Method and system for representing shape of fiber optic sensor

Abstract

A method of representing a shape of an optical fiber sensor (12) having a central core (16) and a plurality of outer cores (14, 18, 20), each core including one or more sensing elements, the method comprising: (a) optically interrogating the cores (14, 16, 18, 20) of the optical fiber sensor (12) from incident light waves in a wavelength range centered on a resonant wavelength of the one or more sensing elements, wherein the wavelength range is associated with detection limited to a minimum radius of curvature along the optical fiber sensor; (b) reconstructing a shape of the optical fiber sensor (12) involving processing an interferometric signal received from the optical interrogation of the cores (14, 16, 18, 20), including reconstructing a shape of at least one out-of-range portion of the optical fiber sensor (12), the at least one out-of-range portion being a portion having a radius of curvature lower than the minimum radius of curvature, wherein reconstructing the shape of the at least one out-of-range portion includes calculating a curvature of the optical fiber sensor (12) in the at least one out-of-range portion from an interferometric signal received from the interrogation of the central core (16) in the at least one out-of-range portion; (c) displaying the shape of the optical fiber sensor (12) including the at least one out-of-range portion. A system performing this method is also described.

Description

Technical Field

[0001] This invention generally relates to methods for representing the shape of an optical fiber sensor. More specifically, the invention relates to methods for representing the shape of an optical fiber sensor having a central core and a plurality of outer cores, each core including one or more sensing elements. The invention also relates to a system for representing the shape of an optical fiber sensor. Furthermore, the invention relates to a computer program suitable for causing said system to perform the above-described methods. Background Technology

[0002] Optical shape sensing (OSS) is a technique that reconstructs the three-dimensional shape of a specialized fiber optic sensor based on the reflection of light within the sensor. This technique enables, for example, real-time 3D visualization of the complete shape of devices such as medical devices like catheters and guidewires. The shape of the medical device can be overlaid on X-ray images or preoperative CT scans. In this way, physicians can navigate the device during procedures without requiring X-ray tracking.

[0003] In optical shape sensing, distributed strain and temperature signals are obtained from backscattered spectra using an interferometer system. This is done for an optical fiber sensor with, for example, three outer cores spirally wound around a fourth core located at the center of the optical fiber sensor. The core's response to strain and temperature is measured as the phase difference of the optical signal from the interferometer, as a function of the position along the optical fiber sensor. The phase difference is obtained relative to a reference measurement, where the optical fiber sensor is in a well-defined shape, such as a perfectly straight shape. From the phase difference, the strain and temperature difference for each core can be derived. The strain signal will be the sum of bending strain in two orthogonal directions, torsional strain, and axial strain, with the axial strain being the strain in the longitudinal direction of the optical fiber sensor. The shape of the optical fiber sensor can be reconstructed from these four position-dependent quantities. Detailed descriptions of shape sensing techniques are provided in documents US 8773650 B1 and US 9784569 B1. For high-accuracy shape sensing, accurate optical fiber sensor properties are required in the shape reconstruction model. These properties can be determined for each individual optical fiber sensor during calibration.

[0004] OSS fiber optic sensors inserted into the lumen of medical devices can experience varying radii of curvature. Medical devices can be pre-formed and will change shape during operation. The minimum radius of curvature encountered by the fiber optic sensor depends on the device design, the fiber optic sensor itself, and the environment in which it is used. For example, the human vascular system can be very tortuous. To access these types of blood vessels, more flexible devices will be used. Furthermore, during processing, medical devices may kink, i.e., experience locally very sharp bends. Therefore, OSS fiber optic sensors within these devices must be able to withstand small radii of curvature. If the radius of curvature is limited to zero, the fiber optic sensor will simply break. However, optical shape sensing technology introduces another limitation related to the minimum measurable bending radius of the fiber optic sensor.

[0005] The minimum measurable bending radius of an optical fiber sensor is proportional to the core distance from the outer core to the center of the sensor and inversely proportional to the scanning wavelength range of the light used to probe the core. Therefore, to reduce the minimum measurable bending radius, increasing the scanning wavelength range or decreasing the outer core distance seems straightforward. Decreasing the outer core distance reduces sensitivity not only to bending strain but also torsional strain, as sensitivity to torsional strain is proportional to the square of the outer core distance. Since the required torsional accuracy is very high, decreasing the outer core distance is disadvantageous. Increasing the scanning wavelength range is disadvantageous for other reasons. It reduces the signal-to-noise ratio because the resonant peak fills the spectrum relatively less. Furthermore, the delay length between two consecutive nodes (data points as a function of position on the optical fiber sensor) decreases, resulting in an increase in data points for the same physical length of the optical fiber sensor. Summary of the Invention

[0006] The purpose of this invention is to provide a method for representing the shape of an optical fiber sensor, which improves the accuracy of shape reconstruction.

[0007] Another object of the present invention is to provide a method for representing the shape of an optical fiber sensor that does not require redundancy in the number of optical fiber sensor cores to achieve high accuracy in shape reconstruction.

[0008] Another object of the present invention is to provide a method for representing the shape of an optical fiber sensor, which enables the representation of a shape having a reduced minimum bending radius with high accuracy.

[0009] Another object of the present invention is to provide a corresponding system for representing the shape of an optical fiber sensor.

[0010] Another object of the present invention is to provide a computer program that enables a system for representing the shape of an optical fiber sensor to perform the above-described method.

