Geometric Reconstruction of Buried Heat Sources from a Surface Thermogram

Attempts to reconstruct the spatial location, size, and form of buried heat sources from the measured pattern of thermograms are, in general, prohibited by the lack of a priori information about the thermal (flow) model and the source structure. In this paper, a method is introduced based on geometric reconstruction of a buried heat source configuration. This configuration must contain point sources and/or sharp edges and be confined to a plane region parallel to the surface. The medium, in which the heat source is embedded, is assumed to be homogeneous, isotropic, and of large size compared to the size of the source and to its depth below the surface. The heat flux from the surface to the ambient is assumed to follow the Newtonian cooling law. The spatial density distribution of the flux can be described by a Green function with coefficients determined by the depth of the source plane. It is possible to approximate a corresponding inverse mapping algorithm (reconstruction filter) for each source plane depth, with only one (depth) scaling parameter. The density distribution of the source structure is optimally deblurred when the reconstruction filter's scaling parameter matches the actual depth of the source plane below the surface. In the reconstruction procedure, this reconstruction filter is consecutively applied for several values of the scaling parameter. The so-called ``deblurring quality'' of the point or edge information is utilized to decide which scaling parameter achieves the sharpest image. This procedure resembles the focusing of a lens.