High-speed high-precision fiber shape measurement method based on phase demodulation

Abstract

The present application relates to a kind of high-speed high-precision optical fiber shape measurement method based on phase demodulation, using the helical multicore optical fiber containing long-period fiber grating, based on the distributed three-dimensional shape sensing measurement device of multi-channel OFDR, channel number is not less than the number of core, including: the differential phase strain demodulation of phase jump removal;(2) the fiber external torsion compensation of multicore optical fiber: the strain caused by fiber external torsion is calculated after the common-mode strain of the average elimination of peripheral core strain;According to the external torsion of fiber and compensation when calculating bending direction is calculated;Shape reconstruction based on rotating minimal frame: the curve is regarded as being composed of many curvature radius fixed small circular arc segments, the radius and direction of circular arc are calculated by the curvature and bending direction angle of curve at the point, the shape of whole optical fiber is obtained by the method of rotating minimal frame to splice each circular arc micro segment.

Description

Technical Field

[0001] This invention relates to the field of fiber optic sensing technology, and in particular to a high-speed, high-precision fiber shape measurement technology based on phase demodulation. Background Technology

[0002] Shape measurement is a general term referring to measuring the specific location of a structure in three-dimensional space. Conventional methods for measuring shape are quite limited, such as physically measuring the coordinates of a position along a rope every inch or taking pictures with a camera. However, neither of these methods can accurately obtain the three-dimensional shape information of an object. On the other hand, if the object cannot be physically touched or seen, such as if it is contained in a sealed box, then how to perform such a measurement becomes a problem. This is where the advantages of fiber optic shape sensing (FOSS) become apparent.

[0003] The conventional method for measuring fiber optic shape is to use strain as the basic measurement signal. When the fiber is bent, the material on the outer side of the bend is stretched, while the material on the inner side is compressed. If the local strain changes throughout the fiber and the fiber's initial position are known, the fiber's shape and position information can be calculated. High-precision fiber optic shape measurement has applications in many fields, such as civilian, mechanical, aerospace, biological, and medical fields. In most of these applications, the shape sensing system must be able to accurately determine the fiber's position, for example, requiring a relative position error of less than one percent of its length. Currently, many methods exist for shape measurement, but none fully meet the requirements of most applications because they are too slow to meet real-time measurement needs, or they cannot adequately compensate for fiber torsion, resulting in insufficient accuracy. These factors diminish the practical application value of fiber optic shape sensing.

[0004] To achieve high-speed and high-precision shape and position measurement, several key issues must be addressed. First, Optical Frequency Domain Reflectometry (OFDR), with its high resolution and measurement accuracy over short distances, has become one of the most ideal methods for fiber optic shape measurement. However, the most classic strain demodulation method in OFDR is based on the cross-correlation principle, which has a very long computation time, making it unsuitable for real-time shape measurement. Therefore, a new method capable of fast and high-precision strain demodulation must be found.

[0005] Secondly, optical fibers inevitably introduce torsion during practical applications, which directly leads to errors in the calculation of bending direction angles. Therefore, it is essential to measure the torsion present in the fiber with high precision and compensate for it in subsequent shape calculations. Torsion can be sensed by using a helical multi-core fiber with a central core. However, the problem is that for tightly wound helical multi-core fibers, there is a force interaction between the outer cores and the central core. Therefore, measurements cannot be performed based on the traditional torsion model of helical multi-core fibers; a new torsion measurement model needs to be established.

[0006] Third, traditional shape reconstruction methods are spatial differential geometry reconstruction methods based on the Frenet-Serret framework. However, this method has its limitations. For example, the reconstruction accuracy of this method is very low for curves containing line segments and singular points. In addition, because it requires solving differential equations numerically, the calculation speed of this method is very slow and it is not suitable for real-time shape detection. Therefore, we hope to have a method that can perform shape reconstruction quickly. Summary of the Invention

[0007] The purpose of this invention is to provide a high-speed, high-precision method for measuring the shape of optical fibers. This method detects the optical phase change along the fiber in each core of a multi-core optical fiber. Based on the detected optical phase change and combined with a phase-hopping filtering method, the strain magnitude at that point on the multi-core fiber is calculated. Furthermore, the curvature and bending direction angle at that location are calculated. By comprehensively comparing the strain magnitudes in each fiber core, the external torsion of the fiber is calculated, and the bending direction angle is compensated. Finally, based on the compensated curvature and bending direction angle, the shape is reconstructed using the rotating minimum frame method to achieve the optical fiber shape measurement. The technical solution is as follows:

[0008] A high-speed, high-precision fiber shape measurement method based on phase demodulation is implemented using a helical multi-core fiber with a long-period fiber grating and a distributed three-dimensional shape sensing and measurement device based on a multi-channel OFDR, wherein the number of channels is not less than the number of fiber cores. The method is characterized by the following steps:

[0009] (1) Demodulation of differential phase strain to remove phase jump, the method is as follows:

[0010] S1.1: Two sets of experiments were conducted. One set of optical fibers was in a straight state, i.e., without any strain, as the reference set; the other set of optical fibers was in a bent state as the measurement set. The two sets of beat frequency signals were converted to the distance domain by fast Fourier transform and the optical phase information was extracted.