[0011] According to a first aspect of the present invention, a method for representing the shape of an optical fiber sensor is provided, the optical fiber sensor having a central core and a plurality of outer cores, each core including one or more sensing elements, the method comprising:

[0012] (a) Optically probing the core of the fiber optic sensor from incident light waves within a wavelength range centered on the resonant wavelength of the one or more sensing elements, wherein the wavelength range is associated with detection limited to the minimum radius of curvature of the fiber optic sensor.

[0013] (b) Reconstructing the shape of the fiber optic sensor involves processing an interferometric measurement signal received from the optical interrogation of the core, including reconstructing the shape along at least one out-of-range portion of the fiber optic sensor, the at least one out-of-range portion being a portion having a radius of curvature lower than the minimum radius of curvature, wherein reconstructing the shape of the at least one out-of-range portion includes calculating the curvature of the fiber optic sensor in the at least one out-of-range portion based on the interferometric measurement signal received from the interrogation of the central core in the at least one out-of-range portion;

[0014] (c) Displaying the shape of the fiber optic sensor including the at least one portion outside the range.

[0015] This invention enables the representation of the shape of an optical fiber sensor even in sections where the radius of curvature along the optical fiber sensor is smaller than the minimum measurable bending radius. In this disclosure, the portion along the optical fiber sensor where the radius of curvature is smaller than the minimum measurable bending radius is referred to as the "out-of-range portion." To represent the shape of the optical fiber sensor in the out-of-range portion, this invention does not require redundancy in the number of outer cores, nor does it require an increased scanning wavelength range or a reduced distance between the outer cores and the center. In the out-of-range portion, one or more of the outer cores of the optical fiber sensor do not provide interferometric measurement signals. Probing can be performed when the wavelength offset of one or more shape sensing elements in one or more outer cores exceeds the limit of the scanning wavelength range in the out-of-range portion. Therefore, in the out-of-range portion, shape reconstruction cannot be based on strain measured in the outer cores. This invention proposes deriving the strain in the out-of-range portion from the signal received from optical probing of the central core in the out-of-range portion, and calculating the curvature based on the strain caused by bending in the central core. Calculating the curvature of the optical fiber sensor in at least one out-of-range portion may include calculating the curvature of the optical fiber sensor at multiple locations along the out-of-range portion.

[0016] As a preferred embodiment, the invention can be based on the insight that a nonlinear effect exists in the relationship between stress and strain applied due to bending. While this nonlinear effect is negligible for small strains, it is observable for high strain values, such as in portions outside the range where the radius of curvature is very small. Therefore, the signal from the central core provides a measurable contribution to the strain due to curvature, and the radius of curvature (bending radius) can be derived from this measurable contribution, despite the fact that the resonant wavelength of one or more outer cores shifts beyond the limits of the scanning wavelength range. Although the central core has no observable contribution to the strain signal in portions with larger bending radii, this is different in portions outside the range where one or more bending radii are very small.

[0017] The fiber optic sensor used in the method according to the invention can be a standard fiber optic sensor having three outer cores and one central core. The outer cores can be spirally wound around the central core. The sensing element of the core can be a fiber Bragg grating (FBG). The number of outer cores and the type of sensing element can differ from those previously indicated.

[0018] The method according to the invention enables the shape of a fiber optic sensor to be represented with high accuracy in one or more ranges outside of conventional methods of shape representation.

[0019] Since the method according to the invention does not require redundancy in the number of fiber optic sensor cores, it also saves costs.

[0020] Preferred embodiments are described in the dependent claims or in the subsequent parts of the specification.

[0021] In an embodiment, reconstructing the shape of the at least one out-of-range portion may further include interpolating one or more quantities of the at least one out-of-range portion from one or more quantities of the same type from at least one portion adjacent to the at least one out-of-range portion.

[0022] In the portion adjacent to the outer limit section, i.e., the portion with a radius of curvature not less than the minimum measurable bending radius, strain measurements can be performed as usual and with high accuracy. Based on these measurements, one or more quantities of the same type as those in the adjacent portion can be interpolated (particularly linearly) in the outer limit section. Phase measurements in two adjacent portions before and after the outer limit section can be used for interpolation.

[0023] Preferably, the one or more quantities may include one or more quantities that vary slowly along the portion outside the range.

[0024] Besides curvature or bending radius, these quantities can be anything required for shape reconstruction. While the bending radius would be too small in the out-of-range portion, the length of that portion would also be limited, for example, when the fiber optic sensor bends at an angle no greater than, for example, a U-turn or kink. Therefore, it is reasonable to assume that most quantities (except curvature) will exhibit only minor variations in that portion. Thus, interpolation (especially linear interpolation) of one or more of these quantities will be sufficient for accurate shape reconstruction.

[0025] One or more quantities that typically vary slowly in the outer portion can be the bending angle (bending direction), the torsional angle, and / or common-mode strain. Common-mode strain is the strain common to all cores and typically includes both thermal strain and axial strain.

[0026] In an embodiment, step a) may include measuring position-related strain by optical probing of the central core in the at least one out-of-range portion.

[0027] As mentioned above, when the bending radius is very small, there is a non-negligible nonlinear effect between the stress and strain applied due to bending. Therefore, while the outer core does not provide a strain signal useful for shape reconstruction due to its relatively larger core distance from the center of the fiber optic sensor, the central core, conversely, provides a measurable contribution to the strain due to curvature. This contribution to strain can be measured and used for shape reconstruction of the portion of the fiber optic sensor outside its range. In this embodiment, the curvature of the fiber optic sensor can be calculated based on the derivative of the position-related phase difference of the signal received from the interferometer from the central core.

