Simulation tool for 3D shape sensors based on Fiber Bragg gratings and optimization of measurement points

3D shape sensing using Fiber Bragg gratings has attracted the interest of several research groups in recent years, but so far no possibility has been presented to optimize the sensing system by simulation. Almost always, the gratings (the points of strain measurement) are distributed equidistantly, and the reconstruction algorithm has not been verified by simulation. In this paper we present our simulation tool that works on a mathematical basis and includes two parts: the first part describes how to determine the strains of Fiber Bragg gratings mounted along a given shape. The second part describes our algorithm to reconstruct the shape from this strain data using theory of differential geometry. This reconstruction algorithm is evaluated within the simulation environment and can be adapted to different system behaviors like circular bending of the instrument, cubic bending or bending according to the Euler beam theory. Furthermore, the gratings can be optimized with respect to their position and designated Bragg wavelength. To demonstrate the effectiveness of the simulation tool, an optimization has been conducted for the grating positions along a shape with two independent bendable segments. For each configuration of the shape, the reconstruction results using the optimized grating positions were significantly better than when using equidistantly distributed gratings.