Incremental shape measurement with fiber Bragg gratings in a multi-core fiber for three-dimensional paths

A multi-core fiber (MCF) provides a compact solution for three-dimensional (3D) shape measurement. In this Letter, an incremental shape measurement method for 3D paths is proposed, using an MCF based on fiber Bragg gratings (FBGs). A few FBG sets can iteratively provide plenty of strain information about the 3D path during navigation. The overall continuities of the curvature and torsion are improved based on intensive strain calculations. Meanwhile, the transformation matrix algorithm is used to reconstruct the shape of 3D paths. Dynamic measurement experiments of a seven-core fiber with two FBG sets are carried out to verify the incremental shape measurement method. This method shows a great performance of the different paths, with a maximum incremental position error of 4.68%.