[0011] S1.2: Assuming that the initial wavelengths of the light sources are strictly equal, the difference between the two sets of phase signals is used to obtain the optical phase change caused by strain, thus obtaining the differential phase;

[0012] S1.3: Perform phase unwrapping on the differential phase, and differentiate the differential phase data after unwrapping. The phase change rate after differentiation reflects the strain magnitude at each position in the optical fiber.

[0013] S1.4 Removes singular points;

[0014] S1.5: Use the surrounding normal points to interpolate the singular points to obtain the de-jumped differential phase data;

[0015] S1.6: Combine zero-phase low-pass filtering to remove high-frequency noise and achieve strain data demodulation.

[0016] (2) External torsion compensation of multi-core optical fibers

[0017] Based on the demodulated strain data obtained in step (1), the strain caused by the external torsion of the optical fiber is calculated by averaging the strain of the outer core and eliminating the common-mode strain. The common-mode strain is obtained by calculating the average strain value in multiple cores. The external torsion of the optical fiber is calculated according to the torsion parameters and compensation is performed when calculating the bending direction.

[0018] (3) Shape reconstruction based on rotation minimum frame: The curve is regarded as a series of small arc segments with fixed curvature radii. The radius and direction of the arc are calculated by the curvature and bending direction angle of the curve at that point. The shape of the whole optical fiber is obtained by splicing each arc segment by rotating minimum frame.

[0019] Furthermore, the method for identifying singular points in S1.4 is as follows:

[0020] The phase change rate after differentiation of S1.4 reflects the strain magnitude at various locations in the optical fiber, denoted as .

[0021] S1.4: Will Divide the optical fiber into several segments, each with a length of N. Calculate the length of each segment. The absolute median difference (MAD);

[0022] S1.5: Set a determination coefficient q greater than 1, and calculate the absolute deviation δ of each data point from the median in each data segment. abs When δ abs If the value is greater than q*MAD, the point is considered a singular point; otherwise, it is considered a normal point.

[0023] Furthermore, it is characterized by q = 1.4826.

[0024] Furthermore, the specific steps of step (2) are as follows:

[0025] S2.1: Demodulate and acquire strain data of the central fiber core and each peripheral fiber core;

[0026] S2.2: Common mode strain is obtained from the average strain value in each fiber core and is denoted as ε. a ;

[0027] S2.3: Calculate the strain ε caused by torsion in the outer fiber core. twist ;

[0028] S2.4: Calculate the external torsion rate of the multi-core optical fiber:

[0029]

[0030] Where, ε c γ0 is the strain of the central fiber core, γ0 is the initial nominal spin rate of the optical fiber, obtained by γ0 = 2π / h, h is the initial pitch of the optical fiber, r is the core pitch of the multi-core optical fiber, and γ reflects the external torsion rate at various positions of the optical fiber.

[0031] S2.5: Obtain external torsion compensation for the optical fiber.

[0032] Furthermore, the method for calculating the external torsion rate of the multi-core optical fiber in step S2.4 is as follows:

[0033]

[0034] Where, ε c γ is the strain of the central fiber core, γ0 is the initial nominal spin rate of the optical fiber, obtained by γ0 = 2π / h, h is the initial pitch of the optical fiber, r is the core pitch of the multi-core optical fiber, and γ reflects the external torsion rate at various positions of the optical fiber.

[0035] Furthermore, in step S2.5, the formula for external torsion compensation of the optical fiber bending direction using the calculated external torsion angle is as follows:

[0036] θ=θ0-∫γds

[0037] Where θ0 is the bending direction angle before uncompensated torsion, and θ is the bending direction angle after compensated torsion.

[0038] Furthermore, the specific steps of step (3) are as follows:

[0039] S3.1: Calculate the relative coordinates of each point: Consider the curve as a series of tiny circular arcs with fixed radii of curvature, and calculate the relative coordinates of each point with respect to the previous point based on the curvature of each position of the optical fiber.

