from a less elastic material with a smaller Young's modulus, allowing for finer measurement resolution.

[0008] Other and further embodiments and features of the present invention will become apparent during the course of the following discussion and by reference to the accompanying drawings.

[0009] Reference is now made to the drawings, in which like numerals represent like parts in the several views. [Brief description of the drawings]

[0010] [Figure 1] FIG. 1 is an isometric view of a cross section of a twisted multi-core optical fiber useful in a multi-core sensing fiber according to the present invention. [Diagram 2] FIG. 2 is an end view of the multi-core sensing fiber of FIG. [Diagram 3] FIG. 3 is a block diagram of an exemplary system for sensing and measuring deformation in three-dimensional space associated with the position of a multicore sensing fiber. [Figure 4] FIG. 4 is a close-up cross-sectional view of bend locations along a multicore sensing fiber showing the presence of both compression and expansion between the various offset cores. [Diagram 5] FIG. 5 is a graph showing the reduction in standard deviation of fiber geometry measurements as a function of the number of measurements. [Figure 6A] FIG. 6A is a photo reproduction of a loop of a multicore sensing fiber illustrating the improvement in shape reconstruction associated with performing multiple measurements. [Figure 6B] FIG. 6B illustrates the improvement in shape reconstruction associated with performing multiple measurements versus reconstruction based on a single measurement. [Figure 6C] FIG. 6C illustrates the improvement in shape reconstruction associated with performing multiple measurements, the reconstruction being based on a set of 10 separate measurements. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] 1 is an isometric view of an exemplary twisted multi-core optical fiber 10 that may be used to perform detection of microbends (and generally various other microdeformations) in three-dimensional space in accordance with the principles of the present invention. FIG. 2 is an end view of the fiber 10 of FIG. 1, specifically illustrating the arrangement of a set of offset cores within the multi-core fiber 10. In this embodiment, the multi-core fiber 10 is configured such that the cores are all offset by the same amount (R 0 ) radially offset by 12 1 ~12 6As shown, the cores are equally spaced from each other and the set of six cores provides an angular displacement Z of 60° between adjacent cores.

[0012] As best shown in FIG. 1, the sensing cores 12 follow a helical pattern along the length of the multicore fiber 10 (hence the meaning of "twisted" when describing the design of the sensing fiber 10). Such a fiber can be formed during the process of drawing an optical preform into the fiber, where the preform is continuously rotated, resulting in the offset cores 12 extending helically around the central axis of the fiber with a constant "twist frequency." Thus, the defined twist frequency, which can be characterized as turns per meter, is denoted in FIG. 1 as Λ s , which forms a defined spatial twist period denoted as

[0013] Each offset core 12 i is a continuous FBG that can be written into the core during the process of drawing the preform into the final fiber. i Each FBG14 is formed to include i are all reflective of the same Bragg wavelength λ so that they all reflect light of the same wavelength in the absence of any local bending or deformation that would result in a shift in the Bragg wavelength value. Bragg is created to show:

[0014] Figure 3 shows an exemplary distributed shape sensing system 100 utilizing the multicore sensing fiber 10 of Figures 1 and 2. The system 100 includes an optical backscattering reflectometer (OBR) 20 that utilizes optical frequency domain reflectometry (OFDR) measurements in a manner described more fully below to ascertain the presence of micro-deformations along the multicore sensing fiber 10, providing detailed information regarding their location and shape. The ability to collect measurements from multiple offset cores 12 at any lateral location along the span of the multicore sensing fiber 10 provides the resolution necessary to provide highly accurate sensing of microbends in the fiber.

[0015] The OBR20 itself is the Bragg wavelength (λ Bragg ) is a tunable laser source 22 configured as a swept wavelength (frequency) source centered around λ Bragg For example, λ may be configured to provide a narrow linewidth output that is swept through a wavelength range of ±10 nm on either side of λ (i.e., a wavelength range of 20 nm). Bragg For a wavelength of 1531 nm to 1551 nm, the tunable laser source may be configured to provide an output beam that is scanned over a wavelength range of 1531 nm to 1551 nm. A tuning bandwidth of 20 nm is exemplary only, and larger bandwidths may be desirable, as described below.

[0016] The output beam from the tunable laser 22 then passes through a beam splitter 24 of the OBR 20, which directs a majority of the beam (sometimes called the “probe beam” or “probe signal”) out of the OBR 20 and into a 1×N optical switch 30. The switch 30 directs the probe beam into a selected offset core 12 of the multicore sensing fiber 10, as described in more detail below. i The target object is controlled to be directed toward the target object.

