ORIGINAL RESEARCH article
Front. Phys.
Sec. Optics and Photonics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1665822
This article is part of the Research TopicAcquisition and Application of Multimodal Sensing Information, Volume IIIView all 3 articles
High-Precision Shape Reconstruction for Optical Fiber Sensors Based on Cubic Spline Interpolation and Tangent Angle Recursion
Provisionally accepted
Yixiao Liu
Haining Ji*- Xiangtan University, Xiangtan, China
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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.
Keywords: optical fiber sensor, reconstruction, Cubic spline interpolation, tangentangle recursion algorithm, High-precision
Received: 14 Jul 2025; Accepted: 05 Sep 2025.
Copyright: © 2025 Liu and Ji. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Haining Ji, Xiangtan University, Xiangtan, China
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