Thermal-strain-based calibration for high-accuracy shape reconstruction of fiber Bragg grating sensors

Fiber Bragg grating (FBG) shape sensors play a crucial role in three-dimensional (3D) shape sensing fields such as medical robotics and aerospace. However, existing methods suffer from a fundamental contradiction: the strain coefficient, temperature coefficient, and encapsulation angle must be calibrated in separate steps, making the process cumbersome and prone to error accumulation, while simultaneously compensating for temperature drift and encapsulation deviations remains challenging. To fill this gap, we propose a two-stage thermal-strain-based framework that simultaneously decouples the strain and temperature coefficients in a single thermal-variation experiment, fundamentally eliminating the error propagation of multi-step calibration. The method consists of two stages: (1) a thermal-variation experiment that decouples and determines the strain and temperature coefficients for all sensing units, and (2) a simplified bending test that identifies the actual encapsulation angles without requiring repeated maximum strain point identification. Experimental validation shows that this integrated approach greatly improves reconstruction accuracy, reducing the endpoint error (EPE) to a range of 1.70 mm to 4.48 mm, corresponding to 0.4-1.1% of the 0.4 m sensor length under room temperature conditions. More importantly, the method exhibits exceptional robustness in thermally varying environments (10-25°C), effectively compensating for thermal drift. This work establishes a robust, efficient, and high-precision calibration paradigm, paving the way for the reliable deployment of FBG shape sensors in complex real-world applications.