Formal derivation of an inversion formula for the approximation of interface defects by means of active thermography

TL;DR

This paper derives an inversion formula for detecting interface defects in composite conductors using active thermography, employing Laplace transforms and symmetry properties to improve nondestructive evaluation.

Contribution

It presents a novel mathematical derivation of an inversion formula for interface defect detection via active thermography, enhancing nondestructive testing methods.

Findings

Numerical inversion from simulated data shows promising results.

The inversion formula effectively detects interface perturbations.

The method leverages Laplace transforms and symmetries for improved accuracy.

Abstract

Thermal properties of a two-layered composite conductor are modified in case the interface is damaged. The present paper deals with nondestructive evaluation of perturbations of interface thermal conductance due to the presence of defects. The specimen is heated by means of a lamp system or a laser while its surface temperature is measured with an infrared camera in the typical framework of Active Thermography. Defects affecting the interface are evaluated using an inversion formula obtained by means of Laplace transformation and suitable symmetries of parabolic differential operators (reciprocity). Results of numerical inversion from simulated data are encouraging