Thermal-wave slice diffraction tomography (TSDT) is a photothermal imaging technique for non-destructive evaluation (NDE), leading to the detection of subsurface cross sectional defects in opaque solids in the very-near-surface region ( - mm). An exact, Green's-function based mathematical model that represents the behaviour of a three-dimensional thermal wave is developed and correlated with a numerical reconstruction technique. The computational technique utilizes the well known Tikhonov regularization method to invert almost singular matrices resulting from the ill-posedness of the inverse thermal-wave problem for the reconstruction of thermal diffusivity cross sectional images in materials. Numerical calculations of the inverse problem are carried out using the Born approximation and simulated reconstructions in back scattering and transmission are presented.