[0017] Returning to the discussion 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 the backscattered reflections from the multicore sensing fiber 10 are combined in the beam splitter 24 (acting as a combiner in this direction) and direct an interfering combination of these signals to a photodetector 28 contained within the OBR 20. The output from the photodetector 28 is then applied as an input to a Fourier analyzer 29, which performs a frequency domain analysis and converts the frequency domain measurements from the photodetector 28 into spatial domain measurements of phase and amplitude as a function of length along the multicore sensing fiber 10.

[0018] If the multi-core sensing fiber 10 is flat and straight, with no microbends (or other types of minute deformations), then all of the FBGs 14 will be focused at the reference Bragg wavelength λ Bragg , and consistently reflects the probe beam light only at this wavelength, allowing the remaining wavelengths to continue propagating along the multi-core sensing fiber 10. Thus, λ Bragg Since there is no change in the frequency content of the output of the photodetector 28, there is also no change. Thus, the Fourier analyzer 29 provides a constant linear output signal indicative of an "unperturbed" multi-core sensing fiber 10. Once any microbend / deformation is present in the fiber 10, the Bragg wavelength of one or more offset cores 12 will change (see FIG. 4 described below), and the output from the Fourier analyzer 29 will contain a set of peaks associated with the microbend. The output from the Fourier analyzer 29 can be considered as the output sensing signal from the OBR system 20.

[0019] Thus, according to the principles of OFDR, each offset core 12 is scanned with a probe beam that is scanned over a defined wavelength range. i By illuminating the multi-core sensing fiber 10 with a Fourier transform, deformations / microbends along the multi-core sensing fiber 10 are identified in an interference signal that is processed by the Fourier analyzer 29. That is, by performing a Fourier transform of the interfering beam, the spectral information can be used to detect and measure the microdeformations along the multi-core sensing fiber 10. The Fourier transform converts the spectral information in the received interference signal into spatial (temporal) information in the form of distributed Bragg wavelength changes at the locations where the microbends / deformations are present.

[0020] The Fourier relationship inversely correlates the wavelength scan range of the tunable laser source 22 to the longitudinal spatial domain measurements of strain (and therefore curvature and shape). For example, a wavelength scan range of 20 nm translates to a measurement resolution of 40 μm. Increasing the wavelength scan range to 80 nm (still centered on the given Bragg wavelength) would lead to a resolution of 10 μm in the measurement of localized microbends, albeit at the cost of requiring a tunable laser source 22 capable of generating such a large swept wavelength range.

[0021] Continuing with the description of the components of system 100, the tunable probe beam exiting OBR 20, as described above, is provided as an input to a 1×N optical switch 30. Optical switch 30 has a single input / output port 32 and a plurality of N connection ports 34. 1 ~34 N Each connection port includes 34 i Has a unique offset core 12 i The N number of outputs from the optical switch 30 are related to the offset core 12 in a one-to-one relationship. 1 ~12 N 38 A plurality of separate optical fibers associated with 1 ~38 N The distal end of the multicore sensing fiber 10 is immersed in an index-matching gel 50 to suppress unwanted Fresnel reflections at the distal end face of the fiber 10 from re-entering one or more of the multiple offset cores 12.

[0022] FIG. 3 also illustrates an exemplary configuration for coupling the output from the optical switch 30 to the multicore sensing fiber 10. In particular, FIG. 3 illustrates the use of a tapered fiber bundle (TFB) 40 to provide efficient optical coupling between a fiber 38 (from the optical switch 30) and the offset core 12 of the fiber 10. In accordance with known principles of operation of a given TBF, the TBF 40 functions to reduce the overall diameter of a "bundle" of input fibers 38 to an output taper 42 that matches the end face of the multicore sensing fiber 10 (as shown in FIG. 2 above). The output taper 42 is oriented such that the core region of each fiber 38 aligns with a separate core region of the offset core 12. That is, the cross-sectional shape of the output end face 44 of the TBF 40 is matched to the end face of the multicore sensing fiber 10, as shown in FIG. 2. The use of the TBF 40 allows for efficient delivery of a probe signal into the multicore sensing fiber 10, as well as collection of a backscattered signal therefrom.

