Optical fiber shape reconstruction algorithm based on 3D Euler spiral model

Abstract This paper presents a reconstruction algorithm that uses a 3D Euler spiral model to construct the microsegment of a 3D space curve to improve the reconstruction efficiency. Euler spiral is a curve whose shape information changes linearly with arc length, which improves the current assumption of the reconstruction algorithms that the shape information of the micro-segment is constant, and effectively reduces the number of interpolations required, and thus improves the efficiency of the shape algorithm. To verify the effectiveness of this algorithm, a method for constructing random space curves is proposed. Three random space curves of different lengths are reconstructed and the results are compared with the reconstruction algorithms based on the homogeneous transformation matrix and Bishop frame. The results show that this model can significantly improve the efficiency of the algorithm. Under the random space curves of 1 m, 10 m, and 100 m, the efficiency is enhanced by about 15, 27, and 30 times respectively. Prepare a shape sensor with a length of 1465 mm to verify the highest reconstruction accuracy of 3D Euler spiral model, which is consistent with the simulation results. The results provide a solid foundation for further research in the field of shape sensing, and show potential for promoting the development of applications that rely on real-time shape measurements.