Stimulated infrared thermography applied to the local thermal characterization of fresco

In this work, we present a new method for estimating the local thermal diffusivity of fresco. This method uses a temporal analysis of the thermal response of a work of art submitted to a local laser excitation. First, we present the principle of the estimation method. Then, we show theoretically with the help of numerical simulations, the feasibility of the method. Finally, we show experimentally, that the method allows a good estimation of the thermal diffusivity of an academic plaster sample and of an academic fresco. The field of restoration and conservation of heritage artworks requests various non-destructive and characterization techniques. Among these NDT methods we can cite stimulated infrared thermography. The scientific literature already shows that this method is very efficient for the detection and localization of structural changes affecting the heritage artwork such as delamination [1-50]. The request of geometric characterization of these defects pushes the research teams to develop thermophysical properties estimation tools usable in situ. For example, wanting estimate by stimulated infrared thermography, the depth of a delamination, requires local knowledge of the thermal diffusivity of the artwork. In previous studies [51 – 53], we proposed three methods for local measurement of thermal diffusivity. They used a local laser excitation associated with a mathematical post treatment. The principles of these techniques were the followings: In the first case [51], the post treatment implemented, was an analysis of the spatial Fourier transform of the infrared thermogram obtained. In the second case [52], the post treatment was a temporal analysis of the characteristic radius of the thermal signature of the laser spot. Finally, in the third case [53], the post treatment was carried out in the temporal analysis of the maximum temperature of the thermal signature. The work presented here, aims to purpose a fourth estimation method. First it uses as the previous ones, a local laser excitation, providing an in situ analysis. Then it analyzes the temporal evolution of the area located under the spatial profile of the thermal signature of the laser spot. In this paper we present the results then obtained. We present first the principle of the estimation method. Then, we show theoretically, using numerical simulations, the feasibility of the method. Finally, we show experimentally that the method allows a good estimation of the thermal diffusivity of an academic plaster sample and of an academic fresco. 2. Local thermal diffusivity measurement method The principle of the local thermal diffusivity measurement method developed for the study is the following: A sample is subjected on its front face to a localized laser excitation. This excitation is temporally close to a Dirac function δ (t) and is spatially Gaussian shape. The measurement of the spatiotemporal evolution of the temperature field induced by this excitation, using an infrared camera and a mathematical post-processing leads an estimation of the thermal diffusivity of the studied material. Let us examine the mathematical post-processing which is based on this measurement technique. Given a plate having thickness L. It is radially semi-infinite. Given a very short thermal excitation (Dirac function δ (t)). Its spatial shape is Gaussian. At the initial time t = 0 s, this excitation is applied in the center of the plate in order to eliminate edge effects. Given R, the characteristic radius of this exciting spot (measured at Qmax / e 2 ). Given λ, ρ, C and a, respectively, the thermal conductivity, the density, the heat capacity and the thermal diffusivity of the studied material. The sample is initially in thermal balance with its environment. Finally, in this model we neglect the radiative - convective exchanges between the studied sample and the environment. The mathematical translation of these hypotheses leads to the following differential system (1):