[0040] S3.2: Calculate the coordinate rotation matrix of the minimum frame of each point: The minimum frame of each point is a Cartesian coordinate system for that point. The x, y, and z axes of the coordinate system are defined as the tangent vector direction, principal normal vector direction, and binormal vector direction of that point, respectively. The minimum frame of the next point is obtained by rotating the minimum frame of the previous point. The rotation angle along the x-axis is the change in the bending direction angle of that point, and the rotation angle along the z-axis is the central angle corresponding to the arc segment. Thus, the coordinate rotation matrix of each point relative to the previous point is constructed, and the coordinate rotation matrix of the minimum frame of each point is calculated.

[0041] S3.3: Calculate the absolute coordinates of each point to obtain the three-dimensional shape coordinates of the optical fiber.

[0042] Further, the method of step S3.3 is as follows: given the relative coordinates of each point and the minimum frame rotation matrix, the relative position coordinates of each point are transformed into absolute coordinates relative to the geodetic coordinate system through coordinate transformation, which are the three-dimensional shape coordinates of the optical fiber. Attached Figure Description

[0043] Figure 1 This is a diagram of a three-dimensional shape measurement system based on a four-channel OFDR.

[0044] Figure 2 This is a flowchart of the differential phase strain demodulation algorithm for phase transition removal.

[0045] Figure 3 This displays differential phase data within a 1m range of a certain outer core of a multi-core optical fiber.

[0046] Figure 4 Displays differential phase data after unwinding.

[0047] Figure 5 Yes Figure 4 The phase change rate curve obtained after differentiation

[0048] Figure 6 This is a graph of the phase change rate after processing with a phase jump removal filtering algorithm.

[0049] Figure 7 This is a schematic diagram of the spiral multi-core optical fiber structure used.

[0050] Figure 8 This shows the strain distribution of each fiber core when the optical fiber is in a torsional state.

[0051] Figure 9 A schematic diagram showing the twisted outer core unfolding along the fiber surface is shown.

[0052] Figure 10 This is a schematic diagram of the shape reconstruction algorithm for the minimum rotating frame. Detailed Implementation

[0053] In the following description, specific details, such as particular nodes, functional entities, technologies, protocols, standards, etc., are set forth for the purpose of explanation and not limitation in order to understand the described techniques. It will be apparent to those skilled in the art that other embodiments besides the specific details disclosed below may be employed. In other instances, detailed descriptions of well-known methods, apparatuses, technologies, etc., have been omitted to avoid obscuring this specification with unnecessary detail, and various functional blocks are shown in the accompanying drawings.

[0054] This invention utilizes a helical multi-core optical fiber with a long-period fiber grating to achieve precise shape measurement. In fact, the shape and position information of the optical fiber can be determined by demodulating back Rayleigh scattering within the fiber. This measurement method enables high-precision, high-speed shape measurement.

[0055] The following section first introduces the distributed three-dimensional shape sensing and measurement system based on four-channel OFDR used in this invention.

[0056] This invention includes a distributed three-dimensional shape sensing and measurement device based on a four-channel OFDR using a helical multi-core optical fiber containing a long-period fiber grating. For example... Figure 1 As shown, the measuring device includes: a tunable laser 1, a computer 2, a 1:99 optical beam splitter 3, a four-channel high-speed data acquisition card 11, a clock triggering device 4 based on an additional interferometer, and four main interferometer modules, each corresponding to one of the four cores of a multi-core optical fiber.

[0057] The clock triggering device 4 based on the additional interferometer includes: a first circulator 5, a first 50:50 coupler 6, a first balanced detector 7, a delay fiber 8, a first Faraday rotating mirror 9, and a second Faraday rotating mirror 10. The clock triggering device 4 based on the additional interferometer is used to achieve equal optical frequency spacing sampling, the purpose of which is to suppress nonlinear scanning of the light source.

[0058] The four master interferometers are connected to the four channels of the four-channel high-speed data acquisition card 11, and are improved Mach-Zehnder interferometers. Each master interferometer includes: a 20:80 coupler (24, 25, 26, 27), a circulator (20, 21, 22, 23), a 50:50 coupler (16, 17, 18, 19), and a balanced detector (12, 13, 14, 15).

