Error analysis of multi-core fiber shape sensing

The reconstruction accuracy of multi-core fiber shape sensing is influenced by multiple factors, and a systematic error analysis is currently lacking. Finite element models of a three-core fiber were established under unidirectional bending, U-shaped bending, S-shaped bending, and three-dimensional spatial bending. The axial strain data of the fiber cores under each model were extracted. Shape reconstruction was performed using a three-dimensional reconstruction algorithm based on the Frenet-Serret framework. The relationships between reconstruction error and factors such as sampling resolution, bending shape, and fiber length were analyzed. The results indicate that the shape reconstruction error exhibits an exponential relationship with sampling resolution and a significantly linear positive correlation with the overall fiber strain. Furthermore, the unit-length error of shape reconstruction demonstrates scale invariance. The findings of this study provide theoretical and methodological support for the design of multi-core fiber shape sensing algorithms and hold certain engineering value for on-demand configuration of testing resources in different application scenarios.