Groove-Based Calibration of Multicore Fiber Bragg Grating Shape Sensors with Rotation-Angle Correction

Fiber-optic shape sensors require accurate calibration of the spatial orientation and effective core distances of their sensing planes. We present a rotation-angle correction procedure for sinusoidal calibration of multicore fiber Bragg grating (MCF-FBG) shape sensors. The method is demonstrated using a constant-radius groove template and a single rotation stage. Within the groove fixture, groove-fiber friction, finite torsional stiffness, and non-ideal boundary conditions may contribute to deviations between the local sensor-plane rotation and the motor-imposed angle, resulting in distorted sinusoidal wavelength responses and biased curvature estimation. The proposed method addresses deviations from the assumed sinusoidal response by jointly correcting the effective rotation angle assigned to the four FBG responses in each sensor plane while leaving the measured wavelength shifts unchanged. The method was demonstrated using a 20 cm four-core single-mode fiber containing 200 femtosecond-laser-inscribed FBGs arranged in 50 sensor planes at 4 mm spacing. Quantitative validation with planar constant-curvature templates showed tip-position errors of approximately 2-5 mm, compared with approximately 6-13 mm for conventional sine calibration. An additional endpoint-position test of the 50-plane sensor yielded a mean error of 11.28 mm and an RMSE of 13.73 mm, compared with 19.03 mm and 21.55 mm, respectively, for conventional sine calibration. Additional non-planar bending tests qualitatively illustrated the sensor's three-dimensional reconstruction capability. The results show that rotation-angle correction can improve calibration accuracy while retaining a single-rotation-stage groove fixture.