Reconstruction error model of distributed shape sensing based on the reentered frame in OFDR

At present, the reconstruction error of optical fiber shape sensing is commonly represented by Euclidean distance error. However, the Euclidian error of shape reconstruction will be dependent on the shape complexity, which depends on length, curvature and torsion. In this paper, we establish a reconstruction error model of distributed shape sensing in optical frequency domain reflectometry (OFDR) based on the Frenet-Serret frame and the error delivering theory, which illustrates the relationship between the reconstruction error and parameters such as curvature, torsion, fiber length and strain measurement error. We experimentally verify the feasibility and applicability of the proposed reconstruction error model by distributed optical fiber shape sensing system based on OFDR. The proposed reconstruction error model can provide a prediction of the maximal reconstruction error when the estimated range of curvature, torsion, fiber length of a shape needs to be reconstructed and strain measurement errors of OFDR system are known. It is very useful to judge whether the shape reconstruction error meets the requirement according to the shape to be reconstructed.