[0028] In an embodiment, calculating the curvature of the fiber optic sensor in the at least one range outside the range may include using a nonlinear relationship between strain and curvature to calculate the curvature.

[0029] Preferably, calculating the curvature of the fiber optic sensor in the at least one portion outside the range includes using a linear relationship between strain and square curvature (or in other words, a quadratic relationship between strain and curvature) to calculate the curvature.

[0030] Therefore, using the linear relationship between strain and square curvature utilizes the lowest order of the nonlinear relationship between applied stress and strain, namely, the second order of the nonlinear effect. Although higher orders than the second order of the nonlinear relationship between strain and curvature could also be used, using the second-order (quadratic) relationship reduces computational complexity while achieving high accuracy.

[0031] To find the scaling factor between strain and square curvature, in another embodiment, it can be provided that the scaling factor is determined by calibrating the fiber optic sensor before probing the fiber optic sensor.

[0032] Calibrating the fiber optic sensor may include bending the fiber optic sensor to a plurality of different bending radii equal to or greater than the minimum radius of curvature in a small length region along the length of the fiber optic sensor, optically probing the core to obtain interference signals from the core at a plurality of locations along the fiber optic sensor, calculating common-mode strain and curvature based on the interference signals along the fiber optic sensor, and calculating the scaling factor from the common-mode strain and square curvature.

[0033] In this way, the scaling factor can be determined with high accuracy.

[0034] When the position-dependent curvature in the outer part of the range is known from the distributed strain measurement of the central core in the outer part, the position-dependent derivative of the phase difference (strain) of the outer core in the outer part can be calculated using the known position-dependent curvature.

[0035] In another embodiment, step b) may further include identifying at least one of the beginning and end of the at least one out-of-range portion.

[0036] Identifying the start and / or end of at least one out-of-range portion further improves the method according to the invention, because the steps of interpolating one or more quantities in at least one out-of-range portion and / or using strain measurements from the central core based on the nonlinear effect between applied stress and strain can be started and / or completed at the correct location along the fiber optic sensor, while in the non-out-of-range portion, shape measurement and reconstruction can be performed with high accuracy as usual.

[0037] The identification step may include setting at least one of the following: a curvature threshold, a threshold for the absolute value of the phase difference between two consecutive sample points in the signal received from the interrogation.

[0038] This embodiment utilizes the concept that, in a portion of the fiber optic sensor not far before the out-of-range portion, the curvature increases and begins to approach its maximum achievable value. Furthermore, the absolute value of the phase difference between two consecutive sample points begins to increase to π rad in the same portion of the fiber optic sensor. A similar concept applies to the out-of-range portion of the fiber optic sensor. In this embodiment, thresholds can advantageously be set for both curvature and phase difference to mark the start and / or end positions of the out-of-range portion.

[0039] The step of identifying the beginning of the at least one out-of-range portion may include identifying when at least one of the absolute values ​​of curvature and phase difference increases and begins to approach at least one of the curvature threshold and the threshold value of the absolute value of phase difference. The step of identifying the end of the at least one out-of-range portion may include identifying when at least one of the absolute values ​​of curvature and phase difference decreases and begins to fall below at least one of the curvature threshold and the threshold value of the absolute value of phase difference.

[0040] According to a second aspect, a system for representing the shape of an optical fiber sensor is provided, the optical fiber sensor having a central core and a plurality of outer cores, each core including one or more sensing elements, the system comprising:

[0041] (a) A probing module configured to optically probing the core of the fiber optic sensor from incident light waves in a wavelength range centered on the resonant wavelength of the one or more sensing elements, wherein the wavelength range is associated with detection limited to the minimum radius of curvature of the fiber optic sensor.

[0042] (b) A reconstruction module configured to reconstruct the shape of the fiber optic sensor, involving processing an interferometric measurement signal received from the optical interrogation of the core, including reconstructing the shape along at least one out-of-range portion of the fiber optic sensor, the at least one out-of-range portion being a portion having a radius of curvature lower than the minimum radius of curvature, wherein the reconstruction module is configured to reconstruct the shape of the at least one out-of-range portion by calculating the curvature of the fiber optic sensor in the at least one out-of-range portion based on the interferometric measurement signal received from the interrogation of the central core in the at least one out-of-range portion;

[0043] (c) A display unit configured to display the shape of the fiber optic sensor, including the at least one portion outside the range.

[0044] It should be understood that the system for which protection is sought may have similar and / or identical preferred embodiments to the method for which protection is sought and, as particularly, defined in the dependent claims and disclosed herein.

[0045] According to a third aspect of the invention, a computer program including program code units is provided, which, when executed on a system, are configured to cause the system according to the second aspect to perform the steps of the method according to the first aspect. Attached Figure Description

[0046] These and other aspects of the invention will be apparent and illustrated with reference to one or more embodiments described below. In the accompanying drawings:

[0047] Figure 1A block diagram illustrating the shape of a fiber optic sensor is shown.

[0048] Figure 2 It shows the use of in Figure 1 A perspective view of the fiber optic sensors used in the system;

[0049] Figure 3 It shows Figure 2 The cross-section of the fiber optic sensor in the image;

[0050] Figure 4 a) shows a graph of an example curvature as a function of the position along the fiber optic sensor;

[0051] Figure 4 b) shows the target Figure 4 a) Curves of bending signals of various cores of the fiber optic sensor with curvature.