[0023] The system 100 shown in Figure 3 is used to recognize microbends along a multicore sensing fiber 10, which are recognized by the local asymmetric stresses generated within the fiber cross section at the location of a given microbend B. Figure 4 is an enlarged cross-sectional isometric view of the multicore sensing fiber 10 at a particular location B that is experiencing a deformation. This particular bend is caused by the cores 12 2 Therefore, FBG14 2 In accordance with the known properties of Bragg gratings, this reduction in the grating period also reduces the spacing between adjacent gratings in the FBG14. 2 Reduces the Bragg wavelength experienced by the core 12 3 is in the mid-plane of the fiber 10 (as shown in FIG. 4), and therefore FBG 14 3 The Bragg wavelength of the core 12 is not affected by this bending since it remains constant. 4 undergoes expansion at this bending position, and FBG14 4 By increasing the space between adjacent gratings, FBG14 4 The grating period and Bragg wavelength are reduced.

[0024] An optical switch 30 is used to switch the swept-wavelength probe beam to each individual offset core 12. i By sequentially illuminating the fiber 10 with multiple offset cores 12, the change in Bragg wavelength associated with a particular core at a given transverse location allows the type of shape deformation to be recreated. That is, the inclusion of switching functionality within the system 100 allows data to be collected from multiple offset cores 12, one at a time, to obtain cross-sectional deformations at selected locations along the fiber 10. Repeating this process along the extent of the multicore sensing fiber 10 allows for a complete reconstruction of the various microbends (and other types of deformations) occurring along its span.

[0025] Once all measurements are completed by the Fourier analyzer 29, the associated three-dimensional spatial distribution curvature and shape can be created by the reconstruction module 27 coupled to the output of the Fourier analyzer 29, as shown in Fig. 3. The distribution curvature of the multi-core sensing fiber 10 is a vector quantity κ(z), whose phase provides information about the direction of the local microbend, which helps to reconstruct the distribution shape of the sensing multi-core fiber 10. In general, the spatially dependent curvature κ(z) depends on the local distortion and the geometric shape of the offset core 12.

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[0026] Each offset core 12 1 ~12 N By utilizing an optical switch 30 to sequentially illuminate the offset cores 12, the strain information from a number N (e.g., N=6) of offset cores 12 is summed in the reconstruction module 29 as indicated by the definition of the spatially dependent curvature κ(z) to develop both the magnitude and phase of the distributed fiber curvature. The bending orientation of each curve along the multi-core sensing fiber 10 is represented by the phase portion of the curvature. It should be understood that the number of individual offset cores 12 included in the multi-core sensing fiber 10 directly affects the accuracy of the calculated distributed curvature, and increasing the number of offset cores increases the amount of data captured and recorded by the Fourier analyzer 29.

[0027] Finally, the profile shape S of the deformed fiber may also be provided as an output from the reconstruction module 27. In particular, the profile shape is reconstructed from the calculated spatially dependent curvature κ(z) using the Frenet-Serret formulas (which are a set of differential equations that describe three-dimensional (3D) curves) to provide the profile shape output from module 27. Specifically, the Frenet-Serret equations relate local shape parameters including the tangent T(x,y,z), principal normal N(x,y,z), and binormal B(x,y,z) vectors to the fiber curvature and twist measured at closely spaced locations. Mathematically, this is expressed as follows:

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[0028] It is important to note that the initial condition for solving the above equations assumes no curvature and no twist at the input to the multicore sensing fiber 10 at position z(=0), i.e., κ(0)=τ(0)=0. Furthermore, the tangent T(x,y,z), principal normal N(x,y,z) and binormal B(x,y,z) vectors are defined as three orthonormal unit vectors in an arbitrarily chosen three-dimensional spatial reference frame at z=0. The tangent vector at any position is assumed to "point" in the direction of increasing fiber length, indicating the local fiber orientation. Thus, the concatenation of the tangent vectors at closely spaced positions along the length of the multicore sensing fiber 10 represents the fiber distribution shape.

[0029] The measurement sensitivity of the system of the present invention can be increased by increasing the signal-to-noise ratio (SNR) of the OBR 20, or by widening the tuning range of the tunable laser 22 to increase the measurement resolution (as described above). The SNR can be increased by increasing the signal-to-noise ratio (SNR) of the reference beam (

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[0030] Increasing the sensitivity of measurements in the cross-section of the multicore sensing fiber 10 also requires increasing the radial offset R between the cores 12 and the central axis of the fiber 10 while maintaining the same outer diameter of the fiber. 0 The amount of Bragg wavelength shift (=Δλ) in the presence of bending-induced fiber strain can be Bragg ) is expressed by the following relationship: 0 is directly related to the value of

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[0031] Another alternative approach to increasing the measurement sensitivity is to reduce the overall diameter of the multi-core sensing fiber 10. Because the fiber is cylindrical, reducing the diameter reduces the moment of inertia I (I=π / 4*R 4) (R is the radius of the fiber 10). As a result, by reducing the moment of inertia, the flexibility (and therefore bending) of the multi-core sensing fiber 10 itself is increased, leading to a larger shift in the Bragg wavelength in the FBG 14. Increasing I can improve the sensitivity of the local strain, local curvature, and ultimately the profile measurement. Specifically, by reducing the fiber diameter by 50%, the value of I50% decreases to about 0.0625I, and the resulting bending amplitude y 0 and the associated Bragg wavelength shift ΔλBragg is increased by a factor of 16.

