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Let $\Omega_\epsilon$ be a metallic plate whose top inaccessible surface hasbeen damaged by some chemical or mechanical agent. We heat the opposite sideand collect a sequence of temperature maps $u^\epsilon$. Here, we construct aformal explicit approximation of the damage $\epsilon\theta$ by solving anonlinear inverse problem for the heat equation in three steps: (i) smoothingof temperature maps, (ii) domain derivative of the temperature, (iii) thinplate approximation of the model and perturbation theory.  Our inversion formula is tested with realistic synthetic data and used in areal laboratory experiment.

A procedure for detecting hidden surface defects in a plate from real thermal data by means of active thermography