Effect of Thermal Noise on the Strain Gradient Sensor Using Cascaded Fiber Bragg Gratings

Abstract

Understanding the distribution and gradient of longitudinal strain is essential for accurately assessing the structural integrity and mechanical behavior of materials and components under deformation. In this study, we investigate the impact of thermal noise on the performance of a strain gradient sensor based on fiber Bragg grating (FBG) technology. The proposed sensor architecture employs a series of $M$ cascaded uniform FBGs (UniFBGs), evenly spaced along a fiber-under-test (FUT), enabling spatially resolved strain measurement along the entire length of the structure. An analytical model is rigorously developed to characterize the sensor′s response to strain, incorporating the physical and optical behavior of the cascaded FBG array. The model accounts for wavelength shifts induced by strain and the corresponding changes in reflected spectra. Building on this foundation, we conduct a detailed numerical analysis of the sensor's signal-to-noise ratio (SNR), focusing specifically on the influence of thermal noise at the photodetection stage. The results provide valuable insights into the trade-offs between sensor resolution, reflectivity, interrogation configuration, and noise-induced limitations, contributing to the practical design and optimization of high-resolution distributed strain gradient sensing systems.