Straightforward Reconstruction of Smooth Concave Diffusivity Profiles from Photothermal Phase

This article introduces a fast and easy way to retrieve smooth concave thermal-diffusivity profiles from the photothermal (PT) response of a semi-infinite solid with concave depth-dependent thermal diffusivity, such as case-hardened steels. The approach is based on the exact asymptotic behavior of the PT phase and on the position, height, and width of the phase maximum. The resulting procedure, which only requires PT phase data at relatively few frequencies, is unambiguous and involves only simple algebraic formulae and no tweaking. The method is successfully applied to the inversion of some simulated profiles, including the demanding piecewise linear one, proving the value of the method.