基于Frenet-Serret框架的OFDR三维形状重构算法研究

Research on OFDR 3D shape reconstruction algorithm based on Frenet-Serret framework

为了更深入地研究光频域反射法(optical frequency domain reflectometry, OFDR)在形状检测,有效计算变形监测等应用场景下光纤的形状和位置,设计了一种利用分布式光频域反射技术测得的光纤应变数据来重构三维形状的算法。与已有算法相比,在数据处理环节加入了样条插值,从而使得形状还原精度提高,并利用仿真实验对算法进行了验证。首先设计了通过应变数据得到三芯光纤曲率和弯曲方向采样值的计算方法,结合Frenet-Serret公式构造了曲线方程;然后利用有限元分析软件对空间S形应变数据进行建模并提取,带入已设计的算法求解,在三维空间中重建S形光纤;最后得出位置误差随着光纤长度的增加逐渐增加,均方根误差计算结果为0.996 mm,单位长度误差最大值为0.082 4%。结果表明,该算法能较好地恢复原始曲线,具有一定的工程价值。

In order to further study the shape detection of optical frequency domain reflectometry(OFDR),and effectively calculate the shape and position of optical fiber in application scenarios such as deformation monitoring,this paper designed an algorithm to reconstruct three-dimensional shape using the optical fiber strain data measured by distributed optical frequency domain reflection technology.Compared with the existing algorithm,spline interpolation was added to the data processing,which improved the precision of shape reduction,and the simulation experiments were used to verify the algorithm.Firstly,a calculation method was designed to obtain the sampling values of curvature and bending direction of three-core optical fiber from the strain data,and the curve equation was constructed by combining the Frenet-Serret formula.Then the finite element analysis software was used to model and extract the S-shape strain data and the S-shape fiber was reconstructed in the three-dimensional space.The results show that the position error increases with the increase of fiber length.The root mean square error is 0.996 mm,and the maximum error per unit length is 0.0824%.The results show that the algorithm can recover the original curve well.