Simultaneous Measurement of Axial Strain, Bending and Torsion With a Single Fiber Bragg Grating in CYTOP Fiber

This paper presents the development of a three-dimensional (3-D) displacement sensor based on one fiber Bragg grating (FBG). In order to obtain higher sensitivity and dynamic range, the FBG is inscribed in low-loss, multimode, cyclic transparent amorphous fluoropolymers using the direct-write, plane-by-plane femtosecond laser inscription method. The proposed sensor is based on the influence of each displacement condition, namely, axial strain, torsion, and bending on the FBG reflection spectrum. Such influence is analyzed with respect to the FBG wavelength shift, reflectivity, and full width half maximum. The operation principle and theoretical background of the proposed approach is numerically analyzed by means of finite element analysis for the strain along the grating length and coupled-mode theory with a modified transfer matrix formulation for the FBG spectrum. The sensor is experimentally characterized and validated in which the results show good agreement between the applied axial strain, bending, and torsion with relative errors below 5.5%. Thus, the proposed sensor is an interesting alternative for measuring displacements in 3-D applications, such as movement analysis and the instrumentation of novel soft robots.