A Review of Mathematical Methods for the Evaluation of Defects in a Layered Specimen by Means of Active Thermography: Perturbation Theory, Linearization, and Reciprocity Gap

The thermal properties of a two-layered composite conductor are modified in the case that the interface is damaged. The present paper deals with the nondestructive evaluation of the perturbations of interface thermal conductance due to the presence of defects. The specimen was heated by means of a lamp system or a laser while its temperature was measured with an infrared camera in the typical framework of active thermography. The evaluation of the defects affecting the interface was made in the past using thin plate approximation or standard numerical techniques for inverse problems. Here, we show an explicit inversion formula obtained from the reciprocity property of parabolic equations.