[0032] Fabricating the multi-core sensing fiber 10 from an optical material with a smaller Young's modulus (E) than conventional silica glass (E=~70 GPa) also leads to improved SNR. Soft glasses, such as chalcogenide and fluoride glasses, provide a suitable platform for reducing the Young's modulus of the multi-core sensing fiber 10. On the other hand, the longitudinal sensitivity of the shape sensing measurement can be increased proportionately by increasing the accuracy of the estimated group delay for the distributed backscattered signal. A set of distributed measurements of the refractive index of the fiber 10 can be used to determine the estimated group delay.

[0033] It has also been found that by performing repeated measurements of each offset core, it is possible to reduce the noise present in the average value. For example, switch 30 has port 34 1 to port 34 NThe offset 12 may be controlled to perform multiple switching to, forming multiple measurement scans of the multi-core sensing fiber 10. That is, by performing multiple scans of each offset 12, the noise contribution associated with a single scan is reduced by averaging over multiple scans. That is, the repeated measurements result in suppressing the noise present in the measurement data by averaging the data over multiple scans, thereby effectively improving the SNR and improving the accuracy of the fiber shape measurement. Figure 5 shows the reduction in the standard deviation of the strain measurements as a function of the number of averaging scans. When the data was averaged over 10 separate measurements, a suppression of more than 3 dB in the standard deviation was observed. The effect of this multi-scan noise suppression has also been analyzed with respect to the accuracy of the shape reconstruction.

[0034] FIG. 6A is a photographic reproduction of an exemplary multicore sensing fiber bent into a circular loop, with the loop having a diameter of approximately 40 cm. FIG. 6B is a reconstruction formed in accordance with the teachings of the present invention when only a single set of measurements was obtained (i.e., a single scan), while the reconstruction shown in FIG. 6C was obtained by averaging the results of 10 separate scans. The reconstructed shape of the fiber was found to exhibit a fairly high error relative to the actual layout of the fiber when measurements were not averaged over multiple scans, clearly demonstrating the effect of noise. This is especially true under gentle bend and small curvature settings where the strain signal is not substantially larger than the noise.

[0035] It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the present invention. Therefore, the present invention is intended to cover modifications and variations of the above-described embodiments, all of which are deemed to be within the spirit and scope of the present invention as defined by the claims appended hereto.

Claims

1. A distributed system for sensing and measuring microbends and small deformations in three-dimensional (3D) space, comprising: A multi-core sensing fiber, R in the radial direction from the center of the multi-core sensing fiber ０ a plurality of offset cores spaced apart by a distance; A plurality of continuous fiber Bragg gratings (FBGs) inscribed in the plurality of offset cores in a one-to-one relationship, each FBG having a common Bragg wavelength, λ Ｂｒａｇｇ a multi-core sensing fiber having a plurality of FBGs configured to reflect light at 1. An optical backscatter reflectometer comprising: λ Ｂｒａｇｇ a tunable laser source generating a swept wavelength output beam over a wavelength range encompassing an optical beam splitter / combiner that splits the swept-wavelength output beam into a swept-wavelength probe beam directed to the multicore sensing fiber and a swept-wavelength reference beam directed to a reflector, the optical beam splitter / combiner also combining the swept-wavelength return beam from the multicore sensing fiber and the reflected swept-wavelength reference beam to generate an interferometric FBG sensing beam; a photodetector responsive to the interferometric FBG sensing beam to generate an electronic version thereof; an optical backscattering reflectometer comprising: an optical detector coupled to the optical detector and configured to perform a Fourier transform on the electronic version of the interferometric FBG sensing beam to generate measurements of local variations in Bragg wavelength between offset cores at identified locations along an axial length of the multicore sensing fiber and to use the measurements to reconstruct a shape in the three-dimensional space; an optical switching arrangement disposed along a path of the swept-wavelength probe beam for sequentially illuminating each individual core with the swept-wavelength probe beam to collect data from the plurality of offset cores one at a time; A reconstruction processor for determining a distribution curvature κ(z) in the three-dimensional space, the distribution curvature being a vector quantity having a phase that provides information about a direction of a local microbend, the distribution curvature being defined by Equation 1: [0010] R 0 is the radial offset between the center of the multicore sensing fiber and the center of each offset core of the plurality of offset cores, u defines an individual core, ρ u (z) is the unit vector of the associated offset core, and ε u (z) is the strain induced in the associated offset core, defined in Equation 2: [0025] and a reconstruction processor, wherein η is a distortion optical coefficient related to a composition of the multi-core sensing fiber.

