A Procedure for Detecting Hidden Surface Defects in a Thin Plate by Means of Active Thermography

Let ?_\epsilon be a metallic plate whose top inaccessiblesurface has been damaged by some chemical or mechanicalagent. We heat the opposite side and collect a sequence oftemperature maps u^\epsilon . Here, we construct a formal explicitapproximation of the damage \epsilon ? by solving a nonlinearinverse problem for the heat equation in three steps: (i)smoothing of temperature maps, (ii) domain derivative ofthe temperature, (iii) thin plate approximation of the modeland perturbation theory. Our inversion formula is tested withrealistic synthetic data and used in a real laboratory experiment.