Nonlinear least-squares curve fitting method for detection of overlapped FBG temperature sensor spectra

Abstract

This study introduces a novel approach to address the challenge of separating partially and fully overlapped spectra in Fiber Bragg Grating (FBG) sensors. Leveraging the Nonlinear Least-Squares Curve Fitting method with the Levenberg-Marquardt algorithm (LMA), the proposed algorithm successfully detects distinct FBG peaks even in complex spectral superpositions. This investigation utilized two Fiber Bragg Grating (FBG) sensors, with one subjected to varying temperatures and the other maintained at a constant temperature as a reference. The reflection spectra from the FBG sensors were analyzed across 20 distinct temperature values, and the proposed algorithm accurately identified the peak wavelengths of both sensors with precision. Examination of the relative errors in the detected peak wavelengths revealed a maximum percentage error of 0.0025%. This finding underscores the capability of the proposed algorithm to achieve highly accurate peak detection in densely multiplexed FBG sensors, particularly in applications demanding precise measurements across numerous points within a sensor network.