Simultaneous shape reconstruction and twist measurement based on optical frequency domain reflectometry

Shape reconstruction and twist measurement in fiber optic shape sensing (FOSS) exhibits significant value for applications in medical surgery, robotic manipulation, and other advanced fields. In this study, we propose a method for simultaneous shape reconstruction and twist measurement based on optical frequency domain reflectometry (OFDR), enabling the successful decoupling of bending and twist strains in spun multiple single-core fibers (MFS). These separated strain components are utilized for curvature estimation and twist angle measurement, respectively. Experimental results demonstrate that the proposed method enables accurate measurement of twist angles in both two-dimensional (2D) and three-dimensional (3D) complex fiber shapes. Meanwhile, a more accurate orientation measurement is guaranteed in complex shape reconstruction by the proposed method. The mean absolute error (MAE) of twist measurement is 3.787°, while the mean relative error (MRE) of Euclidean distance in simultaneous shape reconstruction is 0.896%, respectively. This capability also expands the potential for advanced positioning applications involving angular variations, particularly in fields such as medical and surgical robotics.