2. The plurality of offset cores are arranged in a helical pattern along the axial length of the multicore sensing fiber, the helical pattern having a predetermined period Λ ｓ 2. The distributed system of claim 1, wherein the distributed system is periodic.

3. 2. The distribution system of claim 1, wherein the optical switching arrangement comprises a 1×N optical switch, the plurality of offset cores comprises a plurality of N offset cores, the 1×N optical switch configured to couple a plurality of N switch ports and the plurality of N offset cores in a one-to-one relationship, and the optical switching arrangement further comprises a plurality of N output fibers coupled to the plurality of N switch ports and used to couple to the multicore sensing fiber.

4. 4. The distribution system of claim 3, wherein the 1×N optical switch is controlled to sequentially couple the swept-wavelength probe beam to each switch port of the plurality of N switch ports and to sequentially couple the swept-wavelength probe beam to each offset core to perform a scanning sequence of the multi-core sensing fiber over a period of time.

5. 5. The dispersion system of claim 4, wherein multiple scans of each offset core are performed to improve the signal-to-noise ratio of measurements produced by the Fourier transform analyzer.

6. the plurality of N output fibers are configured to couple with a tapered fiber bundle; 5. The distribution system of claim 4, wherein the tapered fiber bundle reduces the physical size of the plurality of N output fibers exiting the 1×N optical switch to a diameter substantially equal to a diameter of the multicore sensing fiber.

7. The distributed system according to claim 1 , wherein the reconstruction processing unit further determines a distribution shape S in a three-dimensional space based on the determined distribution curvature vector κ(z) and Equation 3. [0030] Where: [0045] where T(x,y,z) is the tangent to the distribution curvature vector, N(x,y,z) is the principal normal to the distribution curvature vector, and B(x,y,z) is the binomial of the distribution curve vector. [0050] and τ(z) is the twist, which quantifies how rapidly the bending direction changes along the axial length of the multicore sensing fiber.

8. A distributed system for sensing and measuring microbends and small deformations in three-dimensional (3D) space, comprising: A multi-core sensing fiber, a plurality of offset cores spaced radially apart from a center of the multi-core sensing fiber by a distance R 0 ; a multi-core sensing fiber comprising a plurality of continuous fiber Bragg gratings (FBGs) inscribed in said plurality of offset cores in a one-to-one relationship, each FBG configured to reflect light at a common Bragg wavelength, λ Bragg ; 1. An optical backscatter reflectometer comprising: a tunable laser source that produces a swept-wavelength output beam over a range of wavelengths encompassing λ Bragg; an optical beam splitter / combiner that splits the swept-wavelength output beam into a swept-wavelength probe beam directed to the multicore sensing fiber and a swept-wavelength reference beam directed to a reflector, the optical beam splitter / combiner also combining the swept-wavelength return beam from the multicore sensing fiber and the reflected swept-wavelength reference beam to generate an interferometric FBG sensing beam; a photodetector responsive to the interferometric FBG sensing beam to generate an electronic version thereof; an optical backscattering reflectometer comprising: an optical detector coupled to the optical detector and configured to perform a Fourier transform on the electronic version of the interferometric FBG sensing beam to generate measurements of local variations in Bragg wavelength between offset cores at identified locations along an axial length of the multicore sensing fiber and to use the measurements to reconstruct a shape in the three-dimensional space; an optical switching arrangement disposed along a path of the swept-wavelength probe beam for sequentially illuminating each individual core with the swept-wavelength probe beam to collect data from the plurality of offset cores one at a time; R ０ is the desired change in Bragg wavelength Δλ in the presence of deformation. Ｂｒａｇｇ selected to provide [006] where η is a constant representing the strain optical coefficient of the material forming the multi-core sensing fiber, and y ０ is the local displacement in the transverse plane of the deformation relative to the linear neutral plane, and k ｄ is the period of the deformation applied along the length of the multicore sensing fiber.

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