Development of a photothermal measurement model to determine layer thickness of multi-layered coating systems with unknown thermal properties

In this article, a general model for 1D thermal wave interference is derived for multi-layered coating systems on a thermally thick substrate using the same principles as for the well established one-layered and two-layered coating cases. Using the lock-in thermography principle, an illumination source modulates the surface of those systems periodically by a planar, sinusoidal wave form with a fixed frequency. The coating systems absorb the optical energy on its surface and convert it into thermal energy, resulting in the propagation of a spatially and temporally periodic thermal wave with the same frequency. These thermal waves, originating at the surface, are reflected and transmitted at each interface leading to infinitely many wave trains that need to be tracked in order to formulate the final surface temperature as a superposition of all these waves. The heat transfer inside the object depends on the layer thickness of each coating, but also on the thermal properties of each layer material. The goal is to have a mathematical and physical model which describes the phase angle data measured by an infrared camera. Having these data, the main objective of this paper is to determine the thickness of each coating layer. In practice, the thermal properties of the layers usually are unknown, which makes the process even more difficult. For that reason, this article presents a concept to determine the thermal properties in advance.