[0059] During operation, the light emitted from the tunable laser 1 is split into two paths by a 1:99 fiber coupler 3. One portion enters the auxiliary interferometer 4, then passes through the circulator 5 and the 50:50 coupler 6, before entering the reference arm and measurement arm of the auxiliary interferometer, respectively. After reflection by Faraday mirrors 9 and 10, a beat frequency signal is generated at coupler 6. This signal is converted into an electrical signal by the balanced detector 7 and provides an external clock for the data acquisition card 11. The clock trigger signal (f-clock) samples the beat frequency signal output by the main interferometer at equal optical frequency intervals to compensate for the nonlinear sweep frequency effect of the TLS. The remaining 99% of the light passes through three 50:50 couplers 28, 29, and 30 and is split into four paths, each corresponding to one of the four cores of the multi-core fiber. Each master interferometer consists of a reference arm and a measurement arm. The optical signal from the measurement arm passes through circulators 20, 21, 22, and 23 and is connected to the cores 31, 32, 33, and 34 of the multi-core fiber, respectively. The backscattered Rayleigh light in the cores and the reference light form beat interference within couplers 16, 17, 18, and 19, respectively. After passing through balanced detectors 12, 13, 14, and 15, the signals are converted into electrical signals and connected to the four channels of the acquisition card 11. The shape-sensing fiber 35 includes a central core coaxial with three spirally wound outer cores. The cross-sectional view of fiber 35 shows that the outer cores 31, 32, and 33 are evenly spaced at 120° angles and tightly wound with the central core 34.

[0060] The technical solution of the present invention will be described below.

[0061] This invention achieves precise measurement of the position and shape of an optical fiber based on the aforementioned measuring device. It detects the optical phase change along the fiber in each core of a multi-core optical fiber. Based on the detected optical phase change and combined with a phase-hopping filtering method, it calculates the strain magnitude at that point on the multi-core optical fiber, and further calculates the curvature and bending direction angle at that location. By comprehensively comparing the strain magnitudes in each fiber core, it calculates the external torsion of the optical fiber and compensates for the bending direction angle. Finally, based on the compensated curvature and bending direction angle, it uses the rotating minimum frame method to reconstruct the shape and achieve optical fiber shape measurement. This includes several aspects:

[0062] (1) Differential phase strain demodulation to remove phase jump

[0063] Step 1: Conduct two sets of experiments. One set of optical fibers is in a straight state (i.e., no strain is applied) as the reference set; the other set of optical fibers is in a bent state as the measurement set. The acquired beat frequency signals are converted to the distance domain using Fast Fourier Transform and the optical phase information is extracted and denoted as follows: and

[0064] Step 2: Assuming the initial wavelengths of the light sources are strictly equal, the difference between the two sets of phase signals is used to obtain the optical phase change caused by strain.

[0065] Step 3: Unwrap the differential phase. Due to the presence of light source phase noise, the phase curve at this point has a large number of transition points. To eliminate the influence of these transition points on the demodulation results, the derivative of the unwrapped differential phase data is calculated. The phase change rate after differentiation reflects the strain magnitude at various locations in the fiber, denoted as .

[0066] Step 4: The fiber is divided into several segments, each with a length of N. Then, the length of each segment is calculated. The absolute median deviation (MAD)

[0067] MAD = median(|A i -median(A i )|) (1)

[0068] The median is the absolute value of the new data obtained by subtracting the median from the original data. It is a robust measure of the variation in a data sample. Compared to the standard deviation, it is less susceptible to the influence of a few erroneous data points, and therefore more suitable as a threshold for identifying outliers.

[0069] Step 5: Calculate the absolute deviation δ of each data point from the median in each data segment. abs When δ abs A value greater than 1.4826 * MAD is considered a singular point; otherwise, it is considered a normal point. For more detailed information on this step, please refer to the following literature:

[0070] T.Pham-Gia, and TLHung, "The mean and median abso lute deviations," Mathematical and Computer Modelling, vol.34, no.7-8, pp.921-936, Oct, 2001.

[0071] Step 6: Use the surrounding normal points to interpolate the singular points to obtain the de-jumped differential phase data.

[0072] Step 7: At this point, the phase data still has some small noise fluctuations. Combine this with zero-phase low-pass filtering to remove high-frequency noise and achieve accurate strain data demodulation.

[0073] (2) External torsion compensation of optical fiber based on the characteristics of tightly wound spiral multi-core optical fiber

[0074] Unlike traditional helical multi-core fibers where there is a certain gap between the outer cores and the central core, the multi-core fiber used here has three outer cores tightly wrapped around a fourth core along the center of the fiber. This results in strain transfer between the central core and the surrounding cores. The strain caused by torsion can be calculated by averaging the strain of the outer cores and eliminating common-mode strain. The common-mode strain is obtained by calculating the average strain of all four cores. Then, the external torsion of the fiber is calculated based on the torsion parameters, and compensation is made when calculating the bending direction. The specific steps are as follows:

[0075] Step 1: Demodulate and acquire the strain data of each fiber core. The three outer fiber cores are denoted as ε1, ε2, and ε3, respectively, and the central fiber core is denoted as ε. c

[0076] Step 2: Due to the close contact between the outer and central fiber cores, the strain of the central fiber core cannot be eliminated as a common-mode strain. The common-mode strain at this point is obtained by averaging the strains in all four fiber cores, denoted as ε. a .

