Thermal effusivity profile characterization from pulse photothermal data

An inversion method is proposed for depth profiling of the thermal effusivity from the surface temperature evolution after an excitation. Focus is on pulse heating. The effusivity profile is obtained through a Laplace inversion. The Stehfest method is implemented and we propose to use the number of elements in the Stehfest series N as a regularizing parameter. The optimum N value is defined by plotting a characteristic C curve with the norm of the solution derivative and the norm of the residues of the so-called apparent effusivity function. Examples of inversion results are given for linear and Gaussian effusivity profiles. For this purpose, we extended the formalism of thermal quadrupoles to the case of linearly varying effusivity. A statistical analysis is performed to assess the influence of noise on the inversion results. Recommendations on the thermogram minimum duration are derived therefrom. Experimental results obtained with a case-hardened steel sample show the potential of the present nondestru...

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