[0052] Figure 5 a) shows a cross-section of the fiber optic sensor subjected to curvature;

[0053] Figure 5 b) Explained the nonlinear relationship between applied stress and strain;

[0054] Figure 6 A graph showing the phase derivative and curvature of the measurement as a function of the position along the fiber optic sensor is presented.

[0055] Figure 7 based on Figure 6 A graph of the phase derivative as a function of square curvature is shown;

[0056] Figure 8 The graphs show the phase derivatives of various cores of the fiber optic sensor in the high curvature region;

[0057] Figure 9 a) A graph showing the shape of an optical fiber sensor with a ring having a radius of curvature of 16.7 mm is shown, wherein shape reconstruction has been performed using conventional methods;

[0058] Figure 9 b) shows the representation having with Figure 9 a) A graph showing the shape of the fiber optic sensor with the same ring as in a), wherein shape reconstruction has been performed using the method according to the invention;

[0059] Figure 9 c) shows a graph representing the shape of an optical fiber sensor with a curvature that is smaller than the smallest radius that can be measured by conventional methods.

[0060] Figure 9 d) shows the representation having with Figure 9c) A graph showing the shape of the fiber optic sensor with the same curvature, while shape reconstruction has been performed using the method according to the invention. Detailed Implementation

[0061] Figure 1 A portion of the system 10 configured to represent the shape of the fiber optic sensor 12 is shown schematically.

[0062] System 10 can be configured as a distributed strain sensing system based on a multi-channel optical frequency domain reflectometer (OFDR) for probing the fiber optic sensor 12 and reconstructing the shape of the fiber optic sensor 12. The fiber optic sensor may have multiple fiber cores 14, 16, 18, 20 embedded therein; in this embodiment, it has four cores with one central core 16 and three outer cores 14, 18, 20. The fiber optic sensor 12 can be a standard fiber optic sensor known in the field of optical shape sensing.

[0063] Figure 2 A section of fiber optic sensor 12 and cores 14, 16, 18, and 20 are shown. Figure 3 A cross-section of the fiber optic sensor 12 in a plane perpendicular to its longitudinal central axis is shown. Outer cores 14, 18, and 20 are spirally arranged around a central core 16. The central core 16 is positioned on the central axis of the fiber optic sensor 12. The outer cores 14, 18, and 20 are angularly spaced from each other in the azimuth direction around the longitudinal central axis of the fiber optic sensor 12. The longitudinal central axis coincides with the central core 16. Depending on the number of four cores in this embodiment, the angular spacing between adjacent outer cores can be 120°. Figure 3 In this context, 'a' represents the distance from the outer core to the center. The distance 'a' can be the same for all outer cores 14, 18, and 20, or it can be different.

[0064] Refer again Figure 1 System 10 includes an interrogation unit 21 and a reconstruction unit 23. The interrogation unit 21 and the reconstruction unit can be integrated as follows: Figure 1 The apparatus is shown. The interrogation unit 21 may include a tunable light source 22 that can sweep across an optical frequency range, also known as a scanning wavelength range. Light emitted by the light source 22 is coupled into an optical interferometry network 24 having optical channels 24a, 24b, 24c, and 24d, depending on the number of fiber cores 14, 16, 18, and 20 of the fiber optic sensor 12. If the fiber optic sensor 12 has fewer or more than four cores, the optical interferometry network 24 may have a correspondingly fewer or more optical channels.

[0065] When the tunable light source 22 sweeps across a range of optical frequencies, each channel 24a, 24b, 24c, 24d of the fiber optic sensor 12, and therefore each fiber core 14, 16, 18, 20, is simultaneously and independently optically probed, and the interferometric measurement signal based on the reflection spectrum returned from each fiber core 14, 16, 18, 20 is routed to the processing unit or data acquisition unit 26 via the corresponding photodetector 25. The processing unit can also reconstruct the 3D shape of the fiber optic sensor 12 based on the distributed strain measurement results from the cores 14, 16, 18, 20. The reconstructed shape can be visually displayed on the display unit 27. The system 10 is specifically configured to perform the method according to this disclosure.

[0066] In embodiments of the fiber optic sensor 12, fiber optic sensor cores 14, 16, 18, and 20 may have fiber optic sensor Bragg gratings (FBGs) formed by periodic variations in refractive index. For simplicity, this document considers an FBG with a single resonant wavelength. The FBG reflects light at a specific wavelength (resonant wavelength) depending on the grating period of the FBG and transmits all other wavelengths. Due to the bending of the fiber optic sensor 12, the grating period is affected by strain, and measurements of the reflected wavelength at any location along the fiber optic sensor allow determination of the local strain of the fiber optic sensor 12.

[0067] In the method of representing the shape of the fiber optic sensor 12, the cores 14, 16, 18, and 20 of the fiber optic sensor 12 are optically probed from incident light waves supplied by the light source 22. Optical probing of the fiber optic sensor 12 provides the information needed, in principle, to reconstruct the three-dimensional shape of the entire fiber optic sensor 12 in real time. Given an appropriate reference strain, the exact orientation and position of the complete fiber optic sensor 12 can be known in real time.

