Photothermal testing of composite materials: Virtual wave concept with prior information for parameter estimation and image reconstruction

In this paper, we propose a new parameter estimation and image reconstruction approach for the photothermal testing of composite materials. Therefore, the full multidimensional evaluation method, virtual wave concept, is extended to estimate the orthotropic thermal diffusivity tensor and to reconstruct the initial temperature distribution after a laser spot heating in an orthotropic material. We establish a formal relationship between the virtual speed of sound tensor and the thermal diffusivity tensor. Furthermore, we show how prior information in the form of positivity and sparsity can be incorporated in the regularization process to improve the solution of the inverse imaging problem. In a second step, the initial temperature distribution is reconstructed by applying ultrasonic imaging methods on the calculated 3D bimodal virtual wave field. This new approach is validated on simulation and experimental data of a unidirectional carbon fiber reinforced polymer. The information loss that results from entropy production during heat diffusion can be partly compensated by including prior information. This allows an accurate parameter estimation and a high-resolution image reconstruction.