Phototermal Spectra of Inhomogeneous Coatings

In this paper we demonstrate a theoretical study for photothermal measurements on inhomogeneous coatings. First, a general photothermal mathematical model for thermal gradient materials is presented. Then, we discuss the effects of inhomogeneous thermal properties in photothermal amplitude and phase spectra of coatings. Finally, a method for quantitative depth profiling that makes use of prior knowledge about the type of profile existing in a sample to reduce the instabilities associated with the mathematically ill conditioned task is demonstrated.