High-Precision Endoscopic Shape Sensing Using Two Calibrated Outer Cores of MC-FBG Array

We present a high-precision endoscopic shape-sensing method using only two calibrated outer cores of a multicore fiber Bragg grating (MC-FBG) array. By leveraging the geometric relationship among two non-collinear outer cores and the central core, the method estimates curvature and bending angle without relying on multiple outer-core channels, thereby reducing complexity and error propagation. On canonical shapes, the proposed method achieves maximum relative reconstruction errors of 1.62% for a 2D circular arc and 2.81% for a 3D helix, with the corresponding RMSE values reported for completeness. In addition, representative endoscope-relevant configurations including the α-loop, reversed α-loop, and N-loop are accurately reconstructed, and temperature tests over 25–81 °C further verify stable reconstruction performance under thermal disturbances. This work provides a resource-efficient and high-fidelity solution for endoscopic shape sensing with strong potential for integration into next-generation image-guided and robot-assisted surgical systems.