[0068] The response of the cores to strain and temperature is measured by system 10 as the phase difference of the optical signal from interferometric network 24, as a function of the delay (position) along the fiber optic sensor 12. The phase difference is obtained relative to a reference measurement, where the fiber optic sensor is in a well-defined shape, such as a perfectly straight shape. Based on the phase differences of cores 14, 16, 18, and 20 relative to the reference measurement, the strain and temperature difference for each core can be derived. The strain signal will be the sum of bending strain in two orthogonal directions, torsional strain, and axial strain, with the axial strain being the strain in the longitudinal direction of the fiber optic sensor 12. Based on these four position-related quantities, the shape of the fiber optic sensor 12 can be reconstructed.

[0069] Therefore, the shape of the fiber optic sensor 12 can be calculated based on the position-related strain signals measured for several cores 14, 16, 18, and 20 inside the fiber optic sensor 12. For example, if the core is arranged at a certain distance from the center of the fiber optic sensor 12, bending the fiber optic sensor 12 in the plane defined by the outer core and the center of the fiber optic sensor 12 will result in strain on the core:

[0070]

[0071] Here, ε is the strain experienced by the core at a distance a from the center of the fiber optic sensor due to the bending of radius r. The bending strain is measured relative to the straight and unstrained cases of the fiber optic sensor 12. The magnitude of the strain can be inferred from the amount of spectral shift of the reflected light received from the core of the fiber optic sensor 12. When the fiber optic sensor 12 includes an FBG as a sensing element, and due to the periodic nature of the FBG, the fiber optic sensor 12 will reflect light of a specific wavelength (i.e., the resonant wavelength). When the fiber optic sensor core elongates (positive strain) relative to a reference measurement, the period of the FBG will increase, resulting in an increase in the resonant wavelength. In the case of compressive (negative) strain, the period of the FBG will decrease, thus decreasing the resonant wavelength. The smaller the radius of curvature, the greater the shift in the resonant wavelength δλ (in the positive or negative direction, depending on the position of the core in the bend):

[0072]

[0073] Where λ0 is the resonant wavelength of the FBG in the unstrained state, and ξ is the strain optics number, which can be approximately 0.8, taking into account the strain-induced change in refractive index that affects the relationship between the Bragg period and wavelength. The sin function in Equation (2) describes the change in position of the outer cores 14, 18, or 20 as they spirally twist around the center of the fiber optic sensor. z is the position along the length of the fiber optic sensor 12. θ twist dθ is the cumulative twist angle of the corresponding core, which is the sum of the inherent twist in the spin fiber sensor and the externally applied twist. For example, for a fiber sensor with 50 turns per meter, dθ twist / dz=314rad / m. It is the offset angle related to the orientation of the bending plane and the angle of the core at the reference position. For clarity, only the strain due to bending is assumed in Equation (2).

[0074] When fiber optic sensors (such as fiber optic sensor 12) are used, for example, in medical devices (such as catheters or guidewires), the device will change its shape during operation. For example, if the device is a catheter intended for insertion into a person's vascular system (which may be very tortuous), the device, and therefore the fiber optic sensor 12, will undergo bending along its length, which may have a very small radius of curvature. However, in optical shape sensing techniques, there are limitations associated with the minimum measurable bending radius of the fiber optic sensor 12. In this disclosure, the portion along the fiber optic sensor 12 where the radius of curvature is lower than the minimum radius of curvature measurable by probing the outer core is referred to as the out-of-range portion.

[0075] The minimum bending radius r of an optical fiber sensor that still resonates within the measurement spectrum and is therefore measurable. min It can be given as:

[0076]

[0077] For example, for a scan range of the outer core with Δλ = 17 nm and λ0 = 1545 nm, ξ = 0.8, and a = 35 μm, the minimum measurable radius of curvature would be 5.1 mm. If the fiber optic sensor 12 is bent to a lower radius of curvature, then for a given scan wavelength range and a given core distance from the center, no signal will be measured for the outer core in the bent plane.

[0078] Figure 4 An example is shown where the fiber optic sensor 12 bends over a short distance, where the radius of curvature is too small for detection within the scanning wavelength range. Figure 4 a) shows the curvature of the fiber optic sensor along the fiber optic sensor. Figure 4 b) shows the corresponding bending signals for various cores, denoted here as cores 0 to 3, where core 0 is the center core and cores 1, 2 and 3 are the outer cores. Figure 4 The dashed lines in b) represent unmeasurable signals that exceed the scanning wavelength range Δλ, where the wavelength offset δλ exceeds the scanning wavelength range. The scanning wavelength range is determined by... Figure 4 The gray background in b) is shown. Figure 4 (b) It can be seen that, due to the small distance of the sharp bend extension, the sinusoidal behavior of the signals received from the outer cores 1, 2, and 3 exists only within a limited positional range. Furthermore, the signal becomes discontinuous when the strain exceeds the wavelength range.

[0079] According to formula (3), increasing the scanning wavelength range Δλ and / or decreasing the distance a of the outer core from the center would be straightforward. However, this disclosure provides a different method than increasing the scanning wavelength range and decreasing the distance a of the outer core from the center to achieve high-accuracy shape reconstruction of the fiber optic sensor 12 along its entire length, and therefore also in the portion of the fiber optic sensor outside the range where the radius of curvature of the fiber optic sensor 12 is below the minimum measurable radius of curvature. The method according to this disclosure also does not require redundancy in the number of outer cores, and is applicable, for example, to standard fiber optic sensors with one central core and three outer cores. It should be understood that this disclosure is not limited to the use of standard fiber optic sensor designs.

[0080] The method for representing the shape of an optical fiber sensor (such as optical fiber sensor 12) according to this disclosure includes reconstructing the shape along the outer portion of the optical fiber sensor based on interferometric measurement signals received from optical interrogation of a central core in the outer portion, preferably at multiple locations along at least one outer portion. The shape reconstruction may further be based on one or more quantities obtained by interpolating one or more quantities of the same type from one or two portions adjacent to the outer portion.

