Improved KLT Algorithm for High-Precision Wavelength Tracking of Optical Fiber Bragg Grating Sensors

Fiber Bragg Gratings (FBGs) are among the most popular optical fiber sensors. FBGs are well suited for direct detection of temperature and strain and can be functionalized for pressure, humidity, and refractive index sensing. Commercial setups for FBG interrogation are based on white-light sources and spectrometer detectors, which are capable of decoding the spectrum of an FBG array. Low-cost spectrometers record the spectrum on a coarse wavelength grid (typically 78–156 pm), whereas wavelength shifts of 1 pm or lower are required by most of the applications. Several algorithms have been presented for detection of small wavelength shift, even with coarse wavelength sampling; most notably, the Karhunen-Loeve Transform (KLT) was demonstrated. In this paper, an improved algorithm based on KLT is proposed, which is capable of further expanding the performances. Simulations show that, reproducing a commercial spectrometer with 156 pm grid, the algorithm estimates wavelength shift with accuracy well below 1 pm. In typical signal-to-noise ratio (SNR) conditions, the root mean square error is 22–220 fm, while the accuracy is 0.22 pm, despite the coarse sampling. Results have been also validated through experimental characterization. The proposed method allows achieving exceptional accuracy in wavelength tracking, beating the picometer level resolution proposed in most commercial and research software, and, due to fast operation (>5 kHz), is compatible also with structural health monitoring and acoustics