Method-of-images formulation of the inverse problem of depth profiling the thermal reflection coefficient in an impulse heated solid

Karanicolas, J.; Fu, S.-W.; Power, J. F.
May 2000
AIP Conference Proceedings;2000, Vol. 509 Issue 1, p595
Academic Journal
The problem of depth profiling the thermal effusivity of a material, based on the detection of thermal waves has many applications in manufacturing. We introduce a theory of the one-dimensional thermal backscattering response in a surface impulse heated solid. The solid consists of discrete layers of constant diffusivity but variable conductivity. No weak scattering assumption is made (as in most past works). An analytical solution to this problem is outlined in the literature but detailed expressions for the summations accounting for all thermal propagation paths (and their respective weightings) are not easily extracted from the published mathematical framework. Our analysis greatly simplifies the problem, based on the Method-of-Images, the finite number of layers thermally probed in fixed time, and a set of simple parity rules which identify all thermal propagation sequences returning significant energy to the sample surface. This leads to a new and unexpectedly simple, linear formulation of the inverse problem, which reconstructs a stable depth profile of thermal effusivity. © 2000 American Institute of Physics.


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