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

We presented 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 between two non-collinear outer cores and the central core, the approach determines curvature and bending angle without multiple outer-core measurements, reducing computational complexity and error propagation. Experimental results demonstrate that the proposed method achieves maximum relative reconstruction errors of 1.62% and 2.81% for 2D circular and 3D helical shapes, respectively. Furthermore, arbitrary endoscopic configurations such as α-loops and N-loops are accurately reconstructed, validating the robustness of the method under realistic clinical conditions. 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.