[0077] Step 3: Calculate the strain caused by torsion in the outer fiber core.

[0078]

[0079] Step 4: Calculate the external torsion rate of the optical fiber:

[0080]

[0081] Where γ0 is the initial nominal spin rate of the optical fiber, obtained by γ0 = 2π / h, r is the core pitch of the multi-core optical fiber, and γ reflects the external twist rate at various positions of the optical fiber. If you want to know the cumulative twist angle from the initial position, you can calculate it by integrating γ along the length of the optical fiber.

[0082] Step 5: Compensate for the bending direction of the optical fiber using the calculated external twist angle:

[0083] θ=θ0-∫γds (4)

[0084] Where θ0 is the bending direction angle before uncompensated torsion, and θ is the bending direction angle after compensated torsion.

[0085] (3) Shape reconstruction algorithm based on rotation minimum frame

[0086] The algorithm treats the curve as composed of many tiny arc segments with fixed radii of curvature. The radius and direction of each arc can be calculated from the curvature and bending direction angle of the curve at that point. Finally, by using a minimum rotating frame method, each arc segment is spliced ​​together to obtain the shape of the entire optical fiber. The advantages of this method are that it remains applicable to curves with singularities or straight line segments, and because it only requires simple matrix operations, the processing speed is very fast. The specific steps are as follows:

[0087] Step 1: Calculate the relative coordinates of each point. Consider the curve as composed of many tiny circular arc segments with fixed radii of curvature, and calculate the relative coordinates of each point with respect to the previous point based on the curvature of each position in the optical fiber.

[0088] Step 2: Calculate the coordinate rotation matrix of the minimum frame at each point. The minimum frame at each point is a Cartesian coordinate system for that point, where the x, y, and z axes are defined as the tangent vector direction, principal normal vector direction, and binormal vector direction, respectively. The minimum frame of a subsequent point can be obtained by rotating the minimum frame of the previous point. The rotation angle along the x-axis represents the change in the bending direction angle at that point, and the rotation angle along the z-axis represents the central angle corresponding to the arc segment. This allows us to construct the coordinate rotation matrix of each point relative to the previous point. Continuous coordinate rotations are mathematically represented by the continuous multiplication of rotation matrices, thus allowing us to calculate the coordinate rotation matrix of the minimum frame at each point.

[0089] Step 3: Calculate the absolute coordinates of each point. Given the relative coordinates of each point and the minimum frame rotation matrix, the relative position coordinates of each point can be transformed into absolute coordinates relative to the geodetic coordinate system through coordinate transformation, which are the three-dimensional shape coordinates of the optical fiber.

[0090] The present invention will be further described below with reference to embodiments.

[0091] (1) Differential phase de-jump filtering algorithm

[0092] This embodiment provides a phase jump filtering method in the differential phase strain demodulation process, which corresponds to the three-dimensional shape sensing measurement system in Embodiment 1.

[0093] Since strain in optical fibers causes a phase shift in the Rayleigh scattering signal in the fiber core, the phase change caused by strain is determined by calculating the optical phase at various locations on the multi-core fiber and subtracting it from the phase of the reference signal. Theoretically, the differential wrapped phase result should be limited to the range of ±2π radians, at which point phase expansion can obtain a continuous absolute phase. However, the presence of light source phase noise can cause jump points during phase expansion. This phase noise may be caused by the laser linewidth or by residual nonlinearity during laser tuning. These jump points are further amplified during subsequent differentiation, resulting in many clutter peaks in the phase change curve after differentiation, ultimately leading to strain demodulation errors. Therefore, de-jump filtering is required for the differential phase data. The specific algorithm processing flow is as follows: Figure 2 As shown.

[0094] Step 1: First, conduct two sets of experiments using the system in Example 1. One set of optical fibers is in a straight state (i.e., no strain is applied) as the reference set; the other set of optical fibers is in a bent state as the measurement set, where bending strain exists in the fiber core. The two sets of beat frequency signals are then converted to the distance domain using Fast Fourier Transform and their phase information is extracted.

[0095] Step 2: Subtract the optical phase signals from the reference group and the measurement group to obtain the optical phase change caused by strain. The differential phase within a 1m range in a certain fiber core is as follows: Figure 3 As shown.

