Thermal-wave slice tomography using wave field reconstruction

Abstract

Thermal-wave Slice Diffraction Tomography (TSDT) was introduced as a photothermal imaging instrumentation technique [I-31 for the detection of sub-surface defects in solid material along crosssectional planes perpendicular to the laser-beam scanned surface. The first TSDT instrument was based on contacting photopyroelectric tomographic detection [2,3] followed by ray-optic reconstruction of the cross-sectional thermal-wave image of the thermal diffusivity of the chosen slice [2]. The one-dimensional ray-optic based reconstruction technique was quite successful in illustrating the TSDT principle. However, using only ray-optic methods has many limitations, especially in highly dispersive wave fields, such as thermal waves. For this reason techniques familiar from X-ray cross-sectional tomography, such as the recovery of a 2-D image from an oversampled I-D projection, cannot be applied to TSDT with satisfactory image contrast, spatial resolution and low distortion. We therefore present a novel Computational Slice Diffraction Tomography based on the matrix methodology of Ref. [4]. The physical methodology is described and the computational technique allowing slice reconstruction and imaging is given for experimental situations involving both back-propagation as well as forward (transmission) thermal-wave data numerically manufactured from the solution to the direct problem (Helmholtz pseudo-wave equation [51).