[0081] In the following description, the use of quantities obtained from the signal received from the optical interrogation of the central core in the out-of-range portion for shape reconstruction of the fiber optic sensor 12 in the out-of-range portion will be described in more detail.

[0082] A second-order nonlinear effect exists in the relationship between stress and strain applied due to bending. This effect is negligible for small strains, but becomes readily observable for high strain values. Therefore, the signal from the central core provides a measurable contribution to the strain due to curvature, and the bending radius can be derived from this measurable contribution, despite the fact that the resonant wavelengths of the outer cores (e.g., cores 14, 18, 20) deviate beyond the scanning wavelength range. This can be explained as follows.

[0083] For small stresses σ (the amount of force per unit cross-sectional area), the relationship with the subsequent strain ε (relative elongation) is linear with a proportionality constant E known as Young's modulus. For large strains, Young's modulus depends on the strain given by the following formula:

[0084]

[0085] The modulus E0 is Young's modulus at small strain values. The nonlinear term γε / 2 describes the strain dependence of Young's modulus, and γ is a proportionality constant. In steady state, the stress σ = E0. The integral over the cross-section should always be zero; otherwise, the fiber optic sensor will deform and / or shift. For a fiber optic sensor with bending and considering only linear terms, the requirement of zero integral stress is satisfied when exactly half of the cross-section has negative (compressive) strain and the other half has positive (tensile) strain. Zero strain is exactly at the midpoint of the cross-section. Including nonlinear terms shifts the neutral line of zero strain towards the tensile portion to compensate for the quadratic term, which increases the absolute value of the stress in the tensile portion and decreases the absolute value of the stress in the compressive portion (γ>0). Figure 5 Graphical representations of these aspects are given in a) and 5b). R is the radius of the fiber optic sensor, and κ is the curvature. The strain at the center of the fiber optic sensor due to bending is not zero, and is equal to... This means that the central core in the fiber optic sensor will undergo secondary curvature-dependent strain. This signal can be measured and used to recover regions beyond the scanning wavelength range (i.e., Figure 4 The signal of the outer core in the area outside the dashed line shown in b) is then used. Subsequently, the shape of the fiber optic sensor 12 can be calculated even in regions with excessive curvature (i.e., bending radii below the minimum measurable bending radius).

[0086] In order to evaluate curvature from the signal at the center core, the proportionality constant β (i.e., factor) between the square of curvature and the common-mode strain is used. The requirement is known. The factor β can be found through a calibration procedure performed on the fiber optic sensor. Calibration can be performed as follows: the fiber optic sensor is bent to various bending radii over a small region of interest, such that the subsequent signal remains within the wavelength scan range, i.e., also for the outer core. Based on the signals from a total of 4 cores, the common-mode strain and curvature are calculated. An example of this measurement is shown in... Figure 6 It is given in [the document]. Figure 6 In the diagram, the shape curvature and common-mode phase derivative are plotted relative to the location along the fiber optic sensor. Due to the small radius of curvature, the curvature in this example reaches a maximum of 150m near the location of 2.15m. -1 . Figure 6 The common-mode phase derivative from which the common-mode strain can be calculated is shown. In a practical example, the scaling constant between the common-mode strain and the phase derivative can be approximately -0.106 με / (rad / m). Figure 6 In this example, the curvature reaches a maximum of 150m at a position of approximately 2.15m. -1 Furthermore, the phase derivative reaches a maximum of 550 rad / m.

[0087] Figure 7 It is shown as follows Figure 6 The phase derivative of the interference signal shown is as follows Figure 6Common-mode strain of the square of curvature shown. From Figure 7 it can be seen that the graph is linear, with a slope of =0.025rad x m. This corresponds to a γ value of the strain dependence of Young's modulus of 5.4.

[0088] When not only the bending strain is linear with respect to curvature but also the common-mode strain caused by bending is quadratic with respect to curvature, the corresponding phase derivative representing strain on the core of an optical fiber sensor can be written as follows:

[0089]

[0090] In formula (5), is the phase difference between the measurement of the actual shape and the reference shape (usually a straight shape) of the optical fiber sensor; a is the distance of the corresponding core from the center of the optical fiber sensor. SF is a constant describing the relationship between curvature and phase derivative; θ bend gives the bending direction, θ helix represents the angle of helical winding of the outer core inherent in the optical fiber sensor; θ twist is an additional angle caused by the twist of the optical fiber sensor due to external torque; and Δ represents the angular (azimuthal) position of the corresponding core in the cross-section of the optical fiber sensor relative to the reference axis. The second term on the right-hand side of formula (5) represents axial strain and temperature strain (i.e., common-mode strain), while the last term in formula (5) is the strain caused by nonlinear bending proportional to the square of curvature. The quantities a, SF, θ helix and Δ can be determined in a conventional calibration procedure applied to each optical fiber sensor under consideration.

[0091] For sensors with the same radius R, the scaling factor β (see above) generally does not vary significantly between different optical fiber sensors, because the stress / strain nonlinearity represents a property of the glass material. For each of various cores in an optical fiber sensor (for example, four cores as shown in Figure 2 and 3 ), a formula such as formula (5) can be written with the following concept: for each core and the measured phase derivative on the left-hand side of formula (5), the values of a and Δ will be different.

