多芯光纤光栅形状传感性能与重构误差研究

多芯光纤光栅形状传感技术利用空分复用以及应变监测的优势，结合不同的栅点布设方案，实现待测对象的连续曲率和形状传感。首先介绍了多芯光纤光栅曲率和挠率传感原理，提出采用齐次矩阵变换的三维重构算法实现光纤的三维形状重构。为了探究不同光栅密度对实验精度的影响，利用算法编程模拟了不同光栅间距下的三维形状重构精度，依据模拟仿真的结果，建立了不同光栅间距与三维重构误差之间的关系。三维形状传感实验使用光栅间距为10 cm和5 cm的七芯光纤光栅串。实验结果表明，最大误差出现在尾点处，分别为2.56 cm和1.15 cm，占全长的3.2%和1.4%，平均误差为1.32 cm和0.62 cm，占全长的1.7%和0.8%。实验结果与仿真值比较接近，说明可以依据仿真结果对不同光栅间距下的三维形状误差进行预测。结合具体的应用场景合理配置测点资源，在较低的成本范围内实现高性能的检测。

Research on shape sensing performance and reconstruction error of multi-core fiber grating

  Objective   At present, shape sensing technology based on multi-core fiber grating is mainly divided into two categories, one is the optical frequency domain reflectometry (OFDR) demodulation technology based on the all-same weak grating. The other is multi-core grating or integrated grating shape sensing technology based on wavelength demodulation mode, and the multi-core grating array sensing system based on wavelength demodulation mode has the advantages of small size, high signal-to-noise ratio, fast acquisition speed and high real-time demodulation. In view of the diverse shape sensing needs in the actual application, the multi-core grating array multi-core sensing system using wavelength demodulation can be flexibly configured according to the actual needs of the number and spacing of the grating, which can realize the shape monitoring of the measured object with more flexible sensing distance and more diverse shape change span, which has a wider application prospect. However, because the multi-core grating measurement point cannot be continuously in space, the shape of the blank grating area between the measurement points cannot be obtained, and there is a blind zone of the measurement point. In practical applications, in order to improve the accuracy of shape sensing, it is necessary to study the shape deformation characteristics of the object to be measured, and design a reasonable grating distribution configuration scheme under the premise of taking into account the measurable key points and the full range of measurable areas to be measured.  Methods   Based on the strain sensing characteristics of seven-core fiber gratings, this paper adopts a three-dimensional shape reconstruction method based on homogeneous transformation matrix to reconstruct the shape of two seven-core fiber gratings with different grating spacing, solve the curvature and torsion of the region where the grating measurement point is located by the relative change value of the wavelength of the grating point, and obtain the curvature and torsion of the blank grating region between the FBG measurement points by cubic spline interpolation, and finally integrate the curvature and torsion of all points into the same coordinate system. The three-dimensional shape reconstruction of the object to be measured is realized. In order to explore the influence of grating spacing on shape reconstruction accuracy, the three-dimensional shape reconstruction error under different grating spacing based on this algorithm principle is simulated by algorithm programming, and the experimental verification is completed by building a three-dimensional shape sensing system, and the rationality of the error and simulation error in the experiment is discussed.  Results and Discussions   The simulation calculation selects the raster spacing L of 12.5 cm, 10 cm, 8 cm, 5 cm and 1 cm, and plots the 3D reconstruction curve and the real curve under these raster spacing. Both the simulation assumes that the curvature and torsion measurement error of the gate measurement point is 0. The results show that when the grating spacing L is 12.5 cm, 10 cm, 8 cm, 5 cm and 1 cm, the spatial position error shows a gradual increasing trend with the length of the fiber, and the larger the grating spacing is, the larger the error is. The maximum reconstruction error falls at the end point of the analog length, which is 7.75 cm, 4.35 cm, 2.63 cm, 0.94 cm and 0.25 cm, accounting for 4.8%, 2.7%, 1.6%, 0.6% and 0.16% of the total length (Fig.4). In the experiment, a grating string with a grating spacing of 5 cm and 10 cm was selected to carry out a three-dimensional shape sensing experiment. The experimental results show that the reconstructed three-dimensional shape matches the real shape well (Fig.7). The maximum error at a raster spacing of 5 cm is 1.15 cm, accounting for 1.4% of the total length, and the average error is 0.62 cm, accounting for 0.8% of the total length. The maximum error at a raster spacing of 10 cm is 2.56 cm, accounting for 3.2% of the total length, and the average error is 1.32 cm, accounting for 1.7% of the total length (Tab.1).  Conclusions   Whether it is simulation or experimental verification, the overall trend of error value and relative length of the object to be measured is in line with the trend of linear growth. The maximum error points all occur at the end point. By establishing the variation relationship between the raster spacing and the slope of the linear fit, the correspondence between different raster spacing and the 3D reconstruction error can be explored. According to this relationship, the three-dimensional shape reconstruction error of any grating spacing and any length of optical fiber under similar shapes can be predicted, so that the appropriate grating spacing and demodulation method can be selected in combination with specific application scenarios, reasonable allocation of measurement point resources, and improvement of detection performance in a lower cost range.