Distributed Fiber Sensing Of Three-Dimensional Shape Sensing And Its Error Model Based On OFDR

Optical frequency domain reflectometry(OFDR)measures the optical frequency shift of Rayleigh back scattering in optical fiber to realize the sensing of external vibration,temperature and strain.Compared with traditional optical fiber sensing,distributed optical fiber sensing based on OFDR has high spatial resolution and high measurement sensitivity,which is very suitable for shape sensing.OFDR based shape sensing has great application prospects in micro manipulator control of surgical robot,shape sensing of interventional catheter,three-dimensional shape sensing of satellite sail,shape sesnsing of aircraft wing and flexible skin.This paper intends to carry out the research on two-dimensional and three-dimensional shape with a large curvature radius reconstruction and error model based on OFDR.The main work is as follows:1.Starting with OFDR distributed sensing principle,this paper focuses on the analysis of OFDR three-dimensional shape sensing principle.We establish the relationship between the optical frequency shift of Rayleigh backscattering spectrum in optical fiber and bending radius.We parameterizes the spatial curve based on curve theory and use Frenet-Serret frame to connect the spatial curve with the strain of multi-core optical fiber in shape sensing.We realize the reconstruction of three-dimensional space curve,which provides a theoretical basis for the subsequent experiments and algorithms in this paper.We derive the analytical formula of curve reconstruction based on Frenet-Serret framework.We conclude that curvature and torsion are the key factors of curve reconstruction.At the same time,we analyze the influence of initial value and torsion of frame on curve reconstruction by numerical simulation.2.We propose a three-dimensional shape sensor with large curvature radius using OFDR in multi-core fiber.We establish the theoretical models of strain measurement error and curvature radius reconstruction error under different curvature radius of optical fiber.In the experiment,we construct a distributed shape sensing experimental system based on OFDR.The strain of three cores in multi-core fiber is measured and submitted to the Frenet-Serret frame to reconstruct the three-dimensional shape of fiber.By optimizing the measurable strain resolution and sensing spatial resolution,we realize two-dimensional shapes reconstruction with large curvature radius from 5cm to 100 cm.In order to verify the accuracy of 3D curve reconstruction,we propose a 3D shape sensing verification method and error evaluation method based on 3D printing technology.We design and fabricate a 3D printing model with accurate spatial positions of 3D spatial curve.Through experiments,we realize reconstruction of three-dimensional curves with large curvature radius from 5 cm to 100 cm.The root mean square error between the reconstructed curve and the set curve is 7.2 mm and the average Euclidean distance between them is 3.4 mm.3.We construct and verify the Euclidean distance error model for 3D shape reconstruction based on Frenet-Serret frame.Firstly,We analyze the influencing factors of Euclidean distance error of reconstructed spatial curve and establish the corresponding error theory and simulation model.Secondly,we simulate and analyze the variation of Euclidean distance error of reconstructed spatial curve with fiber length under different curvature.We also simulate and analyze the relationship between strain measurement error and Euclidean distance error of reconstructed spatial curve under different curvature radius and torsion.In the experiment,by designing and making 3D printing models with different curvature and torsion,We use the control variable method to fix the length,curvature and torsion of the reconstructed curve respectively and acquire the relationship between Euclidean distance error and strain error.The experimental results are basically consistent with the simulation results.We find that the Euclidean distance error of the reconstructed space curve increases nonlinearly with the length of the reconstructed curve,nonlinearly with the radius of curvature and linearly with the torsion.Finally,we analyze the error sources and limitations in shape sensing.