[0096] Step 3: Put Figure 3 The differential phase results are directly unwrapped, and the result is as follows: Figure 4 As shown, due to the presence of fiber self-helix, the outer fiber core is continuously stretched and compressed, causing the differential phase to exhibit periodic sinusoidal fluctuations. Simultaneously, the DC component in the phase curve is caused by the axial stretching or compression of the fiber as a whole. Theoretically, this should be a continuously changing curve; however, from... Figure 4 As can be seen, the curve has many abrupt transitions. This can be observed more intuitively by differentiating the differential phase curve, such as... Figure 5 As shown, the phase curve after differentiation reflects the phase change rate at various positions in the fiber core. It has a proportional relationship with the strain at that position. At this time, the phase change rate curve has many clutter peaks and high-frequency noise. This is because the differential phase curve after direct unwinding has a large number of jump points.

[0097] Step 4: First, Figure 5The phase change rate curve shown is segmented along the optical fiber. In the example, each segment has 30 data points. The absolute value of the difference between each of these data points and its median is calculated, resulting in a new set of data called the median difference. Then, the median of this new set of data is calculated to obtain the absolute median difference (MAD). Similar to variance, MAD reflects the dispersion of data, but it is less susceptible to the influence of a single erroneous data point than variance. Therefore, a certain proportion of MAD is often used as a threshold for identifying outliers.

[0098] Step 5: Calculate the absolute deviation of each data point in each data segment from the median, and compare it sequentially with 1.4826 times the MAD. If the median deviation exceeds this threshold, the point is considered an outlier; otherwise, it is considered a normal point. The following literature can be referenced here:

[0099] T.Pham-Gia, and TLHung, "The mean and median absolute deviations," Mathematical and Computer Modelling, vol.34, no.7-8, pp.921-936, Oct, 2001.

[0100] Step 6: Next, interpolate the singular point using the surrounding normal points to obtain the phase change rate curve after removing the singular point. If you want to obtain the differential phase curve after de-jumping, simply integrate it.

[0101] Step 7: Even after removing singular points, the phase change rate curve still contains some high-frequency noise. At this point, a simple low-pass filter is sufficient to achieve accurate strain data demodulation. This embodiment uses a zero-phase digital IIR filter for low-pass filter design. The filter order is set to 5, and the normalized cutoff frequency is set to 0.0182 based on the nominal pitch of the multi-core fiber. The filtered result is as follows... Figure 6 As shown.

[0102] (2) Fiber external torsion compensation

[0103] This embodiment employs an external torsion compensation method for tightly wound helical multi-core optical fibers. The torsional force applied to the fiber causes rotational displacement of the outer core, leading to errors in the calculated bending direction angle. To properly map the core strain signal to the corrected bending direction, the torsion applied along the entire length of the sensing fiber must be measured. The geometry of the helical multi-core fiber allows for direct measurement of the torsion and strain caused by bending along this section of the fiber.

[0104] The structural diagram of the tightly wound spiral multi-core optical fiber used in this embodiment is shown below. Figure 7As shown, the optical fiber consists of a central core and three outer cores, forming a tightly wound helical structure. Each core has a diameter of 150 μm, and the relative positions of the outer cores are fixed at 120° angles to each other. The fiber pitch is 1 cm. This optical fiber can be used to achieve torsion compensation for the entire fiber. The technical solution is as follows:

[0105] Step 1: Demodulate and obtain the strain data of each fiber core using the strain demodulation method in Example 2. The strains of the three outer fiber cores are denoted as ε1, ε2, and ε3, respectively, and the strain of the central fiber core is denoted as ε. c .

[0106] Step 2: Calculate the axial strain ε experienced by the entire optical fiber. a , Figure 8 The strain distribution of each fiber core is shown when the optical fiber is in a torsional state. It can be seen that when the optical fiber is subjected to only torsional force, the central fiber core and the outer fiber cores produce opposite strains. This indicates that there is an interaction force between the central fiber core and the outer fiber core during the torsional process. At this time, the axial strain of the optical fiber as a whole can be calculated from the average strain of the four fiber cores.

[0107]

[0108] Step 3: Calculate the strain ε caused by torsion in the outer fiber core using the formula. twist .

[0109] Step 4: Calculate the external torsion rate of the optical fiber. For example... Figure 9 As shown, a multi-core optical fiber is considered as a cylinder and unfolded into a rectangle along its axis. l0 represents the initial length of the outer cores before twisting, r is the fiber core pitch, and h is the initial helical pitch. Assuming a torsional force exists in the fiber with the torque direction opposite to the initial helical direction, the outer cores experience negative strain due to compression. Simultaneously, due to the close contact between the outer and central cores, the outer cores exert a positive strain on the central core, causing it to stretch by a length ε. c h. According to Figure 9 The geometric relationships given can be used to derive the formula relating the strain in each fiber core to the torsion experienced by the fiber. After calculating the torsion rate γ at each position of the fiber, the cumulative torsion angle of the fiber from the initial position can be obtained by integrating it along the fiber length.