[0092] With reference to Figure 8 , consider now a region z1<z<z2 of an optical fiber sensor with high curvature, such that outer cores (such as cores 14, 18, 20) will experience a strain that is too large to be measured within a given scanning wavelength range. Within the region z1<z<z2, it is necessary to recover the phase of the outer cores, because no measurable bending signal exists in this region, as indicated by the dashed line. For regions z<z1 and z>z2, all information is available to reconstruct the shape based on the measurement of the distributed strain (phase derivative) of the outer cores, that is, the bending angle θbend , torsion angle θ twist and curvature κ are known as functions of the distance along the optical fiber sensor and the common-mode effect caused by axial strain and temperature .

[0093] When reconstructing the shape of the optical fiber sensor in the out-of-range portion, the shape representing method according to the present disclosure may also use one or more quantities obtained by interpolating one or more quantities of the same type from one or two portions adjacent to the out-of-range portion. In this example, the out-of-range portion is the area between z1 and z2. In the interpolated area, the bending radius will be small, and therefore, when the optical fiber sensor is bent at an angle that is not greater than, for example, a U-turn or a kink, the length of the interpolation will also be limited. Therefore, it is reasonable to assume that in this area, most quantities (except curvature) will exhibit a small amount of change, and thus change only slowly. Therefore, the method according to the present disclosure proposes to obtain the bending angle θ from the region before z1 and / or after z2 bend , torsion angle θ twist and / or common-mode signal interpolate (especially linear interpolation) the bending angle θ in the region between z=z1 and z=z2 bend , torsion angle θ twist and / or common-mode signal It should be noted here that bending angle should not be confused with curvature.

[0094] Since the phase derivative in formula (5) can be measured for the central core ( Figure 8 core 0 therein), all quantities in formula (5) are known through measurement, calibration or linear interpolation, except for curvature κ. Therefore, formula (5) can be solved for the curvature κ at each node in the region z1<z<z2 of the central core.

[0095] For the outer core ( Figure 8 cores 1, 2, 3 therein), all quantities of formula (5) are now known except for the phase derivative on the left-hand side of formula (5). However, since all quantities on the right-hand side of formula (5) are known for the outer core, including the curvature known from strain measurements on the central core, the phase derivative on the left-hand side of formula (5) for each outer core in the region z1<z<z2 can now be calculated using the quantities on the right-hand side obtained from the previous step. If necessary, an offset can be added so that the phase and its derivative are sufficiently continuous.

[0096] Since all phases of all cores are now known, the standard procedure for shape reconstruction can now be applied in the out-of-range portion.

[0097] The method according to this disclosure may further include the step of identifying the start and / or end of the out-of-range portion. Identification of the start and / or end of the out-of-range portion can be performed as follows: In the portion of the fiber optic sensor preceding the out-of-range portion, the curvature will increase and begin to approach a maximum achievable value. For a typical interrogator, this value could be approximately 200m. -1 Furthermore, the absolute value of the phase difference between two consecutive sample points begins to increase to π rad within the same portion of the fiber optic sensor. A similar consideration applies to portions of the fiber optic sensor beyond the region of interest, i.e., at or after the ends of the out-of-range portion.

[0098] It is advantageous to set the thresholds for both curvature and phase difference to, for example, 180m. -1 And 2.8 rad, to mark the start and end positions of the out-of-phase region.

[0099] refer to Figure 9 Experiments demonstrating the efficiency of the method according to this disclosure will be described. Figure 9 In the first experiments a) and b), an optical fiber sensor is provided, and the top end of the optical fiber sensor is folded back onto the optical fiber sensor, thereby creating a loop. The shape of the optical fiber sensor is reconstructed twice, once without small bending radius correction in the shape reconstruction according to this disclosure, and once with small bending radius correction in the shape reconstruction according to this disclosure. The small bending radius correction is based on a second-order nonlinear effect in the relationship between the applied bending stress and strain as described above. Figure 9 a) and 9b) show representations of the shape of an optical fiber sensor with the top folded back onto the optical fiber sensor. Since the minimum radius of curvature present in the region of the loop is 16.7 mm, according to this disclosure, without correction for small bending radii (… Figure 9 In the case of a)) and with correction for a small bending radius ( Figure 9 In case b), the shape representation did not show any difference.

[0100] In the second experiment, the tip of the fiber optic sensor was folded back onto the fiber optic sensor with a sharper curvature than in the first experiment (i.e., with a minimum radius of curvature of 2.7 mm). According to Figure 9 d) When using the method according to this disclosure, the shape of the fiber optic sensor can be accurately reconstructed. Without using the method according to this disclosure, the actual shape cannot be accurately represented, and incorrect results are given. Using the method according to this disclosure, the shape of a fiber optic sensor with a bending radius as small as 2.7 mm can be represented with high accuracy, which is approximately twice the smallest measurable radius of curvature, without increasing the scanning wavelength range, without reducing the distance of the outer core from the center, and without any redundancy in the number of outer cores.

[0101] The computer program includes program code units that, when executed on system 10, cause system 10 to perform steps of the method according to this disclosure. The computer program may be stored / distributed on a suitable non-transient medium, such as an optical storage medium or solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunications systems.

[0102] Although the invention has been illustrated and described in detail in the accompanying drawings and the foregoing description, such illustrations and descriptions should be considered illustrative or exemplary, and not restrictive; the invention is not limited to the disclosed embodiments. Those skilled in the art, through studying the drawings, the disclosure, and the claims, will understand and implement other variations of the disclosed embodiments in practicing the claimed invention.

