High-precision shape reconstruction for optical fiber sensors based on cubic spline interpolation and tangent angle recursion

Accurate reconstruction of optical fiber curves has important applications in fields like medicine, aerospace, and infrastructure monitoring. However, it faces challenges such as insufficient reconstruction accuracy. In this paper, a novel method for optical fiber plane curve reconstruction, based on cubic spline interpolation and the tangent angle recursion algorithm, is proposed. First, the optical fiber sensor demodulation system is utilized to acquire strain information on the surface of the flexible substrate. Then, based on the approximate relationship between wavelength and curvature, discrete curvature values are calculated from experimental data. Next, the cubic spline interpolation is applied to convert the discrete curvature into a continuous profile, ensuring the smoothness of the curve. Finally, the tangent-angle recursive algorithm is employed to derive the coordinates of arbitrary points on the fiber deformation curve, thereby realizing precise reconstruction of the optical fiber curve. Additionally, the Frenet-Serret framework is introduced, which can be employed for 3D reconstruction, and a sensitivity analysis of the key parameters is conducted, exploring the impact of the number of sampling and interpolation points on the reconstruction accuracy. The reconstruction results show that the curves have a high degree of smoothness and physical realism. With 50 sampling points and no interpolation, the mean absolute error (MAE) reaches 0.000892 m, approximately 72% lower than with 20 sampling points and no interpolation. The root mean square error (RMSE) is 0.001127 m, about 75% lower than with 20 sampling points and no interpolation, thereby verifying the feasibility of the method. This study offers theoretical foundations and experimental validation for the optimization of optical fiber shape sensing technology, thus holding significant importance for enhancing measurement accuracy and advancing engineering applications in related domains.