[0110] Step 5: Based on the calculated fiber twist angle and the formula, external torsion compensation of the fiber is achieved.

[0111] (3) Rotation Minimum Frame Shape Reconstruction Algorithm

[0112] This embodiment employs a shape reconstruction algorithm based on a rotational minimum frame. The algorithm treats the curve as composed of many tiny arc segments with fixed radii of curvature. The radius and direction of the arcs can be calculated from the curvature and bending direction angle of the curve at that point. Finally, the shape of the entire optical fiber is obtained by splicing together each arc segment using the rotational minimum frame method.

[0113] Algorithm principle as follows Figure 10 As shown, P i P i+1 P i+2 Let P be any three adjacent points on the optical fiber. i P i+1 The radius of curvature and the bending direction angle of the point are ρ, respectively. i , ρ i+1 and θ i θ i+1 The smallest frame is Ψ i and Ψ i+1 The minimum frame is a Cartesian coordinate system for that point, with the x, y, and z axes pointing towards the tangent vector, principal normal vector, and binormal vector directions, respectively. s represents the length of each fiber optic segment, and Ψ0 represents the geodetic coordinate system. The technical method is as follows:

[0114] Step 1: First, calculate the relative coordinates of each point on the optical fiber with respect to the previous point. For example... Figure 10 As shown, P i+1 Relative to P i The coordinates are

[0115] P i i+1 =[ρ i sin(α i ) -ρ i (1-cos(α i )) 0] (6)

[0116] Where α i It is the central angle of that arc segment, and it is related to the radius of curvature of the optical fiber at that point.

[0117]

[0118] Step 2: Calculate the coordinate rotation matrix of the minimum frame at each point. The minimum frame at each point is a Cartesian coordinate system for that point, where the x, y, and z axes are defined as the tangent vector direction, principal normal vector direction, and binormal vector direction, respectively. The minimum frame of a subsequent point can be obtained by rotating the minimum frame of the previous point. The rotation angle along the x-axis represents the change in the bending direction angle at that point, and the rotation angle along the z-axis represents the central angle corresponding to the arc segment. This allows us to construct the coordinate rotation matrix of each point relative to the previous point. Continuous coordinate rotations are mathematically represented by the continuous multiplication of rotation matrices, thus allowing us to calculate the coordinate rotation matrix of the minimum frame at each point. This implementation example... Figure 10 As shown, calculate the minimum frame Ψ at each point. i The coordinate rotation matrix, where Ψ i+1 It can be made by Ψ i Obtained by coordinate rotation, Ψ i Rotate dθ along the x-axis respectively i Rotate α along the z-axis i You can get Ψ i+1 , where dθ i It is P i Change in the bending direction angle of the point fiber

[0119]

[0120] Where R i It is P i Rotation matrix of coordinates at the point.

[0121] Step 3: Based on the relative coordinates and rotation matrix of each point, transform them into absolute spatial coordinates using coordinate transformation.

[0122]

[0123] in P represents i+1 The absolute coordinates of a point relative to the Earth's coordinate system, i.e., the three-dimensional shape coordinates of the optical fiber.

[0124] The aforementioned 3D shape reconstruction algorithm can be understood as first dividing the curve into many small arc segments, and then stitching together each arc segment by rotating the coordinate system to obtain the shape of the entire optical fiber. The advantages of this method are that it remains applicable to curves with singularities or straight line segments, and because only simple matrix operations are performed throughout the process, it is very fast, making it suitable for scenarios requiring high-speed shape measurement.

