Scattering matrix approach to thermal wave propagation in layered structures

Abstract

In this paper we describe a new technique, based on Fourier optics, to explain the propagation, as well as loss, of three-dimensional thermal waves in isotropic, homogeneous materials. Using this, the dependence of temperature distribution at any arbitrary infinite parallel plane on the aperture distribution is derived. In addition, the temperature distribution at the aperture plane, due to a given perpendicular source is formulated, by applying the boundary conditions in the spatial frequency domain. A scattering matrix theory is developed to analyze the propagation of thermal waves in multilayered structures. This directly relates the heat source characteristics to the temperature distribution at any level. The contrast mechanism in the subsurface mode of operation is explained, and the dependence of the response of a typical system on depth is explored. In addition, the theoretical amplitude and phase images of a cylindrical void are presented; the results are in good agreement with the published experimental subsurface images of voids. Finally, transform techniques in both temporal and spatial frequency domains are employed to analyze the pulse response of layered structures. It is found that the decay rate of the surface temperature is strongly influenced by the presence of inclusions within a sample.