Spatial Short-Term Fourier Transform Based Single-Channel Single-Fiber 3D Shape Sensing

Abstract

Accurate three-dimensional (3D) shape sensing is vital for continuum robots in minimally invasive surgery. Conventional optical fiber methods depend on multi-fiber or multicore configurations, increasing integration complexity and associated costs. Single-fiber approaches support miniaturization, but struggle to decouple 3D bending and twist. We propose a single-channel single-fiber framework based on the spatial short-term Fourier transform (SSTFT) for real-time 3D reconstruction. A helically wrapped fiber encodes multiple deformation modes into periodic strain patterns, which localized Fourier domain analysis converts into curvature, direction, and twist parameters. These parameters feed a piecewise constant curvature and torsion model to efficiently reconstruct the backbone. Experiments on a 1.45 m sensor achieve average shape errors of 2.15 % (bending), 5.32 % (3D helix), and 7.90 % (twist). Compared to multi-fiber Frenet–Serret methods, our approach improves accuracy and robustness while reducing system complexity, demonstrating a promising low-cost, miniaturized shape sensing approach with potential applications in surgical navigation.