Claims

1. A high-speed, high-precision fiber shape measurement method based on phase demodulation, using a helical multi-core fiber containing a long-period fiber grating, implemented using a distributed three-dimensional shape sensing and measurement device based on a multi-channel OFDR, wherein the number of channels is not less than the number of fiber cores, characterized in that... Includes the following steps: (1) Demodulation of differential phase strain without phase jump, the method is as follows: S1.1: Two sets of experiments were conducted. One set of optical fibers was in a straight state, i.e., without any strain, as the reference set; the other set of optical fibers was in a bent state as the measurement set. The two sets of beat frequency signals were converted to the distance domain by fast Fourier transform and the optical phase information was extracted. S1.2: Assuming that the initial wavelengths of the light sources are strictly equal, the difference between the two sets of phase signals is used to obtain the optical phase change caused by strain, thus obtaining the differential phase; S1.3: Perform phase unwrapping on the differential phase, and differentiate the unwrapped differential phase data. The phase change rate after differentiation reflects the strain magnitude at each position in the optical fiber. S1.4 Remove singular points; S1.5: Use the surrounding normal points to interpolate the singular points to obtain the de-jumped differential phase data; S1.6: Combine zero-phase low-pass filtering to remove high-frequency noise and achieve strain data demodulation; (2) External torsion compensation of multi-core fiber: Based on the demodulated strain data obtained in step (1), the strain generated by torsion in the outer core of the fiber is calculated by eliminating the common mode strain by the average strain of the outer core. The common mode strain is obtained by calculating the average strain of multiple cores. The external torsion rate of the multi-core fiber is calculated according to the relationship between the strain generated by torsion in the outer core and the torsion. The fiber torsion angle is calculated according to the external torsion rate and compensation is performed when calculating the bending direction. (3) Shape reconstruction based on the rotation minimum frame: The curve corresponding to the whole optical fiber is regarded as composed of multiple small arc segments with fixed curvature radii. The radius and direction of the arc are calculated by the curvature and bending direction angle at the data point of the small arc segment. The shape of the whole optical fiber is obtained by splicing each arc segment by the rotation minimum frame method.

2. The high-speed, high-precision optical fiber shape measurement method according to claim 1, characterized in that, The method for identifying singular points in S1.4 is as follows: The phase change rate after differentiation of S1.4 reflects the strain magnitude at various locations in the optical fiber, denoted as . ; S1.4: Will Divide the optical fiber into several segments, each with a length of N. Calculate the length of each segment. The absolute median difference (MAD); S1.5: Set a determination coefficient q greater than 1, and calculate the absolute deviation of each data point from the median in each data segment. ,when If a point is considered an outlier, it is considered a normal point.

3. The high-speed, high-precision fiber shape measurement method according to claim 2, characterized in that, q= 。 4. The high-speed, high-precision optical fiber shape measurement method according to claim 1, characterized in that, Step (2) is as follows: S2.1: Demodulate and acquire strain data of the central fiber core and each peripheral fiber core; S2.2: Common mode strain is obtained through the average strain value in each fiber core, denoted as S2.

2. ; S2.3: Calculate the strain caused by torsion in the outer fiber core. ; S2.4: Calculate the external torsion rate of the multi-core optical fiber, using the following formula: in, For strain in the central fiber core. It is the initial nominal spin rate of the optical fiber, determined by... get, h It is the initial pitch of the optical fiber. r The core pitch of a multi-core optical fiber. γ It reflects the external torsion rate at various locations of the optical fiber; S2.5: Obtain external torsion compensation for the optical fiber.

5. The high-speed, high-precision optical fiber shape measurement method according to claim 4, characterized in that, In step S2.5, the formula for external torsion compensation of the fiber bending direction using the calculated external torsion angle is as follows: in It is the bending direction angle before uncompensated torsion. It is the bending direction angle after compensation torsion.

6. The high-speed, high-precision optical fiber shape measurement method according to claim 1, characterized in that, The specific steps for step (3) are as follows: S3.1: Calculate the relative coordinates of each point: Consider the curve as a series of tiny circular arcs with fixed radii of curvature, and calculate the relative coordinates of each point with respect to the previous point based on the curvature of each position of the optical fiber. S3.2: Calculate the coordinate rotation matrix of the minimum frame of each point: The minimum frame of each point is a Cartesian coordinate system of that point, and the x, y, z coordinate axes are defined as the tangent vector direction, principal normal vector direction, and binormal vector direction of that point, respectively; the minimum frame of the next point is obtained by rotating the minimum frame of the previous point; where the rotation angle along the x-axis is the change of the bending direction angle of that point, and the rotation angle along the z-axis is the central angle corresponding to the arc segment. Thus, the coordinate rotation matrix of each point relative to the previous point is constructed, and the coordinate rotation matrix of the minimum frame of each point is calculated. S3.3: Calculate the absolute coordinates of each point to obtain the three-dimensional shape coordinates of the optical fiber.

7. The high-speed, high-precision optical fiber shape measurement method according to claim 6, characterized in that, The method for step S3.3 is as follows: Given the relative coordinates of each point and the minimum frame rotation matrix, the relative position coordinates of each point are transformed into absolute coordinates relative to the geodetic coordinate system through coordinate transformation, which are the three-dimensional shape coordinates of the optical fiber.

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