Dynamic shape sensing using a fiber Bragg grating mesh

When fiber Bragg gratings (FBG) are tightly packed in a mesh and their peaks get close at a distance on the order of individual FBG spectrum widths, they start overlapping and there is a distance below which both peaks won't be detectable anymore using standard peak detection method. Ability to determine locations of individual peaks even after they overlap allows more gratings in a mesh and an increase in shape sensing resolution. We use a linear interpolation method to estimate peak locations when peaks overlap and become undetectable with standard peak finding technique. We test this algorithm on experimentally obtained data and compare peak locations obtained by the algorithm to exact peak locations. We analyze the error to show that algorithm performs well when velocity of peaks stays uniform during peak crossing. However, the error rapidly increases if the velocity changes during crossing and the maximum error can occur in a situation when peaks change direction during peak crossing.