On the Trade-off Between Spatial Resolution and High Curvature Bending in FBG-based Shape Sensing.

Fiber Bragg grating (FBG)-based shape sensing is an emerging technology used for the navigation of flexible medical instruments, such as needles, catheters, and endoscopes. FBG-based sensors operate by measuring strain-induced wavelength shifts in the reflected light, which are used to determine the curvature along a fiber's length. While an increased number of gratings enhances shape-sensing accuracy, incorporating many within a fixed spectrum can induce interference in wavelength shifts, specifically during high curvature bending, limiting the detectable bending range. Such interference severely compromises shape estimation, posing challenges for instruments requiring high curvature bends. In this article, we study this tradeoff between resolution and bending curvature. Next, we introduce an algorithm that leverages the reflectivity and full-width half maximum (FWHM) of FBG nodes for improved bend estimation, even in high-curvature scenarios. To this end, first, we provide a model of reflectivity of uniform gratings using coupled-mode theory. The model is used to match spectrum measurements with FBG nodes. Second, we develop an algorithm using the proposed model and random walk model to estimate the relative probability of a given reflected wavelength corresponding to each FBG node. This algorithm then uses variants of the Hungarian algorithm to solve an assignment problem and classify FBG nodes. We then collected three datasets with FBGs experiencing varying curvature. One of the datasets validates the proposed model and the latter two demonstrate that relative to a commercially available interrogator, our approach classifies FBG nodes with 14% higher accuracy, 13% higher precision, 35% higher recall, and 4% higher specificity.</p