[0103] In the claims, the word "comprising" does not exclude other elements or steps, and the words "a" or "an" do not exclude a plurality. A single element or other unit can perform the functions of several items recited in the claims. Although specific measures are recited in different dependent claims, this does not indicate that combinations of these measures cannot be advantageously used.

[0104] No reference numerals in the claims should be construed as limiting the scope.

Claims

1. A method for representing the shape of an optical fiber sensor (12), the optical fiber sensor having a central core (16) and a plurality of outer cores (14, 18, 20), each core including one or more sensing elements, the method comprising: (a) Optically probing the core (14, 16, 18, 20) of the fiber optic sensor (12) from incident light waves within a wavelength range centered on the resonant wavelength of the one or more sensing elements, wherein the wavelength range is associated with detection limited to the minimum measurable radius of curvature of the fiber optic sensor. (b) Reconstructing the shape of the fiber optic sensor (12) involves processing interferometric measurement signals received from the optical interrogation of the cores (14, 16, 18, 20), including reconstructing the shape along at least one out-of-range portion of the fiber optic sensor (12), the at least one out-of-range portion being a portion having a radius of curvature lower than the minimum measurable radius of curvature, wherein reconstructing the shape of the at least one out-of-range portion includes calculating the curvature of the fiber optic sensor (12) in the at least one out-of-range portion based on the interferometric measurement signals received from the interrogation of the central core (16) in the at least one out-of-range portion; (c) Showing the shape of the fiber optic sensor (12) including the at least one portion outside the range.

2. The method according to claim 1, wherein, Reconstructing the shape of the at least one out-of-range portion further includes interpolating one or more quantities of the same type in the at least one out-of-range portion from one or more quantities in at least one portion adjacent to the at least one out-of-range portion.

3. The method according to claim 2, wherein, The one or more quantities include one or more quantities that change slowly along the portion outside the range.

4. The method according to claim 3, wherein, The one or more quantities include one or more of the following: bending angle, torsion angle, common mode strain.

5. The method according to claim 1, wherein, Step a) includes measuring position-dependent strain by optical probing of the central core (16) in at least one out-of-range portion.

6. The method according to claim 1, wherein, Calculating the curvature of the fiber optic sensor (12) in at least one portion outside the range involves using a nonlinear relationship between strain and curvature to calculate the curvature.

7. The method according to claim 1, wherein, Calculating the curvature of the fiber optic sensor (12) in the at least one portion outside the range involves using a linear relationship between strain and square curvature to calculate the curvature.

8. The method of claim 7 further comprises, prior to step (a), calibrating the fiber optic sensor (12) to determine the scaling factor between strain and square curvature.

9. The method according to claim 8, wherein, Calibrating the fiber optic sensor (12) includes: bending the fiber optic sensor (12) into a plurality of different bending radii equal to or greater than the minimum measurable radius of curvature in a small length region along the length of the fiber optic sensor (12); optically probing the cores (14, 16, 18, 20) to obtain interference signals from the cores (14, 16, 18, 20) from a plurality of locations along the fiber optic sensor (12); calculating common-mode strain and curvature based on the interference signals along the fiber optic sensor (12); and calculating the scaling factor based on the common-mode strain and square curvature.

10. The method according to claim 1, wherein, Step (b) further includes identifying at least one of the start and end of the at least one out-of-range portion.

11. The method according to claim 10, wherein, The identification steps include setting at least one of the following: a curvature threshold, a threshold for the absolute value of the phase difference between two successive sample points in the signal received from the interrogation.

12. The method according to claim 11, wherein, The step of identifying the start of the at least one out-of-range portion includes identifying when at least one of the absolute values ​​of curvature and phase difference increases and begins to approach at least one of the curvature threshold and the threshold value of the absolute value of phase difference.

13. The method according to claim 11, wherein, The step of identifying the end of the at least one out-of-range portion includes identifying when at least one of the absolute values ​​of curvature and phase difference decreases and begins to fall below at least one of the curvature threshold and the absolute value of phase difference.

14. A system for representing the shape of an optical fiber sensor (12), the optical fiber sensor having a central core (16) and a plurality of outer cores (14, 18, 20), each core including one or more sensing elements, the system comprising: (a) A probing module (21) configured to optically probing the core (14, 16, 18, 20) of the fiber optic sensor (12) from incident light waves within a wavelength range centered on the resonant wavelength of the one or more sensing elements, wherein the wavelength range is associated with detection limited to the minimum measurable radius of curvature along the fiber optic sensor (12). (b) A reconstruction module (23) configured to reconstruct the shape of the fiber optic sensor (12) involving processing interferometric measurement signals received from the optical interrogation of the cores (14, 16, 18, 20), including reconstructing the shape along at least one out-of-range portion of the fiber optic sensor (12), the at least one out-of-range portion being a portion having a radius of curvature lower than the minimum measurable radius of curvature, wherein the reconstruction module (23) is configured to reconstruct the shape of the at least one out-of-range portion by calculating the curvature of the fiber optic sensor (12) in the at least one out-of-range portion based on the interferometric measurement signals received from the interrogation of the central core (16) in the at least one out-of-range portion; (c) A display unit configured to display the shape of the fiber optic sensor, including the at least one portion outside the range.

15. A computer program product comprising program code units, wherein when the computer program is executed on a system according to claim 14, the program code units are configured to cause the system to perform the steps of the method according to claim 1.

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