Analysis of Strain Transfer in FBG-Based Embedded Optical Fiber 3-D Shape Sensor

The FBG-based embedded optical fiber 3-D shape sensor (FBG-EOFSS) composed of several different materials finds potential applications in various industrial and medical applications. The strain loss during the strain transfer affects the change of the fiber Bragg grating (FBG) sensor's wavelength, which in turn deteriorates the position accuracy. In this article, first, we analyzed the strain transfer in FBG-EOFSS and derived the optical-mechanical transformation equation. Then, a strain transfer model combining mechanics, materials, and optics is developed based on the finite-element analysis (FEA) method. The FEA simulation results show that the strain transfer rate decreases by 27.7%/mm with the increase of the adhesive thickness under FBG. The optimal average strain transfer rate is about 0.97 when the elastic modulus of the adhesive is in the range of 109-1014 Pa. Moreover, the effect of the strain transfer on the position accuracy is analyzed. The relative position error of 3-D shape reconstruction increases by 8.4% with the strain transfer rate decreasing by 10%. Finally, an experimental system composed of the clamp, the displacement stage, and the FBG demodulator is developed. The strain sensitivity coefficients of bare FBGs and FBG sensors were tested quantitatively. The corresponding average strain transfer rate was calculated by the strain sensitivity coefficients. The results can potentially conduce to the design of 3-D shape sensors and improve the positioning accuracy.