Diagnostics of Micropores in a Polymer Material with a Built-In Fiber-Optic Bragg Grating

A mathematical model for the diagnostics of technological defects (micropores) in a polymer material using built-in fiber-optic sensor with a long low-reflective Bragg grating is presented. The diagnostics is based on measuring the informative reflection spectrum of the Bragg grating at the output of the optical fiber. An algorithm for processing the strain spectrum was developed for the cases where the sensitive part of the optical fiber is located in the polymeric material in the deformation "disturbance zone" of the defect in the form of a spherical cavity. The diagnosable parameters were the defect size and location relative to the known length and location of the sensitive part. Results of a mathematical simulation of light and strain spectra along the sensitive part of the optical fiber, at various diagnosed distances from the optical fiber to the center of the spherical cavity in the polymer material are presented. A direct numerical solution (deconvolution) of the Fredholm integral equation is not considered here, and the reflection spectra, are obtained as convolutions with corresponding known strain spectra for the sensitive part of the fiber. The strain spectra were found using the solution of an elasticity theory problem for a "defective medium/fiber" domain.